Heuristic methods and performance bounds for photonic design
Abstract
In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical optimization problem that is computationally difficult to solve globally. Because of this, several heuristic methods have been developed to approximately solve such problems. These methods often produce very good designs, and, in many practical applications, easily outperform ‘traditional’ designs that rely on human intuition. Yet, because these heuristic methods do not guarantee that the approximate solution found is globally optimal, the question remains of just how much better a designer might hope to do. This question is addressed by performance bounds or impossibility results, which determine a performance level that no design can achieve. We focus on algorithmic performance bounds, which involve substantial computation to determine. We illustrate a variety of both heuristic methods and performance bounds on two examples. In these examples (and many others not reported here) the performance bounds show that the heuristic designs are nearly optimal, and can be considered globally optimal in practice. This review serves to clearly set up the photonic design problem and unify existing approachesmore »
- Publication Date:
- Sponsoring Org.:
- USDOE Advanced Research Projects Agency - Energy (ARPA-E)
- OSTI Identifier:
- 1760056
- Grant/Contract Number:
- AR0001212
- Resource Type:
- Published Article
- Journal Name:
- Optics Express
- Additional Journal Information:
- Journal Name: Optics Express Journal Volume: 29 Journal Issue: 2; Journal ID: ISSN 1094-4087
- Publisher:
- Optical Society of America
- Country of Publication:
- United States
- Language:
- English
Citation Formats
Angeris, Guillermo, Vučković, Jelena, and Boyd, Stephen. Heuristic methods and performance bounds for photonic design. United States: N. p., 2021.
Web. doi:10.1364/OE.415052.
Angeris, Guillermo, Vučković, Jelena, & Boyd, Stephen. Heuristic methods and performance bounds for photonic design. United States. https://doi.org/10.1364/OE.415052
Angeris, Guillermo, Vučković, Jelena, and Boyd, Stephen. Fri .
"Heuristic methods and performance bounds for photonic design". United States. https://doi.org/10.1364/OE.415052.
@article{osti_1760056,
title = {Heuristic methods and performance bounds for photonic design},
author = {Angeris, Guillermo and Vučković, Jelena and Boyd, Stephen},
abstractNote = {In the photonic design problem, a scientist or engineer chooses the physical parameters of a device to best match some desired device behavior. Many instances of the photonic design problem can be naturally stated as a mathematical optimization problem that is computationally difficult to solve globally. Because of this, several heuristic methods have been developed to approximately solve such problems. These methods often produce very good designs, and, in many practical applications, easily outperform ‘traditional’ designs that rely on human intuition. Yet, because these heuristic methods do not guarantee that the approximate solution found is globally optimal, the question remains of just how much better a designer might hope to do. This question is addressed by performance bounds or impossibility results, which determine a performance level that no design can achieve. We focus on algorithmic performance bounds, which involve substantial computation to determine. We illustrate a variety of both heuristic methods and performance bounds on two examples. In these examples (and many others not reported here) the performance bounds show that the heuristic designs are nearly optimal, and can be considered globally optimal in practice. This review serves to clearly set up the photonic design problem and unify existing approaches for calculating performance bounds, while also providing some natural generalizations and properties.},
doi = {10.1364/OE.415052},
journal = {Optics Express},
number = 2,
volume = 29,
place = {United States},
year = {Fri Jan 15 00:00:00 EST 2021},
month = {Fri Jan 15 00:00:00 EST 2021}
}
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Works referenced in this record:
Maximizing band gaps in two-dimensional photonic crystals by using level set methods
journal, July 2005
- Kao, C. Y.; Osher, S.; Yablonovitch, E.
- Applied Physics B, Vol. 81, Issue 2-3
Real-coded genetic algorithm for Bragg grating parameter synthesis
journal, January 2001
- Cormier, Gabriel; Boudreau, Roger; Thériault, Sylvain
- Journal of the Optical Society of America B, Vol. 18, Issue 12
On-chip integrated laser-driven particle accelerator
journal, January 2020
- Sapra, Neil V.; Yang, Ki Youl; Vercruysse, Dries
- Science, Vol. 367, Issue 6473
Derivative-free optimization: a review of algorithms and comparison of software implementations
journal, July 2012
- Rios, Luis Miguel; Sahinidis, Nikolaos V.
