Minimax refining of optical multilayer systems

Amedeo Premoli; Maria Luisa Rastello

doi:10.1364/AO.31.001597

Applied Optics
Vol. 31,
Issue 10,
pp. 1597-1605
(1992)
•https://doi.org/10.1364/AO.31.001597

Minimax refining of optical multilayer systems

Amedeo Premoli and Maria Luisa Rastello

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Amedeo Premoli and Maria Luisa Rastello, "Minimax refining of optical multilayer systems," Appl. Opt. 31, 1597-1605 (1992)

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Abstract

A new minimax method for refining optical multilayer systems is presented. It minimizes the maximum deviation of the spectral transmittance from the desired specifications. These are assigned in such a general way that any shape can be approximated. The algorithm consists of iterating optimization steps that are obtained by developing the transmittance in the Taylor expansion versus the known parameters and solved by piecewise-linear programming. The investigation is limited to the design of lossless multilayers with assigned refractive indices and undetermined thicknesses. Some minimax-refined designs are compared favorably with those reported in the literature.

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Layer	n	Case 3A, M = 7		Case 2E, M = 13		Case 3C, M = 17
Layer	n	Starting	Refined	Starting	Refined	Starting	Refined
Substrate	4.00	—	—	—	—	—	—
1	2 20	0.34773	0.36641	0.35595	0.34521	0.23368	0.25089
2	4.20	0.18274	0.17603	0.26952	0.27476	0.23429	0.22884
3	2 20	1.23068	1.24937	0.55336	0.54262	1.30259	1.27245
4	4.20	0.20298	0.21931	1.20929	1.21779	0.07831	0.09618
5	2.20	0.34318	0.32539	1.87832	1.87274	0.68545	0.65532
6	4.20	0.64048	0.62179	0.20769	0.19766	0.60493	0.59735
7	2 20	1.09205	1.10436	0.28827	0.29407	0.31877	0.34891
8	4 20	—	—	0.39907	0.40553	0.24248	0.22464
9	2.20	—	—	2.46973	2.47313	1.22859	1.25765
10	4.20	—	—	0.21021	0.21967	0.33338	0.33733
11	2.20	—	—	2.59586	2.59468	0.15673	0.12767
12	4.20	—	—	0.27867	0.28184	0.64671	0.67372
13	2.20	—	—	1.28759	1.29332	1.25682	1.28696
14	4.20	—	—	—	—	0.11507	0.11419
15	2.20	—	—	—	—	0.50886	0.47957
16	4.20	—	—	—	—	0.60648	0.63306
17	2.20	—	—	—	—	1.08609	1.07404
Air	1.00	—	—	—	—	—	—

Layer	n	Case 3D, M = 15
		Starting	Refined
		Starting	0.99–0.99	0.98–0.98	0.96–0.96
Substrate	4.00	—	—	—	—
1	2.20	0.09091	0.09985	0.17026	0.12269
2	4.20	0.34702	0.32890	0.28440	0.30694
3	2.20	0.45682	0.47839	0.59380	0.48089
4	4.20	0.14702	0.13632	0.08318	0.12621
5	2.20	1.65795	1.64571	1.77477	1.66017
6	4.20	0.04940	0.05806	0.07770	0.04487
7	2.20	2.71477	2.69320	2.61833	2.69033
8	4.20	0.40000	0.42157	0.43856	0.39421
9	2.20	0.04318	0.02327	0.02191	0.07197
10	4.20	0.69524	0.69568	0.68000	0.65588
11	2.20	1.22955	1.25112	1.22705	1.23808
12	4.20	0.12440	0.12966	0.12774	0.11658
13	2.20	0.48750	0.46855	0.48380	0.50267
14	4.20	0.60893	0.60618	0.60694	0.61115
15	2.20	1.08977	1.08730	1.08867	1.08495
Air	1.00	—	—	—	—

