Steven G. Johnson
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View article: Sufficient conditions for localized vibrational modes in one- and two-dimensional discrete lattices
Sufficient conditions for localized vibrational modes in one- and two-dimensional discrete lattices Open
This paper presents a rigorous proof that arbitrarily weak perturbations produce localized vibrational (phonon) modes in one- and two-dimensional discrete lattices, inspired by analogous results for the Schr{ö}dinger and Maxwell equations,…
View article: Hyperparameter-free minimum-lengthscale constraints for topology optimization
Hyperparameter-free minimum-lengthscale constraints for topology optimization Open
The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it …
View article: Unifying and accelerating level-set and density-based topology optimization by subpixel-smoothed projection
Unifying and accelerating level-set and density-based topology optimization by subpixel-smoothed projection Open
We introduce a “subpixel-smoothed projection” (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and sl…
View article: Efficient first-principles inverse design of nanolasers
Efficient first-principles inverse design of nanolasers Open
We develop and demonstrate a first-principles approach, based on the nonlinear Maxwell-Bloch equations and steady-state ab-initio laser theory (SALT), for inverse design of nanostructured lasers, incorporating spatial hole-burning correcti…
View article: Time-reversal-symmetry bounds on electromagnetic fields
Time-reversal-symmetry bounds on electromagnetic fields Open
For linear electromagnetic systems possessing time-reversal symmetry, we present an approach to bound ratios of internal fields excited from different ports, using only the scattering matrix (S matrix), improving upon previous related boun…
View article: Inverse design for robust inference in integrated computational spectrometry
Inverse design for robust inference in integrated computational spectrometry Open
We propose an inverse-design approach for computational spectrometers in which the scattering media are topology-optimized to achieve better performance in inference of unknown spectra. Unlike traditional end-to-end approaches, our inverse…
View article: Scalable Freeform Optimization of Wide-Aperture 3D Metalenses by Zoned Discrete Axisymmetry
Scalable Freeform Optimization of Wide-Aperture 3D Metalenses by Zoned Discrete Axisymmetry Open
We introduce a novel framework for design and optimization of 3D freeform metalenses that attains nearly linear scaling of computational cost with diameter, by breaking the lens into a sequence of radial “zones” with 𝑛-fold discrete axisym…
View article: Sum-of-squares bounds on surface-enhanced Raman scattering
Sum-of-squares bounds on surface-enhanced Raman scattering Open
Surface-enhanced Raman scattering (SERS) is a critical tool for chemical sensing and spectroscopy, and a key question is how to optimally design nanostructures for maximizing SERS. We present fundamental limits on spatially averaged SERS v…
View article: Efficient Calculation of Modified Bessel Functions of the First Kind, $I_ν (z)$, for Real Orders and Complex Arguments: Fortran Implementation with Double and Quadruple Precision
Efficient Calculation of Modified Bessel Functions of the First Kind, $I_ν (z)$, for Real Orders and Complex Arguments: Fortran Implementation with Double and Quadruple Precision Open
We present an efficient self-contained algorithm for computing the modified Bessel function of the first kind $I_ν(z)$, implemented in a robust Fortran code supporting double and quadruple (quad) precision. The algorithm overcomes the limi…
View article: Inverse design of multiresonance filters via quasi-normal mode theory
Inverse design of multiresonance filters via quasi-normal mode theory Open
We present a practical methodology for inverse design of compact high-order/multiresonance filters in linear passive 2-port wave-scattering systems, targeting any desired transmission spectrum (such as standard pass/stop-band filters). Our…
View article: End‐to‐End Metasurface Design for Temperature Imaging via Broadband Planck‐Radiation Regression
End‐to‐End Metasurface Design for Temperature Imaging via Broadband Planck‐Radiation Regression Open
A theoretical framework is presented for temperature imaging from long‐wavelength infrared (LWIR) thermal radiation (e.g., 8–12 µm) through the end‐to‐end design of a metasurface‐optics frontend and a computational‐reconstruction backend. …
View article: Inverse design of 3D-printable metalenses with complementary dispersion for terahertz imaging
Inverse design of 3D-printable metalenses with complementary dispersion for terahertz imaging Open
This study formulates a volumetric inverse-design methodology to generate a pair of complementary focusing metalenses for terahertz imaging: the two lenses exhibit equal and opposite shifts in focal length with frequency. An asymmetry aris…
View article: Sum-of-Squares Bounds on Surface-Enhanced Raman Scattering
Sum-of-Squares Bounds on Surface-Enhanced Raman Scattering Open
Surface-enhanced Raman scattering (SERS) is a critical tool for chemical sensing and spectroscopy, and a key question is how to optimally design nanostructures for maximizing SERS. We present fundamental limits on spatially-averaged SERS v…
View article: Scalable freeform optimization of wide-aperture 3D metalenses by zoned discrete axisymmetry
Scalable freeform optimization of wide-aperture 3D metalenses by zoned discrete axisymmetry Open
We introduce a novel framework for design and optimization of 3D freeform metalenses that attains nearly linear scaling of computational cost with diameter, by breaking the lens into a sequence of radial "zones" with $n$-fold discrete axis…
