Index of refraction measurement on sapphire at low temperatures and visible wavelengths

A. C. DeFranzo; B. G. Pazol

doi:10.1364/AO.32.002224

Applied Optics
Vol. 32,
Issue 13,
pp. 2224-2234
(1993)
•https://doi.org/10.1364/AO.32.002224

Index of refraction measurement on sapphire at low temperatures and visible wavelengths

A. C. DeFranzo and B. G. Pazol

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A. C. DeFranzo and B. G. Pazol, "Index of refraction measurement on sapphire at low temperatures and visible wavelengths," Appl. Opt. 32, 2224-2234 (1993)

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Abstract

The ordinary and extraordinary refractive index of two samples of sapphire, which differed in the way each was grown, was measured. The measurements were made over a wavelength range of 477–701 nm and a temperature range of 20–295 K. A three-term Sellmeier dispersion equation was fit to the data to permit refractive-index interpolation within several parts in 10⁴. The data of index versus temperature were fit to a model and the results of dn/dT versus temperature are given along with certain physical constants that were extracted from the model.

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Temperature (K)	477 nm		502 nm		552 nm		603 nm		654 nm		701 nm

	O	E	O	E	O	E	O	E	O	E	O	E
20	1.7765	1.7683	1.7747	1.7663	1.7710	1.7625	1.7683	1.7596	1.7659	1.7574	1.7638	1.7556
50	1.7768	1.7686	1.7751	1.7664	1.7715	1.7629	1.7684	1.7600	1.7662	1.7578	1.7642	1.7559
77	1.7768	1.7687	1.7749	1.7665	1.7714	1.7626	1.7685	1.7597	1.7660	1.7576	1.7641	1.7559
120	1.7769	1.7687	1.7750	1.7665	1.7713	1.7627	1.7684	1.7599	1.7660	1.7577	1.7643	1.7560
170	1.7768	1.7692	1.7753	1.7670	1.7716	1.7631	1.7687	1.7604	1.7663	1.7581	1.7645	1.7563
200	1.7775	1.7693	1.7756	1.7671	1.7719	1.7634	1.7690	1.7607	1.7668	1.7584	1.7648	1.7568
220	1.7776	1.7698	1.7759	1.7677	1.7723	1.7639	1.7694	1.7612	1.7669	1.7589	1.7650	1.7571
240	1.7779	1.7699	1.7761	1.7676	1.7726	1.7641	1.7697	1.7614	1.7674	1.7591	1.7653	1.7574
260	1.7778	1.7698	1.7759	1.7676	1.7725	1.7639	1.7693	1.7614	1.7672	1.7590	1.7651	1.7571
280	1.7783	1.7700	1.7764	1.7679	1.7727	1.7641	1.7697	1.7613	1.7674	1.7590	1.7653	1.7572
295	1.7787	1.7702	1.7767	1.7682	1.7723	1.7643	1.7698	1.7615	1.7675	1.7590	1.7655	1.7573

Temperature (K)	477 nm		502 nm		552 nm		603 nm		654 nm		701 nm

	O	E	O	E	O	E	O	E	O	E	O	E
20	1.7752	1.7667	1.7732	1.7645	1.7695	1.7608	1.7664	1.7579	1.7642	1.7558	1.7620	1.7538
50	—	—	—	—	—	—	—	—	—	—	—	—
77	1.7746	1.7668	1.7731	1.7645	1.7698	1.7609	1.7667	1.7582	1.7643	1.7559	1.7621	1.7539
120	1.7751	1.7668	1.7737	1.7646	1.7695	1.7612	1.7667	1.7583	1.7645	1.7561	1.7620	1.7540
170	1.7754	1.7672	1.7734	1.7651	1.7698	1.7615	1.7670	1.7587	1.7647	1.7565	1.7625	1.7546
200	1.7757	1.7677	1.7739	1.7653	1.7701	1.7619	1.7672	1.7589	1.7649	1.7568	1.7630	1.7549
220	1.7760	1.7680	1.7740	1.7657	1.7704	1.7622	1.7676	1.7594	1.7653	1.7572	1.7632	1.7552
240	1.7761	1.7681	1.7742	1.7657	1.7704	1.7624	1.7677	1.7593	1.7653	1.7572	1.7634	1.7553
260	1.7765	1.7683	1.7742	1.7661	1.7707	1.7625	1.7678	1.7597	1.7654	1.7574	1.7635	1.7555
280	1.7766	1.7685	1.7743	1.7667	1.7708	1.7627	1.7680	1.7599	1.7656	1.7576	1.7635	1.7557
295	1.7767	1.7685	1.7749	1.7665	1.7712	1.7629	1.7683	1.7602	1.7660	1.7579	1.7641	1.7560