Layer	n	Case 1B, M = 21
		Starting	Refined
		Starting	M = 17	M = 19	M = 21
Substrate	4.00	—	—	—	—
1	2.20	0.325	0.17613	0.16209	0.25481
2	4.20	0.183	0.17984	0.35899	0.30877
3	2.20	0.332	0.09397	0.45049	0.47179
4	4.20	0.186	0.10921	0.35678	0.25119
5	2.20	0.332	0.11709	0.27288	0.20907
6	4.20	0.183	0.00390	0.57617	0.32919
7	2.20	0.325	0.77683	0.01638	0.23957
8	4.20	0.183	0.11362	0.23691	0.26516
9	2.20	0.500	0.78684	0.46127	0.33496
10	4.20	0.035	0.58795	0.17445	0.12911
11	2.20	0.500	0.17785	1.03605	0.84560
12	4.20	0.073	0.37695	0.47231	0.25371
13	2.20	0.748	1.32691	0.11767	0.46429
14	4.20	0.073	0.15474	0.56271	0.34535
15	2.20	0.500	0.41518	1.17951	0.43712
16	4.20	0.035	0.62475	0.14321	0.07569
17	2.20	1.966	1.09321	0.48314	0.96021
18	4.20	0.139	—	0.62660	0.16909
19	2.20	2.733	—	1.09109	0.41822
20	4.20	0.330	—	—	0.56895
21	2.20	1.272	—	—	1.11728
Air	1.00	—	—	—	—
p			1.051	0.862	1.108

Layer	n	Refined
Layer	n	M = 15	M = 17
Substrate	4.00	—	—
1	2.20	0.17813	0.17331
2	4.20	0.17325	0.35185
3	2.20	0.08018	0.48176
4	4.20	0.11174	0.34499
5	2.20	0.89065	0.28966
6	4.20	0.11159	0.80248
7	2.20	0.78481	0.44737
8	4.20	0.60938	0.18432
9	2.20	0.15930	1.03913
10	4.20	0.37930	0.45996
11	2.20	1.31473	0.10086
12	4.20	0.15304	0.59457
13	2.20	0.41628	1.23525
14	4.20	0.62221	0.13353
15	2.20	1.09278	0.47979
16	4.20	—	0.61877
17	2.20	—	1.09150
Air	1.00	—	—
p		1.094	0.882

Layer	n	Case 3A, M = 7		Case 2E, M = 13		Case 3C, M = 17
Layer	n	Starting	Refined	Starting	Refined	Starting	Refined
Substrate	4.00	—	—	—	—	—	—
1	2 20	0.34773	0.36641	0.35595	0.34521	0.23368	0.25089
2	4.20	0.18274	0.17603	0.26952	0.27476	0.23429	0.22884
3	2 20	1.23068	1.24937	0.55336	0.54262	1.30259	1.27245
4	4.20	0.20298	0.21931	1.20929	1.21779	0.07831	0.09618
5	2.20	0.34318	0.32539	1.87832	1.87274	0.68545	0.65532
6	4.20	0.64048	0.62179	0.20769	0.19766	0.60493	0.59735
7	2 20	1.09205	1.10436	0.28827	0.29407	0.31877	0.34891
8	4 20	—	—	0.39907	0.40553	0.24248	0.22464
9	2.20	—	—	2.46973	2.47313	1.22859	1.25765
10	4.20	—	—	0.21021	0.21967	0.33338	0.33733
11	2.20	—	—	2.59586	2.59468	0.15673	0.12767
12	4.20	—	—	0.27867	0.28184	0.64671	0.67372
13	2.20	—	—	1.28759	1.29332	1.25682	1.28696
14	4.20	—	—	—	—	0.11507	0.11419
15	2.20	—	—	—	—	0.50886	0.47957
16	4.20	—	—	—	—	0.60648	0.63306
17	2.20	—	—	—	—	1.08609	1.07404
Air	1.00	—	—	—	—	—	—

Abstract

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Tables (4)

Equations (33)

Applied Optics