- Journal of Global Optimization, Vol. 56, Issue 3
Generative Deep Neural Networks for Inverse Materials Design Using Backpropagation and Active Learning
journal, January 2020
- Chen, Chun‐Teh; Gu, Grace X.
- Advanced Science, Vol. 7, Issue 5
Deep learning enabled inverse design in nanophotonics
journal, February 2020
- So, Sunae; Badloe, Trevon; Noh, Jaebum
- Nanophotonics, Vol. 9, Issue 5
Limits to the Optical Response of Graphene and Two-Dimensional Materials
journal, August 2017
- Miller, Owen D.; Ilic, Ognjen; Christensen, Thomas
- Nano Letters, Vol. 17, Issue 9
Optimization of thermal design of heat sinks: A review
journal, March 2018
- Ahmed, Hamdi E.; Salman, B. H.; Kherbeet, A. Sh.
- International Journal of Heat and Mass Transfer, Vol. 118
Demonstration of systematic photonic crystal device design and optimization by low-rank adjustments: an extremely compact mode separator
journal, January 2005
- Jiao, Yang; Fan, Shanhui; Miller, David A. B.
- Optics Letters, Vol. 30, Issue 2
Inverse-designed stretchable metalens with tunable focal distance
journal, February 2018
- Callewaert, Francois; Velev, Vesselin; Jiang, Shizhou
- Applied Physics Letters, Vol. 112, Issue 9
Design of resonant-cavity-enhanced photodetectors using genetic algorithms
journal, March 2000
- Jervase, J. A.; Bourdoucen, H.
- IEEE Journal of Quantum Electronics, Vol. 36, Issue 3
Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers, Part 2
journal, January 1999
- Reuther, James J.; Jameson, Antony; Alonso, Juan J.
- Journal of Aircraft, Vol. 36, Issue 1
Fundamental limits to radiative heat transfer: Theory
journal, January 2020
- Molesky, Sean; Venkataram, Prashanth S.; Jin, Weiliang
- Physical Review B, Vol. 101, Issue 3
Comparison between genetic and gradient-based optimization algorithms for solving electromagnetics problems
journal, May 1995
- Haupt, R.
- IEEE Transactions on Magnetics, Vol. 31, Issue 3
Ultimate Absorption in Light Scattering by a Finite Obstacle
journal, January 2018
- Miroshnichenko, Andrey E.; Tribelsky, Michael I.
- Physical Review Letters, Vol. 120, Issue 3
Robust topology optimization of three-dimensional photonic-crystal band-gap structures
journal, January 2014
- Men, H.; Lee, K. Y. K.; Freund, R. M.
- Optics Express, Vol. 22, Issue 19
An integrated-nanophotonics polarization beamsplitter with 2.4 × 2.4 μm2 footprint
journal, May 2015
- Shen, Bing; Wang, Peng; Polson, Randy
- Nature Photonics, Vol. 9, Issue 6
Data-driven acceleration of photonic simulations
journal, December 2019
- Trivedi, Rahul; Su, Logan; Lu, Jesse
- Scientific Reports, Vol. 9, Issue 1
Optimum Aerodynamic Design Using the Navier-Stokes Equations
journal, January 1998
- Jameson, A.; Martinelli, L.; Pierce, N. A.
- Theoretical and Computational Fluid Dynamics, Vol. 10, Issue 1-4
GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
journal, July 1986
- Saad, Youcef; Schultz, Martin H.
- SIAM Journal on Scientific and Statistical Computing, Vol. 7, Issue 3
Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices
journal, November 2018
- Hughes, Tyler W.; Minkov, Momchil; Williamson, Ian A. D.
- ACS Photonics, Vol. 5, Issue 12
Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer
journal, May 2015
- Piggott, Alexander Y.; Lu, Jesse; Lagoudakis, Konstantinos G.
