Graphical aids in the use of equivalent index in multilayer-filter design

Curtis Ufford; Philip Baumeister

doi:10.1364/JOSA.64.000329

Journal of the Optical Society of America
Vol. 64,
Issue 3,
pp. 329-334
(1974)
•https://doi.org/10.1364/JOSA.64.000329

Graphical aids in the use of equivalent index in multilayer-filter design

Curtis Ufford and Philip Baumeister

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Curtis Ufford and Philip Baumeister, "Graphical aids in the use of equivalent index in multilayer-filter design," J. Opt. Soc. Am. 64, 329-334 (1974)

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Abstract

The equivalent index of a symmetrical nonabsorbing three-layer stack is plotted vs the thickness ratio and index ratio of the high-index and low-index layers. This furnishes some useful insight into the behavior of the equivalent index and is useful in the design of antireflection coatings and edge filters.

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Type of design	Example
Type of design	a l h l	b h l h	c h l h	d l h l
n_l	1.38	1.38	1.40	1.40
n_h	2.23	2.23	2.07	1.74
h_l, nm	63.4	67.1	43.4	33.9
h_h, nm	31.4	33.5	7.3	52.9
Ω	1.615	1.615	1.48	1.24
Λ	2.5	1.62	0.5	1.0
n_re	1.23	1.23	0.86	0.86
λ₀, nm	1000	1000	250	250
β_e	90°	90°	135°	270°
n_e	1.70	1.70	1.20	1.20

		1	2	3	4	5
Nonsimulated design	Opt. Tkns.	0.25λ₀	0.25λ₀	0.5λ₀	0.25λ₀	0.25λ₀
	Index	1.38	1.90	2.30	1.96	1.66
Simulated design	Opt. Tkns nm	135		135		135
	Index	1.38		2.30		1.63
Simulated design.	Opt. Tkns. of l, nm		48.3		40.9
Layer is simulated with h l h	n_l		1.63		1.63
	Opt. Tkns. of h, nm		43.3		47.0
	n_h		2.30		2.30
Simulated design.	Opt. Tkns. of l, nm		47.2		42.5
Layer is simulated with l h l	n_l		1.63		1.63
	Opt. Tkns. of h, nm		40.5		50.0
	n_h		2.30		2.30

Layer number	Optical thickness, nm	Refractive index
Incident medium	Massive	1.00
1	136.75	1.38
2	42.5	2.30
3	35.5	1.63
4	243.5	2.30
5	38.25	1.63
6	42	2.30
7	148	1.63
Substrate, emergent medium	Massive	1.517

Fig.	2	3	4	5	6	7	8	9
Type	l h l	l h l	l h l	l h l	l h l	l h l	l h l	l h l
A	1.02	1.02	1.02	0.55	1.01	0.92	0.80	1.02
B	1.05	1.05	1.05	0.60	1.02	0.93	0.82	1.05
C	1.08	1.10	1.10	0.65	1.03	0.94	0.84	1.10
D	1.11	1.15	1.15	0.70	1.04	0.95	0.86	1.15
E	1.15	1.20	1.20	0.75	1.06	0.96	0.88	1.20
F	1.20	1.25	1.25	0.80	1.08	0.97	0.90	1.25
G	1.25	1.30	1.30	0.85	1.10	0.98	0.92	1.30
H	1.30	1.35	1.35	0.90	1.15	0.99	0.94	1.35
I	1.35	1.40	1.40	0.95	1.20	1.00	0.96	1.40
J	1.40	1.50	1.50	0.98	1.25	1.01	0.98	1.50
K	1.45	1.60	1.60	1.02	1.30	1.02	0.99	1.60
L	1.50	1.70	1.70	1.05	1.35	1.04	1.01	1.70
M	1.55	1.80	1.80	1.10	1.40	1.06	1.02	1.80
N	1.60	1.90	1.90	1.15	1.45	1.08	1.04	2.00
O	1.65	2.00	2.00	1.20	1.50	1.10	1.06	2.20
P	1.70	2.10	2.15	1.30	1.55	1.15	1.08	2.40
Q	1.75		2.30	1.40		1.20	1.10	2.60
R	1.80		2.45			1.25	1.12	2.80
S	1.85					1.30	1.15	3.00
T	1.90					1.35	1.20	3.40
U						1.40	1.25	3.80
V							1.00
β_e	90	120	135	270	90	120	135	270

Type of design	Example
Type of design	a l h l	b h l h	c h l h	d l h l
n_l	1.38	1.38	1.40	1.40
n_h	2.23	2.23	2.07	1.74
h_l, nm	63.4	67.1	43.4	33.9
h_h, nm	31.4	33.5	7.3	52.9
Ω	1.615	1.615	1.48	1.24
Λ	2.5	1.62	0.5	1.0
n_re	1.23	1.23	0.86	0.86
λ₀, nm	1000	1000	250	250
β_e	90°	90°	135°	270°
n_e	1.70	1.70	1.20	1.20

Abstract

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Figures (14)

Tables (4)

Equations (6)

Journal of the Optical Society of America