@article{SoyarsJo94,
author = {W. M. Soyars and Steven G. Johnson},
title = {Simulating the {Tevatron} liquid {Helium} satellite refrigerators},
journal = {Advances in Cryogenic Engineering},
year = 1994,
volume = 39,
pages = {1231--1235}
}
@article{MorrisonLe96,
pdf = {MorrisonLe96.pdf},
author = {Rick L. Morrison and Anthony L. Lentine and Steven G. Johnson and Wayne H. Knox},
title = {Design and demonstration of a high-speed, multichannel, optical-sampling oscilloscope},
journal = {Applied Optics},
year = 1996,
volume = 35,
pages = {1187--1194},
abstract = {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.}
}
@article{MorrisonJo96,
pdf = {MorrisonJo96.pdf},
author = {Rick L. Morrison and Steven G. Johnson and Anthony L. Lentine and Wayne H. Knox},
title = {Multichannel optical oscilloscope for sampling broadband free-space optoelectronic circuits },
journal = {Proc. SPIE},
year = 1996,
volume = 2692,
pages = {158--163},
abstract = {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.}
}
@article{FrigoJo05,
pdf = {FrigoJo05.pdf},
author = {Frigo, Matteo and Johnson, Steven G.},
title = {The Design and Implementation of {FFTW3}},
journal = {Proceedings of the IEEE},
year = 2005,
month = {February},
volume = 93,
number = 2,
pages = {216--231},
note = {Invited paper, special issue on ``Program Generation, Optimization, and Platform Adaptation''.},
abstract = {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.}
}
@inproceedings{FrigoJo98,
pdf = {FrigoJo98.pdf},
author = {Frigo, Matteo and Johnson, Steven G.},
title = {{FFTW}: An adaptive software architecture for the {FFT}},
booktitle = {Proc. 1998 IEEE Intl. Conf. Acoustics Speech and Signal Processing},
pages = {1381--1384},
year = 1998,
volume = 3,
publisher = {IEEE},
abstract = {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.}
}
@techreport{FrigoJo97,
pdf = {FrigoJo97.pdf},
author = {Frigo, Matteo and Johnson, Steven G.},
title = {The Fastest {Fourier} Transform in the {West}},
institution = {Massachusetts Institute of Technology},
year = 1997,
number = {MIT-LCS-TR-728},
month = {September},
abstract = {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.}
}
@article{JohnsonFr07,
pdf = {JohnsonFr07.pdf},
author = {Steven G. Johnson and Matteo Frigo},
title = {A modified split-radix {FFT} with fewer arithmetic operations},
journal = {IEEE Transactions on Signal Processing},
year = 2007,
month = {January},
volume = 55,
number = 1,
pages = {111--119},
abstract = {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.}
}
@article{VilleneuveFa98,
pdf = {VilleneuveFa98.pdf},
author = {P. R. Villeneuve and S. Fan and S. G. Johnson and J. D. Joannopoulos},
title = {Three-dimensional photon confinement in photonic crystals of low-dimensional periodicity},
journal = {IEE Proceedings: Optoelectronics},
year = 1998,
volume = 145,
number = 6,
pages = {384--390},
abstract = {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.}
}
@article{JohnsonMa98,
pdf = {JohnsonMa98.pdf},
author = {Steven G. Johnson and Christina Manolatou and Shanhui Fan and PierreR. Villeneuve and J. D. Joannopoulos and H. A. Haus},
title = {Elimination of cross talk in waveguide intersections},
journal = {Optics Letters},
year = 1998,
volume = 23,
number = 23,
pages = {1855--1857},
abstract = {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.}
}
@article{ManolatouJo99,
pdf = {ManolatouJo99.pdf},
author = {C. Manolatou and Steven G. Johnson and Shanhui Fan and Pierre R. Villeneuve and H. A. Haus and J. D. Joannopoulos},
title = {High-density integrated optics},
journal = {Journal of Lightwave Technology},
year = 1999,
volume = 17,
number = 9,
pages = {1682--1692},
abstract = {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.}
}
@article{JohnsonFa99,
pdf = {JohnsonFa99.pdf},
author = {Steven G. Johnson and Shanhui Fan and Pierre R. Villeneuve and J. D. Joannopoulos and L. A. Kolodziejski},
title = {Guided modes in photonic crystal slabs },
journal = {Physical Review~B},
year = 1999,
volume = 60,
pages = {5751--5758},
abstract = {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.}
}
@article{LinCh00,
pdf = {LinCh00.pdf},
author = {S. Y. Lin and E. Chow and S. G. Johnson and J. D. Joannopoulos},
title = {Demonstration of highly efficient waveguiding in a photonic crystal slab at the 1.5-$\mu$m wavelength},
journal = {Optics Letters},
year = 2000,
volume = 25,
pages = {1297--1299},
abstract = {Highly efficient transmission of 1.5-$\mu$m 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.}
}
@article{JohnsonVi00,
pdf = {JohnsonVi00.pdf},
author = {Steven G. Johnson and Pierre R. Villeneuve and Shanhui Fan and J. D. Joannopoulos},
title = {Linear waveguides in photonic-crystal slabs },
journal = {Physical Review~B},
year = 2000,
volume = 62,
pages = {8212--8222},
abstract = {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.}
}
@article{ChowLi00,
pdf = {ChowLi00.pdf},
author = {Edmond Chow and S. Y. Lin and S. G. Johnson and P. R. Villeneuve and J. D. Joannopoulos and J. R. Wendt and G. A. Vawter and W. Zubrzycki and H. Hou and A. Alleman},
title = { Three-dimensional control of light in a two-dimensional photonic crystal slab},
journal = {Nature},
year = 2000,
volume = 497,
pages = {983--986},
abstract = {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 $\mu$m, 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.}
}
@article{JohnsonJo00,
pdf = {JohnsonJo00.pdf},
author = {Steven G. Johnson and J. D. Joannopoulos},
title = {Three-dimensionally periodic dielectric layered structure with omnidirectional photonic band gap},
journal = {Applied Physics Letters},
year = 2000,
volume = 77,
pages = {3490--3492},
abstract = {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/SiO$_2$).}
}
@article{JohnsonJo01,
pdf = {JohnsonJo01.pdf},
author = {Steven Johnson and John Joannopoulos},
title = {Block-iterative frequency-domain methods for {Maxwell}'s equations in a planewave basis},
journal = {Optics Express},
year = 2001,
volume = 8,
pages = {173--190},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-8-3-173},
abstract = {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 $O(\Delta x^2)$ 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.}