- Nature Photonics, Vol. 9, Issue 6, p. 374-377
Nanophotonic inverse design with SPINS: Software architecture and practical considerations
journal, March 2020
- Su, Logan; Vercruysse, Dries; Skarda, Jinhie
- Applied Physics Reviews, Vol. 7, Issue 1
Light Trapping Textures Designed by Electromagnetic Optimization for Subwavelength Thick Solar Cells
journal, January 2014
- Ganapati, Vidya; Miller, Owen D.; Yablonovitch, Eli
- IEEE Journal of Photovoltaics, Vol. 4, Issue 1
Optimization of Multilayer Optical Films with a Memetic Algorithm and Mixed Integer Programming
journal, December 2017
- Shi, Yu; Li, Wei; Raman, Aaswath
- ACS Photonics, Vol. 5, Issue 3
Nanophotonic computational design
journal, January 2013
- Lu, Jesse; Vučković, Jelena
- Optics Express, Vol. 21, Issue 11
Training Deep Neural Networks for the Inverse Design of Nanophotonic Structures
journal, January 2018
- Liu, Dianjing; Tan, Yixuan; Khoram, Erfan
- ACS Photonics, Vol. 5, Issue 4
Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures
journal, March 2019
- Amestoy, Patrick R.; Buttari, Alfredo; L'Excellent, Jean-Yves
- ACM Transactions on Mathematical Software, Vol. 45, Issue 1
Fundamental Limitations of Small Antennas
journal, December 1947
- Wheeler, H. A.
- Proceedings of the IRE, Vol. 35, Issue 12
Julia: A Fresh Approach to Numerical Computing
journal, January 2017
- Bezanson, Jeff; Edelman, Alan; Karpinski, Stefan
- SIAM Review, Vol. 59, Issue 1
Aerodynamic design via control theory
journal, September 1988
- Jameson, Antony
- Journal of Scientific Computing, Vol. 3, Issue 3
A repository of convex quadratic programming problems
journal, January 1999
- Maros, István; Mészáros, Csaba
- Optimization Methods and Software, Vol. 11, Issue 1-4
Methods of conjugate gradients for solving linear systems
journal, December 1952
- Hestenes, M. R.; Stiefel, E.
- Journal of Research of the National Bureau of Standards, Vol. 49, Issue 6
Adjoint shape optimization applied to electromagnetic design
journal, January 2013
- Lalau-Keraly, Christopher M.; Bhargava, Samarth; Miller, Owen D.
- Optics Express, Vol. 21, Issue 18
Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes
journal, January 2012
- Lu, Jesse; Vučković, Jelena
- Optics Express, Vol. 20, Issue 7
Global Optimization of Dielectric Metasurfaces Using a Physics-Driven Neural Network
journal, July 2019
- Jiang, Jiaqi; Fan, Jonathan A.
- Nano Letters, Vol. 19, Issue 8
Inverse Designed Metalenses with Extended Depth of Focus
journal, March 2020
- Bayati, Elyas; Pestourie, Raphaël; Colburn, Shane
- ACS Photonics, Vol. 7, Issue 4
Inverse design in nanophotonics
journal, October 2018
- Molesky, Sean; Lin, Zin; Piggott, Alexander Y.
