Optical Properties of Thin Absorbing Films*

F. Abelès

doi:10.1364/JOSA.47.000473

Journal of the Optical Society of America
Vol. 47,
Issue 6,
pp. 473-482
(1957)
•https://doi.org/10.1364/JOSA.47.000473

Optical Properties of Thin Absorbing Films

F. Abelès

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F. Abelès, "Optical Properties of Thin Absorbing Films*," J. Opt. Soc. Am. 47, 473-482 (1957)

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Abstract

Equations are given for the reflectances, transmittances, and phase changes by reflection and transmission of very thin absorbing films, i.e., films with a thickness d very small compared with the wavelength λ of the incident radiation. The similarities and differences between very thin homogeneous and inhomogeneous films are discussed, and some experimental results obtained on very thin gold and chromium films are presented. We measured the reflectance and transmittance of these films as a function of the angle of incidence φ₀ and of the state of polarization of the incident light. A new method is given for obtaining the optical constants of ionic crystals in the infrared. The optical properties of thick metallic films, with some new photometric methods for the determination of their optical constants, are discussed. The theory of the optical absorption of metals is briefly presented.

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Equations (58)

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	λ=546 mμ				λ=640 mμ
φ₀	R_\|\|%	R_⊥%	T_\|\|%	T_⊥%	R_⊥%	T_\|\|%	T_⊥%	R_\|\|%
5	19.3	18.8	63.6	63.5	28.7	57	56.8	28.6
10	19.2	18.9	63.5	63.1	29	57.2	46.4	28.2
15	18.8	19.4	63.5	62.8	29.5	57.5	56	28
20	18.1	20.3	64	61.2	30.6	58.2	54.3	27.2
25	17.5	21.5	65.2	60.2	32.6	59.7	52.1	26
30	16.6	23.2	66.5	58.2	34	61.3	50.7	25.4
35	15.6	24.6	67.5	56.4	36.1	63	48.8	24
40	14.3	26.8	68.6	54.6	38.4	64.2	46.7	22.4
45	12.8	29.6	70.7	50.7	40.8	66.3	44	20.9
50	11.4	32.7	71.3	47.8	44.2	68.4	41	18.7
52	10.8	34.3	72	46.3	45.5	69.3	39.6	17.9
55	9.99	37.2	72.6	43.6	47.9	70.2	37.6	16.7
57	9.56	38.8	⋯	41.3	50.1	71.4	36.1	16.1
58	9.14	⋯	74	⋯	⋯	⋯	⋯	⋯
60	8.72	41.5	74.4	39	52.4	71.9	33.7	15.6
62	⋯	44.3	⋯	36.4	55	72.2	31.8	14.7
63	8.52	⋯	74.5	⋯	⋯	⋯	⋯	⋯
65	8.99	48	74.2	33	59.2	72.4	28	14.5
67	9.36	51	73.6	30.1	61	71.6	25.2	14.7
70	10.8	55.5	72.4	26.2	67.1	70.6	21.4	15.7
72	12.5	58.8	69.6	23.4	69	68.5	19.1	16.8
73	13.6	⋯	67.7	⋯	⋯	66.7	⋯	18.1
74	⋯	63.6	⋯	⋯	⋯	⋯	⋯	⋯
75	16.6	65.2	63.8	19	74.4	64.4	15.8	19.8

	λ=546 mμ		λ=640 mμ
φ₀	a	b	a	b
30	0.714	1.144	0.663	2.320
35	0.722	1.117	0.654	2.323
40	0.723	1.138	0.649	2.312
45	0.737	1.161	0.664	2.265
50	0.705	1.162	0.667	2.222
55	0.695	1.217	0.640	2.218
60	0.699	1.178	0.621	2.182
65	0.695	1.258	0.630	2.340
70	0.709	1.311	0.683	2.582
75	0.669	1.471	0.676	2.560

