Inverse design coupled with adjoint optimization is a powerful method to design on-chip nanophotonic devices with multi-wavelength and multi-mode optical functionalities. Although only two simulations are required in each iteration of this optimization process, these simulations still make up the vast majority of the necessary computations and render the design of complex devices with large footprints computationally infeasible. Here, we introduce a multi-faceted factorization caching approach to drastically simplify the underlying computations in finite-difference frequency-domain (FDFD) simulations and significantly reduce the time required for device optimization. Specifically, we cache the numerical and symbolic factorizations for the solution of the corresponding system of linear equations in discretized FDFD simulations and re-use them throughout the device design process. As proof-of-concept demonstrations of the resulting computational advantage, we present simulation speedups reaching as high as 9.2× in the design of broadband wavelength and mode multiplexers compared to conventional FDFD methods. We also show that factorization caching scales well over a broad range of footprints independent of the device geometry, from as small as 16μm2 to over 7000μm2. Our results present significant enhancements in the computational efficiency of inverse photonic design and can greatly accelerate the use of machine-optimized devices in future photonic systems.

1.
K. Y.
Yang
,
C.
Shirpurkar
,
A. D.
White
,
J.
Zang
,
L.
Chang
,
F.
Ashtiani
,
M. A.
Guidry
,
D. M.
Lukin
,
S. V.
Pericherla
,
J.
Yang
et al, “
Multi-dimensional data transmission using inverse-designed silicon photonics and microcombs
,”
Nat. Commun.
13
,
7862
(
2022
).
2.
E.
Luan
,
H.
Shoman
,
D. M.
Ratner
,
K. C.
Cheung
, and
L.
Chrostowski
, “
Silicon photonic biosensors using label-free detection
,”
Sensors
18
,
3519
(
2018
).
3.
K.
Vandoorne
,
P.
Mechet
,
T.
Van Vaerenbergh
,
M.
Fiers
,
G.
Morthier
,
D.
Verstraeten
,
B.
Schrauwen
,
J.
Dambre
, and
P.
Bienstman
, “
Experimental demonstration of reservoir computing on a silicon photonics chip
,”
Nat. Commun.
5
,
3541
(
2014
).
4.
E. S.
Magden
,
N.
Li
,
M.
Raval
,
C. V.
Poulton
,
A.
Ruocco
,
N.
Singh
,
D.
Vermeulen
,
E. P.
Ippen
,
L. A.
Kolodziejski
, and
M. R.
Watts
, “
Transmissive silicon photonic dichroic filters with spectrally selective waveguides
,”
Nat. Commun.
9
,
3009
(
2018
).
5.
N.
Singh
,
M.
Xin
,
N.
Li
,
D.
Vermeulen
,
A.
Ruocco
,
E. S.
Magden
,
K.
Shtyrkova
,
E.
Ippen
,
F. X.
Kärtner
, and
M. R.
Watts
, “
Silicon photonics optical frequency synthesizer
,”
Laser Photonics Rev.
14
,
1900449
(
2020
).
6.
A. Y.
Piggott
,
J.
Lu
,
K. G.
Lagoudakis
,
J.
Petykiewicz
,
T. M.
Babinec
, and
J.
Vučković
, “
Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer
,”
Nat. Photonics
9
,
374
377
(
2015
).
7.
S.
Molesky
,
Z.
Lin
,
A. Y.
Piggott
,
W.
Jin
,
J.
Vucković
, and
A. W.
Rodriguez
, “
Inverse design in nanophotonics
,”
Nat. Photonics
12
,
659
670
(
2018
).
8.
T. W.
Hughes
,
M.
Minkov
,
I. A.
Williamson
, and
S.
Fan
, “
Adjoint method and inverse design for nonlinear nanophotonic devices
,”
ACS Photonics
5
,
4781
4787
(
2018
).
9.
C. M.
Lalau-Keraly
,
S.
Bhargava
,
O. D.
Miller
, and
E.
Yablonovitch
, “
Adjoint shape optimization applied to electromagnetic design
,”
Opt. Express
21
,
21693
21701
(
2013
).
10.
J.
Lu
and
J.
Vučković
, “
Objective-first design of high-efficiency, small-footprint couplers between arbitrary nanophotonic waveguide modes
,”
Opt. Express
20
,
7221
7236
(
2012
).
11.