Temperature (K)	477 nm		502 nm		552 nm		603 nm		654 nm		701 nm

	ΔO	ΔE	ΔO	ΔE	ΔO	ΔE	ΔO	ΔE	ΔO	ΔE	ΔO	ΔE
20	0.0013	0.0016	0.0015	0.0018	0.0015	0.0017	0.0019	0.0017	0.0017	0.0016	0.0018	0.0018
50	—	—	—	—	—	—	—	—	—	—	—	—
77	0.0022	0.0019	0.0019	0.0020	0.0016	0.0017	0.0018	0.0015	0.0017	0.0017	0.0020	0.0020
120	0.0018	0.0019	0.0017	0.0019	0.0018	0.0015	0.0017	0.0016	0.0015	0.0016	0.0023	0.0020
170	0.0014	0.0020	0.0019	0.0019	0.0018	0.0016	0.0017	0.0017	0.0016	0.0016	0.0020	0.0017
200	0.0018	0.0016	0.0017	0.0018	0.0018	0.0015	0.0018	0.0018	0.0019	0.0016	0.0019	0.0019
220	0.0016	0.0018	0.0019	0.0020	0.0019	0.0017	0.0018	0.0018	0.0016	0.0017	0.0018	0.0019
240	0.0018	0.0018	0.0019	0.0019	0.0022	0.0017	0.0020	0.0021	0.0021	0.0019	0.0019	0.0021
260	0.0013	0.0015	0.0017	0.0015	0.0018	0.0014	0.0015	0.0017	0.0018	0.0016	0.0016	0.0016
280	0.0017	0.0015	0.0021	0.0012	0.0019	0.0014	0.0017	0.0014	0.0018	0.0014	0.0018	0.0015
295	0.0020	0.0017	0.0018	0.0017	0.0011	0.0014	0.0015	0.0013	0.0015	0.0014	0.0014	0.0013

Temperature (K)	χ² × 10⁻⁷	A₀	(λ₀)² μm²	A₁	(λ₁)² μm²	A₂	(λ₂)² μm²
20 O	5.67	1.081	0.0039	1.025	0.0089	10.63	232.8
E	6.29	1.054	0.0051	0.996	0.0119	0.459	70.79
50 O	11.8	1.080	0.0042	1.025	0.0089	8.55	200.4
E	11.5	1.054	0.0047	0.995	0.0125	0.486	172.3
77 O	1.57	1.080	0.0044	1.025	0.0087	10.72	239.7
E	1.43	1.053	0.0038	0.995	0.0136	0.639	286.9
120 O	5.14	1.076	0.0042	1.020	0.0103	6.88	229.7
E	1.49	1.051	0.0041	0.999	0.0129	0.928	215.7
170 O	15.6	1.080	0.0045	1.025	0.0087	6.36	159.7
E	2.29	1.052	0.0041	1.000	0.0129	0.965	161.4
200 O	6.26	1.078	0.0049	1.023	0.0090	7.21	207.3
E	0.883	1.053	0.0039	1.001	0.0127	1.04	162.2
220 O	5.62	1.083	0.0034	1.027	0.0095	6.44	139.2
E	5.14	1.056	0.0042	1.004	0.0119	1.51	111.7
240 O	5.43	1.085	0.0030	1.029	0.0093	6.87	140.4
E	1.24	1.058	0.0040	1.005	0.0116	1.47	103.5
260 O	9.56	1.081	0.0040	1.026	0.0093	6.66	160.7
E	9.13	1.059	0.0033	1.007	0.0119	1.91	89.8
280 O	3.81	1.081	0.0027	1.026	0.0109	6.19	153.0
E	2.52	1.056	0.0024	1.004	0.0137	1.69	124.3
295 O	4.04	1.077	0.0033	1.025	0.0114	5.04	151.2
E	5.76	1.041	0.0004	1.030	0.0141	3.55	123.8

Temperature (K)	χ² × 10⁻⁷	A₀	(λ₀)² μm²	A₁	(λ₁)² μm²	A₂	(λ₂)²μm²
20 O	8.59	1.073	0.0063	1.019	0.0080	5.82	156.5
E	9.42	1.051	0.0041	0.993	0.0130	0.421	79.5
77 O	11.1	1.085	0.0029	1.032	0.0073	7.43	104.7
E	4.90	1.052	0.0062	1.003	0.0090	2.75	123.0
120 O	17.2	1.078	0.0050	1.023	0.0079	5.27	110.3
E	3.56	1.056	0.0036	1.007	0.0105	1.81	55.5
170 O	6.13	1.078	0.0027	1.023	0.0102	6.36	140.8
E	2.29	1.055	0.0056	1.003	0.0095	0.677	29.99
200 O	6.79	1.076	0.0032	1.017	0.0111	5.20	162.5
E	3.70	1.060	0.0041	0.9954	0.0117	0.608	36.52
220 O	1.50	1.077	0.0036	1.021	0.0101	4.73	128.5
E	3.52	1.060	0.0048	1.000	0.0105	2.33	105.7
240 O	5.16	1.075	0.0022	1.020	0.0120	4.94	153.6
E	7.54	1.055	0.0027	1.002	0.0128	1.38	75.8
260 O	1.68	1.074	0.0037	1.018	0.0111	6.25	223.0
E	1.07	1.056	0.0037	1.003	0.0119	1.69	89.2
280 O	5.29	1.076	0.0020	1.021	0.0121	7.41	212.8
E	11.2	1.056	0.0037	1.003	0.0122	1.32	70.5
295 O	8.56	1.076	0.0026	1.026	0.0108	7.63	196.3
E	1.69	1.039	0.0024	1.028	0.0117	3.20	110.7