}
@article{JohnsonIb01,
pdf = {JohnsonIb01.pdf},
author = {Steven Johnson and Mihai Ibanescu and M. Skorobogatiy and Ori Weisberg and Torkel Engeness and Marin Solja{\v{c}}i{\'{c}} and Steven Jacobs and J. Joannopoulos and Yoel Fink},
title = {Low-loss asymptotically single-mode propagation in large-core {OmniGuide} fibers},
journal = {Optics Express},
year = 2001,
volume = 9,
pages = {748--779},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-9-13-748},
abstract = {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 TE$_{01}$ 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.}
}
@article{ChowLi01,
pdf = {ChowLi01.pdf},
author = {Edmond Chow and S. Y. Lin and J. R. Wendt and S. G. Johnson and J. D. Joannopoulos},
title = {Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at $\lambda = 1.55\mu$m wavelengths},
journal = {Optics Letters},
year = 2001,
volume = 26,
pages = {286--288},
abstract = {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 $\sim 1\mu$m at a wavelength of $\lambda \sim 1.55\mu$m. The measured $\eta$ spectrum also agrees well with a finite-difference time-domain simulation.}
}
@article{LinCh01,
pdf = {LinCh01.pdf},
author = {S. Y. Lin and Edmond Chow and S. G. Johnson and J. D. Joannopoulos},
title = {Direct measurement of the quality factor in a two-dimensional photonic-crystal microcavity},
journal = {Optics Letters},
year = 2001,
volume = 26,
pages = {1903--1905},
abstract = {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 $816 \pm 30$ is achieved at $\lambda = 1.55\mu$m. This high-$Q$ cavity will permit the realistic realization of spontaneous-emission modification and on--off optical switches.}
}
@article{JohnsonFa01,
pdf = {JohnsonFa01.pdf},
author = {Steven G. Johnson and Shanhui Fan and Attila Mekis and J. D. Joannopoulos},
title = {Multipole-cancellation mechanism for high-{$Q$} cavities in the absence of a complete photonic band gap},
journal = {Applied Physics Letters},
year = 2001,
volume = 78,
pages = {3388--3390},
note = {Invited paper.},
abstract = {We describe and demonstrate a new mechanism for low radiation losses in structures lacking a complete band gap, and show how resonant cavities with $Q>10^3$ 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.}
}
@article{JohnsonMe01,
pdf = {JohnsonMe01.pdf},
author = {Steven G. Johnson and Attila Mekis and Shanhui Fan and John D. Joannopoulos},
title = {Molding the flow of light},
journal = {Computing in Science and Engineering},
year = 2001,
volume = 3,
number = 6,
pages = {38--47},
note = {Invited paper.},
abstract = {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.}
}
@article{FanJo01,
pdf = {FanJo01.pdf},
author = {Shanhui Fan and S. G. Johnson and J. D. Joannopoulos and C. Manolatou and H. A. Haus},
title = {Waveguide branches in photonic crystals},
journal = {Journal of the Optical Society of America~B},
year = 2001,
volume = 18,
pages = {162--165},
abstract = {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.}
}
@article{PovinelliJo01,
pdf = {PovinelliJo01.pdf},
author = {M. L. Povinelli and Steven G. Johnson and Shanhui Fan and J. D. Joannopoulos},
title = {Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap },
journal = {Physical Review~B},
year = 2001,
volume = 64,
pages = 075313,
abstract = {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.}
}
@article{JohnsonPo01-SPIE,
pdf = {JohnsonPo01-SPIE.pdf},
author = {Steven G. Johnson and Michelle L. Povinelli and John D. Joannopoulos},
title = {New photonic crystal system for integrated optics},
journal = {Proc. SPIE},
year = 2001,
volume = 4532,
pages = {167--179},
note = {Invited paper.},
abstract = {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. }
}
@article{ChowLi01-SPIE,
pdf = {ChowLi01-SPIE.pdf},
author = {Edmond K. Chow and Shawn-Yu Lin and Steven G. Johnson and John D. Joannopoulos and James A. Bur and Pierre R. Villeneuve},
title = {Demonstration of high waveguide bending efficiency ($>90$\%) in a photonic-crystal slab at 1.5-$\mu$m wavelengths},
journal = {Proc. SPIE},
year = 2001,
volume = 4283,
pages = {453--461},
abstract = {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 ($\eta$) is measured within the photonic band gap. As high as 90\% bending efficency is observed at some frequencies.}
}
@article{LinCh02,
pdf = {LinCh02.pdf},
author = {S. Y. Lin and E. Chow and J. Bur and S. G. Johnson and J. D. Joannopoulos},
title = {Low-loss, wide-angle {Y} splitter at approximately $\sim 1.6 \mu$m wavelengths built with a two-dimensional photonic crystal},
journal = {Optics Letters},
year = 2002,
volume = 27,
pages = {1400--1402},
abstract = {We report a successful experimental realization of a photonic-crystal Ysplitter operating at $\lambda \sim 1.6\mu$m. Our device has a large splitting angle of $120^\circ$ and a miniature size of $\sim 3\mu\mathrm{m}\times 3\mu\mathrm{m}$. Furthermore, the Y-splitter loss is measured to be 0.5--1dB at $\lambda$ = 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.}
}
@article{WattsJo02,
pdf = {WattsJo02.pdf},
author = {M. R. Watts and S. G. Johnson and H. A. Haus and J. D. Joannopoulos},
title = {Electromagnetic cavity with arbitrary {$Q$} and small modal volume without a complete photonic bandgap},
journal = {Optics Letters},
year = 2002,
volume = 27,
pages = {1785--1787},
abstract = {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. $Q$ values in excess of $10^5$ 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.}
}
@article{LuoJo02,
pdf = {LuoJo02.pdf},
author = {Chiyan Luo and Steven G. Johnson and J. D. Joannopoulos},
title = {All-angle negative refraction without negative effective index },
journal = {Physical Review~B},
year = 2002,
volume = 65,
pages = 201104,
abstract = {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.}
}
@article{JohnsonIb02,
pdf = {JohnsonIb02.pdf},
author = {Steven G. Johnson and M. Ibanescu and M. A. Skorobogatiy and O. Weisberg and J. D. Joannopoulos and Y. Fink},
title = {Perturbation theory for {Maxwell}'s equations with shifting material boundaries},
journal = {Physical Review~E},
year = 2002,