	λ=546 mμ				λ=640 mμ
φ₀	R_\|\|%	R_⊥%	T_\|\|%	T_⊥%	R_\|\|%	R_⊥%	T_\|\|%	T_⊥%
5	15.5	15.4	52.1	52.1	14.9	15	53	53.3
10	15.1	15.8	52.3	51.7	14.6	15.3	53.4	53
15	14.5	16.2	52.7	50.7	14	15.6	54.3	52.5
20	13.8	16.9	53.6	49.9	13.4	16.4	55	51.9
25	13.1	17.8	54.7	48.5	12.8	17.4	55.9	51.1
30	12.2	19.2	56	47.3	11.6	18.4	57.1	49.7
35	10.7	20.5	57.7	45.3	10.4	20.1	58.1	47.8
40	9.16	22.5	59.4	43.6	8.87	22.3	59.8	45.8
45	7.40	25.3	60.4	41.6	6.94	24.9	61.8	43.3
50	5.54	28	62.9	38.6	5.11	27.8	63.6	40.3
52	4.80	30	⋯	37.3	4.34	29.5	64.7	39
55	3.98	31.6	64.6	35.4	⋯	31.6	66.1	36.4
57	2.74	33.2	65.4	33.9	⋯	33.1	67	34.1
60	1.71	35.5	66.3	31.6	⋯	36.1	68.5	31.8
62	⋯	⋯	66.8	29.1	⋯	39.2	69.1	30
65	⋯	41.5	67.2	26.4	⋯	42.8	69.1	26.7
67	⋯	43.4	66.5	23.9	⋯	46	68.9	24.6
70	⋯	47.9	65.8	20.5	⋯	50.2	67.2	20.9
72	⋯	50.9	64.3	18.1	⋯	54	65.8	18.5
73	⋯	52.7	63.2	16.8	⋯	55.4	64.5	17.2
74	2.09	⋯	⋯	⋯	⋯	⋯	⋯	⋯
75	2.89	56.2	61.5	14.3	⋯	59.5	62	14.6

	λ=546 mμ		λ=640 mμ
φ₀	a	b	a	b
30	1.735	0.582	1.551	0.521
35	1.772	0.548	1.567	0.536
40	1.744	0.561	1.545	0.568
45	1.672	0.617	1.532	0.593
50	1.697	0.571	1.523	0.587
55	1.664	0.562	1.550	0.586
60	1.645	0.485	1.596	0.556
65	1.655	0.503	1.567	0.644
70	1.730	0.390	1.568	0.668
75	1.743	0.288	1.555	0.707

φ₀	R_⊥	R_\|\|	n	k
0	0.431	0.431	⋯	⋯
10	0.432	0.430	⋯	⋯
20	0.450	0.412	⋯	⋯
30	0.481	0.380	⋯	⋯
35	0.506	0.362	⋯	⋯
40	0.523	0.336₅	⋯	⋯
45	0.550	0.304	⋯	⋯
50	0.583₅	0.273	⋯	⋯
55	0.615	0.241	⋯	⋯
60	0.660	0.205	2.52	2.31
65	0.704	0.170	2.48₅	2.31
70	0.751	0.144	2.43	2.28
75	0.806₅	0.139	2.50₅	2.30
78	⋯	0.164	⋯	⋯

φ₀	R_⊥	R_\|\|	n	k
10	0.433	0.429	⋯	⋯
20	0.452	0.420	⋯	⋯
30	0.482	0.381₅	⋯	⋯
35	0.498₅	0.362	⋯	⋯
40	0.518	0.334	⋯	⋯
45	0.547	0.303₅	⋯	⋯
50	0.581	0.271	⋯	⋯
55	0.620₅	0.233₅	⋯	⋯
60	0.658	0.192	3.28	2.19
62	0.681₅	0.175₅	3.29	2.20
67	0.722	0.135	3.16₅	2.24
72	0.775	0.104₅	3.11	2.27
74	0.800	0.099₅	3.16	2.33
75	0.811	0.098₅	3.15	2.33

Abstract

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Figures (5)

Tables (6)

Equations (58)

Journal of the Optical Society of America