Anisotropy of thermo-optic properties of beryllium hexaaluminate crystal doped with chromium ions

K. V. Yumashev; V. I. Goman; L. K. Pavlovski; E. V. Vilejshikova; A. V. Yukhnouskaya; A. M. Malyarevich

doi:10.1364/JOSAB.448569

Journal of the Optical Society of America B
Vol. 39,
Issue 4,
pp. 962-967
(2022)
•https://doi.org/10.1364/JOSAB.448569

Anisotropy of thermo-optic properties of beryllium hexaaluminate crystal doped with chromium ions

K. V. Yumashev, V. I. Goman, L. K. Pavlovski, E. V. Vilejshikova, A. V. Yukhnouskaya, and A. M. Malyarevich

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K. V. Yumashev, V. I. Goman, L. K. Pavlovski, E. V. Vilejshikova, A. V. Yukhnouskaya, and A. M. Malyarevich, "Anisotropy of thermo-optic properties of beryllium hexaaluminate crystal doped with chromium ions," J. Opt. Soc. Am. B 39, 962-967 (2022)

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Abstract

We determined the thermo-optic coefficients of ${\rm{C}}{{\rm{r}}^{3 +}}$-doped beryllium hexaaluminate crystal (${\rm{C}}{{\rm{r}}^{3 +}}:{\rm{BeA}}{{\rm{l}}_6}{{\rm{O}}_{10}}$) for light polarizations ${\textbf{E}}\;||\;{N_p}$, ${{\rm{N}}_m}$, and ${{\rm{N}}_g}$, and present the thermo-optic dispersion formulas for the principal thermo-optic coefficients of ${\rm{C}}{{\rm{r}}^{3 +}}:{\rm{BeA}}{{\rm{l}}_6}{{\rm{O}}_{10}}$. We also measured the linear thermal expansion coefficients for this crystal in the directions of optical indicatrix axes ${{\rm{N}}_p}$, ${{\rm{N}}_m}$, and ${{\rm{N}}_g}$. Finally, we modeled the thermo-optic dispersion data in accordance with theory, taking into account contributions both from the change of the electronic bandgap with temperature and from the volumetric thermal expansion coefficient.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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		TCOP			$d n / d T$