volume = 65,
pages = 066611,
abstract = {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.}
}
@article{SoljacicIb02,
pdf = {SoljacicIb02.pdf},
author = {Marin Solja{\v{c}}i{\'{c}} and Mihai Ibanescu and Steven G. Johnson and Yoel Fink and J. D. Joannopoulos},
title = {Optimal bistable switching in nonlinear photonic crystals },
journal = {Physical Review~E},
year = 2002,
volume = 66,
pages = 055601,
abstract = {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 $\omega_\mathrm{res}$, the quality factor $Q$, and parameter $\kappa$ 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.}
}
@article{JohnsonBi02,
pdf = {JohnsonBi02.pdf},
author = {Steven G. Johnson and Peter Bienstman and M. A. Skorobogatiy and Mihai Ibanescu and Elefterios Lidorikis and J. D. Joannopoulos},
title = {Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals},
journal = {Physical Review~E},
year = 2002,
volume = 66,
pages = 066608,
abstract = {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.}
}
@article{LuoJo02-3d,
pdf = {LuoJo02-3d.pdf},
author = {Chiyan Luo and Steven G. Johnson and J. D. Joannopoulos},
title = {All-angle negative refraction in a three-dimensionally periodic photonic crystal},
journal = {Applied Physics Letters},
year = 2002,
volume = 81,
pages = {2352--2354},
abstract = {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.}
}
@article{SkorobogatiyJa02,
pdf = {SkorobogatiyJa02.pdf},
author = {Maksim Skorobogatiy and Steven Jacobs and Steven Johnson and Yoel Fink},
title = {Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates},
journal = {Optics Express},
year = 2002,
volume = 10,
pages = {1227--1243},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-10-21-1227},
abstract = {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.}
}
@article{SoljacicJo02,
pdf = {SoljacicJo02.pdf},
author = {Marin Solja{\v{c}}i{\'{c}} and Steven G. Johnson and Shanhui Fan and Mihai Ibanescu and Erich Ippen and J. D. Joannopoulos},
title = {Photonic-crystal slow-light enhancement of nonlinear phase sensitivity},
journal = {Journal of the Optical Society of America~B},
year = 2002,
volume = 19,
pages = {2052--2059},
abstract = {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 $20\mu\mathrm{m} \times 200\mu\mathrm{m}$ in size by using readily available materials and at modest levels of power. With this approach, one could have $\sim 10^5$ such devices on a surface that is $2 \mathrm{cm} \times 2 \mathrm{cm}$, making it an important step towards large-scale all-optical integration.}
}
@article{SkorobogatiyIb02,
pdf = {SkorobogatiyIb02.pdf},
author = {Maksim Skorobogatiy and Mihai Ibanescu and Steven G. Johnson and Ori Weisberg and Torkel D. Engeness and Marin Solja{\v{c}}i{\'{c}} and Steven A. Jacobs and Yoel Fink},
title = {Analysis of general geometric scaling perturbations in a transmitting waveguide: Fundamental connection between polarization-mode dispersion and group-velocity dispersion},
journal = {Journal of the Optical Society of America~B},
year = 2002,
volume = 19,
pages = {2867--2875},
abstract = {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 $\tau$ becomes proportional to group-velocity dispersion $D$ such that $\tau = \lambda \delta |D|$, where $\delta$ is a measure of the fiber elipticity and $\lambda$ 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.}
}
@article{JohnsonIb02-SPIE,
pdf = {JohnsonIb02-SPIE.pdf},
author = {Steven G. Johnson and Mihai Ibanescu and Maksim A. Skorobogatiy and Ori Weisberg and Torkel D. Engeness and Marin Solja{\v{c}}i{\'{c}} and Steven A. Jacobs and John D. Joannopoulos and Yoel Fink},
title = {Breaking the glass ceiling: Hollow {OmniGuide} fibers},
journal = {Proc. SPIE},
year = 2002,
volume = 4655,
pages = {1--15},
abstract = {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 TE$_{01}$ mode propagating in an effectively single-mode
fashion. Finally, because this TE$_{01}$ 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.}
}
@article{SoljacicJo02-SPIE,
pdf = {SoljacicJo02-SPIE.pdf},
author = {Marin Solja{\v{c}}i{\'{c}} and Steven G. Johnson and Shanhui Fan and Mihai Ibanescu and Erich P. Ippen and John D. Joannopoulos},
title = {Enhancement of phase sensitivity by exploring slow light in photonic crystals},
journal = {Proc. SPIE},
year = 2002,
volume = 4870,
pages = {248--258},
abstract = {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 $\sim 10^5$ such devices on a surface 2*2
square cm, making it an important step towards large-scale all-optical
integration.}
}
@article{ChowLi02-SPIE,
pdf = {ChowLi02-SPIE.pdf},
author = {Edmond K. Chow and Shawn-Yu Lin and Steven G. Johnson and John D. Joannopoulos},
title = {Transmission measurement of quality factor in two-dimensional photonic-crystal microcavity},
journal = {Proc. SPIE},
year = 2002,
volume = 4646,
pages = {199--204},
abstract = {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 $816 \pm 30$ is achieved at $\lambda=1.55\mu$m. This
high-$Q$ cavity will enable realistic realization of spontaneous
emission modification and on-off optical switches.}
}
@article{LuoIb03,
pdf = {LuoIb03.pdf},
author = {Chiyan Luo and Mihai Ibanescu and Steven G. Johnson and J. D. Joannopoulos},
title = {Cerenkov Radiation in Photonic Crystals},
journal = {Science},
year = 2003,
volume = 299,
pages = {368--371},
abstract = {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.}
}
@article{SoljacicIb03,
pdf = {SoljacicIb03.pdf},
author = {Marin Solja{\v{c}}i{\'{c}} and Mihai Ibanescu and Steven G. Johnson and J. D. Joannopoulos and Yoel Fink},
title = {Optical bistability in axially modulated {OmniGuide} fibers},
journal = {Optics Letters},
year = 2003,
volume = 28,
pages = {516--518},
abstract = {We demonstrate the feasibility of optical bistability in an axially modulated nonlinear OmniGuide fiber through analytical theory and detailed numerical experiments. At 1.55-$\mu$m 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 $\mu$m .}
}
@article{LuoJo03,
pdf = {LuoJo03.pdf},
author = {Chiyan Luo and Steven Johnson and J. Joannopoulos and J. Pendry},
title = {Negative refraction without negative index in metallic photonic crystals},