View article: Matrix Calculus (for Machine Learning and Beyond)
Matrix Calculus (for Machine Learning and Beyond) Open
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and …
View article: Designing structures that maximize spatially averaged surface-enhanced Raman spectra: erratum
Designing structures that maximize spatially averaged surface-enhanced Raman spectra: erratum Open
This erratum corrects a misstatement regarding the absence of non-integrable singularities in 2d distributed Raman sensing applications and a formula [Eq. (9)] for one case of Raman enhancement. These changes do not impact the other result…
View article: End-to-end metasurface design for temperature imaging via broadband Planck-radiation regression
End-to-end metasurface design for temperature imaging via broadband Planck-radiation regression Open
We present a theoretical framework for temperature imaging from long-wavelength infrared thermal radiation (e.g. 8-12 $μ$m) through the end-to-end design of a metasurface-optics frontend and a computational-reconstruction backend. We intro…
View article: End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing
End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing Open
We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (e.g…
View article: Towards optimal spatiotemporal wavefront shaping for the cocktail party problem with inverse design of an acoustic reconfigurable metasurface in disordered media
Towards optimal spatiotemporal wavefront shaping for the cocktail party problem with inverse design of an acoustic reconfigurable metasurface in disordered media Open
Multiple-user multiple-input multiple-output applications have recently gained a lot of attention. Here, we show an efficient optimization formulation for the design of all the temporal and spatial degrees of freedom of an acoustic reconfi…
View article: Multimaterial fiber as a physical simulator of a capillary instability
Multimaterial fiber as a physical simulator of a capillary instability Open
Capillary breakup of cores is an exclusive approach to fabricating fiber-integrated optoelectronics and photonics. A physical understanding of this fluid-dynamic process is necessary for yielding the desired solid-state fiber-embedded mult…
View article: Predicting the effect of pallet overhang on the box compression strength
Predicting the effect of pallet overhang on the box compression strength Open
A corrugated box's compression strength can easily be affected by how the box is used, including pallet overhang which reduces a box's effective compression strength (BCT). The specific impact of a given amount of overhang on BCT remains p…
View article: Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics
Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics Open
Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. …
View article: Inverse-Designed Lithium Niobate Nanophotonics
Inverse-Designed Lithium Niobate Nanophotonics Open
National Natural Science Foundation of China, Research Grants Council, University Grants Committee (City Univ. Hong Kong), Croucher Foundation, Simons Foundation
View article: Multimaterial Fiber is a Physical Simulator of a Capillary Instability
Multimaterial Fiber is a Physical Simulator of a Capillary Instability Open
The capillary breakup of cores is an exclusive approach to fabricating fiber-integrated optoelectronics and photonics. A physical understanding of this fluid-dynamic process is necessary for yielding the desired solid-state fiber-embedded …
View article: Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics
Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics Open
Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. …
View article: Methods and apparatus for broadband angular selectivity of electromagnetic waves
Methods and apparatus for broadband angular selectivity of electromagnetic waves Open
A filter to transmit incident radiation at a predetermined incidence angle includes a plurality of photonic crystal structures disposed substantially along a surface normal direction of the filter. The photonic crystal structure includes a…
View article: Thermophotovoltaic energy generation
Thermophotovoltaic energy generation Open
Inventive systems and methods for the generation of energy using thermophotovoltaic cells are described. Also described are systems and methods for selectively emitting electromagnetic radiation from an emitter for use in thermophotovoltai…
View article: Dielectric waveguide with transverse index variation that support a zero group velocity mode at a non-zero longitudinal wavevector
Dielectric waveguide with transverse index variation that support a zero group velocity mode at a non-zero longitudinal wavevector Open
Optical components including a laser based on a dielectric waveguide extending along a waveguide axis and having a refractive index cross-section perpendicular to the waveguide axis, the refractive index cross-section supporting an electro…
View article: Inverse-designed lithium niobate nanophotonics
Inverse-designed lithium niobate nanophotonics Open
Lithium niobate-on-insulator (LNOI) is an emerging photonic platform that exhibits favorable material properties (such as low optical loss, strong nonlinearities, and stability) and enables large-scale integration with stronger optical con…
View article: Nonlinear exceptional-point lasing with <i>ab initio</i> Maxwell–Bloch theory
Nonlinear exceptional-point lasing with <i>ab initio</i> Maxwell–Bloch theory Open
We present a general analysis for finding and characterizing nonlinear exceptional point (EP) lasers above threshold using steady-state ab initio Maxwell–Bloch equations. For a system of coupled slabs, we show that a nonlinear EP is obtain…