Global optimization and modeling techniques for planar multilayered dielectric structures

R. F. Oulton; C. S. Adjiman

doi:10.1364/AO.45.005910

Applied Optics
Vol. 45,
Issue 23,
pp. 5910-5922
(2006)
•https://doi.org/10.1364/AO.45.005910

Global optimization and modeling techniques for planar multilayered dielectric structures

R. F. Oulton and C. S. Adjiman

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R. F. Oulton and C. S. Adjiman, "Global optimization and modeling techniques for planar multilayered dielectric structures," Appl. Opt. 45, 5910-5922 (2006)

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Abstract

We present a multilevel global optimization strategy for synthesizing planar multilayered dielectric structures. A low discrepancy sequence of sample points with uniform variable space coverage allows a global-level search while systematic refinement using gradient-based techniques identifies optima at the local level. Since efficient local optimization is important for this method, a fast calculation approach based on mode matching is presented; this also facilitates the compact derivation of analytical gradients. The approach is compared with genetic and simulated annealing algorithms through an antireflection coating design. The method proves to be competitive in terms of its performance, nonadaptive algorithm, and ability to track local solutions.

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Rank	ℱ	Method	R̄ ^a (%)	t_T ^b (μm)	t _opt ^c (μm)
17 layers:
1^d	0.64	ML	0.63	12.0	38
2^d	0.65	GA	0.63	10.4	31
3	0.66	ML	0.64	11.9	39
4	0.66	ML	0.65	11.7	39
5	0.68	ML	0.66	12.0	38
⫶	⫶	⫶	⫶	⫶	⫶
11	0.69	ML	0.65	9.8	31
12^d	0.69	SA	0.65	10.8	31
20 layers:
1^d	0.59	ML	0.58	13.6	44
2	0.62	ML	0.60	12.2	37
3	0.62	ML	0.60	11.9	36
4	0.63	ML	0.61	12.6	37
5	0.63	ML	0.61	13.0	43
⫶	⫶	⫶	⫶	⫶	⫶
13	0.65	ML	0.64	14.8	49
14^d	0.66	GA	0.63	10.5	32
⫶	⫶	⫶	⫶	⫶	⫶
45^d	0.70	SA	0.69	9.6	29

Layer	17 Layers		20 Layers
Layer	Index	Thickness (μm)	Index	Thickness (μm)
Air	1	∞	1	∞
1	2.2	1.0905	2.2	1.0851
2	4.2	0.6073	4.2	0.6007
3	2.2	0.5294	2.2	0.5533
4	4.2	0.1217	4.2	0.0997
5	2.2	1.1719	2.2	1.2353
6	4.2	1.3287	4.2	0.7047
7	2.2	0.2290	2.2	0.2252
8	4.2	0.9317	4.2	0.3021
9	2.2	0.3893	2.2	0.7903
10	4.2	0.1889	4.2	1.2260
11	2.2	0.9297	2.2	0.7377
12	4.2	1.1795	4.2	0.1727
13	2.2	1.2290	2.2	0.2650
14	4.2	0.1000	4.2	0.9940
15	2.2	0.5591	2.2	1.0354
16	4.2	1.3823	4.2	0.0905
17	2.2	0.0594	2.2	0.6772
18	–	–	4.2	1.3999
19	–	–	2.2	0.0981
20	–	–	4.2	1.2808
Substrate	4	∞	4	∞

Rank	ℱ	Method	R̄ ^a (%)	t_T ^b (μm)	t _opt ^c (μm)
17 layers:
1^d	0.64	ML	0.63	12.0	38
2^d	0.65	GA	0.63	10.4	31
3	0.66	ML	0.64	11.9	39
4	0.66	ML	0.65	11.7	39
5	0.68	ML	0.66	12.0	38
⫶	⫶	⫶	⫶	⫶	⫶
11	0.69	ML	0.65	9.8	31
12^d	0.69	SA	0.65	10.8	31
20 layers:
1^d	0.59	ML	0.58	13.6	44
2	0.62	ML	0.60	12.2	37
3	0.62	ML	0.60	11.9	36
4	0.63	ML	0.61	12.6	37
5	0.63	ML	0.61	13.0	43
⫶	⫶	⫶	⫶	⫶	⫶
13	0.65	ML	0.64	14.8	49
14^d	0.66	GA	0.63	10.5	32
⫶	⫶	⫶	⫶	⫶	⫶
45^d	0.70	SA	0.69	9.6	29

Layer	17 Layers		20 Layers
Layer	Index	Thickness (μm)	Index	Thickness (μm)
Air	1	∞	1	∞
1	2.2	1.0905	2.2	1.0851
2	4.2	0.6073	4.2	0.6007
3	2.2	0.5294	2.2	0.5533
4	4.2	0.1217	4.2	0.0997
5	2.2	1.1719	2.2	1.2353
6	4.2	1.3287	4.2	0.7047
7	2.2	0.2290	2.2	0.2252
8	4.2	0.9317	4.2	0.3021
9	2.2	0.3893	2.2	0.7903
10	4.2	0.1889	4.2	1.2260
11	2.2	0.9297	2.2	0.7377
12	4.2	1.1795	4.2	0.1727
13	2.2	1.2290	2.2	0.2650
14	4.2	0.1000	4.2	0.9940
15	2.2	0.5591	2.2	1.0354
16	4.2	1.3823	4.2	0.0905
17	2.2	0.0594	2.2	0.6772
18	–	–	4.2	1.3999
19	–	–	2.2	0.0981
20	–	–	4.2	1.2808
Substrate	4	∞	4	∞

Abstract

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Equations (36)

Applied Optics