Index of refraction of germanium

John H. Burnett; Eric C. Benck; Simon G. Kaplan; Erik Stover; Adam Phenis

doi:10.1364/AO.382408

Applied Optics
Vol. 59,
Issue 13,
pp. 3985-3991
(2020)
•https://doi.org/10.1364/AO.382408

Index of refraction of germanium

John H. Burnett, Eric C. Benck, Simon G. Kaplan, Erik Stover, and Adam Phenis

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John H. Burnett, Eric C. Benck, Simon G. Kaplan, Erik Stover, and Adam Phenis, "Index of refraction of germanium," Appl. Opt. 59, 3985-3991 (2020)

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Abstract

Measurements of the index of refraction of a sample of high-quality, single-crystal germanium using the minimum deviation refractometry method are presented for temperatures near 22°C and for wavelengths in the range 2 to 14 µm. The standard uncertainty for the measurements ranges from ${1.5} \times {{10}^{ - 5}}$ to ${4.2} \times {{10}^{ - 5}}$, generally increasing with wavelength. A Sellmeier formula fitting the data for this range is provided. Details of the custom system and procedures are presented, along with a detailed analysis of the uncertainty. These results are compared with previous measurements.

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$λ^{v a c}$ (µm)	$λ^{a i r}$ (µm)	${I n d e x}^{v a c}$	${I n d e x}^{a i r}$	$u_{c} (n)$ ( $10^{- 5}$ )
2.00000	1.99947	4.109725	4.108630	1.6
2.12500	2.12443	4.095492	4.094401	1.5
2.25000	2.24940	4.084070	4.082982	1.5
2.37500	2.37437	4.074715	4.073629	1.5
2.50000	2.49933	4.066925	4.065842	1.5
2.75000	2.74927	4.054785	4.053705	1.5
3.00000	2.99920	4.045796	4.044719	1.6
3.39224	3.39133	4.035736	4.034661	1.6
4.00000	3.99894	4.025816	4.024744	1.7
4.50000	4.49880	4.020584	4.019514	1.8
5.00000	4.99867	4.016867	4.015798	1.9
5.50000	5.49854	4.014131	4.013062	2.0
6.00000	5.99840	4.012071	4.011003	2.2
7.00000	6.99814	4.009192	4.008126	2.4
8.00000	7.99787	4.007321	4.006255	2.6
9.00000	8.99761	4.006019	4.004953	2.9
10.00000	9.99734	4.005079	4.004013	3.1
11.00000	10.99707	4.004360	4.003294	3.4
12.00000	11.99681	4.003824	4.002758	3.7
13.00000	12.99654	4.003358	4.002293	4.0
14.00000	13.99627	4.002979	4.001914	4.2

Sources $x$	Magnitude of Uncertainty $u (x)$	Index Uncertainty $u_{x} (n) (10^{- 5})$
Peak position	(0.7 to 5) arcseconds (1/10th of diffracted peak width FWHM)	0.6–4
Prism apex angle	0.15 arcseconds [including $λ / 120$ (at 633 nm) RMS surface flatness error]	0.9
Index inhomogeneity	$0.91 \times 10^{- 5}$ RMS for 10 mm thickness at $λ = 3.39 µ m$	0.91
Encoder angle	0.15 arcseconds	0.17
Prism temperature	0.005°C	0.26–0.20
Wavelength calibration	0.05 nm	0.6–0.002
Alignment	0.05 arcseconds	0.08
$N_{2}$ gas and air dispersion formulas	$2 \times 10^{- 7}$	0.08
$N_{2}$ gas temperature	0.02°C	0.01
$N_{2}$ gas pressure	0.02 kPa	0.02

Sellmeier Constants
$K_{1}$	0.362471
$K_{2}$	14.640402
$K_{3}$	0.008175
$L_{1}$	1.243341 µm
$L_{2}$	0.4120985 µm
$L_{3}$	26.5311 µm

$λ^{v a c}$ (µm)	$λ^{a i r}$ (µm)	${I n d e x}^{v a c}$	${I n d e x}^{a i r}$	$u_{c} (n)$ ( $10^{- 5}$ )
2.00000	1.99947	4.109725	4.108630	1.6
2.12500	2.12443	4.095492	4.094401	1.5
2.25000	2.24940	4.084070	4.082982	1.5
2.37500	2.37437	4.074715	4.073629	1.5
2.50000	2.49933	4.066925	4.065842	1.5
2.75000	2.74927	4.054785	4.053705	1.5
3.00000	2.99920	4.045796	4.044719	1.6
3.39224	3.39133	4.035736	4.034661	1.6
4.00000	3.99894	4.025816	4.024744	1.7
4.50000	4.49880	4.020584	4.019514	1.8
5.00000	4.99867	4.016867	4.015798	1.9
5.50000	5.49854	4.014131	4.013062	2.0
6.00000	5.99840	4.012071	4.011003	2.2
7.00000	6.99814	4.009192	4.008126	2.4
8.00000	7.99787	4.007321	4.006255	2.6
9.00000	8.99761	4.006019	4.004953	2.9
10.00000	9.99734	4.005079	4.004013	3.1
11.00000	10.99707	4.004360	4.003294	3.4
12.00000	11.99681	4.003824	4.002758	3.7
13.00000	12.99654	4.003358	4.002293	4.0
14.00000	13.99627	4.002979	4.001914	4.2

Sources $x$	Magnitude of Uncertainty $u (x)$	Index Uncertainty $u_{x} (n) (10^{- 5})$
Peak position	(0.7 to 5) arcseconds (1/10th of diffracted peak width FWHM)	0.6–4
Prism apex angle	0.15 arcseconds [including $λ / 120$ (at 633 nm) RMS surface flatness error]	0.9
Index inhomogeneity	$0.91 \times 10^{- 5}$ RMS for 10 mm thickness at $λ = 3.39 µ m$	0.91
Encoder angle	0.15 arcseconds	0.17
Prism temperature	0.005°C	0.26–0.20
Wavelength calibration	0.05 nm	0.6–0.002
Alignment	0.05 arcseconds	0.08
$N_{2}$ gas and air dispersion formulas	$2 \times 10^{- 7}$	0.08
$N_{2}$ gas temperature	0.02°C	0.01
$N_{2}$ gas pressure	0.02 kPa	0.02

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Applied Optics