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Title: Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition

Abstract

Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total computational domain. Here we show that the adjoint variable method can be combined with the Schur complement domain decomposition method. With this combination, in each optimization step, the simulation only involves the degrees of freedom that are inside the design region. Our approach should significantly improve the computational efficiency of adjoint variable method based optimization of photonic structures.

Authors:
; ;
Publication Date:
Research Org.:
Energy Frontier Research Centers (EFRC) (United States). Photonics at Thermodynamic Limits (PTL); Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR)
OSTI Identifier:
1532811
Alternate Identifier(s):
OSTI ID: 1613131
Grant/Contract Number:  
SC0019140; FA9550-17-1-0002
Resource Type:
Published Article
Journal Name:
Optics Express
Additional Journal Information:
Journal Name: Optics Express Journal Volume: 27 Journal Issue: 15; Journal ID: ISSN 1094-4087
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 36 MATERIALS SCIENCE

Citation Formats

Zhao, Nathan Z., Boutami, Salim, and Fan, Shanhui. Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition. United States: N. p., 2019. Web. https://doi.org/10.1364/OE.27.020711.
Zhao, Nathan Z., Boutami, Salim, & Fan, Shanhui. Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition. United States. https://doi.org/10.1364/OE.27.020711
Zhao, Nathan Z., Boutami, Salim, and Fan, Shanhui. Wed . "Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition". United States. https://doi.org/10.1364/OE.27.020711.
@article{osti_1532811,
title = {Accelerating adjoint variable method based photonic optimization with Schur complement domain decomposition},
author = {Zhao, Nathan Z. and Boutami, Salim and Fan, Shanhui},
abstractNote = {Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total computational domain. Here we show that the adjoint variable method can be combined with the Schur complement domain decomposition method. With this combination, in each optimization step, the simulation only involves the degrees of freedom that are inside the design region. Our approach should significantly improve the computational efficiency of adjoint variable method based optimization of photonic structures.},
doi = {10.1364/OE.27.020711},
journal = {Optics Express},
number = 15,
volume = 27,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1364/OE.27.020711

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Works referenced in this record:

Nested Dissection of a Regular Finite Element Mesh
journal, April 1973

  • George, Alan
  • SIAM Journal on Numerical Analysis, Vol. 10, Issue 2
  • DOI: 10.1137/0710032

Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
journal, November 1988


Accelerating simulation of ensembles of locally differing optical structures via a Schur complement domain decomposition
journal, January 2014

  • Verweij, Sacha; Liu, Victor; Fan, Shanhui
  • Optics Letters, Vol. 39, Issue 22
  • DOI: 10.1364/OL.39.006458

A perfectly matched layer for the absorption of electromagnetic waves
journal, October 1994


Feasible adjoint sensitivity technique for EM design optimization
journal, December 2002

  • Georgieva, N. K.; Glavic, S.; Bakr, M. H.
  • IEEE Transactions on Microwave Theory and Techniques, Vol. 50, Issue 12
  • DOI: 10.1109/TMTT.2002.805131

Adjoint Method and Inverse Design for Nonlinear Nanophotonic Devices
journal, November 2018


Adjoint-based optimization of active nanophotonic devices
journal, January 2018


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
  • DOI: 10.1038/nphoton.2015.69

Inverse-designed metastructures that solve equations
journal, March 2019

  • Mohammadi Estakhri, Nasim; Edwards, Brian; Engheta, Nader
  • Science, Vol. 363, Issue 6433
  • DOI: 10.1126/science.aaw2498

Parallel nested dissection
journal, December 1990


Method for sensitivity analysis of photonic crystal devices
journal, January 2004

  • Veronis, Georgios; Dutton, Robert W.; Fan, Shanhui
  • Optics Letters, Vol. 29, Issue 19
  • DOI: 10.1364/OL.29.002288

Design methodology for compact photonic-crystal-based wavelength division multiplexers
journal, January 2011

  • Liu, Victor; Jiao, Yang; Miller, David A. B.
  • Optics Letters, Vol. 36, Issue 4
  • DOI: 10.1364/OL.36.000591

Low-loss and fabrication tolerant silicon mode-order converters based on novel compact tapers
journal, January 2015


Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
journal, June 2004

  • Davis, Timothy A.
  • ACM Transactions on Mathematical Software, Vol. 30, Issue 2
  • DOI: 10.1145/992200.992206

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
  • DOI: 10.1364/OE.21.021693

Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes
journal, January 2012