Optimum conditions for ultraviolet-laser generation based on self-frequency sum mixing in Nd<sup>3+</sup>-activated borate crystals

Daniel Jaque

doi:10.1364/JOSAB.19.001326

Journal of the Optical Society of America B
Vol. 19,
Issue 6,
pp. 1326-1334
(2002)
•https://doi.org/10.1364/JOSAB.19.001326

Optimum conditions for ultraviolet-laser generation based on self-frequency sum mixing in Nd³⁺-activated borate crystals

Daniel Jaque

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Daniel Jaque, "Optimum conditions for ultraviolet-laser generation based on self-frequency sum mixing in Nd³⁺-activated borate crystals," J. Opt. Soc. Am. B 19, 1326-1334 (2002)

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Abstract

A simple theoretical model of the ultraviolet laser radiation generated by self-frequency sum mixing in a single argon-pumped ${Nd}^{3 +}$ -doped nonlinear crystal is proposed. Self-absorption by both absorption edge and ${Nd}^{3 +}$ bands lying in the ultraviolet range is taken into account. The model is then applied to ${Nd}^{3 +} : {YAl}_{3} ({BO}_{3})_{4},$ ${Nd}^{3 +} : {GdCa}_{4} O ({BO}_{3})_{3},$ and ${Nd}^{3 +} : {YCa}_{4} O ({BO}_{3})_{3}$ borate laser crystals. The crystal length, pump wavelength, and ${Nd}^{3}$ concentration that optimize the pump to ultraviolet efficiency are determined for each case. The ultraviolet output power is found to be tens of milliwatts for a pump power of 2 W.

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$λ_{Ar}$ (nm)	NYAB Crystal			NYCOB Crystal
$λ_{Ar}$ (nm)	Transition	Wavelength (nm)	Phase-Matching Angle (°)	Transition	Wavelength (nm)	Phase-Matching Angle (°)
514.5	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 46.5$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	$φ_{pm} = 88$
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 40.2$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 58.1$
501.7	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 47.4$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	Not allowed
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 40.8$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 60.1$
496.5	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 47.7$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	Not allowed
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 41.1$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 60.8$
488	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 48.3$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	Not allowed
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 41.5$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 62.2$

$λ_{Ar}$ (nm)	$λ_{IR}$ (nm)	$λ_{UV}$ (nm)	$σ_{Ar}$ (cm^-1/at. %)	$σ_{UV}$ (cm^-1/at. %)	$α_{edge}$ (cm^-1)
514.5	1062	346.6	0.143	0.006	0.513
501.7	1062	340.7	0.012	0	0.576
496.5	1062	338.3	0.005	0	0.645
488	1062	334.3	0.012	0	0.684
514.5	1338	371.6	0.143	0.019	0.299
501.7	1338	364.9	0.012	0.041	0.345
496.5	1338	362.1	0.005	0.173	0.351
488	1338	357.6	0.012	0.154	0.38

Material	d (pm/V)	$τ_{F}$ (µs)	$σ_{em} (^{4} F_{3 / 2} \to^{4} I_{11 / 2})$ $(\times 10^{23} m^{2})$	$σ_{em} (^{4} F_{3 / 2} \to^{4} I_{13 / 2})$ $(\times 10^{23} m^{2})$	L (cm^-1)
NYAB	1.9b	$\frac{60}{1 + 0.02 N}$ c	1.1d	0.24d	0.011d
NYCOB	1.1e	$\frac{104}{1 + 0.008 N}$ e	0.42f	0.16f	0.018e

$λ_{Ar}$ (nm)	$λ_{IR}$ (nm)	$λ_{UV}$ (nm)	$σ_{Ar}$ (cm^-1/at. %)	$σ_{UV}$ (cm^-1/at. %)	$α_{edge}$ (cm^-1)
514.5	1060	346.4	0.296	0.020	0.33
501.7	1060	340.5	0.040	0.012	0.380
496.5	1060	338.1	0.012	0.011	0.396
488	1060	334.1	0.005	0.023	0.424
514.5	1332	371.1	0.296	0.006	0.211
501.7	1332	364.4	0.040	0.097	0.242
496.5	1332	361.7	0.012	0.239	0.254
488	1332	357.1	0.005	0.189	0.273

$λ_{Ar}$ (nm)	NYAB Crystal			NYCOB Crystal
$λ_{Ar}$ (nm)	Transition	Wavelength (nm)	Phase-Matching Angle (°)	Transition	Wavelength (nm)	Phase-Matching Angle (°)
514.5	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 46.5$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	$φ_{pm} = 88$
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 40.2$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 58.1$
501.7	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 47.4$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	Not allowed
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 40.8$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 60.1$
496.5	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 47.7$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	Not allowed
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 41.1$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 60.8$
488	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1062$	$θ_{pm} = 48.3$	$^{4} F_{3 / 2} \to^{4} I_{11 / 2}$	$λ_{IR} = 1060$	Not allowed
	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1338$	$θ_{pm} = 41.5$	$^{4} F_{3 / 2} \to^{4} I_{13 / 2}$	$λ_{IR} = 1332$	$φ_{pm} = 62.2$

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Journal of the Optical Society of America B