Temperature-dependent optical constants of highly transparent solids determined by the combined double optical pathlength transmission-ellipsometry method

X. C. Li; C. C. Wang; J. M. Zhao; L. H. Liu

doi:10.1364/AO.57.001260

Applied Optics
Vol. 57,
Issue 5,
pp. 1260-1266
(2018)
•https://doi.org/10.1364/AO.57.001260

Temperature-dependent optical constants of highly transparent solids determined by the combined double optical pathlength transmission-ellipsometry method

X. C. Li, C. C. Wang, J. M. Zhao, and L. H. Liu

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X. C. Li, C. C. Wang, J. M. Zhao, and L. H. Liu, "Temperature-dependent optical constants of highly transparent solids determined by the combined double optical pathlength transmission-ellipsometry method," Appl. Opt. 57, 1260-1266 (2018)

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- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: November 24, 2017
- Revised Manuscript: January 7, 2018
- Manuscript Accepted: January 13, 2018
- Published: February 9, 2018

Abstract

The optical constants of five highly transparent substrates (polycrystalline ${BaF}_{2}$ , ${CaF}_{2}$ , ${MgF}_{2}$ , ZnSe, and ZnS) were experimentally determined based on a combined technique using both the double optical pathlength transmission method and the ellipsometry method within temperature range 20°C–350°C in the ultraviolet-infrared region (0.2–20 μm). The results show that the refractive index spectra of polycrystalline ${BaF}_{2}$ , ${CaF}_{2}$ , and ${MgF}_{2}$ are similar, but differ from that of polycrystalline ZnSe and ZnS. The thermo-optic coefficient of these highly transparent substrates increases with increasing temperature. The absorption indices show a significant temperature-dependent behavior, which increases with increasing temperature from 20°C to 350°C over the transparent region. For the sake of application, the fitted formulas of the refractive index of the five highly transparent substrates as a function of wavelength and temperature are presented.

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Sample	Thickness (mm)	Standard Deviation (mm)
${BaF}_{2}$	3.997	0.001
${CaF}_{2}$	4.069	0.002
${MgF}_{2}$	2.054	0.001
ZnSe	2.115	0.003
ZnS	1.486	0.002

	$a_{0}$	$a_{1}$	$a_{2}$	$a_{3}$	$a_{4}$	$a_{5}$	$λ_{1}^{2}$	$λ_{2}^{2}$	$λ_{3}^{2}$
${BaF}_{2}$	−0.3381	$- 2.263 \times 10^{- 3}$	2.479	1.302	$3.692 \times 10^{- 8}$	$2.567 \times 10^{- 5}$	0.7279	$5.124 \times 10^{- 3}$	889.7
${CaF}_{2}$	1.706	0.3380	−0.2171	0.1650	$- 2.237 \times 10^{- 8}$	$5.662 \times 10^{- 5}$	$1.650 \times 10^{- 2}$	−79.79	199.1
${MgF}_{2}$	2.314	0.7152	−0.4309	$3.470 \times 10^{- 3}$	$- 3.175 \times 10^{- 8}$	$3.385 \times 10^{- 5}$	230.3	$- 1.999 \times 10^{- 2}$	0.3482
ZnSe	6.558	−1.053	$- 5.687 \times 10^{- 2}$	1.241	$1.440 \times 10^{- 7}$	$- 7.939 \times 10^{- 5}$	−3.920	0.3991	2159
ZnS	5.459	$- 7.082 \times 10^{- 2}$	−1.340	$- 7.056 \times 10^{- 2}$	$1.576 \times 10^{- 7}$	$- 7.071 \times 10^{- 5}$	0.5402	−76.52	0.538

Sample	Thickness (mm)	Standard Deviation (mm)
${BaF}_{2}$	3.997	0.001
${CaF}_{2}$	4.069	0.002
${MgF}_{2}$	2.054	0.001
ZnSe	2.115	0.003
ZnS	1.486	0.002

	$a_{0}$	$a_{1}$	$a_{2}$	$a_{3}$	$a_{4}$	$a_{5}$	$λ_{1}^{2}$	$λ_{2}^{2}$	$λ_{3}^{2}$
${BaF}_{2}$	−0.3381	$- 2.263 \times 10^{- 3}$	2.479	1.302	$3.692 \times 10^{- 8}$	$2.567 \times 10^{- 5}$	0.7279	$5.124 \times 10^{- 3}$	889.7
${CaF}_{2}$	1.706	0.3380	−0.2171	0.1650	$- 2.237 \times 10^{- 8}$	$5.662 \times 10^{- 5}$	$1.650 \times 10^{- 2}$	−79.79	199.1
${MgF}_{2}$	2.314	0.7152	−0.4309	$3.470 \times 10^{- 3}$	$- 3.175 \times 10^{- 8}$	$3.385 \times 10^{- 5}$	230.3	$- 1.999 \times 10^{- 2}$	0.3482
ZnSe	6.558	−1.053	$- 5.687 \times 10^{- 2}$	1.241	$1.440 \times 10^{- 7}$	$- 7.939 \times 10^{- 5}$	−3.920	0.3991	2159
ZnS	5.459	$- 7.082 \times 10^{- 2}$	−1.340	$- 7.056 \times 10^{- 2}$	$1.576 \times 10^{- 7}$	$- 7.071 \times 10^{- 5}$	0.5402	−76.52	0.538

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Applied Optics