Quantum fluctuations give rise to van der Waals and Casimir forces that dominate the interaction between electrically neutral objects at sub-micron separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in micro- and nano-mechanical devices. Nevertheless, utilization of Casimir forces on the chip level remains a major challenge because all experiments so far require an external object to be manually positioned close to the mechanical element. Here by integrating a force-sensing micromechanical beam and an electrostatic actuator on a single chip, we demonstrate the Casimir effect between two micromachined silicon components on the same substrate. A high degree of parallelism between the two near-planar interacting surfaces can be achieved because they are defined in a single lithographic step. Apart from providing a compact platform for Casimir force measurements, this scheme also opens the possibility of tailoring the Casimir force using lithographically defined components of non-conventional shapes.
We predict that the radiative heat-transfer rate between a cylinder and a perforated surface depends non-monotonically on their separation. This anomalous behavior, which arises due to evanescent-wave effects, is explained using a heuristic model based on the interaction of a dipole with a plate. We show that nonmonotonicity depends not only on geometry and temperature but also on material dispersion—for micron and submicron objects, nonmonotonicity is present in polar dielectrics but absent in metals with small skin depths.
We demonstrate the realization of a two-dimensional chiral optical waveguide with an infinite translational symmetry that exhibits asymmetric wave propagation. The low-symmetry geometry of the cross-section that lacks any rotational and mirror symmetries shows emphin-principal directional asymmetric polarization rotation. We use general symmetry arguments to provide qualitative analysis of the waveguide's eigenstates and numerically corroborate this using finite element simulation. We show that despite the only perturbative break of time-reversal symmetry via small modal losses, the structure supports a non-degenerate pair of co-rotating elliptical modes. We fabricated meters long fiber with a spiral structure and studied its optical properties.
This chapter discusses the relationships between current sources and the resulting electromagnetic waves in FDTD simulations. First, the “total-field/scattered-field” approach to creating incident plane waves is reviewed and seen to be a special case of the well-known principle of equivalence in electromagnetism: this can be used to construct equivalent current sources for any desired incident field, including waveguide modes. The effects of dispersion and discretization are discussed, and a simple technique to separate incident and scattered fields is described in order to compensate for imperfect equivalent currents. The important concept of the local density of states (LDOS) is reviewed, which elucidates the relationship between current sources and the resulting fields, including enhancement of the LDOS via mode cutoffs (Van Hove singularities) and resonant cavities (Purcell enhancement). We also address various other source techniques such as covering a wide range of frequencies and incident angles in a small number of simulations for waves incident on a periodic surface, sources to excite eigenmodes in rectangular supercells of periodic systems, moving sources, and thermal sources via a Monte Carlo/Langevin approach.
Advances in photonics and nanotechnology have the potential to revolutionize humanity’s ability to communicate and compute. To pursue these advances, it is mandatory to understand and properly model interactions of light with materials such as silicon and gold at the nanoscale, i.e., the span of a few tens of atoms laid side by side. These interactions are governed by the fundamental Maxwell’s equations of classical electrodynamics, supplemented by quantum electrodynamics.
This book presents the current state-of-the-art in formulating and implementing computational models of these interactions. Maxwell’s equations are solved using the finite-difference time-domain (FDTD) technique, pioneered by the senior editor, whose prior Artech House books in this area are among the top ten most-cited in the history of engineering. You discover the most important advances in all areas of FDTD and PSTD computational modeling of electromagnetic wave interactions.
This cutting-edge resource helps you understand the latest developments in computational modeling of nanoscale optical microscopy and microchip lithography. You also explore cutting-edge details in modeling nanoscale plasmonics, including nonlocal dielectric functions, molecular interactions, and multi-level semiconductor gain. Other critical topics include nanoscale biophotonics, especially for detecting early-stage cancers, and quantum vacuum, including the Casimir effect and blackbody radiation.
We describe a fluctuating surface-current formulation of radiative heat transfer, applicable to arbitrary geometries in both the near and far field, that directly exploits efficient and sophisticated techniques from the boundary-element method. We validate as well as extend previous results for spheres and cylinders, and also compute the heat transfer in a more complicated geometry consisting of two interlocked rings. Finally, we demonstrate how this method can be adapted to compute the spatial distribution of heat flux on the surfaces of the bodies.
We designed and analyzed a “mesh-stack” three-dimensional photonic crystal of a 12.4% bandgap with a dielectric constant ratio of 12∶1. The mesh-stack consists of four offset identical square-lattice air-hole patterned membranes in each vertical period that is equal to the in-plane period of the square lattice. This design is fully compatible with the membrane-stacking fabrication method, which is based on alignment and stacking of large-area single-crystal membranes containing engineered defects. A bandgap greater than 10% is preserved as long as the membranes are subjected to in-plane misalignment less than 3% of the square period. By introducing a linear defect with a nonsymmorphic symmetry into the mesh-stack, we achieved a single-mode waveguide over a wide bandwidth.
Current optical communication systems rely almost exclusively on multimode fibres for short- and medium-haul transmissions, and are now expanding into the long-haul arena. Ultra-high bandwidth applications are the main drive for this expansion, based on the ability to spatially multiplex data channels in multimode systems. Integrated photonics, on the other hand, although largely responsible for today’s telecommunications, continues to operate almost strictly in the single-mode regime. This is because multimode waveguides cannot be compactly routed on-chip without significant inter-mode coupling, which impairs their data rate and prevents the use of modal multiplexing. Here we propose a platform for on-chip multimode devices with minimal inter-mode coupling, opening up the possibilities for integrated multimode optics. Our work combines a novel theoretical approach—large-scale inverse design of transformation optics to maximize performance within fabrication constraints—with unique grayscale-lithography fabrication of an exemplary device: a low-crosstalk multimode waveguide bend.
We investigate the design of taper structures for coupling to slow-light modes of various photonic-crystal waveguides while taking into account parameter uncertainties inherent in practical fabrication. Our short-length (11 periods) robust tapers designed for λ= 1.55μm and a slow-light group velocity of c/34 have a total loss of < 20 dB even in the presence of nanometer-scale surface roughness, which outperform the corresponding non-robust designs by an order of magnitude. We discover a posteriori that the robust designs have smooth profiles that can be parameterized by a few-term (intrinsically smooth) sine series which helps the optimization to further boost the performance slightly. We ground these numerical results in an analytical foundation by deriving the scaling relationships between taper length, taper smoothness, and group velocity with the help of an exact equivalence with Fourier analysis.
The famous Johnson–Nyquist formula relating noise current to conductance has a microscopic generalization relating noise current density to microscopic conductivity, with corollary relations governing noise in the components of the electromagnetic fields. These relations, known collectively in physics as fluctuation–dissipation relations, form the basis of the modern understanding of fluctuation-induced phenomena, a field of burgeoning importance in experimental physics and nanotechnology. In this review, we survey recent progress in computational techniques for modeling fluctuation-induced phenomena, focusing on two cases of particular interest: near-field radiative heat transfer and Casimir forces. In each case we review the basic physics of the phenomenon, discuss semi-analytical and numerical algorithms for theoretical analysis, and present recent predictions for novel phenomena in complex material and geometric configurations.
We propose an optimization-based theoretical approach to tailor the optical response of silver/silica multilayer nanospheres over the visible spectrum. We show that the structure that provides the largest cross-section per volume/mass, averaged over a wide frequency range, is the silver coated silica sphere. We also show how properly chosen mixture of several species of different nanospheres can have an even larger minimal cross-section per volume/mass over the entire visible spectrum.
From drug delivery to chemical and biological catalysis and cosmetics, the need for efficient fabrication pathways for particles over a wide range of sizes, from a variety of materials, and in many different structures has been well established. Here we harness the inherent scalability of fibre production and an in-fibre Plateau–Rayleigh capillary instability for the fabrication of uniformly sized, structured spherical particles spanning an exceptionally wide range of sizes: from 2 mm down to 20 nm. Thermal processing of a multimaterial fibre controllably induces the instability, resulting in a well-ordered, oriented emulsion in three dimensions. The fibre core and cladding correspond to the dispersed and continuous phases, respectively, and are both frozen in situ on cooling, after which the particles are released when needed. By arranging a variety of structures and materials in a macroscopic scaled-up model of the fibre, we produce composite, structured, spherical particles, such as core–shell particles, two-compartment `Janus' particles, and multi-sectioned `beach ball' particles. Moreover, producing fibres with a high density of cores allows for an unprecedented level of parallelization. In principle, 108 50-nm cores may be embedded in metres-long, 1-mm-diameter fibre, which can be induced to break up simultaneously throughout its length, into uniformly sized, structured spheres.
We show that cloaking of isolated objects using transformation-based cloaks is subject to a diameter–bandwidth product limitation: as the size of the object increases, the bandwidth of good (small cross-section) cloaking decreases inversely with the diameter, as a consequence of causality constraints even for perfect fabrication and materials with negligible absorption. This generalizes a previous result that perfect cloaking of isolated objects over a nonzero bandwidth violates causality. Furthermore, we demonstrate broader causality-based scaling limitations on any bandwidth-averaged cloaking cross-section, using complex analysis and the optical theorem to transform the frequency-averaged problem into a single scattering problem with transformed materials.
In this paper we describe a general method to avoid stress-induced buckling of thin and large freestanding membranes. We show that using properly designed supports, in the form of microbeams, we can reduce the out-of-plane deflection of the membrane while maintaining its stiffness. As a proof of principle, we used a silicon-on-insulator (SOI) platform to fabricate 30 μm wide, 220 nm thick, free-standing Si membranes, supported by four 15 μm long and 3 μm wide microbeams. Using our approach, we are able to achieve an out-of-plane deformation of the membrane smaller than 50 nm in spite of 39 MPa of compressive internal stress. Our method is general, and can be applied to different material systems with compressive or tensile internal stress.
We develop a general numerical method to calculate the nonequilibrium radiative heat transfer between a plate and compact objects of arbitrary shapes, making the first accurate theoretical predictions for the total heat transfer and the spatial heat flux profile for three-dimensional compact objects including corners or tips. In contrast to the known sphere-plate heat transfer, we find qualitatively different scaling laws for cylinders and cones at small separations, and, in contrast to a flat or slightly curved object, a sharp cone exhibits a local minimum in the spatially resolved heat flux directly below the tip. Our results may have important implications for near-field thermal writing and surface roughness.
We explore the mechanisms for an efficient light trapping structure for thin-film silicon solar cells. The design combines a distributed Bragg reflector (DBR) and periodic gratings. Using photonic band theories and numerical simulations, we discover that light can be scattered into the DBR by gratings, with an unusual way of light trapping different from metal reflectors and photonic crystals. We further investigate the influence of DBR on generated photocurrent in different device configurations. These results would provide new design rules for photonic structures in thin-film solar cells.
By directly simulating Maxwell’s equations via the finite-difference time-domain (FDTD) method, we numerically demonstrate the possibility of achieving high-efficiency second harmonic generation (SHG) in a structure consisting of a microscale doubly-resonant ring resonator side-coupled to two adjacent waveguides. We find that ≥94% conversion efficiency can be attained at telecom wavelengths, for incident powers in the milliwatts, and for reasonably large bandwidths (Q ∼1000s). We demonstrate that in this high efficiency regime, the system also exhibits limit-cycle or bistable behavior for light incident above a threshold power. Our numerical results agree to within a few percent with the predictions of a simple but rigorous coupled-mode theory framework.
We design an all–dielectric Lüneburg lens as an adiabatic space–variant lattice explicitly accounting for finite film thickness. We describe an all–analytical approach to compensate for the finite height of subwavelength dielectric structures in the pass–band regime. This method calculates the effective refractive index of the infinite–height lattice from effective medium theory, then embeds a medium of the same effective index into a slab waveguide of finite height and uses the waveguide dispersion diagram to calculate a new effective index. The results are compared with the conventional numerical treatment – a direct band diagram calculation, using a modified three–dimensional lattice with the superstrate and substrate included in the cell geometry. We show that the analytical results are in good agreement with the numerical ones, and the performance of the thin–film Lüneburg lens is quite different than the estimates obtained assuming infinite height.
