Multi-solution inverse design in photonics using generative modeling

Preetam Kumar; Aniket Patra; Aniket Patra; E. S. Shivaleela; Vincenzo Caligiuri; Vincenzo Caligiuri; Roman Krahne; Antonio De Luca; Antonio De Luca; T. Srinivas

doi:10.1364/JOSAB.502923

Journal of the Optical Society of America B
Vol. 41,
Issue 2,
pp. A152-A160
(2024)
•https://doi.org/10.1364/JOSAB.502923

Multi-solution inverse design in photonics using generative modeling

Preetam Kumar, Aniket Patra, E. S. Shivaleela, Vincenzo Caligiuri, Roman Krahne, Antonio De Luca, and T. Srinivas

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Preetam Kumar, Aniket Patra, E. S. Shivaleela, Vincenzo Caligiuri, Roman Krahne, Antonio De Luca, and T. Srinivas, "Multi-solution inverse design in photonics using generative modeling," J. Opt. Soc. Am. B 41, A152-A160 (2024)

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Table of Contents Category
- Photonics
Optics & Photonics Topics
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About this Article
History
- Original Manuscript: August 8, 2023
- Revised Manuscript: January 10, 2024
- Manuscript Accepted: January 13, 2024
- Published: January 30, 2024
Virtual Issues
JOSA B Feature Issue: Inverse Design in Photonics (2024)

Abstract

The lack of uniqueness poses a common challenge in the inverse design of nanophotonic structures. This issue arises from the presence of multiple sets of design parameters that yield identical output configurations. Several existing machine learning methods offer promising solutions for enabling flexibility in selecting sets of design variables. However, these approaches still face significant challenges like limited output diversity, and training instability. These issues constrain the variety of solutions attainable for a particular target response. To overcome these challenges in the realm of multi-solution inverse design problems in nanophotonics, we have developed a GA-$\beta $CVAE architecture based on generative models. This approach effectively tackles such problems, thereby expanding the range of distinct solutions achievable in nanophotonics. Our approach combines a genetic algorithm with a $\beta$ conditional variational autoencoder neural network based generative model, capturing multiple distinct solutions for a given target. It provides flexibility in selecting design variables. We successfully applied it to design ${\rm{Ti}}{{\rm{O}}_{{2}}}\text{-}{\rm{Si}}{{\rm{O}}_{{2}}}$ based multilayer thin films in the visible range (400–750 nm), with layer thickness as the design variable. Experimental verification confirmed the effectiveness of our proposed architecture.

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Supplementary Material (1)

Name	Description
Supplement 1	Supplemental document.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	56	99	54	123	151	120	100	60	13
2	89	74	82	41	78	129	136	21	36
3	93	67	76	46	87	121	141	18	38

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	69	106	53	101	106	36	149	19	42
2	70	89	63	98	49	141	92	54	17
3	56	119	48	115	75	50	135	55	20

Solution Set	$σ^{2} ({n m}^{2})$	MAPE
1	20	13.69
2	20	13.55
3	20	15.16
1	40	5.9
2	40	6.17
3	40	6.18
1	60	6.08
2	60	6.09
3	60	6.9

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	56	99	54	123	151	120	100	60	13
2	89	74	82	41	78	129	136	21	36
3	93	67	76	46	87	121	141	18	38

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	69	106	53	101	106	36	149	19	42
2	70	89	63	98	49	141	92	54	17
3	56	119	48	115	75	50	135	55	20

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	56	99	54	123	151	120	100	60	13
2	89	74	82	41	78	129	136	21	36
3	93	67	76	46	87	121	141	18	38

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	69	106	53	101	106	36	149	19	42
2	70	89	63	98	49	141	92	54	17
3	56	119	48	115	75	50	135	55	20

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	56	99	54	123	151	120	100	60	13
2	89	74	82	41	78	129	136	21	36
3	93	67	76	46	87	121	141	18	38

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	69	106	53	101	106	36	149	19	42
2	70	89	63	98	49	141	92	54	17
3	56	119	48	115	75	50	135	55	20

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	56	99	54	123	151	120	100	60	13
2	89	74	82	41	78	129	136	21	36
3	93	67	76	46	87	121	141	18	38

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	69	106	53	101	106	36	149	19	42
2	70	89	63	98	49	141	92	54	17
3	56	119	48	115	75	50	135	55	20

Abstract

Supplementary Material (1)

Data availability

Cited By

Figures (9)

Tables (4)

Equations (5)

Journal of the Optical Society of America B

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	56	99	54	123	151	120	100	60	13
2	89	74	82	41	78	129	136	21	36
3	93	67	76	46	87	121	141	18	38

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	69	106	53	101	106	36	149	19	42
2	70	89	63	98	49	141	92	54	17
3	56	119	48	115	75	50	135	55	20

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	119	33	61	39	99	120	77	18	109
2	98	91	19	95	93	98	92	70	26
3	107	61	41	58	111	86	112	18	79

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	56	99	54	123	151	120	100	60	13
2	89	74	82	41	78	129	136	21	36
3	93	67	76	46	87	121	141	18	38

Solution Set	Layer 1	Layer 2	Layer 3	Layer 4	Layer 5	Layer 6	Layer 7	Layer 8	Layer 9
1	69	106	53	101	106	36	149	19	42
2	70	89	63	98	49	141	92	54	17
3	56	119	48	115	75	50	135	55	20