A.
Michaels
and
E.
Yablonovitch
, “
Leveraging continuous material averaging for inverse electromagnetic design
,”
Opt. Express
26
,
31717
31737
(
2018
).
12.
K.
Wang
,
X.
Ren
,
W.
Chang
,
L.
Lu
,
D.
Liu
, and
M.
Zhang
, “
Inverse design of digital nanophotonic devices using the adjoint method
,”
Photonics Res.
8
,
528
533
(
2020
).
13.
A. M.
Hammond
and
R. M.
Camacho
, “
Designing integrated photonic devices using artificial neural networks
,”
Opt. Express
27
,
29620
29638
(
2019
).
14.
N. Z.
Zhao
,
S.
Boutami
, and
S.
Fan
, “
Accelerating adjoint variable method based photonic optimization with schur complement domain decomposition
,”
Opt. Express
27
,
20711
20719
(
2019
).
15.
W.
Ma
,
Z.
Liu
,
Z. A.
Kudyshev
,
A.
Boltasseva
,
W.
Cai
, and
Y.
Liu
, “
Deep learning for the design of photonic structures
,”
Nat. Photonics
15
,
77
90
(
2021
).
16.
M.
Chen
,
R.
Lupoiu
,
C.
Mao
,
D.-H.
Huang
,
J.
Jiang
,
P.
Lalanne
, and
J. A.
Fan
, “
High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning
,”
ACS Photonics
9
,
3110
3123
(
2022
).
17.
D.
Liu
,
Y.
Tan
,
E.
Khoram
, and
Z.
Yu
, “
Training deep neural networks for the inverse design of nanophotonic structures
,”
ACS Photonics
5
,
1365
1369
(
2018
).
18.
Z.
Liu
,
D.
Zhu
,
L.
Raju
, and
W.
Cai
, “
Tackling photonic inverse design with machine learning
,”
Adv. Sci.
8
,
2002923
(
2021
).
19.
P. R.
Wiecha
,
A.
Arbouet
,
C.
Girard
, and
O. L.
Muskens
, “
Deep learning in nano-photonics: Inverse design and beyond
,”
Photonics Res.
9
,
B182
B200
(
2021
).
20.
O.
Schenk
,
K.
Gärtner
, and
W.
Fichtner
, “
Efficient sparse LU factorization with left-right looking strategy on shared memory multiprocessors
,”
BIT Numer. Math.
40
,
158
176
(
2000
).
21.
T. A.
Davis
,
S.
Rajamanickam
, and
W. M.
Sid-Lakhdar
, “
A survey of direct methods for sparse linear systems
,”
Acta Numer.
25
,
383
566
(
2016
).
22.
N. Z.
Zhao
,
S.
Boutami
, and
S.
Fan
, “
Efficient method for accelerating line searches in adjoint optimization of photonic devices by combining schur complement domain decomposition and born series expansions
,”
Opt. Express
30
,
6413
6424
(
2022
).
23.
J.
Buus
, “
The effective index method and its application to semiconductor lasers
,”
IEEE J. Quantum Electron.
18
,
1083
1089
(
1982
).
24.
C.
Zhu
,
R. H.
Byrd
,
P.
Lu
, and
J.
Nocedal
, “
Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization
,”
ACM Trans. Math. Software
23
,
550
560
(
1997
).
25.
A. O.
Dasdemir
,
A. K.
Koral
,
B.
Kiraz
,
A.
Kiraz
, and
E. S.
Magden
, “
Multi-scale hierarchical topology optimization for nanophotonic design
,” in
Integrated Photonics Research, Silicon and Nanophotonics
(
Optica Publishing Group
,
2020
), p.
ITu4A-11
.
27.
D.
Marchant
, see https://github.com/dwfmarchant/pyMKL for “
pyMKL: Python wrapper of Intel MKL routines
” (
2017
).
28.
V.
Minden
, see https://github.com/Photonic-Architecture-Laboratories/linear-system-solver for “
Linear system solver
” (
2022
).
29.
L.
Su
,
D.
Vercruysse
,
J.
Skarda
,
N. V.
Sapra
,
J. A.
Petykiewicz
, and
J.
Vučković
, “
Nanophotonic inverse design with spins: Software architecture and practical considerations
,”
Appl. Phys. Rev.
7
,
011407
(
2020
).
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