We demonstrate the possibility of achieving enhanced frequency-selective near-field radiative heat transfer between patterned (photonic-crystal) slabs at designable frequencies and separations, exploiting a general numerical approach for computing heat transfer in arbitrary geometries and materials based on the finite-difference time-domain method. Our simulations reveal a tradeoff between selectivity and near-field enhancement as the slab-slab separation decreases, with the patterned heat transfer eventually reducing to the unpatterned result multiplied by a fill factor (described by a standard proximity approximation). We also find that heat transfer can be further enhanced at selective frequencies when the slabs are brought into a glide-symmetric configuration, a consequence of the degeneracies associated with the nonsymmorphic symmetry group.
A new class of multi-material fiber that incorporates micrometer-thickness concentric-cylindrical sheets of glass into polymer matrix has emerged. The ultimate lower limit of feature size and recent observation of interesting instability phenomenon in fiber system motivate us to examine fluid instabilities during the complicated thermal drawing fabrication processing. In this paper, from the perspective of a single instability mechanism, classical Plateau-Rayleigh instabilities in the form of radial fluctuation, we explore the stability of various microstructures (such as shells and filaments) in our composite fibers. The attained uniform structures are consistent with theoretical analysis. Furthermore, a viscous materials map is established from calculations and agrees well with various identified materials. These results not only shed insights into other forms of fluid instabilities, but also provide guidance to achieve more diverse nanostructures (such as filaments, wires, and particles) in the microstructured fibers.
We prove that, for arbitrary three-dimensional transformation-based invisibility cloaking of an object above a ground plane or of isolated object, there are practical constraints that increase with the object size. In particular, we show that the cloak thickness must scale proportional to the thickness of the object being cloaked, assuming bounded refractive indices, and that absorption discrepancies and other imperfections must scale inversely with the object thickness. For isolated objects, we also show that bounded refractive indices imply a lower bound on the effective cross-section.
We give an example of a geometry in which the electrostatic force between a point charge and a neutral metallic object is repulsive. The example consists of a point charge centered above a thin metallic hemisphere, positioned concave up. We show that this geometry has a repulsive regime using both a simple analytical argument and an exact calculation for an analogous two-dimensional geometry. Analogues of this geometry-induced repulsion can appear in many other contexts, including Casimir systems.
Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of N fluids with arbitrary viscosities, thicknesses, densities, and surface tensions in both the Stokes regime and for the full Navier–Stokes problem. Generalising previous work by Tomotika (N=2), Stone & Brenner (N=3, equal viscosities) and others, we present a full linear stability analysis of the growth modes and rates, reducing the system to a linear generalised eigenproblem in the Stokes case. Furthermore, we demonstrate by Plateau-style geometrical arguments that only axisymmetric instabilities need be considered. We show that the N=3 case is already sufficient to obtain several interesting phenomena: limiting cases of thin shells or low shell viscosity that reduce to N=2 problems, and a system with competing breakup processes at very different length scales. The latter is demonstrated with full 3-dimensional simulations. Many N > 3 cases remain to be explored, and as a first step we discuss two illustrative N →∞ cases, an alternating-layer structure and a geometry with a continuously varying viscosity.
We extend a recently introduced method for computing Casimir forces between arbitrarily shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett. 103 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface–surface separation at which finite-size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.
We numerically investigate the light-absorption behavior of thin-film silicon for normal-incident light, using surface textures to enhance absorption. We consider a variety of texture designs, such as simple periodic gratings and commercial random textures, and examine arbitrary irregular periodic textures designed by multi-parameter optimization. Deep and high-index-contrast textures exhibit strong anisotropic scattering that is outside the regime of validity of the Lambertian models commonly used to describe texture-induced absorption enhancement for normal incidence. Over a 900–1100 nm wavelength range, our optimized surface texture in two dimensions (2D) enhances absorption by a factor of 2.7πn, considerably larger than the original πn Lambertian result and exceeding by almost 50% a recent generalization of Lambertian model for periodic structures in finite spectral range. However, the πn Lambertian limit still applies for isotropic incident light, and our structure obeys this limit when averaged over all the angles. Therefore, our design can be thought of optimizing the angle/enhancement tradeoff for periodic textures.
We present numerical experiments showing how coupled-mode theory can be systematically applied to join very dissimilar photonic crystal waveguides with 100% transmission. Our approach relies on appropriately tuning the coupling of the evanescent tail of a cavity mode to each waveguide. The transition region between the waveguides may be as short as a few lattice spacings. Moreover, this technique only requires varying a small number of parameters (two for each waveguide in our example) and the tuning to each waveguide may be done separately, greatly simplifying the computations involved.
We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria—choice of problem, basis, and solution technique—that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.
In this work we theoretically consider the Casimir force between two periodic arrays of nanowires (both in vacuum, and on a substrate separated by a fluid) at separations comparable to the period. Specifically, we compute the dependence of the exact Casimir force between the arrays under both lateral translations and rotations. Although typically the force between such structures is well characterized by the proximity force approximation (PFA), we find that in the present case the microstructure modulates the force in a way qualitatively inconsistent with PFA. We find instead that effective-medium theory, in which the slabs are treated as homogeneous, anisotropic dielectrics, gives a surprisingly accurate picture of the force, down to separations of half the period. This includes a situation for identical, fluid-separated slabs in which the exact force changes sign with the orientation of the wire arrays, whereas PFA predicts attraction. We discuss the possibility of detecting these effects in experiments, concluding that this effect is strong enough to make detection possible in the near future.
We propose an optomechanical structure consisting of a photonic-crystal (holey) membrane suspended above a layered silicon-on-insulator substrate in which resonant bonding/antibonding optical forces created by externally incident light from above enable all-optical control and actuation of stiction effects induced by the Casimir force. In this way, one can control how the Casimir force is expressed in the mechanical dynamics of the membrane, not by changing the Casimir force directly but by optically modifying the geometry and counteracting the mechanical spring constant to bring the system in or out of regimes where Casimir physics dominate. The same optical response (reflection spectrum) of the membrane to the incident light can be exploited to accurately measure the effects of the Casimir force on the equilibrium separation of the membrane.
We show that some previous proposals for perfectly matched layer (PML) absorbers in anisotropic media or for waveguides at oblique incidence are not, in fact true PMLs; in previous work we similarly showed a failure of several PML proposals for periodic media (photonic crystals). We therefore argue that a more careful validation scheme is required for PML proposals, in contrast to past authors who have typically checked only that reflections are small for a fixed resolution, and suggest a simple validation scheme that can be readily applied to any PML proposal regardless of derivation or implementation. We demonstrate this test for a corrected, unsplit-field PML valid for anisotropic, dispersive media, implemented in both planewave-expansion and finite-difference time-domain (FDTD) methods.
Our previous article [Phys. Rev. Lett. 104, 060401 (2010)] predicted that Casimir forces induced by the material-dispersion properties of certain dielectrics can give rise to stable configurations of objects. This phenomenon was illustrated via a dicluster configuration of non-touching objects consisting of two spheres immersed in a fluid and suspended against gravity above a plate. Here, we examine these predictions from the perspective of a practical experiment and consider the influence of non-additive, three-body, and nonzero-temperature effects on the stability of the two spheres. We conclude that the presence of Brownian motion reduces the set of experimentally realizable silicon/teflon spherical diclusters to those consisting of layered micro-spheres, such as the hollow core (spherical shells) considered here.
We show how to compute Casimir forces at nonzero temperatures with time-domain electromagnetic simulations, for example using a finite-difference time-domain (FDTD) method. Compared to our previous zero-temperature time-domain method, only a small modification is required, but we explain that some care is required to properly capture the zero-frequency contribution. We validate the method against analytical and numerical frequency-domain calculations, and show a surprising high-temperature disappearance of a non-monotonic behavior previously demonstrated in a pistonlike geometry.
We propose a design for a conductive wire composed of several mutually insulated coaxial conducting shells. With the help of numerical optimization, it is possible to obtain electrical resistances significantly lower than those of a heavy-gauge copper wire or litz wire in the 2-–20 MHz range. Moreover, much of the reduction in resistance can be achieved for just a few shells; in contrast, litz wire would need to contain ∼104 strands to perform comparably in this frequency range.
We demonstrate theoretical conditions for highly-efficient degenerate four-wave mixing in triply-resonant nonlinear (Kerr) cavities. We employ a general and accurate temporal coupled-mode analysis in which the interaction of light in arbitrary microcavities is expressed in terms a set of coupling coefficients that we rigorously derive from the full Maxwell equations. Using the coupled-mode theory, we show that light consisting of an input signal of frequency ω0-Δω can, in the presence of pump light at ω0, be converted with quantum-limited efficiency into an output shifted signal of frequency ω0 + Δω, and we derive expressions for the critical input powers at which this occurs. We find that critical powers in the order of 10mW assuming very conservative cavity parameters (modal volumes ∼10 cubic wavelengths and quality factors ∼1000. The standard Manley-Rowe efficiency limits are obtained from the solution of the classical coupled-mode equations, although we also derive them from simple photon-counting “quantum” arguments. Finally, using a linear stability analysis, we demonstrate that maximal conversion efficiency can be retained even in the presence of self- and cross-phase modulation effects that generally act to disrupt the resonance condition.
In 1948, Hendrik Casimir predicted that a generalized version of van der Waals forces would arise between two metal plates due to quantum fluctuations of the electromagnetic field. These forces become significant in micromechanical systems at submicrometre scales, such as in the adhesion between movable parts. The Casimir force, through a close connection to classical photonics, can depend strongly on the shapes and compositions of the objects, stimulating a decades-long search for geometries in which the force behaves very differently from the monotonic attractive force first predicted by Casimir. Recent theoretical and experimental developments have led to a new understanding of the force in complex microstructured geometries, including through recent theoretical predictions of Casimir repulsion between vacuum-separated metals, the stable suspension of objects and unusual non-additive and temperature effects, as well as experimental observations of repulsion in fluids, non-additive forces in nanotrench surfaces and the influence of new material choices.
In this paper, we show that bone piezoelectricity—a phenomenon in which bone polarizes electrically in response to an applied mechanical stress and produces a short-range electric field—may be a source of intense blast-induced electric fields in the brain, with magnitudes and timescales comparable to fields with known neurological effects. We compute the induced charge density in the skull from stress data on the skull from a finite-element full-head model simulation of a typical IED-scale blast wave incident on an unhelmeted human head as well as a human head protected by a kevlar helmet, and estimate the resulting electric fields in the brain in both cases to be on the order of 10 V/m in millisecond pulses. These fields are more than 10 times stronger than the IEEE safety guidelines for controlled environments (IEEE Standards Coordinating Committee 28, 2002) and comparable in strength and timescale to fields from repetitive Transcranial Magnetic Stimulation (rTMS) that are designed to induce neurological effects (Wagner et al., 2006a). They can be easily measured by RF antennas, and may provide the means to design a diagnostic tool that records a quantitative measure of the head's exposure to blast insult.
We demonstrate that tunable attractive (bonding) and repulsive (anti-bonding) forces can arise in highly asymmetric structures coupled to external radiation, a consequence of the bonding/anti-bonding level repulsion of guided-wave resonances that was first predicted in symmetric systems. Our focus is a geometry consisting of a photonic-crystal (holey) membrane suspended above an unpatterned layered substrate, supporting planar waveguide modes that can couple via the periodic modulation of the holey membrane. Asymmetric geometries have a clear advantage in ease of fabrication and experimental characterization compared to symmetric double-membrane structures. We show that the asymmetry can also lead to unusual behavior in the force magnitudes of a bonding/antibonding pair as the membrane separation changes, including nonmonotonic dependences on the separation. We propose a computational method that obtains the entire force spectrum via a single time-domain simulation, by Fourier-transforming the response to a short pulse and thereby obtaining the frequency-dependent stress tensor. We point out that by operating with two, instead of a single frequency, these evanescent forces can be exploited to tune the spring constant of the membrane without changing its equilibrium separation.