λ, nm	$k \| \|$	$E / / N_{p}$	$E / / N_{m}$	$E / / N_{g}$	$E / / N_{p}$	$E / / N_{m}$	$E / / N_{g}$	$d n_{p} / d T$	$d n_{m} / d T$	$d n_{g} / d T$
405	$N_{p}$	−	$17.3 \pm 0.4$	$18.6 \pm 0.4$	−	$11.9 \pm 0.6$	$13.2 \pm 0.6$
	$N_{m}$	$21.0 \pm 0.4$	−	$19.0 \pm 0.4$	$16.1 \pm 0.6$	−	$14.0 \pm 0.6$	$15.6 \pm 0.7$	$11.9 \pm 0.6$	$13.6 \pm 0.7$
	$N_{g}$	$20.4 \pm 0.4$	$17.1 \pm 0.4$	−	$15.2 \pm 0.6$	$11.9 \pm 0.6$	−
450	$N_{p}$	−	$14.8 \pm 0.3$	$15.6 \pm 0.3$	−	$9.5 \pm 0.5$	$10.2 \pm 0.6$
	$N_{m}$	$18.4 \pm 0.4$	−	$16.3 \pm 0.4$	$13.5 \pm 0.6$	−	$11.4 \pm 0.6$	$13.0 \pm 0.7$	$9.5 \pm 0.5$	$10.8 \pm 0.7$
	$N_{g}$	$17.8 \pm 0.3$	$14.7 \pm 0.3$	−	$12.6 \pm 0.6$	$9.5 \pm 0.5$	−
532	$N_{p}$	−	$13.2 \pm 0.3$	$13.5 \pm 0.3$	−	$7.9 \pm 0.5$	$8.2 \pm 0.5$
	$N_{m}$	$15.0 \pm 0.3$	−	$14.5 \pm 0.3$	$10.2 \pm 0.5$	−	$9.6 \pm 0.5$	$9.7 \pm 0.6$	$7.9 \pm 0.5$	$8.9 \pm 0.6$
	$N_{g}$	$14.3 \pm 0.3$	$13.0 \pm 0.3$	−	$9.2 \pm 0.5$	$7.9 \pm 0.5$	−
633	$N_{p}$	−	$11.4 \pm 0.3$	$11.8 \pm 0.3$	−	$6.2 \pm 0.5$	$6.5 \pm 0.5$
	$N_{m}$	$13.2 \pm 0.3$	−	$12.1 \pm 0.3$	$8.4 \pm 0.5$	−	$7.2 \pm 0.5$	$7.9 \pm 0.6$	$6.3 \pm 0.5$	$6.9 \pm 0.5$
	$N_{g}$	$12.4 \pm 0.3$	$11.4 \pm 0.3$	−	$7.4 \pm 0.5$	$6.3 \pm 0.5$	−
650	$N_{p}$	−	$11.3 \pm 0.3$	$11.4 \pm 0.3$	−	$6.1 \pm 0.5$	$6.1 \pm 0.5$
	$N_{m}$	$12.5 \pm 0.3$	−	$11.8 \pm 0.3$	$7.7 \pm 0.5$	−	$7.0 \pm 0.5$	$7.7 \pm 0.5$	$6.0 \pm 0.5$	$6.6 \pm 0.6$
	$N_{g}$	$12.8 \pm 0.3$	$11.0 \pm 0.3$	−	$7.7 \pm 0.5$	$5.9 \pm 0.5$	−
800	$N_{p}$	−	$10.2 \pm 0.3$	$10.2 \pm 0.3$	−	$5.0 \pm 0.5$	$5.0 \pm 0.5$
	$N_{m}$	$11.7 \pm 0.3$	−	$10.8 \pm 0.3$	$6.9 \pm 0.5$	−	$6.0 \pm 0.5$	$6.6 \pm 0.6$	$5.0 \pm 0.5$	$5.5 \pm 0.6$
	$N_{g}$	$11.3 \pm 0.3$	$10.1 \pm 0.3$	−	$6.2 \pm 0.5$	$5.0 \pm 0.5$	−
1064	$N_{p}$	−	$9.7 \pm 0.3$	$9.8 \pm 0.3$	−	$4.5 \pm 0.5$	$4.6 \pm 0.5$
	$N_{m}$	$10.9 \pm 0.3$	−	$10.4 \pm 0.3$	$6.2 \pm 0.5$	−	$5.6 \pm 0.5$	$5.8 \pm 0.6$	$4.6 \pm 0.5$	$5.1 \pm 0.6$
	$N_{g}$	$10.3 \pm 0.3$	$9.6 \pm 0.3$	−	$5.3 \pm 0.5$	$4.6 \pm 0.5$	−