- Nature Photonics, Vol. 12, Issue 11
Global operator bounds on electromagnetic scattering: Upper bounds on far-field cross sections
journal, July 2020
- Molesky, Sean; Chao, Pengning; Jin, Weiliang
- Physical Review Research, Vol. 2, Issue 3
Bounds for Scattering from Absorptionless Electromagnetic Structures
journal, July 2020
- Trivedi, Rahul; Angeris, Guillermo; Su, Logan
- Physical Review Applied, Vol. 14, Issue 1
Thermodynamic Upper Bound on Broadband Light Coupling with Photonic Structures
journal, October 2012
- Yu, Zongfu; Raman, Aaswath; Fan, Shanhui
- Physical Review Letters, Vol. 109, Issue 17
Hierarchical Design and Optimization of Silicon Photonics
journal, March 2020
- Michaels, Andrew; Wu, Ming C.; Yablonovitch, Eli
- IEEE Journal of Selected Topics in Quantum Electronics, Vol. 26, Issue 2
A Limited Memory Algorithm for Bound Constrained Optimization
journal, September 1995
- Byrd, Richard H.; Lu, Peihuang; Nocedal, Jorge
- SIAM Journal on Scientific Computing, Vol. 16, Issue 5
Proximal Algorithms
journal, January 2014
- Parikh, Neal
- Foundations and Trends® in Optimization, Vol. 1, Issue 3
Inverse Design and Demonstration of a Compact on-Chip Narrowband Three-Channel Wavelength Demultiplexer
journal, November 2017
- Su, Logan; Piggott, Alexander Y.; Sapra, Neil V.
- ACS Photonics, Vol. 5, Issue 2
Topology optimization of freeform large-area metasurfaces
journal, January 2019
- Lin, Zin; Liu, Victor; Pestourie, Raphael
- Optics Express, Vol. 27, Issue 11
Chordal Graphs and Semidefinite Optimization
journal, January 2014
- Vandenberghe, Lieven; Andersen, Martin S.
- Foundations and Trends® in Optimization, Vol. 1, Issue 4
Fabrication-constrained nanophotonic inverse design
journal, May 2017
- Piggott, Alexander Y.; Petykiewicz, Jan; Su, Logan
- Scientific Reports, Vol. 7, Issue 1
Analytical level set fabrication constraints for inverse design
journal, June 2019
- Vercruysse, Dries; Sapra, Neil V.; Su, Logan
- Scientific Reports, Vol. 9, Issue 1
Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding
journal, February 2016
- O’Donoghue, Brendan; Chu, Eric; Parikh, Neal
- Journal of Optimization Theory and Applications, Vol. 169, Issue 3
Inverse design of nanophotonic structures using complementary convex optimization
journal, January 2010
- Lu, Jesse; Vuckovic, Jelena
- Optics Express, Vol. 18, Issue 4
Binary particle swarm optimized 2 × 2 power splitters in a standard foundry silicon photonic platform
journal, January 2016
- Mak, Jason C. C.; Sideris, Constantine; Jeong, Junho
- Optics Letters, Vol. 41, Issue 16
Inverse design of nanoparticles for enhanced Raman scattering
journal, January 2020
- Christiansen, Rasmus E.; Michon, Jérôme; Benzaouia, Mohammed
- Optics Express, Vol. 28, Issue 4
Inverse design of photonic crystal devices
journal, July 2005
- Hakansson, A.; Sanchez-Deh, J.; Sanchis, L.
- IEEE Journal on Selected Areas in Communications, Vol. 23, Issue 7
Computer-Automated Design of Multifont Print Recognition Logic
journal, January 1963
- Kamentsky, L. A.; Liu, C. N.
- IBM Journal of Research and Development, Vol. 7, Issue 1
Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring
journal, January 2014
- O'Connor, Daniel; Vandenberghe, Lieven
- SIAM Journal on Imaging Sciences, Vol. 7, Issue 3
Inverse Design of Photonic Crystals through Automatic Differentiation
journal, June 2020
- Minkov, Momchil; Williamson, Ian A. D.; Andreani, Lucio C.
- ACS Photonics, Vol. 7, Issue 7
Adjoint-based optimization of active nanophotonic devices
journal, January 2018
- Wang, Jiahui; Shi, Yu; Hughes, Tyler
- Optics Express, Vol. 26, Issue 3
High-NA achromatic metalenses by inverse design
journal, January 2020
- Chung, Haejun; Miller, Owen D.
- Optics Express, Vol. 28, Issue 5
Photonic crystal fiber design by means of a genetic algorithm
journal, January 2004
- Kerrinckx, Emmanuel; Bigot, Laurent; Douay, Marc
- Optics Express, Vol. 12, Issue 9
Physical Limitations of Omni‐Directional Antennas
journal, December 1948
- Chu, L. J.