Fast surface integral equation (SIE) methods seem to be ideal for simulating 3-D nanophotonic devices, as such devices generate fields in both the interior device volume and in the infinite exterior domain. SIE methods were originally developed for computing scattering from structures with finite surfaces, and since SIE methods automatically represent the infinite extent of the exterior scattered field, there was no need to develop numerical absorbers. Numerical absorbers are needed when SIE methods are used to simulate nanophotonic devices that process or couple light, to provide nonreflecting termination at the optical ports of such devices. In this paper, we focus on the problem of developing an approach to absorbers that are suitable for port termination, yet preserve the surface-only discretization and the geometry-independent Green's function properties of the SIE methods. Preserving these properties allows the absorber approach to be easily incorporated in commonly used fast solvers. We describe our solution to the absorber problem, that of using a gradually increasing surface conductivity, and show how to include surface conductivity in SIE methods. We also analyze numerical results using our absorber approach to terminate a finite-length rectangular cross section dielectric waveguide. The numerical results demonstrate that our surface-conductivity absorber can easily achieve a reflected power of less than 10-7, and that the magnitude of the transition reflection is proportional to 1/L2d+2, where L is the absorber length and d is the order of the differentiability of the surface conductivity function.
We examine a recent prediction for the chirality dependence of the Casimir force in chiral metamaterials by numerical computation of the forces between the exact microstructures, rather than homogeneous approximations. Although repulsion in the metamaterial regime is rigorously impossible, it is unknown whether a reduction in the attractive force can be achieved through suitable material engineering. We compute the exact force for a chiral bent-cross pattern, as well as forces for an idealized “omega”-particle medium in the dilute approximation and identify the effects of structural inhomogeneity (i.e., proximity forces and anisotropy). We find that these microstructure effects dominate the force for separations where chirality was predicted to have a strong influence. At separations where the homogeneous approximation is valid, in even the most ideal circumstances the effects of chirality are less than 10−4 of the total force, making them virtually undetectable in experiments.
We propose a method of achieving large temperature T sensitivity in the Casimir force that involves measuring the stable separation between dielectric objects immersed in a fluid. We study the Casimir force between slabs and spheres using realistic material models, and find large >2 nm/K variations in their stable separations (hundreds of nanometers) near room temperature. In addition, we analyze the effects of Brownian motion on suspended objects, and show that the average separation is also sensitive to changes in T. Finally, this approach also leads to rich qualitative phenomena, such as irreversible transitions, from suspension to stiction, as T is varied.
Despite their great promise, small experimental thermophotovoltaic (TPV) systems at 1000 K generally exhibit extremely low power conversion efficiencies (approximately 1%), due to heat losses such as thermal emission of undesirable mid-wavelength infrared radiation. Photonic crystals (PhC) have the potential to strongly suppress such losses. However, PhC-based designs present a set of non-convex optimization problems requiring efficient objective function evaluation and global optimization algorithms. Both are applied to two example systems: improved micro-TPV generators and solar thermal TPV systems. Micro-TPV reactors experience up to a 27-fold increase in their efficiency and power output; solar thermal TPV systems see an even greater 45-fold increase in their efficiency (exceeding the Shockley–Quiesser limit for a single-junction photovoltaic cell).
We give an example of a geometry in which two metallic objects in vacuum experience a repulsive Casimir force. The geometry consists of an elongated metal particle centered above a metal plate with a hole. We prove that this geometry has a repulsive regime using a symmetry argument and confirm it with numerical calculations for both perfect and realistic metals. The system does not support stable levitation, as the particle is unstable to displacements away from the symmetry axis.
We show that the difficulty of cloaking is fundamentally limited by delay-loss and delay-bandwidth limitations that worsen as the size of the object to be cloaked increases relative to the wavelength, using a simple model of ground-plane cloaking. These limitations must be considered when scaling experimental cloaking demonstrations up from wavelength-scale objects.
We derive a correspondence between the contour integration of the Casimir stress tensor in the complex-frequency plane and the electromagnetic response of a physical dissipative medium in a finite real-frequency bandwidth. The consequences of this correspondence are at least threefold: First, the correspondence makes it easier to understand Casimir systems from the perspective of conventional classical electromagnetism, based on real-frequency responses, in contrast to the standard imaginary-frequency point of view based on Wick rotations. Second, it forms the starting point of finite-difference time-domain numerical techniques for calculation of Casimir forces in arbitrary geometries. Finally, this correspondence is also key to a technique for computing quantum Casimir forces at micrometer scales using antenna measurements at tabletop (e.g., centimeter) scales, forming a type of analog computer for the Casimir force. Superficially, relationships between the Casimir force and the classical electromagnetic Green’s function are well known, so one might expect that any experimental measurement of the Green’s function would suffice to calculate the Casimir force. However, we show that the standard forms of this relationship lead to infeasible experiments involving infinite bandwidth or exponentially growing fields, and a fundamentally different formulation is therefore required.
We present a scheme for obtaining stable Casimir suspension of dielectric nontouching objects immersed in a fluid, validated here in various geometries consisting of ethanol-separated dielectric spheres and semi-infinite slabs. Stability is induced by the dispersion properties of real dielectric (monolithic) materials. A consequence of this effect is the possibility of stable configurations (clusters) of compact objects, which we illustrate via a molecular two-sphere dicluster geometry consisting of two bound spheres levitated above a gold slab. Our calculations also reveal a strong interplay between material and geometric dispersion, and this is exemplified by the qualitatively different stability behavior observed in planar versus spherical geometries.
We prove, via an elementary variational method, 1d and 2d localization within the band gaps of a periodic Schrödinger operator for any mostly negative or mostly positive defect potential, V, whose depth is not too great compared to the size of the gap. In a similar way, we also prove sufficient conditions for 1d and 2d localization below the ground state of such an operator. Furthermore, we extend our results to 1d and 2d localization in d dimensions; for example, a linear or planar defect in a 3d crystal. For the case of D-fold degenerate band edges, we also give sufficient conditions for localization of up to D states.
In this letter, we show theoretically how the light-confining properties of triply-resonant photonic resonators can be tailored to enable dramatic enhancements of the conversion efficiency of terahertz (THz) generation via nonlinear frequency down-conversion processes. Using detailed numerical calculations, we predict that this approach can be used to reduce up to three orders of magnitude the pump powers required to reach quantum-limited conversion efficiency of THz generation in conventional nonlinear optical material systems. Furthermore, we propose a realistic design readily accessible experimentally, both for fabrication and demonstration of optimal THz conversion efficiency at sub-W power levels.
This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Padé approximants, and flexible scripting capabilities.
Our previous article [Phys. Rev. A 80, 012115 (2009)] introduced a method to compute Casimir forces in arbitrary geometries and for arbitrary materials that was based on a finite-difference time-domain (FDTD) scheme. In this article, we focus on the efficient implementation of our method for geometries of practical interest and extend our previous proof-of-concept algorithm in one dimension to problems in two and three dimensions, introducing a number of new optimizations. We consider Casimir pistonlike problems with nonmonotonic and monotonic force dependence on sidewall separation, both for previously solved geometries to validate our method and also for new geometries involving magnetic sidewalls and/or cylindrical pistons. We include realistic dielectric materials to calculate the force between suspended silicon waveguides or on a suspended membrane with periodic grooves, also demonstrating the application of perfectly matched layer (PML) absorbing boundaries and/or periodic boundaries. In addition, we apply this method to a realizable three-dimensional system in which a silica sphere is stably suspended in a fluid above an indented metallic substrate. More generally, the method allows off-the-shelf FDTD software, already supporting a wide variety of materials (including dielectric, magnetic, and even anisotropic materials) and boundary conditions, to be exploited for the Casimir problem.
We propose a scheme for efficient cavity-enhanced nonlinear THz generation via difference-frequency generation (DFG) processes using a triply resonant system based on photonic crystal cavities. We show that high nonlinear overlap can be achieved by coupling a THz cavity to a doubly-resonant, dual-polarization near-infrared (e.g. telecom band) photonic-crystal nanobeam cavity, allowing the mixing of three mutually orthogonal fundamental cavity modes through a χ(2) nonlinearity. We demonstrate through coupled-mode theory that complete depletion of the pump frequency – i.e., quantum-limited conversion – We show that the output power at the point of optimal total conversion efficiency is adjustable by varying the mode quality (Q) factors.
Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.
We introduce an efficient technique for computing Casimir energies and forces between objects of arbitrarily complex 3D geometries. In contrast to other recently developed methods, our technique easily handles non-spheroidal, non-axisymmetric objects and objects with sharp corners. Using our new technique, we obtain the first predictions of Casimir interactions in a number of experimentally relevant geometries, including crossed cylinders and tetrahedral nanoparticles.
Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic homogeneous coatings. Detailed investigations of the optimal discretization (e.g., thickness control of each layer, nonlinear factor, etc.) are presented for both linear and nonlinear spherical cloaks and their effects on invisibility performance are also discussed. The cloaking properties and our choice of optimal segmentation are verified by the numerical simulation of not only near-field electric-field distribution but also the far-field radar cross section (RCS).
We present a method to compute Casimir forces in arbitrary geometries and for arbitrary materials based on the finite-difference time-domain (FDTD) scheme. The method involves the time evolution of electric and magnetic fields in response to a set of current sources, in a modified medium with frequency-independent conductivity. The advantage of this approach is that it allows one to exploit existing FDTD software, without modification, to compute Casimir forces. In this paper, we focus on the derivation, implementation choices, and essential properties of the time-domain algorithm, both considered analytically and illustrated in the simplest parallel-plate geometry.
We demonstrate that a holey photonic-crystal fiber with chalcogenide-glass index contrast can be designed to have a complete gap at a propagation constant β= 0 that also extends into the non-zero β region. This type of bandgap (previously identified only at index contrasts unattainable in glasses) opens up a regime for guiding zero–group-velocity modes not possible in holey fibers with the more common finger-like gaps originating from β→∞. Such modes could be used to enhance nonlinear and other material interactions, such as for hollow-core fibers in gas-sensor applications.
We demonstrate that the ratio of group to phase velocity has a simple relationship to the orientation of the electromagnetic field. In nondispersive materials, opposite group and phase velocity corresponds to fields that are mostly oriented in the propagation direction. More generally, this relationship (including the case of dispersive and negative-index materials) offers a perspective on the phenomena of backward waves and left-handed media. As an application of this relationship, we demonstrate and explain an irrecoverable failure of perfectly matched layer absorbing boundaries in computer simulations for constant cross-section waveguides with backward-wave modes and suggest an alternative in the form of adiabatic isotropic absorbers.
We present a comprehensive study of second-order nonlinear difference frequency generation in triply resonant cavities using a theoretical framework based on coupled-mode theory. We show that optimal quantum-limited conversion efficiency can be achieved at any pump power when the powers at the pump and idler frequencies satisfy a critical relationship. We demonstrate the existence of a broad parameter range in which all triply-resonant DFG processes exhibit monostable conversion. We also demonstrate the existence of a geometry-dependent bistable region.
In this work, we present the design of an integrated photonic-crystal polarization beam splitter (PC-PBS) and a low-loss photonic-crystal 60o waveguide bend. Firstly, the modal properties of the PC-PBS and the mechanism of the low-loss waveguide bend are investigated by the two-dimensional finite-difference time-domain (FDTD) method, and then the integration of the two devices is studied. It shows that, although the individual devices perform well separately, the performance of the integrated circuit is poor due to the multi-mode property of the PC-PBS. By introducing deformed airhole structures, a single-mode PC-PBS is proposed, which significantly enhance the performance of the circuit with the extinction ratios remaining above 20dB for both transverse-electric (TE) and transverse-magnetic (TM) polarizations. Both the specific result and the general idea of integration design are promising in the photonic crystal integrated circuits in the future.
This article concerns the design of tapers for coupling power between uniform and slow-light periodic waveguides. New optimization methods are described for designing robust tapers, which not only perform well under nominal conditions, but also over a given set of parameter variations. When the set of parameter variations models the inevitable variations typical in the manufacture or operation of the coupler, a robust design is one that will have a high yield, despite these parameter variations. The ideas of successive refinement, and robust optimization based on multi-scenario optimization with iterative sampling of uncertain parameters, using a fast method for approximately evaluating the reflection coefficient, are introduced. Robust design results are compared to a linear taper, and to optimized tapers that do not take parameter variation into account. Finally, robust performance of the resulting designs is verified using an accurate, but much more expensive, method for evaluating the reflection coefficient.
