Linear- and nonlinear-optical properties of a new gadolinium calcium oxoborate crystal, Ca4GdO(BO3)3

G. Aka; A. Kahn-Harari; F. Mougel; D. Vivien; F. Salin; P. Coquelin; P. Colin; D. Pelenc; J. P. Damelet

doi:10.1364/JOSAB.14.002238

Journal of the Optical Society of America B
Vol. 14,
Issue 9,
pp. 2238-2247
(1997)
•https://doi.org/10.1364/JOSAB.14.002238

Linear- and nonlinear-optical properties of a new gadolinium calcium oxoborate crystal, Ca₄GdO(BO₃)₃

G. Aka, A. Kahn-Harari, F. Mougel, D. Vivien, F. Salin, P. Coquelin, P. Colin, D. Pelenc, and J. P. Damelet

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G. Aka, A. Kahn-Harari, F. Mougel, D. Vivien, F. Salin, P. Coquelin, P. Colin, D. Pelenc, and J. P. Damelet, "Linear- and nonlinear-optical properties of a new gadolinium calcium oxoborate crystal, Ca₄GdO(BO₃)₃," J. Opt. Soc. Am. B 14, 2238-2247 (1997)

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Abstract

Large and good-optical-quality crystals of gadolinium and calcium oxoborate, ${Ca}_{4} GdO ({BO}_{3})_{3}$ (GdCOB) have been grown from a melt by the Czochralski pulling method. The crystal is absolutely insensitive to moisture. Linear- and quadratic nonlinear-optical properties of this new monoclinic biaxial borate crystal are reported. The crystal is transparent in the visible and the near IR (from 0.32 to 2.7 µm), with favorable phase matching conditions for second-harmonic generation. Experimental phase-matching results, measured with a femtosecond broadband pulse parametric generator source tunable from 0.8 to 2.100 µm, are compared with theoretical predictions. The effective nonlinear coefficients are determined, leading to $d_{eff} = 1 pm / V$ for type I crystals in the $ZX$ plane. The damage threshold is as high as $1 GW / {cm}^{2}$ at 0.532 µm. The second-harmonic generation conversion efficiency of a $Q$ -switched Nd:YAG laser with a 15-mm long crystal is greater than 50%. These values together with the possibility of growing large crystals make GdCOB an excellent candidate for the next generation of crystals for frequency conversion and parametric processes.

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λ (µm)	$n_{X}$		$n_{Y}$		$n_{Z}$
λ (µm)	Exp.	Calc.	Exp.	Calc.	Exp.	Calc.
0.4047	1.7209	1.7209	1.7476	1.7477	1.7563	1.7563
0.4358	1.7142	1.7142	1.7409	1.7407	1.7493	1.7493
0.4678	1.7089	1.7087	1.7350	1.7351	1.7436	1.7437
0.4800	1.7068	1.7069	1.7333	1.7333	1.7418	1.7418
0.5086	1.7033	1.7033	1.7295	1.7295	1.7379	1.7380
0.5461	1.6992	1.6993	1.7253	1.7254	1.7340	1.7339
0.5780	1.6966	1.6966	1.7225	1.7226	1.7310	1.7310
0.5876	1.6960	1.6959	1.7218	1.7218	1.7303	1.7302
0.6439	1.6923	1.6922	1.7181	1.7179	1.7265	1.7264
0.6678	1.6910	1.6909	1.7168	1.7166	1.7250	1.7250
0.7290	1.6879	1.6882	1.7133	1.7136	1.7216	1.7221
0.7960	1.6860	1.6858	1.7112	1.7111	1.7197	1.7195

Refractive Index	Sellmeier Coefficients
Refractive Index	$A$	$B$	$C$	$D$
$n_{X}$	2.8065	0.02347	0.01300	0.00356
$n_{Y}$	2.8957	0.02402	0.01395	0.01039
$n_{Z}$	2.9222	0.02471	0.01279	0.00820

