Thermo-optic coefficients and thermal lensing in Nd-doped KGd(WO<sub>4</sub>)<sub>2</sub> laser crystals

Pavel A. Loiko; Konstantin V. Yumashev; Nikolai V. Kuleshov; Anatoly A. Pavlyuk

doi:10.1364/AO.49.006651

Applied Optics
Vol. 49,
Issue 34,
pp. 6651-6659
(2010)
•https://doi.org/10.1364/AO.49.006651

Thermo-optic coefficients and thermal lensing in Nd-doped $KGd ({WO}_{4})_{2}$ laser crystals

Pavel A. Loiko, Konstantin V. Yumashev, Nikolai V. Kuleshov, and Anatoly A. Pavlyuk

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Pavel A. Loiko, Konstantin V. Yumashev, Nikolai V. Kuleshov, and Anatoly A. Pavlyuk, "Thermo-optic coefficients and thermal lensing in Nd-doped KGd(WO₄)₂ laser crystals," Appl. Opt. 49, 6651-6659 (2010)

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Abstract

We measured the thermo-optic coefficients $d n / d T$ of anisotropic $Nd : KGd ({WO}_{4})_{2}$ crystals at the wavelengths of $1.064 μm$ and $532 nm$ ( $300 K$ ) by a beam deflection method. The values of $d n / d T$ are determined to be $d n_{p} / d T = - 16.0 \times 10^{- 6} K^{- 1}$ , $d n_{m} / d T = - 11.8 \times 10^{- 6} K^{- 1}$ , and $d n_{g} / d T = - 19.5 \times 10^{- 6} K^{- 1}$ (at $1.064 μm$ ) and $d n_{p} / d T = - 14.3 \times 10^{- 6} K^{- 1}$ , $d n_{m} / d T = - 10.0 \times 10^{- 6} K^{- 1}$ , and $d n_{g} / d T = - 15.0 \times 10^{- 6} K^{- 1}$ (at $532 nm$ ). Thermal lensing in the flashlamp-pumped $N_{p}$ - and $N_{g}$ -cut $Nd : KGd ({WO}_{4})_{2}$ laser rods was studied at $1.064 μm$ by a probe beam technique in the nonlasing conditions, and the contribution of the photoelastic term to the thermal lens optical power was estimated. Athermal propagation directions with the definitions $d n / d T + (n - 1) α_{T} = 0$ and $d n / d T + n α_{T} = 0$ were found in $Nd : KGd ({WO}_{4})_{2}$ .

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	$λ = 1.064 μm$			$λ = 532 nm$
	$E ∥ N_{p}$	$E ∥ N_{m}$	$E ∥ N_{g}$	$E ∥ N_{p}$	$E ∥ N_{m}$	$E ∥ N_{g}$
Nd:KGW
$k ∥ N_{p}$	—	$- 9.01$	$- 16.56$	—	—	$- 12.09$
$k ∥ N_{m}$	$- 5.07$	—	$- 7.36$	—	—	—
$k ∥ N_{g}$	$+ 0.78$	$+ 4.67$	—	$+ 2.76$	$+ 7.54$	—
KGW
$k ∥ N_{p}$	—	$- 9.39$	$- 14.45$	—	$- 6.68$	$- 12.62$
$k ∥ N_{m}$	$- 4.73$	—	$- 5.82$	$- 2.69$	—	$- 3.55$
$k ∥ N_{g}$	$+ 0.44$	$+ 3.73$	—	$+ 2.98$	$+ 7.46$	—

	$λ = 1.064 μm$			$λ = 632.8 nm$ [37]			$λ = 532 nm$
	$E ∥ N_{p}$	$E ∥ N_{m}$	$E ∥ N_{g}$	$E ∥ N_{p}$	$E ∥ N_{m}$	$E ∥ N_{g}$	$E ∥ N_{p}$	$E ∥ N_{m}$	$E ∥ N_{g}$
Nd:KGW
$k ∥ N_{p}$	—	$- 11.64$	$- 19.31$	—	$- 9.84$	$- 15.89$	—	—	$- 14.98$
$k ∥ N_{m}$	$- 16.46$	—	$- 19.67$	$- 15.02$	—	$- 16.07$	—	—	—
$k ∥ N_{g}$	$- 15.42$	$- 11.99$	—	$- 14.56$	$- 10.43$	—	$- 14.25$	$- 10.01$	—
KGW
$k ∥ N_{p}$	—	$- 12.02$	$- 17.20$	—	$- 9.39$	$- 15.01$	—	$- 9.44$	$- 15.53$
$k ∥ N_{m}$	$- 16.11$	—	$- 18.12$	$- 14.35$	—	$- 16.48$	$- 14.65$	—	$- 16.52$
$k ∥ N_{g}$	$- 15.75$	$- 12.93$	—	$- 14.14$	$- 9.98$	—	$- 14.02$	$- 10.07$	—