We propose a two dimensional (2D) photonic crystal (PhC) structure that supports super-collimation over a large frequency range (over 4 times that of a traditional square lattice of holes). We theoretically and numerically investigate the collimation mechanism in our 2D structure, in comparison to that of two other frequently used related PhC structures. We also point out the potential importance of our proposed structure in the design of super-collimation-based devices for both monochromatic and polychromatic light.
The front-coating (FC) of a solar cell controls its efficiency, determining admission of light into the absorbing material and potentially trapping light to enhance thin absorbers. Single-layer FC designs are well known, especially for thick absorbers where their only purpose is to reduce reflections. Multilayer FCs could improve performance, but require global optimization to design. For narrow bandwidths, one can always achieve nearly 100% absorption. For the entire solar bandwidth, however, a second FC layer improves performance by 6.1% for 256 μm wafer-based cells, or by 3.6% for 2 μm thin-film cells, while additional layers yield rapidly diminishing returns.
We describe a theoretical analysis of the nonlinear dynamics of third-harmonic generation (ω→3ω) via Kerr (χ(3)) nonlinearities in a resonant cavity with resonances at both ω and 3ω. Such a doubly resonant cavity greatly reduces the required power for efficient harmonic generation, by a factor of ∼V/Q2 where V is the modal volume and Q is the lifetime, and can even exhibit 100% harmonic conversion efficiency at a critical input power. However, we show that it also exhibits a rich variety of nonlinear dynamics, such as multistable solutions and long-period limit cycles. We describe how to compensate for self- and cross-phase modulation (which otherwise shifts the cavity frequencies out of resonance), and how to excite the different stable solutions (and especially the high-efficiency solutions) by specially modulated input pulses.
We numerically demonstrate a stable mechanical suspension of a silica cylinder within a metallic cylinder separated by ethanol, via a repulsive Casimir force between the silica and the metal. We investigate cylinders with both circular and square cross sections, and show that the latter exhibit a stable orientation as well as a stable position, via a method to compute Casimir torques for finite objects. Furthermore, the stable orientation of the square cylinder undergoes a 45o transition as the separation length scale is varied, which is explained as a consequence of material dispersion.
We establish rigorous necessary analytical conditions for the existence of single-polarization single-mode (SPSM) bandwidths in index-guided microstructured waveguides (such as photonic-crystal fibers). These conditions allow us to categorize designs for SPSM waveguides into four strategies, at least one of which seems previously unexplored. Conversely, we obtain rigorous sufficient conditions for the existence of two cutoff-free index-guided modes in a wide variety of microstructured dielectric waveguides with arbitrary periodic claddings, based on the existence of a degenerate fundamental mode of the cladding (a degenerate light line). We show how such a degenerate light line, in turn, follows from the symmetry of the cladding.
Discussion of the considerations involved in high-performance FFT implementations, which center largely on memory access and other non-arithmetic concerns, as illustrated by a case study of the FFTW library.
We develop a coupled mode theory (CMT) model of the behavior of a polarization source in a general photonic structure, and obtain an analytical expression for the resulting generated electric field; loss, gain and/or nonlinearities can also be modeled. Based on this treatment, we investigate the criteria needed to achieve an enhancement in various nonlinear effects, and to produce efficient sources of terahertz radiation, in particular. Our results agree well with exact finite-difference time-domain (FDTD) results. Therefore, this approach can also in certain circumstances be used as a potential substitute for the more numerically intensive FDTD method.
Although perfectly matched layers (PMLs) have been widely used to truncate numerical simulations of electromagnetism and other wave equations, we point out important cases in which a PML fails to be reflectionless even in the limit of infinite resolution. In particular, the underlying coordinate-stretching idea behind PML breaks down in photonic crystals and in other structures where the material is not an analytic function in the direction perpendicular to the boundary, leading to substantial reflections. The alternative is an adiabatic absorber, in which reflections are made negligible by gradually increasing the material absorption at the boundaries, similar to a common strategy to combat discretization reflections in PMLs. We demonstrate the fundamental connection between such reflections and the smoothness of the absorption profile via coupled-mode theory, and show how to obtain higher-order and even exponential vanishing of the reflection with absorber thickness (although further work remains in optimizing the constant factor).
We present algorithms for the discrete cosine transform (DCT) and discrete sine transform (DST), of types II and III, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from 2 N log2 N + O(N) to (17)/(9) N log2 N + O(N) for a power-of-two transform size N. Furthermore, we show that a further N multiplications may be saved by a certain rescaling of the inputs or outputs, generalizing a well-known technique for N=8 by Arai et al. These results are derived by considering the DCT to be a special case of a DFT of length 4N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DCT-III, DST-II, and DST-III follow immediately from the improved count for the DCT-II.
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from 2Nlog2N + O(N) to (17)/(9)Nlog2N + O(N) for a power-of-two transform size N, and the exact count is strictly lowered for N ≥8. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.
We derive a sufficient condition for the existence of index-guided modes in a very general class of dielectric waveguides, including photonic-crystal fibers (arbitrary periodic claddings, such as “holey fibers”), anisotropic materials, and waveguides with periodicity along the propagation direction. This condition provides a rigorous guarantee of cutoff-free index-guided modes in any such structure where the core is formed by increasing the index of refraction (e.g. removing a hole). It also provides a weaker guarantee of guidance in cases where the refractive index is increased “on average” (precisely defined). The proof is based on a simple variational method, inspired by analogous proofs of localization for two-dimensional attractive potentials in quantum mechanics.
We describe a three-dimensional geometry in which both attractive and repulsive Casimir forces arise using ordinary metallic materials, as computed via an exact numerical method (no uncontrolled approximations). The geometry consists of a zipperlike, glide-symmetric structure formed of interleaved metal brackets attached to parallel plates—because of the interleaving pattern, a net repulsive force can arise from a combination of attractive interactions. Depending on the separation, the perpendicular force between the plates and brackets varies from attractive (large separations) to repulsive (intermediate distances) and back to attractive (close separations), with one point of stable equilibrium in the perpendicular direction. This geometry was motivated by a simple intuition of attractive interactions between surfaces, and so we also consider how a rough proximity-force approximation of pairwise attractions compares to the exact calculations.
Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwell's equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Bloch's theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no additional computational cost. As a proof of concept, these general ideas are demonstrated for the simple case of one-dimensional quasicrystals, which can also be solved by simple transfer-matrix techniques.
We analyze the Casimir force between two parallel infinite metal cylinders with nearby metal plates using two methods. Surprisingly, the attractive force between cylinders depends nonmonotonically on the separation from the plate(s), and the cylinder-plate force depends nonmonotonically on the separation of the cylinders. These multibody phenomenona do not follow from simple two-body force descriptions. We can explain the nonmonotonicity with the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders and their images on the nearby plate(s).
We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a “localized” coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking a limit in which a coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g. from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a sub-pixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.
Since it was first published in 1995, Photonic Crystals has remained the definitive text for both undergraduates and researchers on photonic band-gap materials and their use in controlling the propagation of light. This newly expanded and revised edition covers the latest developments in the field, providing the most up-to-date, concise, and comprehensive book available on these novel materials and their applications.
Starting from Maxwell's equations and Fourier analysis, the authors develop the theoretical tools of photonics using principles of linear algebra and symmetry, emphasizing analogies with traditional solid-state physics and quantum theory. They then investigate the unique phenomena that take place within photonic crystals at defect sites and surfaces, from one to three dimensions. This new edition includes entirely new chapters describing important hybrid structures that use band gaps or periodicity only in some directions: periodic waveguides, photonic-crystal slabs, and photonic-crystal fibers. The authors demonstrate how the capabilities of photonic crystals to localize light can be put to work in devices such as filters and splitters. A new appendix provides an overview of computational methods for electromagnetism. Existing chapters have been considerably updated and expanded to include many new three-dimensional photonic crystals, an extensive tutorial on device design using temporal coupled-mode theory, discussions of diffraction and refraction at crystal interfaces, and more. Richly illustrated and accessibly written, Photonic Crystals is an indispensable resource for students and researchers.
We present analytical results that shed new light on the properties of photonic-crystal fibers (optical fibers with periodic structures in their cladding). First, we discuss a general theorem, applicable to any periodic cladding structure, that gives rigorous conditions for the existence of cutoff-free guided modes-it lets you look at a structure, in most cases without calculation, and by inspection give a rigorous guarantee that index-guiding will occur. This theorem especially illuminates the long-wavelength limit, which has proved diffcult to study numerically, to show that the index-guided modes in photonic-crystal fibers (like their step-index counterparts) need not have any theoretical cutoff for guidance. Second, we look in the opposite regime, that of very short wavelengths. As previously identified by other authors, there is a scalar approximation that becomes exact in this limit, even for very high contrast fibers. We show that this “scalar” limit has consequences for practical operation at finite wavelengths that do not seem to have been fully appreciated: it tells you when band gaps arise and between which bands, reveals the symmetry and “LP” degeneracies of the modes, and predicts the scaling of cladding-related losses (roughness, absorption, etc.) as the size of a hollow core is increased.
Using the ray-optics approximation, we analyze the Casimir force in a two-dimensional domain formed by two metallic blocks adjacent to parallel metallic sidewalls, which are separated from the blocks by a finite distance h. For h>0, the ray-optics approach is not exact because diffraction effects are neglected. Nevertheless, we show that ray optics is able to qualitatively reproduce a surprising effect recently identified in an exact numerical calculation: the force between the blocks varies nonmonotonically with h. In this sense, the ray-optics approach captures an essential part of the physics of multibody interactions in this system, unlike simpler pairwise-interaction approximations such as proximity force approximations (PFA). Furthermore, by comparison to the exact numerical results, we are able to quantify the impact of diffraction on Casimir forces in this geometry.
We examine differences between various zero-group-velocity modes in photonic crystals, including those that arise from Bragg diffraction, anticrossings, and band repulsion. Zero-group velocity occurs at points where the group velocity changes sign, and therefore is conceptually related to “left-hande” media, in which the group velocity is opposite to the phase velocity. We consider this relationship more quantitatively in terms of the Fourier decomposition of the modes, by defining a measure of how much the “average” phase velocity is parallel to the group velocity—an anomalous region is one in which they are mostly antiparallel. We find that this quantity can be used to qualitatively distinguish different zero-group-velocity points. In one dimension, such anomalous regions are found never to occur. In higher dimensions, they are exhibited around certain zero-group-velocity points, and lead to unusual enhanced confinement behavior in microcavities.
Nonlinear photonic-crystal microresonators offer unique fundamental ways of enhancing a variety of nonlinear optical processes. This enhancement improves the performance of nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic ultrafast integrated optical devices. Here, we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal microcavities. First, we discuss a system in which this enhancement has been successfully demonstrated both theoretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we show how nonlinear photonic crystal cavities can be also used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of materials can be strongly modified via the so-called Purcell effect, present in the resonant cavities under study.
In this paper, we review various numerical methods currently used to model nonlinear optical processes in nanophotonics. Among the different theoretical frameworks that have been used to study nonlinear photonic structures, we particularly focus on the application of both perturbation theory and coupled-mode theory to the analysis of complex nonlinear nanophotonic devices. This description is illustrated on several examples of how these techniques can be used to design photonic-crystal-based nonlinear devices. In addition, in all these examples, we show that the predictions made by the two mentioned techniques are in a good agreement with the numerical results obtained from a nonlinear finite-difference-time-domain approach to these problems.
We describe a numerical method to compute Casimir forces in arbitrary geometries, for arbitrary dielectric and metallic materials, with arbitrary accuracy (given sufficient computational resources). Our approach, based on well-established integration of the mean stress tensor evaluated via the fluctuation-dissipation theorem, is designed to directly exploit fast methods developed for classical computational electromagnetism, since it only involves repeated evaluation of the Green's function for imaginary frequencies (equivalently, real frequencies in imaginary time). We develop the approach by systematically examining various formulations of Casimir forces from the previous decades and evaluating them according to their suitability for numerical computation. We illustrate our approach with a simple finite-difference frequency-domain implementation, test it for known geometries such as a cylinder and a plate, and apply it to new geometries. In particular, we show that a pistonlike geometry of two squares sliding between metal walls, in both two and three dimensions with both perfect and realistic metallic materials, exhibits a surprising non-monotonic “lateral” force from the walls.
