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Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser
Mohammad Sabaeian1, Hamid Nadgaran, Laleh Mousave
1Physics Department, College of Science, Shiraz University, Shiraz 71454, Iran. nadgaran@susc.ac.ir
Applied Optics
|May 2, 2008
Summary
A new analytical solution for temperature distribution in solid-state laser crystals with cubic cross-sections has been developed. This provides accurate thermal lensing and birefringence calculations for laser crystal design.
Area of Science:
- Solid-state laser physics
- Thermal management in optical materials
- Analytical heat transfer solutions
Background:
- Accurate temperature distribution in solid-state laser crystals is crucial for predicting thermal lensing, birefringence, and crystal bending.
- Existing solutions for steady-state heat loading are often limited to simple cylindrical shapes and rely on numerical methods.
Purpose of the Study:
- To derive a comprehensive analytical solution for the heat equation in anisotropic, cubic cross-section solid-state laser crystals.
- To accurately model temperature distribution under Gaussian laser pumping with power attenuation and realistic cooling mechanisms.
Main Methods:
- Developed a full analytical solution to the heat equation for a cubic cross-section crystal.
- Incorporated Gaussian pump profile, pump power attenuation, and convective cooling.
- Utilized series solutions for the analytical model.
Main Results:
- Presented the first full analytical solution for temperature distribution in anisotropic cubic solid-state laser crystals.
- Demonstrated excellent agreement between the analytical solutions and numerical counterparts.
- Showcased the effectiveness of employing only a few terms in the series solutions.
Conclusions:
- The derived analytical solution offers a precise and efficient method for analyzing thermal effects in cubic solid-state laser crystals.
- This work advances the understanding and calculation of thermal phenomena critical for laser performance and design.
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