Thermal lens effect model of Ti:sapphire for use in high-power laser amplifiers

Abstract

We mathematically model the thermal lens effect of Ti:sapphire for use in a high-power laser pulse amplifier. The model enables more accurate prediction with new interpretations and offers simplified equations for the optical path difference and thermally induced focal length. Our model is validated through comparisons with measurements of existing high-power laser facilities. Further, we apply the model to a 2 PW, 10 Hz Ti:sapphire laser amplifier design.

Modeling and Analysis of High-Power Ti:sapphire Laser Amplifiers–A Review

“…The loss of linearly polarized light is small spatially, but the amount of loss is dispersed in time, adversely affecting the temporal contrast ratio. The phase retardation of the medium to be introduced does not form the shape of a single concave lens or a single convex lens [22]. If we express this effect as a Zernike polynomial, we can see that it is convex in the vertical direction and concave in the horizontal direction.…”

“…The atomic phase shift is derived from the classical electron model. Equation (21) expresses the wavenumber, k e , for an excited ion, and the gain and phase shift for the excited ion are obtained from Equations (22) and (23) [23]. In a CPA system, the laser pulse is chirped; specifically, because the frequency is distributed in the time domain, the phase shift and gain, which are functions of time t and frequency ω, can be expressed solely as a functions of time t. ∆N is the population inversion, σ 0 is the peak emission cross-section, L is the length of the laser medium, and ω 0 and ∆ω are the peak angular frequency and bandwidth, respectively.…”

“…In a CPA system, the laser pulse is chirped; specifically, because the frequency is distributed in the time domain, the phase shift and gain, which are functions of time t and frequency ω, can be expressed solely as a functions of time t. ∆N is the population inversion, σ 0 is the peak emission cross-section, L is the length of the laser medium, and ω 0 and ∆ω are the peak angular frequency and bandwidth, respectively. The population inversion over time is considered in Equations (22) and (23); therefore, this model considers the gain depletion effect.…”

“…In addition, we show how to apply the model to a CPA system and describe the analysis method of the square pump condition, which has attracted the interest of many research institutes in recent years [20]. Furthermore, an interpretation of the phase distortion occurring in the active medium, which has a significant impact on the energy and spatio-temporal shape of the pulse, is also included in this review [21,22]. The phase retardation generated inside a high-power laser medium, particularly in the case of Ti:sapphire, is relatively inadequately researched and is now essentially gaining attention for its effect [23].…”

10 W injection-locked single-frequency continuous-wave titanium:sapphire laser

“…When developing a high-power Ti:sapphire laser with increased pump power, one crucial issue is how to manage the thermal lens effect [16], which results from variations in the refractive index in the laser crystal due to the thermo-optic effect caused by absorption of the pump beam [17]. In the case of a collimated pump beam for a pulsed Ti:sapphire laser, the property of the thermal lens and its influence on the laser performance has been reported [18]. However, to the best of our knowledge, injection-locked CW Ti:sapphire lasers with this effect have not been investigated well.…”