We present a method of computing Casimir forces for arbitrary geometries, with any desired accuracy, that can directly exploit the efficiency of standard numerical-electromagnetism techniques. Using the simplest possible finite-difference implementation of this approach, we obtain both agreement with past results for cylinder-plate geometries, and also present results for new geometries. In particular, we examine a pistonlike problem involving two dielectric and metallic squares sliding between two metallic walls, in two and three dimensions, respectively, and demonstrate nonadditive and nonmonotonic changes in the force due to these lateral walls.
We derive general conditions for 100% frequency conversion in any doubly resonant nonlinear cavity, for both second- and third-harmonic generation via χ(2) and χ(3) nonlinearities. We find that conversion efficiency is optimized for a certain “critical” power depending on the cavity parameters, and assuming reasonable parameters we predict 100% conversion using milliwatts of power or less. These results follow from a semi-analytical coupled-mode theory framework which is generalized from previous work to include both χ(2) and χ(3) media as well as inhomogeneous (fully vectorial) cavities, analyzed in the high-efficiency limit where down-conversion processes lead to a maximum efficiency at the critical power, and which is verified by direct finite-difference time-domain (FDTD) simulations of the nonlinear Maxwell equations. Explicit formulas for the nonlinear coupling coefficients are derived in terms of the linear cavity eigenmodes, which can be used to design and evaluate cavities in arbitrary geometries.
Recent results by Van Buskirk et al. have broken the record set by Yavne in 1968 for the lowest exact count of real additions and multiplications to compute a power-of-two discrete Fourier transform (DFT). Here, we present a simple recursive modification of the split-radix algorithm that computes the DFT with asymptotically about 6% fewer operations than Yavne, matching the count achieved by Van Buskirk's program-generation framework. We also discuss the application of our algorithm to real-data and real-symmetric (discrete cosine) transforms, where we are again able to achieve lower arithmetic counts than previously published algorithms.
Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (pixelization). We show that accuracy can be significantly improved by using a subpixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory and compare it with other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.
This paper demonstrates switching of a single signal photon by a single gating photon of a different frequency, via a cross-phase-modulation. This effect is mediated by materials exhibiting electromagnetically induced transparency (EIT), which are embedded in photonic crystals (PhCs). An analytical model based on waveguide-cavity QED is constructed for our system, which consists of a PhC waveguide and a PhC microcavity containing a four-level EIT atom. It is solved exactly and analyzed using experimentally accessible parameters. It is found that the strong coupling regime is required for lossless two-photon quantum entanglement.
We study the radiation emitted by an oscillating dipole moving with a constant velocity in a photonic crystal, and analyze the effects that arise in the presence of a photonic band gap. It is demonstrated through numerical simulations that the radiation strength may be enhanced or inhibited according to the photonic band structure, and anomalous effects in the sign and magnitude of the Doppler shifts are possible, both outside and inside the gap. We suggest that this effect could be used to identify the physical origin of the backward waves in recent metamaterials.
We investigate the extension of optical micromanipulation to integrated optics. In particular, we consider whether propagating light signals can cause mechanical reconfiguration of a device. While such forces are intrinsically weak, we predict theoretically that significant displacements can be achieved using various enhancement mechanisms. These include the use of high-index materials, high-Q (cavity quality factor) enhancement, and slow light in photonic crystals. Silicon optical waveguides have a considerable refractive index contrast with the surrounding air, with a ratio of roughly 3.45/1 at optical communications wavelengths. We show that the strong confinement of light to silicon magnifies optical forces arising from overlap in the guided modes of neighboring waveguides. Silica microsphere resonators are known to have extremely high cavity quality factors, in excess of 108. We show that the quality factor of the resonator magnifies the optical force due to modal overlap between two neighboring spheres. Thirdly, we investigate slow-light enhancement of optical forces using photonic-crystal devices. We show that slow-light velocities give rise to larger forces for the same amount of signal power, enhancing optomechanical coupling effects. In addition to being of fundamental interest, our work suggests that optical manipulation may ultimately provide a route to all-optical conformational control and switching.
Finite-difference time-domain (FDTD) methods suffer from reduced accuracy when modeling discontinuous dielectric materials, due to the inhererent discretization (“pixellization”). We show that accuracy can be significantly improved by using a sub-pixel smoothing of the dielectric function, but only if the smoothing scheme is properly designed. We develop such a scheme based on a simple criterion taken from perturbation theory, and compare it to other published FDTD smoothing methods. In addition to consistently achieving the smallest errors, our scheme is the only one that attains quadratic convergence with resolution for arbitrarily sloped interfaces. Finally, we discuss additional difficulties that arise for sharp dielectric corners.
We study tunable time-delay devices in which the time delay is tuned by changing the group velocity of the propagating signal. The device is designed to place the operating frequency near a photonic band edge. This enhances the change in delay for a given tuning range of the device refractive index. Here we provide an extended explanation of mode symmetry, nomenclature, and the complete band structure of a sample, integrated device to aid the understanding of our previously published work.
We show that two-dimensional photonic crystals can be designed to have dispersion relations with an extended ultraflat cross-section, meaning that for a fixed wave vector wave vector component kx the frequency of a band is almost constant when the other wave vector component ky takes all possible values. these ultra-flat are the result of a non-trivial saddle point in the dispersion relation located in the interior of the Brillouin zone. Interesting consequences include 1D-like behavior, improved super-collimation, and enhanced density of states.
We demonstrate by finite-difference time-domain simulations in 2D and 3D that optical cavities in realistic finite photonic crystals have lifetimes and modal volumes that are essentially insensitive to disorder (of various types, including surface disorder and randomized positions), even with unphysically large disorder. A lifetime Q=108 is demonstrated in a 3D single-mode cavity with a half-wavelength mode diameter using only eight vertical periods of a disordered crystal.
Forces arising from overlap between the guided waves of parallel, microphotonic waveguides are calculated. Both attractive and repulsive forces, determined by the choice of relative input phase, are found. Using realistic parameters for a silicon-on-insulator material system, we estimate that the forces are large enough to cause observable displacements. Our results illustrate the potential for a broader class of optically tunable microphotonic devices and microstructured artificial materials.
We investigate heating from field propagation, coupling, and bending, which are the potential failure mechanisms for an emerging new type of high-power radiation guides-hollow photonic Bragg fibers. Continuous wave (CW) and pulsed radiation sources are considered, assuming continuous operation of the laser source.
We have calculated the optically-induced force between coupled high-Q whispering gallery modes of microsphere resonators. Attractive and repulsive forces are found, depending whether the bi-sphere mode is symmetric or antisymmetric. The magnitude of the force is linearly proportional to the total power in the spheres and consequently linearly enhanced by Q. Forces on the order of 100 nN are found for Q=108, large enough to cause displacements in the range of 1μm when the sphere is attached to a fiber stem with spring constant 0.004 N/m.
We propose the use of slow-light, band-edge waveguides for compact, integrated, tunable optical time delays. We show that slow group velocities at the photonic band edge give rise to large changes in time delay for small changes in refractive index, thereby shrinking device size. Figures of merit are introduced to quantify the sensitivity, as well as the accompanying signal degradation due to dispersion. It is shown that exact calculations of the figures of merit for a realistic, three-dimensional grating structure are well predicted by a simple quadratic-band model, simplifying device design. We present adiabatic taper designs that attain <0.1% reflection in short lengths of 10 to 20 times the grating period. We show further that cascading two gratings compensates for signal dispersion and gives rise to a constant tunable time delay across bandwidths greater than 100GHz. Given typical loss values for silicon-on-insulator waveguides, we estimate that gratings can be designed to exhibit tunable delays in the picosecond range using current fabrication technology.
We present predicted relative scattering losses from sidewall roughness in a strip waveguide compared to an identical waveguide surrounded by a photonic crystal with a complete or incomplete gap in both 2d and 3d. To do so, we develop a new semi-analytical extension of the classic “volume-current method” (Green's functions with a Born approximation), correcting a longstanding limitation of such methods to low-index contrast systems (the classic method may be off by an order of magnitude in high-contrast systems). The resulting loss predictions show that even incomplete gap structures such as photonic-crystal slabs should, with proper design, be able to reduce losses by a factor of two compared to an identical strip waveguide; however, incautious design can lead to increased losses in the photonic-crystal system, a phenomena that we explain in terms of the band structure of the unperturbed crystal.
We propose and demonstrate a mechanism for small-modal-volume high-Q cavities based on an anomalous uniform waveguide mode that has zero group velocity at a nonzero wave vector. In a short piece of a uniform waveguide with a specially designed cross section, light is confined longitudinally by small group-velocity propagation and transversely by a reflective cladding. The quality factor Q is greatly enhanced by the small group velocity for a set of cavity lengths that are separated by approximately π/k0, where k0 is the longitudinal wave vector for which the group velocity is zero.
FFTW is an implementation of the discrete Fourier transform (DFT) that adapts to the hardware in order to maximize performance. This paper shows that such an approach can yield an implementation that is competitive with handoptimized libraries, and describes the software structure that makes our current FFTW3 version flexible and adaptive. We further discuss a new algorithm for real-data DFTs of prime size, a new way of implementing DFTs by means of SIMDmachine-specific instructions, and how a special-purpose compiler can derive optimized implementations of the discrete cosine and sine transforms automatically from a DFT algorithm.
The use of ultra-broadband supercontinuum generated by an all-fiber system to characterize high-index contrast photonic circuits over the wavelength range 1.2–2.0 μm is demonstrated. Efficient, broadband waveguide coupling techniques and sensitive normalized detection enable rapid and high-resolution measurements of nano-scale one-dimensional photonic crystal microcavities. Experimental mappings of bandgaps and cavity mode resonances with a wavelength resolution of 0.1 nm compare well with computer simulations.
Supercontinuum based sources and measurement techniques are developed, enabling optical ultra-broadband studies of nano-scale photonic crystal devices and integrated photonic circuits over 1.2–2.0 μm wavelength range. Experiments involving 1-D periodic photonic crystal microcavity waveguides and 3-D periodic photonic crystals with embedded point defects are described. Experimental findings are compared with rigorous electromagnetic simulations.
We describe the use of high-index-contrast, photonic-crystal wavegides for tunable time delays. The waveguide is designed such that the operating frequency is near a photonic band edge. In this slow light region, a small change in index yields a large change in group velocity, and consequently in time delay. Figures of merit for tunable time delay devices are introduced, including sensitivity, length, and dispersion. We show that a simple quadratic band model is a good predictor of the figures of merit for realistic, 3D, high-index-contrast structures. By cascading two grated waveguides, we can obtain a flat tunable time delay across the operating bandwidth.
A mechanism to reduce radiation loss from integrated optical cavities without a complete photonic bandgap is introduced and demonstrated. It is applicable to any device with a patterned substrate (including both low and high index-contrast systems), when it supports discrete guided or leaky modes through which power escaping the cavity can be channeled into radiation. One then achieves the associated increase in Q by designing the cavity such that the near-field pattern becomes orthogonal to these discrete modes, therefore canceling the coupling of power into them and thus reducing the total radiation loss. The method is independent of any delocalization mechanism and can be used to create high-Q cavities with small modal volume.
We study the radiation pressure on the surface of a waveguide formed by omnidirectionally reflecting mirrors. In the absence of losses, the pressure goes to infinity as the distance between the mirrors is reduced to the cutoff separation of the waveguide mode. This divergence at constant power input is due to the reduction of the modal group velocity to zero, which results in the magnification of the electromagnetic field. Our structure suggests a promising alternative, microscale system for observing the variety of classical and quantum-optical effects associated with radiation pressure in Fabry–Perot cavities.
We derive a general, analytical, coupled-mode theory for disorder-induced scattering in periodic systems that shows that in the experimentally relevant limit of weak disorder, the reflection in a photonic-crystal waveguide is just as low as in a comparable index-guided waveguide. Moreover, since the photonic band gap also blocks radiative loss, the total scattering loss is reduced, and the total transmission is higher. These general results are verified by direct numerical simulations in an example system.