Principal Plane	Type of Interaction	Phase-matching Angle
$XY$	I $(ooe)$	$φ = \arctan \{\frac{n_{x} (2 ω)}{n_{y} (2 ω)} {[\frac{n_{y}^{2} (2 ω) - n_{z}^{2} (ω)}{n_{z}^{2} (ω) - n_{x}^{2} (2 ω)}]}^{1 / 2}\}$
	II $(eoe, oee)$	$φ = \arctan [\frac{n_{x} (2 ω) [n_{z} (ω) + n_{x} (ω)]}{n_{y} (2 ω) [n_{y} (ω) + n_{x} (ω)]} {(\frac{{4 n_{y}^{2} (2 ω) - [n_{y} (ω) + n_{z} (ω)]}}{{[n_{z} (ω) + n_{x} (ω)]^{2} - 4 n_{x}^{2} (2 ω)}})}^{1 / 2}]$
$YZ$	I $(eeo)$	$θ = \arctan \{\frac{n_{z} (ω)}{n_{y} (ω)} {[\frac{n_{x}^{2} (2 ω) - n_{y}^{2} (ω)}{n_{z}^{2} (ω) - n_{x}^{2} (2 ω)}]}^{1 / 2}\}$
	I $(oeo, eoo)$	$θ = \arctan (\frac{n_{z} (ω)}{n_{y} (ω)} {\{\frac{[2 n_{x} (2 ω) - n_{x} (ω)]^{2} - n_{y}^{2} (ω)}{n_{z}^{2} (ω) - [2 n_{x} (2 ω) - n_{x} (ω)]^{2}}\}}^{1 / 2})$
$ZX$ $(θ < V_{z})$	I $(ooe)$	$θ = \arctan \{\frac{n_{z} (2 ω)}{n_{x} (2 ω)} {[\frac{n_{x}^{2} (2 ω) - n_{y}^{2} (ω)}{n_{y}^{2} (ω) - n_{z}^{2} (2 ω)}]}^{1 / 2}\}$
	II $(eoo, oeo)$	$θ = \arctan [\frac{n_{z} (2 ω) [n_{y} (ω) + n_{z} (ω)]}{n_{x} (2 ω) [n_{x} (ω) + n_{y} (ω)]} {(\frac{{4 n_{x}^{2} (2 ω) - [n_{x} (ω) + n_{y} (ω)]^{2}}}{[[n_{y} (ω) + n_{z} (ω)]^{2} - 4 n_{z}^{2} (2 ω)]})}^{1 / 2}]$
$ZX$ $(θ > V_{Z})$	I $(eeo)$	$θ = \arctan (\frac{n_{z} (ω)}{n_{x} (ω)} {[\frac{n_{y}^{2} (2 ω) - n_{x}^{2} (ω)}{n_{z}^{2} (ω) - n_{y}^{2} (2 ω)}]}^{1 / 2})$
	II $(oeo, eoe)$	$θ = \arctan (\frac{n_{z} (ω)}{n_{x} (ω)} {\{\frac{[2 n_{y} (2 ω) - n_{y} (ω)]^{2} - n_{x}^{2} (ω)}{n_{z}^{2} (ω) - [2 n_{y} (2 ω) - n_{y} (ω)]^{2}}\}}^{1 / 2})$

Principal Plane	Type I Crystal	Type II Crystal
$YZ$	$d_{13} {sin}^{2} θ + d_{12} {cos}^{2} θ$	$d_{31} sin θ$
$ZX$	$d_{12} cos θ - d_{32} sin θ$	0
$XY$	$d_{13} sin ϕ$	$d_{31} {sin}^{2} ϕ + d_{32} {cos}^{2} ϕ$

Crystal	Thickness (mm)	Type of Interaction	$d_{eff}$ Relative to That of BBO
BBO	3	I	1
BBO	5	I	1.07
GdCOB $YZ$ plane	2.4	I	0.1
GdCOB $YZ$ plane	2.4	II	0.1
GdCOB $ZX$ plane	2.4	I	0.57
GdCOB $XY$ plane	2.14	I	0.25

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Journal of the Optical Society of America B