journal = {Optics Express},
year = 2003,
volume = 11,
pages = {746--754},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-7-746},
abstract = {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.}
}
@article{EngenessIb03,
pdf = {EngenessIb03.pdf},
author = {Torkel Engeness and Mihai Ibanescu and Steven Johnson and Ori Weisberg and Maksim Skorobogatiy and Steven Jacobs and Yoel Fink},
title = {Dispersion tailoring and compensation by modal interactions in {OmniGuide} fibers},
journal = {Optics Express},
year = 2003,
volume = 11,
pages = {1175--1196},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-10-1175},
abstract = {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 TE$_{01}$ mode immune to polarization-mode dispersion (PMD). We present theoretical calculations for a chalcogenide-based material system that has recently been experimentally drawn.}
}
@article{SkorobogatiyAn03,
pdf = {SkorobogatiyAn03.pdf},
author = {M. Skorobogatiy and C. Anastassiou and Steven Johnson and O. Weisberg and Torkel Engeness and Steven Jacobs and Rokan Ahmad and Yoel Fink },
title = {Quantitative characterization of higher-order mode converters in weakly multimoded fibers},
journal = {Optics Express},
year = 2003,
volume = 11,
pages = {2838--2847},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-11-22-2838},
abstract = {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 LP$_{01}$ mode to the higher order LP$_{11}$ 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.}
}
@article{IbanescuJo03,
pdf = {IbanescuJo03.pdf},
author = {Mihai Ibanescu and Steven G. Johnson and Marin Solja{\v{c}}i{\'{c}} and J. D. Joannopoulos and Yoel Fink and Ori Weisberg and Torkel D. Engeness and Steven A. Jacobs and M. Skorobogatiy},
title = {Analysis of mode structure in hollow dielectric waveguide fibers },
journal = {Physical Review~E},
year = 2003,
volume = 67,
pages = 046608,
abstract = {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 TE$_{01}$ mode as the lowest-loss mode of the OmniGuide fiber.}
}
@article{LidorikisPo03,
pdf = {LidorikisPo03.pdf},
author = {E. Lidorikis and M. L. Povinelli and S. G. Johnson and J. D. Joannopoulos},
title = {Polarization-independent linear waveguides in 3d photonic crystals},
journal = {Physical Review Letters},
year = 2003,
volume = 91,
pages = 023902,
abstract = {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 ($\sim 95\%$) polarization-independent bend transmission is achieved within a certain frequency range.}
}
@article{LuoJo03-subwavelength,
pdf = {LuoJo03-subwavelength.pdf},
author = {Chiyan Luo and Steven G. Johnson and J. D. Joannopoulos},
title = {Subwavelength imaging in photonic crystals },
journal = {Physical Review~B},
year = 2003,
volume = 68,
pages = 045115,
abstract = {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.}
}
@article{PovinelliBr03,
pdf = {PovinelliBr03.pdf},
author = {Povinelli, M. L. and Bryant, R. E. and Assefa, S. and Johnson, S. G. and Shanhui Fan and Erchak, A. A. and Petrich, G. S. and Lidorikis, E. and Joannopoulos, J. D. and Kolodziejski, L. A. and Ippen, E. P.},
title = { Design of a nanoelectromechanical high-index-contrast guided-wave optical switch for single-mode operation at 1.55 $\mu$m},
journal = {IEEE Photonics Technology Letters},
year = 2003,
volume = 15,
number = 9,
pages = {1207--1209},
abstract = {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 $\mu$m, 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.}
}
@article{JohnsonJo03,
pdf = {JohnsonJo03.pdf},
author = {Steven G. Johnson and J. D. Joannopoulos},
title = {Designing synthetic optical media: Photonic crystals},
journal = {Acta Materialia},
year = 2003,
volume = 51,
pages = {5823--5835},
abstract = {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.}
}
@article{LidorikisPo03-SPIE,
pdf = {LidorikisPo03-SPIE.pdf},
author = {Elefterios Lidorikis and Michelle L. Povinelli and Steven G. Johnson and Marin Solja{\v{c}}i{\'{c}} and Mihai Ibanescu and Yoel Fink and John D. Joannopoulos},
title = {Modeling of nanophotonics},
journal = {Proc. SPIE},
year = 2003,
volume = 5225,
pages = {7--19},
note = {Invited paper.},
abstract = {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.}
}
@article{SoljacicIb03-SPIE,
pdf = {SoljacicIb03-SPIE.pdf},
author = {Marin Solja{\v{c}}i{\'{c}} and Mihai Ibanescu and Chiyan Luo and Steven G. Johnson and Shanhui Fan and Yoel Fink and John D. Joannopoulos},
title = {All-optical switching using optical bistability in nonlinear photonic crystals},
journal = {Proc. SPIE},
year = 2003,
volume = 5000,
pages = {200--214},
note = {Invited paper.},
abstract = {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.}
}
@article{SkorobogatiyJo03,
pdf = {SkorobogatiyJo03.pdf},
author = {M. Skorobogatiy and Steven G. Johnson and Steven A. Jacobs and Yoel Fink},
title = {Dielectric profile variations in high-index-contrast waveguides, coupled mode theory, and perturbation expansions},
journal = {Physical Review~E},
year = 2003,
volume = 67,
pages = 046613,
abstract = {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.}
}
@article{PovinelliJo03,
pdf = {PovinelliJo03.pdf},
author = {M. L. Povinelli and Steven G. Johnson and J. D. Joannopoulos and J. B. Pendry},
title = {Toward photonic-crystal metamaterials: Creating magnetic emitters in photonic crystals},
journal = {Applied Physics Letters},
year = 2003,
volume = 82,
pages = {1069--1071},
abstract = {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.}
}
@article{BienstmanAs03,
pdf = {BienstmanAs03.pdf},
author = {Peter Bienstman and Solomon Assefa and Steven G. Johnson and John D. Joannopoulos and Gale S. Petrich and Leslie A. Kolodziejski },
title = {Taper structures for coupling into photonic crystal slab waveguides},
journal = {Journal of the Optical Society of America~B},
year = 2003,
volume = 20,
pages = {1817--1821},
abstract = {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.}
}
@inproceedings{JohnsonPo03-ESPC,
pdf = {JohnsonPo03-ESPC.pdf},
author = {Steven G. Johnson and M. L. Povinelli and P. Bienstman and M. Skorobogatiy and Solja{\v{c}}i{\'{c}}, Marin and M. Ibanescu and E. Lidorikis and J. D. Joannopoulos},
