Preprints — Nanostructures and Computation Group

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A. Pick, A. Cerjan, and S. G. Johnson, “Ab-initio theory of quantum fluctuations and relaxation oscillations in multimode lasers,” e-Print archive, arXiv:1811.00108, October 2018. [ bib | arXiv ]
We present an ab-initio semi-analytical solution for the noise spectrum of complex-cavity micro-structured lasers, including central Lorentzian peaks at the multimode lasing frequencies and additional sidepeaks due to relaxation-oscillation (RO) dynamics. In Ref. 1, we computed the central-peak linewidths by solving generalized laser rate equations, which we derived from the Maxwell-Bloch equations by invoking the fluctuation-dissipation theorem to relate the noise correlations to the steady-state lasing properties; Here, we generalize this approach and obtain the entire laser spectrum, focusing on the RO sidepeaks. Our formulation treats inhomogeneity, cavity openness, nonlinearity, and multimode effects accurately. We find a number of new effects, including new multimode RO sidepeaks and three generalized α factors. Last, we apply our formulas to compute the noise spectrum of single- and multimode photonic-crystal lasers.

H. Shim, L. Fan, S. G. Johnson, and O. D. Miller, “Fundamental limits to near-field optical response, over any bandwidth,” arXiv, arXiv:1805.02140, May 2018. [ bib | arXiv ]
We develop an analytical framework to derive upper bounds to light-matter interactions in the optical near field, where applications ranging from spontaneous-emission amplification to greater-than-blackbody heat transfer show transformative potential. Our framework connects the classic complex-analytic properties of causal fields with newly developed energy-conservation principles, resulting in a new class of power-bandwidth limits. We show that at specific frequency and bandwidth combinations, the bounds can be closely approached by canonical plasmonic geometries, with the opportunity for new designs to emerge away from those frequency ranges. Embedded in the bounds is a material “figure of merit,” which determines the maximum response of any material (metal/dielectric, bulk/2D, etc.), for any frequency and bandwidth. We focus on spontaneous-emission enhancements as encoded in the local density of states (LDOS), and anticipate extensions to Casimir forces, nonlinear Raman scattering, engineered Lamb shifts, and more.

Y. Liu, L. Fan, E. Lee, N. Fang, S. G. Johnson, and O. D. Miller, “Optimality of optical forces and torques on nanoparticles via illumination/scattering channels,” e-Print archive, arXiv:1805.11471, May 2018. [ bib | arXiv ]
A universal property of resonant subwavelength scatterers is that their optical cross-sections are proportional to a square wavelength, λ2, regardless of whether they are plasmonic nanoparticles, two-level quantum systems, or RF antennas. The maximum cross-section is an intrinsic property of the incident field: plane waves, with infinite power, can be decomposed into multipolar orders with finite powers proportional to λ2. In this Letter, we identify λ2/c and λ3/c as analogous force and torque constants, derived within a more general quadratic scattering-channel framework for upper bounds to optical force and torque for any illumination field. This framework also simplifies the reverse problem: computing optimal “holographic” incident beams, for a fixed collection of scatterers. We analyze structures and incident fields that approach the bounds, which for nonspherical, wavelength-scale bodies show a rich interplay between scattering channels. This framework should enable optimal mechanical control of nanoparticles with light.

M. Benzaouia, G. Tokic, O. D. Miller, D. K. P. Yue, and S. G. Johnson, “From solar cells to ocean buoys: Wide-bandwidth limits to absorption by metaparticle arrays,” e-Print archive, arXiv:1804.00600, April 2018. [ bib | arXiv ]
In this paper, we develop an approximate wide-bandwidth upper bound to the absorption enhancement in arrays of metaparticles, applicable to general wave-scattering problems and motivated here by ocean-buoy energy extraction. We show that general limits, including the well-known Yablonovitch result in solar cells, arise from reciprocity conditions. The use of reciprocity in the stochastic regime leads us to a diffusion model from which we derive our main result: an analytical prediction of optimal array absorption that closely matches exact simulations for both random and optimized arrays. This result also enables us to propose and quantify approaches to increase performance through careful particle design and/or using external reflectors.

M. T. H. Reid, O. D. Miller, A. G. Polimeridis, A. W. Rodriguez, E. M. Tomlinson, and S. G. Johnson, “Photon torpedoes and Rytov pinwheels: Integral-equation modeling of non-equilibrium fluctuation-induced forces and torques on nanoparticles,” e-Print archive, arXiv:1708.01985, August 2017. [ bib | arXiv ]
We present new theoretical tools, based on fluctuational electrodynamics and the integral-equation approach to computational electromagnetism, for numerical modeling of forces and torques on bodies of complex shapes and materials due to emission of thermal radiation out of thermal equilibrium. This extends our recently-developed fluctuating-surface-current (FSC) and fluctuating-volume-current (FVC) techniques for radiative heat transfer to the computation of non-equilibrium fluctuation-induced forces and torques; as we show, the extension is non-trivial due to the greater computational cost of modeling radiative momentum transfer, including new singularities that must be carefully neutralized. We introduce a new analytical cancellation technique that addresses these challenges and allows, for the first time, accurate and efficient prediction of non-equilibrium forces and torques on bodies of essentially arbitrary shapes-including asymmetric and chiral particles-and complex material properties, including continuously-varying and anisotropic dielectrics. We validate our approach by showing that it reproduces known results, then present new numerical predictions of non-equilibrium self-propulsion, self-rotation, and momentum-transfer phenomena in complex geometries that would be difficult or impossible to study with existing methods. Our findings indicate that the fluctuation-induced dynamics of micron-size room-temperature bodies in cold environments involve microscopic length scales but macroscopic time scales, with typical linear and angular velocities on the order of microns/second and radians/second; For a micron-scale gear driven by thermal radiation from a nearby chiral emitter, we find a strong and non-monotonic dependence of the magnitude and even the sign of the induced torque on the temperature of the emitter.