Photonic crystals offer unprecedented opportunities for miniaturization and integration of optical devices. They also exhibit a variety of new physical phenomena, including suppression or enhancement of spontaneous emission, low-threshold lasing, and quantum information processing. Various techniques for the fabrication of three-dimensional (3D) crystals photonicsuch as silicon micromachining, wafer fusion bonding, holographic lithography, self-assembly, angled-etching, micromanipulation, glancing-angle deposition, auto-cloning, have been proposed and demonstrated with different levels of success. However, a critical step towards the fabrication of functional 3D devices, that is, the incorporation of microcavities or waveguides in a controllable way, has not been achieved at optical wavelengths. Here we present the fabrication of 3D photonic crystals that are particularly suited for optical device integration using a lithographic layer-by-layer approach. Point-defect microcavities are introduced during the fabrication process and optical measurements show they have resonant signatures around telecommunications wavelengths (1.3–1.5μm). Measurements of reflectance and transmittance at near-infrared are in good agreement with numerical simulations.
We report the design, device fabrication, and measurements of tunable silicon photonic band gap microcavities in optical waveguides, using direct application of piezoelectric-induced strain to the photonic crystal. We show, through first-order perturbation computations and experimental measurements, a 1.54 nm shift in cavity resonances at 1.56 μm wavelengths for an applied strain of 0.04%. The strain is applied through integrated piezoelectric microactuators. For operation at infrared wavelengths, we combine x-ray and electron-beam lithography with thin-film piezoelectric processing. This level of integration permits realizable silicon-based photonic chip devices, such as high-density optical filters, with active reconfiguration.
Photonic-crystal structures consisting of dielectric rods were designed, fabricated, and optically characterized. The combination of the high refractive-index-contrast GaAs/AlxOy material system with electron-beam lithography enabled the fabrication of structures suitable for the optical propagation of 1.5 μm light. Experimental transmission spectra were obtained for structures consisting of a two-dimensional array of rods and line-defect waveguides. Optical measurements confirmed the presence of a photonic band gap, as well as band gap guidance in the line-defect waveguide. A two-stage coupling scheme facilitated efficient optical coupling into the line-defect waveguide.
We present detailed theoretical and numerical analysis of certain novel non-linear optical phenomena enabled by photonic bandgap fibers. In particular, we demonstrate the feasibility of optical bistability in an axially modulated nonlinear photonic bandgap fiber through analytical theory and detailed numerical experiments. At 1.55μm carrier wavelength, the in-fiber devices we propose can operate with only a few tens of mW of power, have a nearly instantaneous response and recovery time, and be shorter than 100μm. Furthermore, we predict existence of gap-like solitons (which have thus-far been described only in axially periodic systems) in axially uniform photonic bandgap fibers.
We show that modes of axially uniform waveguides of arbitrary cross section can be made to have anomalous dispersion relations resulting from strong repulsion between two modes. When the axial wave vector k is 0, the two modes have different TE/TM symmetry and thus can be brought arbitrarily close to an accidental frequency degeneracy. For nonzero k, the symmetry is broken causing the modes to repel. When the modes are sufficiently close together this repulsion leads to unusual features such as extremely flattened dispersion relations, backward waves, zero group velocity for nonzero k, atypical divergence of the density of states, and nonzero group velocity at k = 0.
Group velocity, vg, dependence of propagation loss in single-line-defect photonic crystal waveguides on GaAs membranes, and minimum loss as low as 2.5 dB/mm, are presented. When vg is reduced by a factor of 7, an additional loss is found to be only 5 dB/mm, thus proving a feasible usage of low vg.
The majority of photonic crystals developed till-date are not dynamically tunable, especially in silicon-based structures. Dynamic tunability is required not only for reconfiguration of the optical characteristics based on user-demand, but also for compensation against external disturbances and relaxation of tight device fabrication tolerances. Recent developments in photonic crystals have suggested interesting possibilities for static small-strain modulations to affect the optical characteristics1-3, including a proposal for dynamic strain-tunability4. Here we report the theoretical analysis, device fabrication, and experimental measurements of tunable silicon photonic band gap microcavities in optical waveguides, through direct application of dynamic strain to the periodic structures5. The device concept consists of embedding the microcavity waveguide6 on a deformable SiO2 membrane. The membrane is strained through integrated thin-film piezoelectric microactuators. We show a 1.54 nm shift in cavity resonances at 1.56 μm wavelengths for an applied piezoelectric strain of 0.04%. This is in excellent agreement with our modeling, predicted through first-order semi-analytical perturbation theory7 and finite-difference time-domain calculations. The measured microcavity transmission shows resonances between 1.55 to 1.57 μm, with Q factors ranging from 159 to 280. For operation at infrared wavelengths, we integrate X-ray and electron-beam lithography (for critical 100 nm feature sizes) with thin-film piezoelectric surface micromachining. This level of integration permits realizable silicon-based photonic chip devices, such as high-density optical filters and spontaneous-emission enhancement devices with tunable configurations.
Standard perturbation theory (PT) and coupled mode theory (CMT) formulations fail or exhibit very slow convergence when applied to the analysis of geometrical variations in high index-contrast optical components such as Bragg fibers and photonic crystals waveguides. By formulating Maxwell's equations in perturbation matched curvilinear coordinates, we have derived several rigorous PT and CMT expansions that are applicable in the case of generic non-uniform dielectric profile perturbations in high index-contrast waveguides. In strong fiber tapers and fiber Bragg gratings we demonstrate that our formulation is accurate and rapidly converges to an exact result when used in a CMT framework even in the high index-contrast regime. We then apply our method to investigate the impact of hollow Bragg fiber ellipticity on its Polarization Mode Dispersion (PMD) characteristics for telecom applications. Correct PT expansions allowed us to design an efficient optimization code which we successfully applied to the design of dispersion compensating hollow Bragg fiber with optimized low PMD and very large dispersion parameter. We have also successfully extended this methodology to treat radiation scattering due to common geometric variations in generic photonic crystals. As an example, scattering analysis in strong 2D photonic crystal tapers is demonstrated.
In this work we present an introduction to photonic crystals by discussing the basic concepts and principles behind these artificial materials, as well as their abilities to control light and enable unusual optical phenomena. We will focus on specific examples including (1) negative refraction of light, (2) the superprism effect (anomalous electromagnetic dispersion), and (3) the possibility of superlensing (subwavelength focusing). These are very general results based on direct solutions of Maxwell's equations, and can consequently be of relevance to many areas of science and technology.
In a conventional material, the coherent Cerenkov radiation due to a moving charged particle is associated with a velocity threshold, a forward-pointing radiation cone, and a forward direction of emission. We describe different behavior for the Cerenkov radiation in a photonic crystal. In particular, this radiation is intrinsically coupled with transition radiation and is observable without any threshold. Within one particle-velocity range, we found a radiation pattern with a backward-pointing radiation cone. In another velocity range, backward-propagating Cerenkov radiation can be expected. Potential applications include velocity-sensitive particle detection and radiation generation at selectable frequencies.
We demonstrate the feasibility of optical bistability in an axially modulated nonlinear OmniGuide fiber through analytical theory and detailed numerical experiments. At 1.55-μm carrier wavelength, the in-fiber devices that we propose can operate with only a few tens of milliwatts of power, can have a nearly instantaneous response and recovery time, and can be shorter than 100 μm .
It is shown that certain metallic photonic crystals can enable negative refraction and subwavelength imaging without relying on a negative effective index. These metallic structures are very simple in design and appear straightforward for fabrication. Their unusual electromagnetic response should provide an interesting comparison with the metallic left-handed materials.
We present a method for dispersion-tailoring of OmniGuide and other photonic band-gap guided fibers based on weak interactions (“anticrossings”) between the core-guided mode and a mode localized in an intentionally introduced defect of the crystal. Because the core mode can be guided in air and the defect mode in a much higher-index material, we are able to obtain dispersion parameters in excess of 500,000 ps/nm-km. Furthermore, because the dispersion is controlled entirely by geometric parameters and not by material dispersion, it is easily tunable by structural choices and fiber-drawing speed. So, for example, we demonstrate how the large dispersion can be made to coincide with a dispersion slope that matches commercial silica fibers to better than 1%, promising efficient compensation. Other parameters are shown to yield dispersion-free transmission in a hollow OmniGuide fiber that also maintains low losses and negligible nonlinearities, with a nondegenerate TE01 mode immune to polarization-mode dispersion (PMD). We present theoretical calculations for a chalcogenide-based material system that has recently been experimentally drawn.
We present a rigorous analysis methodology of fundamental to higher order mode converters in step index few mode optical fibers. We demonstrate experimental conversion from a fundamental LP01 mode to the higher order LP11 mode utilizing a multiple mechanical bend mode converter. We perform a quantitative analysis of the measured light intensity, and demonstrate a modal decomposition algorithm to characterize the modal content excited in the fiber. Theoretical modelling of the current mode converter is then performed and compared with experimental findings.
In this paper, we analyze the electromagnetic mode structure of an OmniGuide fiber—hollow dielectric waveguide in which light is confined by a large index-contrast omnidirectional dielectric mirror. In particular, we find that the modes in an OmniGuide fiber are similar to those in a hollow metallic waveguide in their symmetries, cutoff frequencies, and dispersion relations. We show that the differences can be predicted by a model based on a single parameter—the phase shift upon reflection from the dielectric mirror. The analogy to the metal waveguide extends to the transmission properties, resulting in the identification of the TE01 mode as the lowest-loss mode of the OmniGuide fiber.
Using a symmetry-based approach, we have designed polarization-independent waveguides in a 3D photonic crystal. A comprehensive series of numerical experiments, involving the propagation of pulsed signals through long straight waveguide sections and sharp bends, quantitatively evaluates the bend-transmission coefficient over the entire bandwidth of the corresponding guided modes. High (∼95%) polarization-independent bend transmission is achieved within a certain frequency range.
We investigate the transmission of evanescent waves through a slab of photonic crystal and explore the recently suggested possibility of focusing light with subwavelength resolution. The amplification of near-field waves is shown to rely on resonant coupling mechanisms to surface photon bound states, and the negative refractive index is only one way of realizing this effect. It is found that the periodicity of the photonic crystal imposes an upper cutoff to the transverse wave vector of evanescent waves that can be amplified, and thus a photonic-crystal superlens is free of divergences even in the lossless case. A detailed numerical study of the optical image of such a superlens in two dimensions reveals a subtle and very important interplay between propagating waves and evanescent waves on the final image formation. Particular features that arise due to the presence of near-field light are discussed.
A design is presented for a nanoelectromechanical optical switch based on the horizontal deflection of an input waveguide to align with one of two output waveguides. The use of high-index (GaAs) strip waveguides surrounded by air, designed to be single-mode at 1.55 μm, significantly decreases device dimensions as compared to previous designs. Design tradeoffs between optical and mechanical properties of the device are discussed. By means of three-dimensional numerical simulations, optical transmission is optimized for two different design strategies: butt and parallel coupling. High polarization-independent transmission (over 90%) is predicted for realistic design parameters.
A new class of materials, called photonic crystals, affect a photon's properties in much the same way that a semiconductor affects an electron's properties. This represents an ability to mold and guide light that leads naturally to novel applications in several fields, including optoelectronics and telecommunications. We present an introductory survey of the basic concepts and ideas that underlie photonic crystals, and present results and devices that illustrate their potential to circumvent limits of traditional optical systems.
The ability of photonic crystals to mold the flow of light in new ways can lead to a variety of novel and improved designs of optical nanocomponents and nanodevices in photonics. Two examples will be presented: a) Using linear materials, a polarization independent waveguide is designed in a 3D photonic crystal. It is demonstrated that this system provides lossless guiding of light at length-scales approaching the wavelength of the light itself, offering a promising platform for the design of integrated high performance polarization-insensitive waveguide networks. b) Using nonlinear materials, a cylindrical photonic crystal fiber is designed that can exhibit all-optical switching without the need for an axial periodicity. It is shown that this property stems from the unique structure of the cylindrical photonic crystal guidedmode dispersion relation, and can lead to significant improvements in manufacturing ease, operating power usage, and device size requirements, making such a system ideal for integrated all-optical signal processing.
We demonstrate optical bistability in a class of non-linear photonic crystal devices, through the use of detailed numerical experiments, and analytical theory. Our devices are shorter than the wavelength of light in length, they can operate with only a few mW of power, and can be faster than 1ps.
Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electromagnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fails when applied to the problem of shifted material boundaries. In this paper we developed coupled mode and perturbation theory formulations for treating generic perturbations of a waveguide cross section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate beyond the first order and rapidly converges to an exact result when used in a coupled mode theory framework even for the high-index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of such quantities as deterministic PMD and change in the GV and GVD of a mode due to generic profile distortion in a waveguide of arbitrary cross section. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary profile variations in high-index-contrast waveguides.
In this work, we explore the possibility of designing photonic crystals to act as magnetic metamaterials: structures that exhibit magnetic properties despite the nonmagnetic character of their constituents. The building blocks of a magnetic material are microscopic magnetic dipoles, and to create a synthetic analog we employ point-defect modes in a photonic crystal. We begin by identifying a point defect mode in a three-dimensional crystal whose local field pattern resembles an oscillating magnetic moment. By analyzing the far-field pattern of the field radiated from the defect, we prove quantitatively that such modes can be designed with a primarily magnetic character: over 98% of the emitted power goes into magnetic multipole radiation. Unlike the constituents of natural para- and ferromagnetic materials, these synthetic magnetic emitters can be designed to operate without losses even at optical frequencies.
We present an adiabatic taper design in three dimensions for coupling light into photonic crystal defect waveguides in a square lattice of circular dielectric rods. The taper is a two-stage structure in which the first stage makes the transition from a dielectric waveguide to a coupled-cavity waveguide. The second stage subsequently transforms the waveguide mode from an index-guided mode to a band-gap-guided mode. We discuss differences between the two-dimensional device and its three-dimensional slab version.
Although brute-force simulations of Maxwell's equations, such as FDTD methods, have enjoyed wide success in modeling photonic-crystal systems, they are not ideally suited for the study of weak perturbations, such as surface roughness or gradual waveguide transitions, where a high resolution and/or large computational cells are required. Instead, we suggest that these important problems are ideally suited for semi-analytical methods, which employ perturbative corrections (typically only needing the lowest order) to the exactly understood perfect waveguide. However, semi-analytical methods developed for the study of conventional waveguides require modification for high index-contrast, strongly periodic photonic crystals, and we have developed corrected forms of coupled-wave theory, perturbation theory, and the volume-current method for this situation. In this paper, we survey these new developments and describe the most significant results for adiabatic waveguide transitions and disorder losses. We present design rules and scaling laws for adiabatic transitions. In the case of disorder, we show both analytically and numerically that photonic crystals can suppress radiation loss without any corresponding increase in reflection, compared to a conventional strip waveguide with the same modal area, group velocity, and disorder strength.
We show how an electromagnetic cavity with arbitrarily high Q and small (bounded) modal volume can be formed in two or three dimensions with a proper choice of dielectric constants. Unlike in previous work, neither a complete photonic bandgap nor a trade-off in mode localization for Q is required. Rather, scattering and radiation are prohibited by a perfect mode match of the TE-polarized modes in each subsection of a Bragg resonator. Qy values in excess of 105 are demonstrated through finite-difference time-domain simulations of two- and three-dimensional structures with modal areas or volumes of the order of the wavelength squared or cubed.
We report a successful experimental realization of a photonic-crystal Ysplitter operating at λ∼1.6μm. Our device has a large splitting angle of 120o and a miniature size of ∼3μm×3μm. Furthermore, the Y-splitter loss is measured to be 0.5–1dB at λ = 1640–1680 nm , making the Ysplitter promising for integrated photonic- circuit applications. These unique properties are attributed to the new guiding principle made possible by the photonic bandgap.
We describe an all-angle negative refraction effect that does not employ a negative effective index of refraction and involves photonic crystals. A few simple criteria sufficient to achieve this behavior are presented. To illustrate this phenomenon, a microsuperlens is designed and numerically demonstrated.
Perturbation theory permits the analytic study of small changes on known solutions, and is especially useful in electromagnetism for understanding weak interactions and imperfections. Standard perturbation-theory techniques, however, have difficulties when applied to Maxwell's equations for small shifts in dielectric interfaces (especially in high-index-contrast, three-dimensional systems) due to the discontinous field boundary conditions—in fact, the usual methods fail even to predict the lowest-order behavior. By considering a sharp boundary as a limit of anisotropically smoothed systems, we are able to derive a correct first-order perturbation theory and mode-coupling constants, involving only surface integrals of the unperturbed fields over the perturbed interface. In addition, we discuss further considerations that arise for higher-order perturbative methods in electromagnetism.
We present an analytical model and numerical experiments to describe optimal bistable switching in a nonlinear photonic crystal system. It is proved that only three parameters are needed to characterize a bistable switch: the resonant frequency ωres, the quality factor Q, and parameter κ that measures nonlinear “feedback strength.” A photonic crystal enables the device to operate in single-mode fashion, as if it were effectively one dimensional. This provides optimal control over the input and output and facilitates further large-scale optical integration.
We prove that an adiabatic theorem generally holds for slow tapers in photonic crystals and other strongly grated waveguides with arbitrary index modulation, exactly as in conventional waveguides. This provides a guaranteed pathway to efficient and broad-bandwidth couplers with, e.g., uniform waveguides. We show that adiabatic transmission can only occur, however, if the operating mode is propagating (nonevanescent) and guided at every point in the taper. Moreover, we demonstrate how straightforward taper designs in photonic crystals can violate these conditions, but that adiabaticity is restored by simple design principles involving only the independent band structures of the intermediate gratings. For these and other analyses, we develop a generalization of the standard coupled-mode theory to handle arbitrary nonuniform gratings via an instantaneous Bloch-mode basis, yielding a continuous set of differential equations for the basis coefficients. We show how one can thereby compute semianalytical reflection and transmission through crystal tapers of almost any length, using only a single pair of modes in the unit cells of uniform gratings. Unlike other numerical methods, our technique becomes more accurate as the taper becomes more gradual, with no significant increase in the computation time or memory. We also include numerical examples comparing to a well-established scattering-matrix method in two dimensions.
We introduce a photonic crystal that has a large range of effective negative refractive index in three dimensions (3D) and demonstrate its negative-refraction property by numerical simulations. With slight modifications, our design is also amenable to layer-by-layer fabrication. This work should enable experimental observation of negative refraction and related phenomena in 3D at optical frequencies.
Perturbation theory formulation of Maxwell's equations gives a theoretically elegant and computationally efficient way of describing small imperfections and weak interactions in electro-magnetic systems. It is generally appreciated that due to the discontinuous field boundary conditions in the systems employing high dielectric contrast profiles standard perturbation formulations fail when applied to the problem of shifted material boundaries. In this paper we developed a novel coupled mode and perturbation theory formulations for treating generic non-uniform (varying along the direction of propagation) perturbations of a waveguide cross-section based on Hamiltonian formulation of Maxwell equations in curvilinear coordinates. We show that our formulation is accurate and rapidly converges to an exact result when used in a coupled mode theory framework even for the high index-contrast discontinuous dielectric profiles. Among others, our formulation allows for an efficient numerical evaluation of induced PMD due to a generic distortion of a waveguide profile, analysis of mode filters, mode converters and other optical elements such as strong Bragg gratings, tapers, bends etc., and arbitrary combinations of thereof. To our knowledge, this is the first time perturbation and coupled mode theories are developed to deal with arbitrary non-uniform profile variations in high index-contrast waveguides.
We demonstrate how slow group velocities of light, which are readily achievable in photonic-crystal systems, can dramatically increase the induced phase shifts caused by small changes in the index of refraction. Such increased phase sensitivity may be used to decrease the sizes of many devices, including switches, routers, all-optical logical gates, wavelength converters, and others. At the same time a low group velocity greatly decreases the power requirements needed to operate these devices. We show how these advantages can be used to design switches smaller than 20μm ×200μm in size by using readily available materials and at modest levels of power. With this approach, one could have ∼105 such devices on a surface that is 2 cm ×2 cm, making it an important step towards large-scale all-optical integration.
We develop a novel perturbation theory formulation to evaluate polarization-mode dispersion (PMD) for a general class of scaling perturbations of a waveguide profile based on generalized Hermitian Hamiltonian formulation of Maxwell's equations. Such perturbations include elipticity and uniform scaling of a fiber cross section, as well as changes in the horizontal or vertical sizes of a planar waveguide. Our theory is valid even for discontinuous high-index contrast variations of the refractive index across a waveguide cross section. We establish that, if at some frequencies a particular mode behaves like pure TE or TM polarized mode (polarization is judged by the relative amounts of the electric and magnetic longitudinal energies in the waveguide cross section), then at such frequencies for fibers under elliptical deformation its PMD as defined by an intermode dispersion parameter τ becomes proportional to group-velocity dispersion D such that τ= λδ|D|, where δ is a measure of the fiber elipticity and λ is a wavelength of operation. As an example, we investigate a relation between PMD and group-velocity dispersion of a multiple-core step-index fiber as a function of the coreclad index contrast. We establish that in this case the positions of the maximum PMD and maximum absolute value of group-velocity dispersion are strongly correlated, with the ratio of PMD to group-velocity dispersion being proportional to the coreclad dielectric contrast.
We argue that OmniGuide fibers, which guide light within a hollow core by concentric multilayer films having the property of omnidirectional reflection, have the potential to lift several physical limitations of silica fibers. We show how the strong confinement in OmniGuide fibers greatly suppresses the properties of the cladding materials: even if highly lossy and nonlinear materials are employed, both the intrinsic losses and nonlinearities of silica fibers can be surpassed by orders of magnitude. This feat, impossible to duplicate in an index-guided fiber with existing materials, would open up new regimes for long-distance propagation and dense wavelengthdivision multiplexing (DWDM). The OmniGuide-fiber modes bear a strong analogy to those of hollow metallic waveguides; from this analogy, we are able to derive several general scaling laws with core radius. Moreover, there is strong loss discrimination between guided modes, depending upon their degree of confinement in the hollow core: this allows large, ostensibly multi-mode cores to be used, with the lowest-loss TE01 mode propagating in an effectively single-mode fashion. Finally, because this TE01 mode is a cylindrically symmetrical (“azimuthally” polarized) singlet state, it is immune to polarization-mode dispersion (PMD), unlike the doubly-degenerate linearly-polarized modes in silica fibers that are vulnerable to birefringence.
We demonstrate how dramatic increases in the induced phase shifts caused by small changes in the index of refraction can be achieved by using very slow group velocities of light, which are readily achievable in photonic crystal systems. Combined with the fact that small group velocity greatly decreases the power requirements needed to operate a device, enhanced phase sensitivity may be used to decrease the size and power requirements of many devices, including switches, routers, all-optical logical gates, wavelength converters, etc. We demonstrate how these advantages can be used to design switches smaller than 20*200 square microns in size, using readily available materials, and at modest levels of power. With this approach, one could have ∼105 such devices on a surface 2*2 square cm, making it an important step towards large-scale all-optical integration.
A new micro-cavity design is proposed and structures are realized using a 2D photonic-crystal slab. The cavity consists of seven defect holes that encompass a hexagon and is designed to reduce vertical light leakage. From a direct transmission measurement, a Q-value of 816 ±30 is achieved at λ=1.55μm. This high-Q cavity will enable realistic realization of spontaneous emission modification and on-off optical switches.
Photonic Crystals: The Road from Theory to Practice explores the theoretical road leading to the practical application of photonic band gaps. These new optimal devices are based on symmetry and resonance and the benefits and limitations of hybrid “two dimensional” slab systems in three dimensions. The book also explains that they also signify a return to the ideal of an omnidirectional band gap in a structure inspired by and emulating the simplicity of two dimensions. Finally, the book takes a look at computational methods to solve the mathematical problems that underlie all undertakings in this field. Photonic Crystals: The Road from Theory to Practice should rapidly bring the optical professional and engineer up to speed on this intersection of electromagnetism and solid-state physics. It will also provide an excellent addition to any graduate course in optics.
We describe a fully-vectorial, three-dimensional algorithm to compute the definite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor for anisotropic structures, and demonstrate that O(Δx2) convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugate-gradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.
