Abstract
Fundamentally power-limited by thermal effects, the design challenge for end-pumped “bulk” solid-state lasers depends upon knowledge of the temperature gradients within the gain medium. We have developed analytical expressions that can be used to model the temperature distribution and thermal-lens power in end-pumped solid-state lasers. Enabled by the inclusion of a temperature-dependent thermal conductivity, applicable from cryogenic to elevated temperatures, typical pumping distributions are explored and the results compared with accepted models. Key insights are gained through these analytical expressions, such as the dependence of the peak temperature rise in function of the boundary thermal conductance to the heat sink. Our generalized expressions provide simple and time-efficient tools for parametric optimization of the heat distribution in the gain medium based upon the material and pumping constraints.
Highlights
The end-pumped solid-state laser is a mature design architecture exploited for many scientific, industrial, and medical laser applications, in the tens-of-watts power regime
Analytical solutions for the temperature distribution along the length of a side-cooled end-pumped rod are presented for different pump distributions that can be used for practical configurations, such as near-diffraction-limited, to fibre-coupled diode-laser, pumps
We have drawn on the fact that the thermal conductivity of laser gain media is dependent upon their temperature
Summary
The end-pumped solid-state laser is a mature design architecture exploited for many scientific, industrial, and medical laser applications, in the tens-of-watts power regime. Analytical solutions for the temperature distribution along the length of a side-cooled end-pumped rod are presented for different pump distributions that can be used for practical configurations, such as near-diffraction-limited, to fibre-coupled diode-laser, pumps This result provides novel analytical expressions for the thermal-lens strength associated with the pump-induced accumulated optical phase shift, which converge to well-known equations [5] when a temperature-independent thermal conductivity is chosen. The rest of this paper is organized as follows: we start by introducing the model for the thermal conductivity k(T), which matches with actual measurements and provides simple solutions for the Kirchhoff transform, and its dependence over the two main temperature ranges of practical interest Utilizing this form for k(T), the derivation of the exact solutions for the temperature distribution along an end-pumped rod is given.
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