Anisotropy of refractive-index nonlinear change in Cr<sup>4+</sup>:YAG at cw resonant excitation: modeling

Alexander V. Kir’yanov; Juan Carlos Bermudez G.

doi:10.1364/JOSAB.20.002454

Journal of the Optical Society of America B
Vol. 20,
Issue 12,
pp. 2454-2469
(2003)
•https://doi.org/10.1364/JOSAB.20.002454

Anisotropy of refractive-index nonlinear change in Cr⁴⁺:YAG at cw resonant excitation: modeling

Alexander V. Kir’yanov and Juan Carlos Bermudez G.

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Alexander V. Kir’yanov and Juan Carlos Bermudez G., "Anisotropy of refractive-index nonlinear change in Cr⁴⁺:YAG at cw resonant excitation: modeling," J. Opt. Soc. Am. B 20, 2454-2469 (2003)

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Abstract

A model is developed for numerically calculating the nonlinear change of the refractive index in a ${Cr}^{4 +} : YAG$ crystal under the powerful resonant (wavelength 1.06 μm) continuous-wave excitation. The anisotropy features of the ${Cr}^{4 +}$ centers’ population perturbation (bleaching) and the sample inhomogeneous heating (leading to the thermolensing effect) as the basic contributions in the refractive-index nonlinear change are addressed for the first time to our knowledge.

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Number	Parameter	Value
1	Refractive index	$n_{0} = 1.8$
2	Thermal-index gradient	$d n / d T = 9.8 \times 10^{- 6} K^{- 1}$
3	Thermal conductivity	$K = 0.13 W / cm \times K$
4	Poisson coefficient	$υ = 0.3$
5	Convective coefficient	$h = 10^{2}$
6	Thermal-expansion coefficient	$α_{T} = 8.2 \times 10^{- 6} K^{- 1}$
7	Coolant temperature	$T_{C} = 17 ° C$
8	Photoelastic coefficients	$C_{r} = 1.318 C_{t} = - 0.169$ (Ref. 29 )
9	Atomic resonance detuning parameter	$δ = 0.2$ (Ref. 10 )
10	Small-signal resonant absorption coefficient	$α_{0} = 3.362 {cm}^{- 1}$
11	Residual losses	$β = 0.54 {cm}^{- 1}$
12	Crystal length	$L = 0.3 cm$
13	Crystal diameter	$\emptyset = 0.9 cm$
14	Initial and final transmittance	$T 0_{in} = 0.31,$ $T 0_{fin} = 0.85$
15	${Cr}^{4 +}$ fluorescence lifetime	$τ_{f} = 4.3 \times 10^{- 6} s$ (Ref. 34 )
16	Saturation intensity	$I_{S} = 63 kW / {cm}^{2}$
17	Luminescence quantum efficiency	$ε = 0.34$ (Ref. 34 )
18	Stokes losses	$γ = 0.25$
19	Fractional heat-load parameter	$ξ = 0.75$
20	Energy of pump quanta	$h υ = 1.85 \times 10^{- 19} J$
21	Pump wavelength	$λ_{P} = 1.06 \times 10^{- 4} cm$
22	${Cr}^{4 +}$ luminescence wavelength	$λ_{L} = 1.47 \times 10^{- 4} cm$
23	Beam waist $(Z = 0$ position)	$ω_{0} = 15 \times 10^{- 4} cm$

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Journal of the Optical Society of America B