Modern design tools and a new paradigm in optical coating design

Alexander V. Tikhonravov; Michael K. Trubetskov

doi:10.1364/AO.51.007319

Applied Optics
Vol. 51,
Issue 30,
pp. 7319-7332
(2012)
•https://doi.org/10.1364/AO.51.007319

Modern design tools and a new paradigm in optical coating design

Alexander V. Tikhonravov and Michael K. Trubetskov

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Alexander V. Tikhonravov and Michael K. Trubetskov, "Modern design tools and a new paradigm in optical coating design," Appl. Opt. 51, 7319-7332 (2012)

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Abstract

Several modern optical coating designs tools are discussed in the frame of a new design paradigm proposing the search not for a formally optimal solution with the lowest possible merit function value but for the most practical solution that takes into account additional feasibility demands. Considered design tools include a stochastic optimization procedure that takes into account upper and lower constraints for layer optical thicknesses. This procedure allows one to obtain multiple solutions to a design problem, which presents additional opportunities for choosing a practically optimal design. Two special design techniques involving integer optimization also take into account additional demands. The first one is aimed at designing multicavity narrow bandpass filters with quarter wave or multiple quarter wave layer optical thicknesses. It enables obtaining bandpass filters with extremely steep transmittance slopes, bandwidths of several tens of nanometers, and very small ripples in transmission zones. The second technique is aimed at covering design problems that have been traditionally solved using the theory of equivalent layers. One more technique considered in this paper is aimed at reducing the influence of noncorrelated thickness errors on design spectral characteristics.

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Design	MF	TOT
1	0.526	9212.7
2	0.524	9363.9
3	0.516	9409.7
4	0.479	9422.8
5	0.571	9202.9
6	0.599	9391.2
7	0.570	9665.9
8	0.464	9371.8
9	0.524	9226.7
10	0.496	9382.7

Parameters\Design	1	2	3	4	5
$R_{\min}$ , %	99.80	99.81	99.94	99.92	99.87
$N$	73	83	85	83	82
TOT, nm	11285.6	13045.3	13056.3	12732.0	12661.8
$m_{1}$	11	14	13	12	10
$m_{2}$	8	11	12	13	14
$m_{3}$	14	13	14	13	14
$a_{1}$	0.888	0.906	1.657	0.897	0.894
$a_{2}$	1.202	1.208	1.196	1.180	1.179
$a_{3}$	1.512	1.604	0.904	1.581	1.573
$b_{1}$	0.908	$= a_{1}$	1.482	$= a_{1}$	$= a_{1}$
$b_{2}$	1.168	$= a_{2}$	1.181	$= a_{2}$	$= a_{2}$
$b_{3}$	1.578	$= a_{3}$	$= a_{3}$	$= a_{3}$	$= a_{3}$
$c_{1}$	1.035	1.070	1.782	0.552	0.966
$c_{2}$	1.146	1.489	1.198	2.0	0.932
$c_{3}$	0.991	$= a_{2}$	1.263	1.509	1.494
$c_{4}$	2.0	1.982	1.961	0.100	$= 0$
$d_{1}$	0.938	1.752	1.681	0.843	0.847
$d_{2}$	1.308	1.282	1.007	1.964	0.515
$d_{3}$	0.899	1.918	$= a_{3}$	$= a_{3}$	$= a_{3}$

Parameters\Design	AR-6	AR-10	AR-14	AR-Robust
$N$	6	10	14	9
TOT, nm	463.8	943.1	1380.0	1102.1
MF	0.263	0.135	0.129	0.169
E(MF)	0.343	0.295	0.372	0.277

Design	MF	TOT
1	0.526	9212.7
2	0.524	9363.9
3	0.516	9409.7
4	0.479	9422.8
5	0.571	9202.9
6	0.599	9391.2
7	0.570	9665.9
8	0.464	9371.8
9	0.524	9226.7
10	0.496	9382.7

Parameters\Design	1	2	3	4	5
$R_{\min}$ , %	99.80	99.81	99.94	99.92	99.87
$N$	73	83	85	83	82
TOT, nm	11285.6	13045.3	13056.3	12732.0	12661.8
$m_{1}$	11	14	13	12	10
$m_{2}$	8	11	12	13	14
$m_{3}$	14	13	14	13	14
$a_{1}$	0.888	0.906	1.657	0.897	0.894
$a_{2}$	1.202	1.208	1.196	1.180	1.179
$a_{3}$	1.512	1.604	0.904	1.581	1.573
$b_{1}$	0.908	$= a_{1}$	1.482	$= a_{1}$	$= a_{1}$
$b_{2}$	1.168	$= a_{2}$	1.181	$= a_{2}$	$= a_{2}$
$b_{3}$	1.578	$= a_{3}$	$= a_{3}$	$= a_{3}$	$= a_{3}$
$c_{1}$	1.035	1.070	1.782	0.552	0.966
$c_{2}$	1.146	1.489	1.198	2.0	0.932
$c_{3}$	0.991	$= a_{2}$	1.263	1.509	1.494
$c_{4}$	2.0	1.982	1.961	0.100	$= 0$
$d_{1}$	0.938	1.752	1.681	0.843	0.847
$d_{2}$	1.308	1.282	1.007	1.964	0.515
$d_{3}$	0.899	1.918	$= a_{3}$	$= a_{3}$	$= a_{3}$

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Applied Optics