F. Hernández, A. Pick, and S. G. Johnson, “Scalable computation of Jordan chains,” e-Print archive, arXiv:1704.05837, April 2017. [ bib | arXiv ]
We present an algorithm to compute the Jordan chain of a nearly defective matrix with a 2×2 Jordan block. The algorithm is based on a inverse-iteration procedure and only needs information about the invariant subspace corresponding to the Jordan chain, making it suitable for use with large matrices arising in applications, in contrast with existing algorithms which rely on an SVD. The algorithm produces the eigenvector and Jordan vector with O(ε) error, with ε being the distance of the given matrix to an exactly defective matrix. As an example, we demonstrate the use of this algorithm in a problem arising from electromagnetism, in which the matrix has size 2122×2122. An extension of this algorithm is also presented which can achieve higher order convergence [O2)] when the matrix derivative is known.

O. D. Miller, C. W. Hsu, E. Anquillare, J. D. Joannopoulos, M. Soljačić, and S. G. Johnson, “Power-bandwidth limitations of an optical resonance,” e-Print archive, arXiv:1510.06902, October 2015. [ bib | arXiv ]
We present shape-independent upper limits to the power-bandwidth product for a single resonance in an optical scatterer, with the bound depending only on the material susceptibility. We show that quasistatic metallic scatterers can nearly reach the limits, and we apply our approach to the problem of designing N independent, subwavelength scatterers to achieve flat, broadband response even if they individually exhibit narrow resonant peaks.

S. G. Johnson, “Saddle-point integration of C “bump” functions,” e-Print archive, arXiv:1508.04376, August 2015. [ bib | arXiv ]
This technical note describes the application of saddle-point integration to the asymptotic Fourier analysis of the well-known C “bump” function exp[-(1-x2)-1], deriving both the asymptotic decay rate k-3/4 exp(-sqrt(k)) of the Fourier transform F(k) and the exact coefficient. The result is checked against brute-force numerical integration and is extended to generalizations of this bump function.

O. D. Miller, W. Qiu, J. D. Joannopoulos, and S. G. Johnson, “Comment on `A self-assembled three-dimensional cloak in the visible' in scientific reports 3, 2328,” e-Print archive, arXiv:1310.1503, October 2013. [ bib | arXiv ]
Mühlig et. al. propose and fabricate a “cloak” comprised of nano-particles on the surface of a sub-wavelength silica sphere. However, the coating only reduces the scattered fields. This is achieved by increased absorption, such that total extinction increases at all wavelengths. An object creating a large shadow is generally not considered to be cloaked; functionally, in contrast to the relatively few structures that can reduce total extinction, there are many that can reduce scattering alone.

A. P. McCauley, A. W. Rodriguez, M. T. H. Reid, and S. G. Johnson, “Casimir repulsion beyond the dipole regime,” e-Print archive, arXiv:1105.0404, May 2011. [ bib | arXiv ]
We extend a previous result [Phys. Rev. Lett. 105, 090403 (2010)] on Casimir repulsion between a plate with a hole and a cylinder centered above it to geometries in which the central object can no longer be treated as a point dipole. We show through numerical calculations that as the distance between the plate and central object decreases, there is an intermediate regime in which the repulsive force increases dramatically. Beyond this, the force rapidly switches over to attraction as the separation decreases further to zero, in line with the proximity force approximation. We demonstrate that this effect can be understood as a competition between an increased repulsion due to a larger polarizability of the central object interacting with increased fringing fields near the edge of the plate, and attractive forces due primarily to the nonzero thickness of the plate. In comparison with our previous work, we find that using the same plate geometry but replacing the single cylinder with a ring of cylinders, or more generally an extended uniaxial conductor, the repulsive force can be enhanced by a factor of approximately 103. We conclude that this enhancement, although quite dramatic, is still too small to yield detectable repulsive Casimir forces.

A. Rodriguez and S. G. Johnson, “Efficient generation of correlated random numbers using Chebyshev-optimal magnitude-only IIR filters,” e-Print archive, arXiv:physics/0703152, March 2007. [ bib | arXiv ]
We compare several methods for the efficient generation of correlated random sequences (colored noise) by filtering white noise to achieve a desired correlation spectrum. We argue that a class of IIR filter-design techniques developed in the 1970s, which obtain the global Chebyshev-optimum minimum-phase filter with a desired magnitude and arbitrary phase, are uniquely suited for this problem but have seldom been used. The short filters that result from such techniques are crucial for applications of colored noise in physical simulations involving random processes, for which many long random sequences must be generated and computational time and memory are at a premium.

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See also our published papers and our home page.