Interface design methods for two-material optical multilayer coatings

J. A. Dobrowolski; R. A. Kemp

doi:10.1364/AO.31.006747

Applied Optics
Vol. 31,
Issue 31,
pp. 6747-6756
(1992)
•https://doi.org/10.1364/AO.31.006747

Interface design methods for two-material optical multilayer coatings

J. A. Dobrowolski and R. A. Kemp

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J. A. Dobrowolski and R. A. Kemp, "Interface design methods for two-material optical multilayer coatings," Appl. Opt. 31, 6747-6756 (1992)

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Abstract

A method for the design of multilayers is proposed in which the thicknesses of two layers on either side of an interface are simultaneously adjusted. It is therefore possible to shift the boundary between two layers without changing their combined optical thickness. This can be an advantage during the solution of some problems. The method has been implemented for the refinement and the synthesis of systems that are made of two nonabsorbing, dispersive coating materials. A number of numerical examples illustrating the various ways in which the method can be applied are presented. The results are compared with those obtained by a more conventional technique. The interface design method is quite robust and yields solutions that can be implemented readily.

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k	Location	Layer (i + 1)	Layer i
1	Within layer system	0	0
2	Within layer system	−δ_A	0
3	Within layer system	+δ_A	0
4	Within layer system	0	−δ_B
5	Within layer system	0	+δ_B
6	Within layer system	−δ_A	+δ_B
7	Within layer system	+δ_A	−δ_B
8	Within layer system	−δ_A	−δ_B
9	Within layer system	+δ_A	+δ_B
10	Add (δ_A + δ_B) to either end	0	0
11	Add (δ_A + δ_B) at medium	+δ_A	0
12	Add (δ_A + δ_B) at medium	−δ_A	0
13	Add (δ_A + δ_B) at substrate	0	+δ_B
14	Add (δ_A + δ_B) at substrate	0	−δ_B

k	Fig. 3	Fig. 4A	Fig. 4B	Fig. 4C	Fig. 4D	Fig. 5A	Fig. 5B	Fig. 5C	Fig. 6A	Fig. 6B	Fig. 6C	Fig. 6D
1	76.7	68.5	55.3	51.2	67.0	88.7	90.9	86.3	82.3	84.6	84.5	65.0
2	5.1	14.8	4.0	6.5	1.4	4.5	0.0	4.5	10.6	1.4	1.7	6.3
3	5.1	17.2	5.7	8.4	2.2	7.7	0.54	4.0	8.0	3.3	3.6	7.0
4	1.1		7.4	9.2	6.8		2.1	0.3		2.4	2.6	2.2
5	3.0		10.2	10.5	12.1		4.5	0.6		2.3	2.1	3.6
6	4.6		7.4	4.6	4.9		1.4	2.6		2.4	2.0	6.7
7	3.0		8.7	5.4	4.7		1.3	2.1		3.9	3.4	8.9
8	0.2		1.5	2.3	0.8		0.2	1.0		0.5	0.6	0.4
9	0.5		4.8	3.5	0.7		0.0	0.3		1.0	0.6	0.5
10	3.6			0.0	0.0			5.4			0.0	2.7
11	0.0			0.0	0.0			0.0			0.0	0.0
12	0.0			0.0	0.0			0.0			0.0	0.0
13	9.7			0.0	0.7			0.0			1.7	2.1
14	17.7			15.0	5.2			2.2			1.7	1.1
∑ (nt)	4.399	31.8	31.5	31.7	31.2	2.848	2.852	3.854	3.054	3.375	3.375	2.200
MF	0.73	1.19	1.18	1.18	0.79	3.03	3.00	2.75	2.36	1.67	1.56	2.22

k	Location	Layer (i + 1)	Layer i
1	Within layer system	0	0
2	Within layer system	−δ_A	0
3	Within layer system	+δ_A	0
4	Within layer system	0	−δ_B
5	Within layer system	0	+δ_B
6	Within layer system	−δ_A	+δ_B
7	Within layer system	+δ_A	−δ_B
8	Within layer system	−δ_A	−δ_B
9	Within layer system	+δ_A	+δ_B
10	Add (δ_A + δ_B) to either end	0	0
11	Add (δ_A + δ_B) at medium	+δ_A	0
12	Add (δ_A + δ_B) at medium	−δ_A	0
13	Add (δ_A + δ_B) at substrate	0	+δ_B
14	Add (δ_A + δ_B) at substrate	0	−δ_B

k	Fig. 3	Fig. 4A	Fig. 4B	Fig. 4C	Fig. 4D	Fig. 5A	Fig. 5B	Fig. 5C	Fig. 6A	Fig. 6B	Fig. 6C	Fig. 6D
1	76.7	68.5	55.3	51.2	67.0	88.7	90.9	86.3	82.3	84.6	84.5	65.0
2	5.1	14.8	4.0	6.5	1.4	4.5	0.0	4.5	10.6	1.4	1.7	6.3
3	5.1	17.2	5.7	8.4	2.2	7.7	0.54	4.0	8.0	3.3	3.6	7.0
4	1.1		7.4	9.2	6.8		2.1	0.3		2.4	2.6	2.2
5	3.0		10.2	10.5	12.1		4.5	0.6		2.3	2.1	3.6
6	4.6		7.4	4.6	4.9		1.4	2.6		2.4	2.0	6.7
7	3.0		8.7	5.4	4.7		1.3	2.1		3.9	3.4	8.9
8	0.2		1.5	2.3	0.8		0.2	1.0		0.5	0.6	0.4
9	0.5		4.8	3.5	0.7		0.0	0.3		1.0	0.6	0.5
10	3.6			0.0	0.0			5.4			0.0	2.7
11	0.0			0.0	0.0			0.0			0.0	0.0
12	0.0			0.0	0.0			0.0			0.0	0.0
13	9.7			0.0	0.7			0.0			1.7	2.1
14	17.7			15.0	5.2			2.2			1.7	1.1
∑ (nt)	4.399	31.8	31.5	31.7	31.2	2.848	2.852	3.854	3.054	3.375	3.375	2.200
MF	0.73	1.19	1.18	1.18	0.79	3.03	3.00	2.75	2.36	1.67	1.56	2.22

Abstract

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Tables (2)

Equations (5)

Applied Optics