title = {Coupling, scattering and perturbation theory: Semi-analytical analyses of photonic-crystal waveguides},
booktitle = {Proc. 2003 5th Intl. Conf. on Transparent Optical Networks and 2nd European Symp. on Photonic Crystals},
pages = {103--109},
year = 2003,
volume = 1,
abstract = {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.}
}
@article{KaralisJo04,
pdf = {KaralisJo04.pdf},
author = {Aristeidis Karalis and Steven G. Johnson and J. D. Joannopoulos},
title = {Discrete-mode cancellation mechanism for high-{$Q$} integrated optical cavities with small modal volume},
journal = {Optics Letters},
year = 2004,
volume = 29,
pages = {2309--2311},
abstract = {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.}
}
@article{PovinelliIb04,
pdf = {PovinelliIb04.pdf},
author = {M. L. Povinelli and Mihai Ibanescu and Steven G. Johnson and J. D. Joannopoulos},
title = {Slow-light enhancement of radiation pressure in an omnidirectional-reflector waveguide},
journal = {Applied Physics Letters},
year = 2004,
volume = 85,
pages = {1466--1468},
abstract = {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.}
}
@article{PovinelliJo04,
pdf = {PovinelliJo04.pdf},
author = {M. L. Povinelli and Steven G. Johnson and Elefterios Lidorikis and J. D. Joannopoulos and Marin Solja{\v{c}}i{\'{c}}},
title = {Effect of a photonic band gap on scattering from waveguide disorder},
journal = {Applied Physics Letters},
year = 2004,
volume = 84,
pages = {3639--3641},
abstract = {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.}
}
@article{QiLi04,
pdf = {QiLi04.pdf},
author = {Minghao Qi and Elefterios Lidorikis and Peter T. Rakich and Steven G. Johnson and J. D. Joannopoulos and Erich P. Ippen and Henry I. Smith},
title = { A three-dimensional optical photonic crystal with designed point defects},
journal = {Nature},
year = 2004,
volume = 429,
pages = {538--542},
abstract = {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--1.5$\mu$m). Measurements of reflectance and transmittance at near-infrared are in good agreement with numerical simulations.}
}
@article{WongRa04,
pdf = {WongRa04.pdf},
author = {Chee Wei Wong and Peter T. Rakich and Steven G. Johnson and Minghao Qi and Henry I. Smith and Erich P. Ippen and Lionel C. Kimerling and Yongbae Jeon and George Barbastathis and Sang-Gook Kim},
title = {Strain-tunable silicon photonic band gap microcavities in optical waveguides},
journal = {Applied Physics Letters},
year = 2004,
volume = 84,
pages = {1242--1244},
abstract = {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 $\mu$m 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.}
}
@article{AssefaRa04,
pdf = {AssefaRa04.pdf},
author = {Solomon Assefa and Peter T. Rakich and Peter Bienstman and Steven G. Johnson and Gale S. Petrich and John D. Joannopoulos and Leslie A. Kolodziejski and Erich P. Ippen and Henry I. Smith},
title = {Guiding 1.5$\mu$m light in photonic crystals based on dielectric rods},
journal = {Applied Physics Letters},
year = 2004,
volume = 85,
pages = {6110--6112},
abstract = {Photonic-crystal structures consisting of dielectric rods were designed, fabricated, and optically characterized. The combination of the high refractive-index-contrast GaAs/Al$_x$O$_y$ material system with electron-beam lithography enabled the fabrication of structures suitable for the optical propagation of 1.5 $\mu$m 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. }
}
@article{SoljacicLi04,
pdf = {SoljacicLi04.pdf},
author = {Marin Solja{\v{c}}i{\'{c}} and Elefterios Lidorikis and Mihai Ibanescu and Steven Johnson and J. Joannopoulos and Yoel Fink},
title = {Optical bistability and cutoff solitons in photonic bandgap fibers},
journal = {Optics Express},
year = 2004,
volume = 12,
pages = {1518--1527},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-8-1518},
abstract = {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 1.55$\mu$m 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 100$\mu$m. 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.}
}
@article{IbanescuJo04,
pdf = {IbanescuJo04.pdf},
author = {M. Ibanescu and S. G. Johnson and D. Roundy and C. Luo and Y. Fink and J. D. Joannopoulos},
title = {Anomalous dispersion relations by symmetry breaking in axially uniform waveguides},
journal = {Physical Review Letters},
year = 2004,
volume = 92,
pages = 063903,
abstract = {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 $k = 0$.}
}
@article{SasakiOh04,
author = {Y. Sasaki and Y. Ohtera and S. G. Johnson and S. Kawakami},
title = {A reference analytical model of three-dimensional photonic crystal waveguides and their mode spectrum},
journal = {Trans. Inst. Elect. Info. Comm. Eng. C},
year = 2004,
volume = {J87-C},
number = 3,
pages = {328--334}
}
@article{TanakaSu04,
pdf = {TanakaSu04.pdf},
author = {Y. Tanaka and Y. Sugimoto and N. Ikeda and H. Nakamura and K. Asakawa and K. Inoue and S. G. Johnson},
title = {Group velocity dependence of propagation losses in single-line-defect photonic crystal waveguides on {GaAs} membranes},
journal = {Electronics Letters},
year = 2004,
volume = 40,
number = 3,
pages = {174--176},
abstract = {Group velocity, $v_g$, 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 $v_g$ 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 $v_g$.}
}
@article{WongYa04-SPIE,
pdf = {WongYa04-SPIE.pdf},
author = {Chee Wei Wong and Xiaodong Yang and Peter T. Rakich and Steven G. Johnson and Minghao Qi and Yongbae Jeon and George Barbastathis and Sang-Gook Kim},
title = {Strain-tunable photonic bandgap microcavity waveguides in silicon at 1.55 $\mu$m},
journal = {Proc. SPIE},
year = 2004,
volume = 5511,
pages = {156--164},
abstract = {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 $\mu$m 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 $\mu$m, 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.}
}
@article{SkorobogatiyJa04-SPIE,
pdf = {SkorobogatiyJa04-SPIE.pdf},
author = {Maksim Skorobogatiy and Steven A. Jacobs and Steven G. Johnson and Michel Meunier and Yoel Fink},
title = {Modeling the impact of manufacturing imperfections on photonic crystal device performance: design of perturbation-tolerant {PBG} components},