Thermo-optic Coefficient	$A$	$B$ , $µ m^{2}$	$C$ , $µ m^{4}$
$d n_{p} / d T$	4.848	0.8611	0.1518
$d n_{m} / d T$	3.705	0.7813	0.08995
$d n_{g} / d T$	4.141	0.8057	0.1207

	TCOP
	$k \| \| N_{p}$	$k \| \| N_{m}$	$k \| \| N_{g}$	$d n / d T$
$E \| \| N_{p}$	−	$11.2 \pm 0.4$	$11.5 \pm 0.4$	$6.4 \pm 0.6$
$E \| \| N_{m}$	$10.2 \pm 0.4$	−	$10.1 \pm 0.4$	$5.0 \pm 0.5$
$E \| \| N_{g}$	$10.8 \pm 0.4$	$10.4 \pm 0.4$	−	$5.6 \pm 0.6$

		TCOP			$d n / d T$
λ, nm	$k \| \|$	$E / / N_{p}$	$E / / N_{m}$	$E / / N_{g}$	$E / / N_{p}$	$E / / N_{m}$	$E / / N_{g}$	$d n_{p} / d T$	$d n_{m} / d T$	$d n_{g} / d T$
405	$N_{p}$	−	$17.3 \pm 0.4$	$18.6 \pm 0.4$	−	$11.9 \pm 0.6$	$13.2 \pm 0.6$
	$N_{m}$	$21.0 \pm 0.4$	−	$19.0 \pm 0.4$	$16.1 \pm 0.6$	−	$14.0 \pm 0.6$	$15.6 \pm 0.7$	$11.9 \pm 0.6$	$13.6 \pm 0.7$
	$N_{g}$	$20.4 \pm 0.4$	$17.1 \pm 0.4$	−	$15.2 \pm 0.6$	$11.9 \pm 0.6$	−
450	$N_{p}$	−	$14.8 \pm 0.3$	$15.6 \pm 0.3$	−	$9.5 \pm 0.5$	$10.2 \pm 0.6$
	$N_{m}$	$18.4 \pm 0.4$	−	$16.3 \pm 0.4$	$13.5 \pm 0.6$	−	$11.4 \pm 0.6$	$13.0 \pm 0.7$	$9.5 \pm 0.5$	$10.8 \pm 0.7$
	$N_{g}$	$17.8 \pm 0.3$	$14.7 \pm 0.3$	−	$12.6 \pm 0.6$	$9.5 \pm 0.5$	−
532	$N_{p}$	−	$13.2 \pm 0.3$	$13.5 \pm 0.3$	−	$7.9 \pm 0.5$	$8.2 \pm 0.5$
	$N_{m}$	$15.0 \pm 0.3$	−	$14.5 \pm 0.3$	$10.2 \pm 0.5$	−	$9.6 \pm 0.5$	$9.7 \pm 0.6$	$7.9 \pm 0.5$	$8.9 \pm 0.6$
	$N_{g}$	$14.3 \pm 0.3$	$13.0 \pm 0.3$	−	$9.2 \pm 0.5$	$7.9 \pm 0.5$	−
633	$N_{p}$	−	$11.4 \pm 0.3$	$11.8 \pm 0.3$	−	$6.2 \pm 0.5$	$6.5 \pm 0.5$
	$N_{m}$	$13.2 \pm 0.3$	−	$12.1 \pm 0.3$	$8.4 \pm 0.5$	−	$7.2 \pm 0.5$	$7.9 \pm 0.6$	$6.3 \pm 0.5$	$6.9 \pm 0.5$
	$N_{g}$	$12.4 \pm 0.3$	$11.4 \pm 0.3$	−	$7.4 \pm 0.5$	$6.3 \pm 0.5$	−
650	$N_{p}$	−	$11.3 \pm 0.3$	$11.4 \pm 0.3$	−	$6.1 \pm 0.5$	$6.1 \pm 0.5$
	$N_{m}$	$12.5 \pm 0.3$	−	$11.8 \pm 0.3$	$7.7 \pm 0.5$	−	$7.0 \pm 0.5$	$7.7 \pm 0.5$	$6.0 \pm 0.5$	$6.6 \pm 0.6$
	$N_{g}$	$12.8 \pm 0.3$	$11.0 \pm 0.3$	−	$7.7 \pm 0.5$	$5.9 \pm 0.5$	−
800	$N_{p}$	−	$10.2 \pm 0.3$	$10.2 \pm 0.3$	−	$5.0 \pm 0.5$	$5.0 \pm 0.5$
	$N_{m}$	$11.7 \pm 0.3$	−	$10.8 \pm 0.3$	$6.9 \pm 0.5$	−	$6.0 \pm 0.5$	$6.6 \pm 0.6$	$5.0 \pm 0.5$	$5.5 \pm 0.6$
	$N_{g}$	$11.3 \pm 0.3$	$10.1 \pm 0.3$	−	$6.2 \pm 0.5$	$5.0 \pm 0.5$	−
1064	$N_{p}$	−	$9.7 \pm 0.3$	$9.8 \pm 0.3$	−	$4.5 \pm 0.5$	$4.6 \pm 0.5$
	$N_{m}$	$10.9 \pm 0.3$	−	$10.4 \pm 0.3$	$6.2 \pm 0.5$	−	$5.6 \pm 0.5$	$5.8 \pm 0.6$	$4.6 \pm 0.5$	$5.1 \pm 0.6$
	$N_{g}$	$10.3 \pm 0.3$	$9.6 \pm 0.3$	−	$5.3 \pm 0.5$	$4.6 \pm 0.5$	−

Thermo-optic Coefficient	$A$	$B$ , $µ m^{2}$	$C$ , $µ m^{4}$
$d n_{p} / d T$	4.848	0.8611	0.1518
$d n_{m} / d T$	3.705	0.7813	0.08995
$d n_{g} / d T$	4.141	0.8057	0.1207

Abstract

Data availability

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Figures (4)

Tables (3)

Equations (2)

Journal of the Optical Society of America B