We present the light-propagation characteristics of OmniGuide fibers, which guide light by concentric multi-layer dielectric mirrors having the property of omnidirectional reflection. We show how the lowest-loss TE01 mode can propagate in a single-mode fashion through even large-core fibers, with other modes eliminated asymptotically by their higher losses and poor coupling, analogous to hollow metallic microwave waveguides. Dispersion, radiation leakage, material absorption, nonlinearities, bending, acircularity, and interface roughness are considered with the help of leaky modes and perturbation theory, and both numerical results and general scaling relations are presented. We show that cladding properties such as absorption and nonlinearity are suppressed by many orders of magnitude due to the strong confinement in a hollow core, and other imperfections are tolerable, promising that the properties of silica fibers may be surpassed even when nominally poor materials are employed.
Based on a photonic-crystal slab structure, a 60 photonic-crystal waveguide bend is successfully fabricated. Its bending efficiency within the photonic bandgap is measured, and near 100% efficiency is observed at certain frequencies near the valence band edge. The bending radius is ∼1μm at a wavelength of λ∼1.55μm. The measured η spectrum also agrees well with a finite-difference time-domain simulation.
A new microcavity design is proposed and structures are realized with a two-dimensional photonic-crystal slab. The cavity consists of seven defect holes that encompass a hexagon and is designed to reduce vertical light leakage. From a direct transmission measurement, a Q value of 816 ±30 is achieved at λ= 1.55μm. This high-Q cavity will permit the realistic realization of spontaneous-emission modification and on–off optical switches.
We describe and demonstrate a new mechanism for low radiation losses in structures lacking a complete band gap, and show how resonant cavities with Q>103 can be achieved without sacrificing strong localization in 3d. This involves a forced cancellation in the lowest-order term(s) of the multipole far-field radiation expansion. We focus on the system of photonic-crystal slabs, one- to two-dimensionally periodic dielectric structures of finite height with vertical index guiding. Simulations and analytical results in 2d and 3d are presented.
A new class of materials, called photonic crystals, affects a photon's properties in much the same way that a semiconductor affects an electron's properties. The ability to mold and guide light leads naturally to novel applications in several fields, including optoelectronics and telecommunications. The authors present an introductory survey of the basic concepts and ideas, including results for never before possible photon phenomena.
Theoretical and numerical analyses of waveguide branches in a photonic crystal are presented. Conditions for perfect transmission and zero reflection are discussed. Based upon these conditions, numerical simulations of electromagnetic-wave propagation in photonic crystals are performed to identify structures with near-complete transmission.
Using numerical simulations, we demonstrate the construction of two-dimensional- (2D-) like defect modes in a recently proposed 3D photonic crystal structure. These modes, which are confined in all three dimensions by a complete photonic band gap, bear a striking similarity to those in 2D photonic crystals in terms of polarization, field profile, and projected band structures. It is expected that these results will greatly facilitate the observation of widely studied 2D photonic-crystal phenomena in a realistic, 3D physical system.
We describe a new photonic-crystal structure with a complete three-dimensional photonic band gap (PBG) and its potential application to integrated optics. The structure not only has a large band gap and is amenable to layer-by-layer litho-fabrication, but also introduces the feature of high-symmetry planar layers resembling two-dimensional photonic crystals. This feature enables integrated optical devices to be constructed by modification of only a single layer, and supports waveguide and resonant-cavity modes that strongly resemble the corresponding modes in the simpler and well-understood 2d systems. In contrast to previous attempts to realize 2d crystals in 3d via finite-height “slabs,” however, the complete PBG of the new system eliminates the possibility of radiation losses. Thus, it provides a robust infrastructure within which to embed complex optical networks, combining elements such as compact filters, channel-drops, and waveguide bends/junctions that have previously been proposed in 2d photonic crystals.
Using a two-dimensional (2D) photonic-crystal slab structure, we have demonstrated a strong 2D photonic band gap with the capability of fully controlling light in all three dimensions. Our demonstration confirms the predictions on the possibility of achieving 3D light control using 2D band gaps, with strong index guiding providing control in the third dimension, and raise the prospect of being able to realize novel photonic-crystal devices. Based on such slab structure with triangular lattice of holes, a 60-degree photonic-crystal waveguide bend is fabricated. The intrinsic bending efficiency (η) is measured within the photonic band gap. As high as 90% bending efficency is observed at some frequencies.
Highly efficient transmission of 1.5-μm light in a two-dimensional (2D) photonic crystal slab waveguide is experimentally demonstrated. Light waves are shown to be guided along a triple-line defect formed within a 2D crystal and vertically by a strong index-guiding mechanism. At certain wavelength ranges, complete transmission is observed, suggesting lossless guiding along this photonic one-dimensional conduction channel.
Linear waveguides in photonic-crystal slabs, two-dimensionally periodic dielectric structures of finite height, are fundamentally different from waveguides in two-dimensional photonic crystals. The most important distinctions arise from the fact that photonic-crystal slab waveguides must be index-confined in the vertical direction (while a band gap confines them horizontally). We present a systematic analysis of different families of waveguides in photonic-crystal slabs, and illustrate the considerations that must be applied to achieve single-mode guided bands in these systems. In this way, the unusual features of photonic-crystal waveguides can be realized in three dimensions without the fabrication complexity required by photonic crystals with complete three-dimensional band gaps.
Optoelectronic devices are increasingly important in communication and information technology. To achieve the necessary manipulation of light (which carries information in optoelectronic devices), considerable efforts are directed at the development of crystals photonicperiodic dielectric materials that have so-called photonic bandgaps, which prohibit the propagation of photons having energies within the bandgap region. Straightforward application of the bandgap concept is generally thought to require three-dimensional (3D) photonic crystals; their two-dimensional (2D) counterparts confine light in the crystal plane, but not in the perpendicular z direction, which inevitably leads to diffraction losses. Nonetheless, 2D photonic crystals still attract interest because they are potentially more amenable to fabrication by existing techniques and diffraction losses need not seriously impair utility. Here we report the fabrication of a waveguide-coupled photonic crystal slab (essentially a free-standing 2D photonic crystal) with a strong 2D bandgap at wavelengths of about 1.5 μm, yet which is capable of fully controlling light in all three dimensions. These features confirm theoretical calculations on the possibility of achieving 3D light control using 2D bandgaps, with index guiding providing control in the third dimension, and raise the prospect of being able to realize unusual photonic-crystal devices, such as thresholdless lasers.
A three-dimensionally periodic dielectric structure with a large complete photonic band gap (PBG) is presented. The structure is distinguished by a sequence of planar layers, identical except for a horizontal offset, and repeating every three layers to form an fcc lattice. The layers can be thought of as an alternating stack of the two basic two-dimensional (2D) PBG slab geometries: rods in air and air cylinders in dielectric. These high-symmetry planar cross-sections should simplify the integration of optical devices and components by allowing modification of only a single layer, using simple defects of the same form as in the corresponding 2D systems. A process for fabricating the structure with conventional planar microfabrication technology is described. Gaps of over 21% are obtained for Si/air substrates. Reasonable gaps, over 8%, can be achieved even for the moderate index ratio of 2.45 (Si/SiO2).
This paper presents two-dimensional (2-D) finite difference time domain (FDTD) simulations of low-loss rightangle waveguide bends, T-junctions and crossings, based on high index-contrast waveguides. Such structures are essential for the dense integration of optical components. Excellent performance characteristics are obtained by designing the waveguide intersection regions as low-Q resonant cavities with certain symmetries and small radiation loss. A simple analysis, based on coupled mode theory in time, is used to explain the operation principles and agrees qualitatively with the numerical results.
We analyze the properties of two-dimensionally periodic dielectric structures that have a band gap for propagation in a plane and that use index guiding to confine light in the third dimension. Such structures are more amenable to fabrication than photonic crystals with full three-dimensional band gaps, but retain or approximate many of the latter's desirable properties. We show how traditional band-structure analysis can be adapted to slab systems in the context of several representative structures, and describe the unique features that arise in this framework compared to ordinary photonic crystals.
FFT literature has been mostly concerned with minimizing the number of floating-point operations performed by an algorithm. Unfortunately, on present-day microprocessors this measure is far less important than it used to be, and interactions with the processor pipeline and the memory hierarchy have a larger impact on performance. Consequently, one must know the details of a computer architecture in order to design a fast algorithm. In this paper, we propose an adaptive FFT program that tunes the computation automatically for any particular hardware. We compared our program, called FFTW, with over 40 implementations of the FFT on 7 machines. Our tests show that FFTW's self-optimizing approach usually yields significantly better performance than all other publicly available software. FFTW also compares favorably with machine-specific, vendor-optimized libraries.
Photonic crystals of one- or two-dimensional periodicity can be used to achieve three-dimensional photon confinement in dielectric waveguides with modal volumes of the order of a cubic half-wavelength. Since photonic crystals of low-dimensional periodicity do not have full three-dimensional bandgaps, the microcavities undergo increasing radiation losses with decreasing modal volumes. High-Q resonant modes can be generated by reducing the strength of the photon confinement. Increasingly, larger modal volumes lead to lower radiation losses and more efficient coupling to waveguide modes outside the cavity.
We present general criteria for crossing perpendicular waveguides with nearly 100% throughput and 0% cross talk. Our design applies even when the waveguide width is of the order of the wavelength. The theoretical basis for this phenomenon is explained in terms of symmetry considerations and resonant tunneling and is then illustrated with numerical simulations for both a two-dimensional photonic crystal and a conventional high-index-contrast waveguide crossing. Cross-talk reduction by up to 8 orders of magnitude is achieved relative to unmodified crossings.
This paper describes FFTW, a portable C package for computing the one- and multidimensional complex discrete Fourier transform (DFT). FFTW is typically faster than all other publicly available DFT software, including the well-known FFTPACK and the code from Numerical Recipes. More interestingly, FFTW is competitive with or better than proprietary, highly-tuned codes such as Sun's Performance Library and IBM's ESSL library. FFTW implements the Cooley-Tukey fast Fourier transform, and is freely available on the Web at http://theory.lcs.mit/ fftw. Three main ideas are the keys to s performance. First, the computation of the transform is performed by an executor consisting of highly-optimized, composable blocks of C code called codelets. Second, at runtime, a planner finds an efficient way (called ) to compose the codelets. Through the planner, FFTW adapts itself to the architecture of the machine it is running on. Third, the codelets are automatically generated by a codelet generator written in the Caml Light dialect of ML. The codelet generator produces long, optimized, unreadable code, which is nevertheless easy to modify via simple changes to th generator.
Free-space digital optical systems have demonstrated the capability to provide thousands of optical connections between optoelectronic chips. This dense concentration of channels creates substantial challenges in monitoring individual connections for diagnostic purposes without compromising performance. From the concept of stroboscopic techniques, we have designed and constructed a multichannel optical diagnostic tool that operates analogously to an electronic-sampling oscilloscope. The tool is economically constructed by the use of commercially available video cameras and video-enhanced personal computers. An integrated software application operates the tool and displays multiplechannel waveforms. We demonstrate the oscilloscope-sampling optical waveforms of a twodimensional optoelectronic modulator array operating at data rates from 0.5 to 4 Gbits/s.
The advent of large-scale, free-space, optoelecironic interconnections, as demonstrated in recent system prototypes, requires new sampling methods to reveal diagnostic information. Several factors contribute to the difficulty of probing optical communications channels without disrupting their operation. High-speed electronic connections to the chip periphery are not available in sufficient number and would contribute an undesirable thermal load. Electronic and optical physical contact probes would obscure many of the optical channels that are relayed to a common surface of the chip in current systems. Optical sampling provides the better method although many standard techniques are either too time consuming or complex to implement. We will describe a tool we developed that delivers diagnostic information on a large number of high-speed, optical data channels simultaneously and operates analogously to the conventional sampling electronic oscilloscope. The optical oscilloscope is constructed using CCD cameras and video capture boards that are controlled by a software application resident in a personal computer. Sampling is based on a stroboscopic method of using short pulsed laser probe beam synchronized to a data stream to illuminate optical modulators within the opto-elecironic circuit. We have demonstrated and will discuss the tool's capability of simultaneously monitoring arrays of broadband optoelectronic devices operating at speeds from several hundred Megabit/s to a few Gigabit/s.
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