journal = {Proc. SPIE},
year = 2004,
volume = 5450,
pages = {161--172},
abstract = {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.}
}
@article{LuoJo04-SPIE,
pdf = {LuoJo04-SPIE.pdf},
author = {Chiyan Luo and Steven G. Johnson and Marin Solja{\v{c}}i{\'{c}} and John D. Joannopoulos and John B. Pendry},
title = {Novel optical phenomena with photonic crystals},
journal = {Proc. SPIE},
year = 2004,
volume = 5166,
pages = {207--219},
abstract = {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.}
}
@article{JohnsonPo05,
pdf = {JohnsonPo05.pdf},
author = {S. G. Johnson and M. L. Povinelli and M. Solja{\v{c}}i{\'{c}} and A. Karalis and S. Jacobs and J. D. Joannopoulos},
title = {Roughness losses and volume-current methods in photonic-crystal waveguides},
journal = {Applied Physics B},
year = 2005,
month = {July},
volume = 81,
number = {2--3},
pages = {283--293},
note = {Invited paper, special issue on photonic crystals.},
abstract = {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.}
}
@article{IbanescuJo05,
pdf = {IbanescuJo05.pdf},
author = {Mihai Ibanescu and Steven G. Johnson and David Roundy and Yoel Fink and J. D. Joannopoulos},
title = {Microcavity confinement based on an anomalous zero group-velocity waveguide mode},
journal = {Optics Letters},
year = 2005,
month = {March},
volume = 30,
pages = {552--554},
abstract = {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 $\pi/k_0$, where $k_0$ is the longitudinal wave vector for which the group velocity is zero.}
}
@article{RakichSo05,
pdf = {RakichSo05.pdf},
author = {Peter T. Rakich and Hideyuki Sotobayashi and Juliet T. Gopinath and Steven G. Johnson and Jason W. Sickler and Chee Wei Wong and John D. Joannopoulos and Erich P. Ippen},
title = {Nano-scale photonic crystal microcavity characterization with an all-fiber based 1.2--2.0 $\mu$m supercontinuum},
journal = {Optics Express},
year = 2005,
month = {January},
volume = 13,
pages = {821--825},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-3-821},
abstract = {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 $\mu$m 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.}
}
@article{PovinelliLo05,
pdf = {PovinelliLo05.pdf},
author = {Michelle L. Povinelli and Marko Loncar and Mihai Ibanescu and Elizabeth J. Smythe and Steven G. Johnson and Federico Capasso and John D. Joannopoulos },
title = {Evanescent-wave bonding between optical waveguides},
journal = {Optics Letters},
year = 2005,
month = {November},
volume = 30,
pages = {3042--3044},
abstract = {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.}
}
@article{PovinelliJo05-whispering,
pdf = {PovinelliJo05-whispering.pdf},
author = {Michelle Povinelli and Steven Johnson and Marko Loncar and Mihai Ibanescu and Elizabeth Smythe and Federico Capasso and J. Joannopoulos},
title = {High-{$Q$} enhancement of attractive and repulsive optical forces between coupled whispering-gallery-mode resonators},
journal = {Optics Express},
year = 2005,
month = {October},
volume = 13,
pages = {8286--8295},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-20-8286},
abstract = {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 1$\mu$m when the sphere is attached to a fiber stem with spring constant 0.004 N/m.}
}
@article{RodriguezIb05,
pdf = {RodriguezIb05.pdf},
author = {Alejandro Rodriguez and M. Ibanescu and J. D. Joannopoulos and Steven G. Johnson},
title = {Disorder-immune confinement of light in photonic-crystal cavities},
journal = {Optics Letters},
year = 2005,
month = {December},
volume = 30,
pages = {3192--3194},
abstract = {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 $Q=10^8$ is demonstrated in a 3D single-mode cavity with a half-wavelength mode diameter using only eight vertical periods of a disordered crystal.}
}
@article{PovinelliJo05,
pdf = {PovinelliJo05.pdf},
author = {M. Povinelli and Steven Johnson and J. Joannopoulos },
title = {Slow-light, band-edge waveguides for tunable time delays},
journal = {Optics Express},
year = 2005,
month = {September},
volume = 13,
pages = {7145--7159},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-7145},
abstract = {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.}
}
@article{SkorobogatiyJa05,
pdf = {SkorobogatiyJa05.pdf},
author = {M. Skorobogatiy and S. A. Jacobs and S. G. Johnson and C. Anastassiou and B. Temelkuran},
title = {Heating of hollow photonic {Bragg} fibers from field propagation, coupling, and bending},
journal = {Journal of Lightwave Technology},
year = 2005,
month = {November},
volume = 23,
number = 11,
pages = {3517--3525},
abstract = {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.}
}
@article{RakichSo05-SPIE,
pdf = {RakichSo05-SPIE.pdf},
author = {Peter T. Rakich and Hideyuki Sotobayashi and Juliet T. Gopinath and Jason W. Sickler and Chee Wei Wong and Steven G. Johnson and Minghao Qi and Elefterios Lidorikis and Henry I. Smith and John D. Joannopoulos and Erich P. Ippen},
title = {Broadband optical studies of 1-{D} and 3-{D} photonic crystals},
journal = {Proc. SPIE},
year = 2005,
volume = 6017,
pages = 601702,
note = {Invited paper},
abstract = {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 $\mu$m 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.}
}
@article{PovinelliJo05-SPIE,
pdf = {PovinelliJo05-SPIE.pdf},
author = {Michelle L. Povinelli and Steven G. Johnson and John D. Joannopoulos},
title = {High-index-contrast, photonic-band-edge waveguides for tunable time delays},
journal = {Proc. SPIE},
year = 2005,
volume = 5926,
pages = {59260D},
abstract = {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.}
}
@article{LuoIb06,
pdf = {LuoIb06.pdf},
author = {Chiyan Luo and Mihai Ibanescu and Evan J. Reed and Steven G. Johnson and J. D. Joannopoulos},
title = {Doppler radiation emitted by an oscillating dipole moving inside a photonic band-gap crystal},
journal = {Physical Review Letters},
year = 2006,
month = {February},
volume = 96,
pages = 043903,
abstract = {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.}
}
@article{FarjadpourRo06,
pdf = {FarjadpourRo06.pdf},