λ(nm)	χ² × 10⁷	B (eV)	C × 10⁵ (eV/K)	D × 10⁷ (eV/K)³	A (eV)²
477 O	1.80	9.4	−1.38	−3.84	174.0
E	1.92	13.7	−3.68	−3.61	385.4
501 O	1.39	9.3	−1.60	−3.26	174.1
E	2.06	13.6	−4.89	−3.04	380.1
552 O	1.37	9.3	−1.33	−1.01	175.6
E	2.80	13.6	−5.62	−2.78	379.3
603 O	1.35	9.4	−1.10	−3.51	178.0
E	3.57	13.6	−5.83	−2.43	379.4
654 O	1.14	9.4	−1.08	−3.36	178.2
E	4.00	13.6	−6.08	−9.81	376.6
701 O	0.86	9.5	−1.60	−2.72	175.6
E	5.04	13.6	−4.53	−2.33	371.4

λ (nm)	χ² × 10⁷	B (eV)	C × 10⁵ (eV/K)	D × 10⁷ (eV/K)³	A (eV)²
477 O	2.28	9.4	−1.18	−3.99	175.8
E	2.21	13.2	−4.49	−4.45	356.9
501 O	0.78	9.3	−1.37	−3.66	173.9
E	1.09	13.6	−4.73	−4.49	379.5
552 O	0.98	9.3	−1.40	−3.63	175.4
E	0.85	13.7	−5.62	−5.61	382.4
603 O	1.37	9.4	−1.24	−3.22	177.8
E	0.62	13.8	−6.14	−3.38	386.5
654 O	1.18	9.3	−1.19	−4.15	175.9
E	0.77	13.7	−5.79	−3.70	386.9
701 O	2.00	9.3	−1.17	−4.81	174.5
E	1.99	13.6	−5.44	−2.82	374.9

Temperature (K)	dn/dT × 10⁵

	475 nm		502 nm		552 nm		603 nm		654 nm		701 nm

	O	E	O	E	O	E	O	E	O	E	O	E
20	0.20	0.34	0.20	0.45	0.19	0.51	0.15	0.55	0.15	0.44	0.21	0.41
50	0.23	0.36	0.23	0.47	0.22	0.52	0.18	0.56	0.18	0.46	0.24	0.43
77	0.29	0.39	0.29	0.50	0.27	0.55	0.23	0.58	0.22	0.49	0.28	0.45
120	0.47	0.48	0.41	0.56	0.39	0.62	0.35	0.63	0.34	0.57	0.39	0.50
170	0.66	0.62	0.64	0.69	0.60	0.72	0.56	0.72	0.53	0.69	0.56	0.59
200	0.84	0.73	0.81	0.78	0.76	0.81	0.72	0.80	0.68	0.79	0.70	0.67
220	0.98	0.81	0.95	0.85	0.88	0.87	0.83	0.85	0.80	0.86	0.80	0.72
240	1.1	0.91	1.1	0.92	1.0	0.94	0.97	0.91	0.92	0.94	0.91	0.78
260	1.3	1.0	1.3	1.0	1.2	1.0	1.1	0.96	1.1	1.0	1.0	0.84
280	1.5	1.1	1.4	1.1	1.3	1.1	1.3	1.0	1.2	1.1	1.2	0.91
295	1.6	1.2	1.6	1.2	1.4	1.2	1.4	1.1	1.3	1.2	1.3	0.97

Physical Constant	HEM	EFG
$\bar{C} (eV / K) O$	−1.4 × 10⁻⁵	−1.3 × 10⁻⁵
E	−5.1 × 10⁻⁵	−5.5 × 10⁻⁵
$\bar{D} {(eV / K)}_{3} O$	−3.0 × 10⁻¹⁰	−3.4 × 10⁻¹⁰
E	−3.9 × 10⁻¹⁰	−3.4 × 10⁻¹⁰
(dE_g/dT)_T=295(eV/K)O	−9.2 × 10⁻⁵	−1.0 × 10⁻⁴
E	−1.5 × 10⁻⁴	−1.4 × 10⁻⁴
(dE_g/dT)_T=0 (eV/K) O	−1.4 × 10⁻⁵	−1.3 × 10⁻⁵
E	−5.1 × 10⁻⁵	−5.4 × 10⁻⁵

Physical Constant	HEM	EFG
$\bar{A} {(eV / K)}^{2} O$	175.9	175.3
E	381.7	377.5
E_Pe (eV) O	13.3	13.2
E	19.5	19.4

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