Probe Beam Polarization	Measurement Direction	Laser Rods
		$N_{p}$ -cut Nd:KGW		$N_{g}$ -cut Nd:KGW
		M	S	M	S
$E_{probe} ∥ N_{m}$	A	$- 1.05$ ( $- 0.71$ )	0.87 (0.84)	0.97 (0.87)	0.29 (0.53)
$E_{probe} ∥ N_{m}$	B	$- 0.18$ (0.13)	0.87 (0.84)	1.26 (1.4)	0.29 (0.53)
$E_{probe} ⊥ N_{m}$	A	$- 4.01$ ( $- 2.5$ )	3.70 (2.63)	$- 0.47$ (0.38)	0.80 (0.06)
$E_{probe} ⊥ N_{m}$	B	$- 0.31$ (0.13)	3.70 (2.63)	0.33 (0.44)	0.80 (0.06)

Probe Beam Polarization	Meridional Plane	$d n / d T$	$P_{stress}$	$Q_{dist}$	$d n / d T + P_{stress} + Q_{dist}$
$N_{p}$ -cut Nd:KGW
$E_{probe} ∥ N_{m}$	A	$- 11.82$ ( $- 10.14$ )	9.0 (8.2)	0.17 (0.17)	$- 2.64$ ( $- 1.78$ )
$E_{probe} ∥ N_{m}$	B	$- 11.82$ ( $- 10.14$ )	11.2 (10.3)	0.17 (0.17)	$- 0.45$ (0.33)
$E_{probe} ∥ N_{g}$	A	$- 19.49$ ( $- 15.98$ )	9.2 (9.5)	0.18 (0.18)	$- 10.07$ ( $- 6.28$ )
$E_{probe} ∥ N_{g}$	B	$- 19.49$ ( $- 15.98$ )	18.5 (16.1)	0.18 (0.18)	$- 0.78$ (0.33)
$N_{g}$ -cut Nd:KGW
$E_{probe} ∥ N_{m}$	A	$- 11.82$ ( $- 10.14$ )	11.5 (11.2)	1.06 (1.09)	2.43 (2.18)
$E_{probe} ∥ N_{m}$	B	$- 11.82$ ( $- 10.14$ )	13.9 (12.6)	1.06 (1.09)	3.16 (3.52)
$E_{probe} ∥ N_{m}$	A	$- 15.94$ ( $- 14.79$ )	13.7 (14.7)	1.03 (1.06)	$- 1.18$ (0.95)
$E_{probe} ∥ N_{m}$	B	$- 15.94$ ( $- 14.79$ )	15.7 (14.8)	1.03 (1.06)	0.83 (1.11)

	$λ = 1.064 μm$			$λ = 532 nm$
	$E ∥ N_{p}$	$E ∥ N_{m}$	$E ∥ N_{g}$	$E ∥ N_{p}$	$E ∥ N_{m}$	$E ∥ N_{g}$
Nd:KGW
$k ∥ N_{p}$	—	$- 9.01$	$- 16.56$	—	—	$- 12.09$
$k ∥ N_{m}$	$- 5.07$	—	$- 7.36$	—	—	—
$k ∥ N_{g}$	$+ 0.78$	$+ 4.67$	—	$+ 2.76$	$+ 7.54$	—
KGW
$k ∥ N_{p}$	—	$- 9.39$	$- 14.45$	—	$- 6.68$	$- 12.62$
$k ∥ N_{m}$	$- 4.73$	—	$- 5.82$	$- 2.69$	—	$- 3.55$
$k ∥ N_{g}$	$+ 0.44$	$+ 3.73$	—	$+ 2.98$	$+ 7.46$	—

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Applied Optics