- Journal of Applied Physics, Vol. 19, Issue 12, p. 1163-1175
Integrated optical devices design by genetic algorithm
journal, May 2004
- Sanchis, L.; Håkansson, A.; López-Zanón, D.
- Applied Physics Letters, Vol. 84, Issue 22
Bridge topology optimisation with stress, displacement and frequency constraints
journal, February 2003
- Guan, Hong; Chen, Yin-Jung; Loo, Yew-Chaye
- Computers & Structures, Vol. 81, Issue 3
A Simplex Method for Function Minimization
journal, January 1965
- Nelder, J. A.; Mead, R.
- The Computer Journal, Vol. 7, Issue 4
Sum rules for optical scattering amplitudes
journal, January 1982
- McKellar, Bruce H. J.; Box, Michael A.; Bohren, Craig F.
- Journal of the Optical Society of America, Vol. 72, Issue 5
Gradient-based learning applied to document recognition
journal, January 1998
- Lecun, Y.; Bottou, L.; Bengio, Y.
- Proceedings of the IEEE, Vol. 86, Issue 11
Limits to surface-enhanced Raman scattering near arbitrary-shape scatterers: erratum
journal, January 2020
- Michon, Jérôme; Benzaouia, Mohammed; Yao, Wenjie
- Optics Express, Vol. 28, Issue 15
JuMP: A Modeling Language for Mathematical Optimization
journal, January 2017
- Dunning, Iain; Huchette, Joey; Lubin, Miles
- SIAM Review, Vol. 59, Issue 2
An Introduction to the Adjoint Approach to Design
journal, December 2000
- Giles, Michael B.; Pierce, Niles A.
- Flow, Turbulence and Combustion, Vol. 65, Issue 3/4, p. 393-415
Fundamental limits to optical response in absorptive systems
journal, January 2016
- Miller, Owen D.; Polimeridis, Athanasios G.; Homer Reid, M. T.
- Optics Express, Vol. 24, Issue 4
Optical theorem and beyond
journal, July 1976
- Newton, Roger G.
- American Journal of Physics, Vol. 44, Issue 7
Inverse-designed non-reciprocal pulse router for chip-based LiDAR
journal, March 2020
- Yang, Ki Youl; Skarda, Jinhie; Cotrufo, Michele
- Nature Photonics, Vol. 14, Issue 6
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
journal, October 2008
- Chen, Yanqing; Davis, Timothy A.; Hager, William W.
- ACM Transactions on Mathematical Software, Vol. 35, Issue 3
The method of moving asymptotes—a new method for structural optimization
journal, February 1987
- Svanberg, Krister
- International Journal for Numerical Methods in Engineering, Vol. 24, Issue 2
Topology design of tensegrity structures via mixed integer programming
journal, March 2010
- Ehara, Shintaro; Kanno, Yoshihiro
- International Journal of Solids and Structures, Vol. 47, Issue 5
Optimization by Simulated Annealing
journal, May 1983
- Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P.
- Science, Vol. 220, Issue 4598
Fundamental limit of nanophotonic light trapping in solar cells
journal, September 2010
- Yu, Zongfu; Raman, Aaswath; Fan, Shanhui
- Proceedings of the National Academy of Sciences, Vol. 107, Issue 41, p. 17491-17496
Genetic optimization of photonic bandgap structures
journal, January 2007
- Goh, Joel; Fushman, Ilya; Englund, Dirk
- Optics Express, Vol. 15, Issue 13
Computational Bounds for Photonic Design
journal, April 2019
- Angeris, Guillermo; Vučković, Jelena; Boyd, Stephen P.
- ACS Photonics, Vol. 6, Issue 5
Automated Antenna Design with Evolutionary Algorithms
conference, June 2012
- Hornby, Gregory; Globus, Al; Linden, Derek
- Space 2006
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005
- Wächter, Andreas; Biegler, Lorenz T.
- Mathematical Programming, Vol. 106, Issue 1