Refractive-index measurements of moderately reflecting substrates using a wedged film technique

William T. Beauchamp; James D. Rancourt

doi:10.1364/AO.19.003239

Applied Optics
Vol. 19,
Issue 18,
pp. 3239-3244
(1980)
•https://doi.org/10.1364/AO.19.003239

Refractive-index measurements of moderately reflecting substrates using a wedged film technique

William T. Beauchamp and James D. Rancourt

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William T. Beauchamp and James D. Rancourt, "Refractive-index measurements of moderately reflecting substrates using a wedged film technique," Appl. Opt. 19, 3239-3244 (1980)

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Abstract

A method is described whereby the complex index of refraction can be determined for a strongly absorbing substrate material by measurement of reflectance maxima and minima at a given wavelength, as a function of the thickness of a wedged nonabsorbing thin film layer deposited on the substrate. The procedure for determination of the complex index n − ik employs the reflectance extremum and correlated film thickness to construct graphically the complex reflectance amplitude of the substrate material. Subsequently, the Fresnel equations for reflectance amplitude can be used to calculate the values of n and k. Examples of the successful use of the method to determine the far-IR indices of fused silica and sapphire are given. The limitations of the method are discussed, and examples of the expected errors for n and k for the two specific cases calculated are given.

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λ (μm)	This work		Literature values3,4
λ (μm)	n	k	n	k
2.5	1.45	0	1.45	0
7.0	1.19	0	1.10–1.05	0.01–0.14
8.1	0.41	0.44	0.20–0.37	0.25–0.40
8.7	0.38	1.26	0.13–0.39	1.70–1.26
9.1	1.26	2.64	0.50–1.64	4.40–2.50
9.3	2.56	1.87	5.00–2.35	0.70–2.44
9.5	2.97	1.47	3.90–2.98	0.50–1.52
9.7	3.04	0.86	3.20–2.98	0.10–0.90
9.9	2.45	0.24	2.50–2.77	0.05–0.40
10.2	2.33	0.09	2.20–2.36	0.04–0.19
10.6	2.06	0.05	2.10–2.00	0.02–0.12
11.0	1.91	0.05	2.00–1.93	0.02–0.14
11.6	1.70	0.06	1.75–1.79	0.02–0.20
12.3	1.72	0.33	1.25–1.76	0.43–0.34
14.0	1.75	0.06	1.70	0.02

λ (μm)	This work		Published data
λ (μm)	n	k	n	k
2.5	1.71	0	1.71	6.9E-7
8.1	1.4	0	1.21	8.8E-3
8.7	1.24	0.08	1.13	0.01
9.0	1.18	0.10	1.09	0.02
9.3	1.14	0.04	1.05	0.02
9.7	1.04	0.03	1.00	0.02
10.5	0.75	0.06	0.53	0.04
11.2	0.37	0.33	0.02	0.47
11.6	0.14	0.58	0.01	0.81
12.2	0.15	1.03	0.01	1.20
12.8	0.16	1.30	0.01	1.55
13.2	0.13	1.54	0.01	1.77
14.0	. 0.11	2.10	0.01	2.00
14.1	0.10	2.13	0.01	2.31
14.2	0.01	2.28	0.01	2.39
14.4	0.10	2.31	0.01	2.56
14.5	0.18	2.41	0.01	2.64
15.0	0.18	2.98	0.01	2.97
15.5	0.33	3.50	0.45	3.73
16.0	0.65	3.83	0.65	3.28
17.0	2.49	4.95	0.64	7.36

λ	ρ	θ	$\frac{{Δ n}_{s}}{n_{s}}$ ^b	$\frac{{Δ k}_{s}}{k_{s}}$ ^c
2.5	0.185	0	2.0	—
8.1	0.497	54.2°	3.6	4.5
9.0	0.820	42.1	8.5	5.3
9.7	0.536	10.7	3.3	18.0
10.6	0.346	1.6°	2.4	125.0
11.6	0.262	3.72°	2.2	54.0
14.0	0.275	3.13	2.2	60.0

λ	ρ^b	θ^b	$\frac{{Δ n}_{s}}{n_{s}}$ ^c	$\frac{{Δ k}_{s}}{k_{s}}$ ^d
9.0	0.44	168	3.0	17.4
10.5	0.289	83.6	3.0	3.0
14.0	0.996	108.4	126.2	3.0
15.0	0.998	142.8	356.0	5.0
17.0	0.970	164.6	71.3	12.9

λ (μm)	This work		Literature values3,4
λ (μm)	n	k	n	k
2.5	1.45	0	1.45	0
7.0	1.19	0	1.10–1.05	0.01–0.14
8.1	0.41	0.44	0.20–0.37	0.25–0.40
8.7	0.38	1.26	0.13–0.39	1.70–1.26
9.1	1.26	2.64	0.50–1.64	4.40–2.50
9.3	2.56	1.87	5.00–2.35	0.70–2.44
9.5	2.97	1.47	3.90–2.98	0.50–1.52
9.7	3.04	0.86	3.20–2.98	0.10–0.90
9.9	2.45	0.24	2.50–2.77	0.05–0.40
10.2	2.33	0.09	2.20–2.36	0.04–0.19
10.6	2.06	0.05	2.10–2.00	0.02–0.12
11.0	1.91	0.05	2.00–1.93	0.02–0.14
11.6	1.70	0.06	1.75–1.79	0.02–0.20
12.3	1.72	0.33	1.25–1.76	0.43–0.34
14.0	1.75	0.06	1.70	0.02

Abstract

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Applied Optics