author = {Ardavan Farjadpour and David Roundy and Alejandro Rodriguez and Mihai Ibanescu and Peter Bermel and J. D. Joannopoulos and Steven G. Johnson and Geoffrey Burr},
title = {Improving accuracy by subpixel smoothing in {FDTD}},
journal = {Optics Letters},
year = 2006,
month = {October},
volume = 31,
pages = {2972--2974},
abstract = {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.}
}
@article{BermelRo06,
pdf = {BermelRo06.pdf},
author = {Peter Bermel and Alejandro Rodriguez and Steven G. Johnson and John D. Joannopoulos and Marin Solja{\v{c}}i{\'{c}}},
title = {Single-photon all-optical switching using waveguide-cavity quantum electrodynamics},
journal = {Physical Review~A},
year = 2006,
month = {October},
volume = 74,
pages = 043818,
abstract = {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.}
}
@article{PovinelliLo06-SPIE,
pdf = {PovinelliLo06-SPIE.pdf},
author = {M. L. Povinelli and M. Lon{\v{c}}ar and E. J. Smythe and M. Ibanescu and S. G. Johnson and F. Capasso and J. D. Joannopoulos},
title = {Enhancement mechanisms for optical forces in integrated optics},
journal = {Proc. SPIE},
year = 2006,
volume = 6326,
pages = 632609,
abstract = {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.}
}
@article{FarjadpourRo06-SPIE,
pdf = {FarjadpourRo06-SPIE.pdf},
author = {A. Farjadpour and D. Roundy and A. Rodriguez and M. Ibanescu and P. Bermel and J. D. Joannopoulos and S. G. Johnson and G. W. Burr},
title = {Improving accuracy by sub-pixel smoothing in {FDTD}},
journal = {Proc. SPIE},
year = 2006,
volume = 6322,
pages = {63220G},
abstract = {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.}
}
@article{PovinelliJo06-SPIE,
pdf = {PovinelliJo06-SPIE.pdf},
author = {M. L. Povinelli and S. G. Johnson and J. D. Joannopoulos },
title = {Tunable time delays in photonic-crystal waveguides},
journal = {Proc. SPIE},
year = 2006,
volume = 6128,
pages = {61280R},
abstract = {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.}
}
@article{IbanescuSo06-SPIE,
pdf = {IbanescuSo06-SPIE.pdf},
author = {Mihai Ibanescu and Marin Solja{\v{c}}i{\'{c}} and Steven G. Johnson and J. D. Joannopoulos},
title = {Ultra-flat bands in two-dimensional photonic crystals},
journal = {Proc. SPIE},
year = 2006,
volume = 6128,
pages = 612808,
note = {Invited paper.},
abstract = {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 $k_x$ the frequency of a band is almost constant when the other wave vector component $k_y$ 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.}
}
@article{RodriguezSo07,
pdf = {RodriguezSo07.pdf},
author = {Alejandro Rodriguez and Marin Solja{\v{c}}i{\'{c}} and J. D. Joannopoulos and Steven G. Johnson},
title = {$\chi^{(2)}$ and $\chi^{(3)}$ harmonic generation at a critical power in inhomogeneous doubly resonant cavities},
journal = {Optics Express},
year = 2007,
volume = 15,
number = 12,
pages = {7303--7318},
eprint = {arXiv:0704.1890v1},
month = {May},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-12-7303},
abstract = {We derive general conditions for 100\% frequency conversion in any doubly resonant nonlinear cavity, for both second- and third-harmonic generation via $\chi^{(2)}$ and $\chi^{(3)}$ 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 $\chi^{(2)}$ and $\chi^{(3)}$ 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.}
}
@article{RodriguezIb07,
pdf = {RodriguezIb07.pdf},
author = {Alejandro Rodriguez and Mihai Ibanescu and Davide Iannuzzi and Federico Capasso and J. D. Joannopoulos and Steven G. Johnson},
title = {Computation and visualization of {Casimir} forces in arbitrary geometries: Nonmonotonic lateral-wall forces and the failure of proximity-force approximations},
journal = {Physical Review Letters},
year = 2007,
volume = 99,
pages = 080401,
month = {August},
abstract = {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.}
}
@article{AbadFa07,
pdf = {AbadFa07.pdf},
author = {Jorge Bravo-Abad and Shanhui Fan and Steven G. Johnson and John D. Joannopoulos and Marin Solja{\v{c}}i{\'{c}}},
title = {Modeling nonlinear optical phenomena in nanophotonics},
journal = {Journal of Lightwave Technology},
year = 2007,
volume = 25,
number = 9,
pages = {2539--2546},
month = {September},
note = {Invited paper},
abstract = {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.}
}
@article{RodriguezIb07-pra,
pdf = {RodriguezIb07-pra.pdf},
author = {Alejandro Rodriguez and Mihai Ibanescu and Davide Iannuzzi and John D. Joannopoulos and Steven G. Johnson},
title = {Virtual photons in imaginary time: Computing exact {Casimir} forces via standard numerical-electromagnetism techniques},
journal = {Physical Review~A},
year = 2007,
volume = 76,
pages = {032106},
eprint = {arXiv:0705.3661},
month = {September},
abstract = {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.}
}
@article{AbadRo07,
pdf = {AbadRo07.pdf},
author = {Jorge Bravo-Abad and Alejandro Rodriguez and Peter Bermel and Steven G. Johnson and John D. Joannopoulos and Marin Solja{\v{c}}i{\'{c}}},
title = {Enhanced nonlinear optics in photonic-crystal microcavities},
journal = {Optics Express},
year = 2007,
month = {November},
volume = 15,
number = 24,
pages = {16161--16176},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-24-16161},
abstract = {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.}
}
@article{ZaheerRo07,
pdf = {ZaheerRo07.pdf},
author = {Saad Zaheer and Alejandro W. Rodriguez and Steven G. Johnson and Robert L. Jaffe},
title = {Optical-approximation analysis of sidewall-spacing effects on the force between two squares with parallel sidewalls},
journal = {Physical Review~A},
year = 2007,
volume = 76,
pages = 063816,
month = {December},
abstract = {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.}
}
@article{GhebrebrhanIb07,
pdf = {GhebrebrhanIb07.pdf},
author = {M. Ghebrebrhan and M. Ibanescu and Steven G. Johnson and M. Solja{\v{c}}i{\'{c}} and J. D. Joannopoulos},
title = {Distinguishing zero-group-velocity modes in photonic crystals},
journal = {Physical Review~A},
year = 2007,
volume = 76,
pages = 063810,
month = {December},
abstract = {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.}
}
@article{LeeFa08-SPIE,
pdf = {LeeFa08-SPIE.pdf},
author = {Karen K. Lee and Ardavan Farjadpour and Yehuda Avniel and J. D. Joannopoulos and Steven G. Johnson},
title = {A tale of two limits: fundamental properties of photonic-crystal fibers},
journal = {Proc. SPIE},
year = 2008,
volume = 6901,
pages = {69010K},
month = {January},
doi = {doi:10.1117/12.778570},
note = {Invited paper},
abstract = {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. }
}
@incollection{JohnsonJo04,
author = {S. G. Johnson and J. D. Joannopoulos},
title = {Photonic Crystals: Electromagnetic Theory},
booktitle = {Encyclopedia of Modern Optics},
pages = {120--127},
publisher = {Elsevier},
year = 2004,
editor = {B. D. Guenther and D. G. Steel and L. Bayvel},
address = {Oxford},
month = {November},
doi = {doi:10.1016/B0-12-369395-0/00926-X}
}
@incollection{JohnsonSo04,
author = {S. G. Johnson and Marin Solja{\v{c}}i{\'{c}} and J. D. Joannopoulos},
title = {Photonic crystals},
booktitle = {Encyclopedia of Nonlinear Science},
publisher = {Routledge, Taylor and Francis Group},
year = 2005,
editor = {Alwyn Scott},
address = {New York},
month = {July}
}
@incollection{JacobsTe06,
author = {Steven A. Jacobs and Burak Temelkuran and Ori Weisberg and Mihai Ibanescu and Steven G. Johnson and Marin Solja{\v{c}}i{\'{c}}},
title = {Hollow Core Fibers},
booktitle = {Specialty Optical Fibers Handbook},
publisher = {Elsevier},
year = 2006,
editor = {Alexis Mendez and T. Morse},
chapter = 11,
address = {New York},
month = {December}
}
@incollection{JoannopoulosFa01,
author = {J. D. Joannopoulos and S. Fan and A. Mekis and S. G. Johnson},
title = {Novelties of Light with Photonic Crystals},
booktitle = {Photonic Crystals and Light Localization in the 21st Century},
pages = {1--24},
publisher = {Kluwer},
year = 2001,
editor = {Costas M. Soukoulis},
volume = 563,
series = {NATO Science Series C: Mathematical and Physical Sciences},
address = {Dordrecht, Netherlands},
month = {May},
url = {http://books.google.com/books?id=y8O7cfQl9ogC}
}
@article{ShaoJo07-dct2,
author = {Xuancheng Shao and Steven G. Johnson},
title = {Type-{II}/{III} {DCT}/{DST} algorithms with reduced number of arithmetic operations},
journal = {Signal Processing},
volume = 88,
pages = {1553--1564},
year = 2008,
month = {June},
url = {http://arxiv.org/abs/cs.DS/0703150},
doi = {doi:10.1016/j.sigpro.2008.01.004},
abstract = {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 $2 N \log_2 N + O(N)$ to $\frac{17}{9} N \log_2 N + O(N)$ 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.}
}
@article{ShaoJo07-dct4,
author = {Xuancheng Shao and Steven G. Johnson},
title = {Type-{IV} {DCT}, {DST}, and {MDCT} algorithms with reduced numbers of arithmetic operations},
journal = {Signal Processing},
volume = 88,
pages = {1313--1326},
year = 2008,
month = {June},
url = {http://arxiv.org/abs/0708.4399},
doi = {doi:10.1016/j.sigpro.2007.11.024},
abstract = {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 $2N\log_{2}N + O(N)$ to $\frac{17}{9}N\log_{2}N + O(N)$ for a power-of-two transform size $N$, and the exact count is strictly lowered for $N \geq 8$. 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.}
}
@book{JoannopoulosJo08-book,
author = {John D. Joannopoulos and Steven G. Johnson and Joshua N. Winn and Robert D. Meade},
title = {Photonic Crystals: Molding the Flow of Light},
publisher = {Princeton University Press},
year = 2008,
edition = {second},
month = {February},
url = {http://ab-initio.mit.edu/book},
abstract = {Since it was first published in 1995, {\it 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, {\it Photonic Crystals} is an indispensable resource for students and researchers.}
}
@article{RodriguezMc08,
pdf = {RodriguezMc08.pdf},
author = {Alejandro W. Rodriguez and Alexander P. McCauley and Yehuda Avniel and Steven G. Johnson},
title = {Computation and visualization of photonic quasicrystal spectra via {Bloch}'s theorem},
journal = {Physical Review~B},
year = 2008,
volume = 77,
pages = {104201},
url = {http://link.aps.org/abstract/PRB/v77/e104201},
month = {March},
abstract = {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.}
}
@article{RahiRo08,
pdf = {RahiRo08.pdf},
author = {Sahand Jamal Rahi and Alejandro W. Rodriguez and Thorsten Emig and Robert L. Jaffe and Steven G. Johnson and Mehran Kardar},
title = {Nonmonotonic effects of parallel sidewalls on {Casimir} forces between cylinders},
journal = {Physical Review~A},
year = 2008,
volume = 77,
pages = {030101(R)},
eprint = {arXiv:0711.1987},
month = {March},
url = {http://link.aps.org/abstract/PRA/v77/e030101},
abstract = {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).}
}
@article{KottkeFa08,
pdf = {KottkeFa08.pdf},
author = {Chris Kottke and Ardavan Farjadpour and Steven G. Johnson},
title = {Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods},
journal = {Physical Review~E},
year = 2008,
volume = 77,
pages = {036611},
url = {http://link.aps.org/abstract/PRE/v77/e036611},
month = {March},
abstract = {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.}
}
@article{LeeAv08,
pdf = {LeeAv08.pdf},
author = {Karen K. Y. Lee and Yehuda Avniel and Steven G. Johnson},
title = {Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides},
journal = {Optics Express},
year = 2008,
volume = {16},
pages = {9261--9275},
month = {June},
url = {http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-13-9261},
doi = {doi:10.1364/OE.16.009261},
abstract = {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.}
}
@article{RodriguezJo08,
pdf = {RodriguezJo08.pdf},
author = {Alejandro W. Rodriguez and John D. Joannopoulos and Steven G. Johnson},
title = {Repulsive and attractive {Casimir} forces in a glide-symmetric geometry},
journal = {Physical Review~A},
year = 2008,
volume = 77,
pages = {062107},
month = {June},
url = {http://link.aps.org/abstract/PRA/v77/e062107},
abstract = {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 platesābecause 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.},
note = {Invited paper in June 30, 2008, issue of the {\it Virtual Journal of Nanoscale Science & Technology}.}
}
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