Temperature distribution in side- and end-pumped laser crystal rods: temporal and spatial variations

Area of Science:

• Laser physics
• Thermal engineering
• Materials science

Background:

• Laser rods are susceptible to thermal stress and damage, especially when end-pumped.
• Accurate temperature prediction is vital for laser system design and reliability.
• Existing models may not fully account for dynamic pumping conditions and cooling effects.

Purpose of the Study:

• To develop a comprehensive mathematical model for predicting the temperature distribution in end-pumped laser rods.
• To analyze the impact of spatial and temporal pump variations on laser rod temperature.
• To provide a tool for predicting quasi-steady-state temperatures in various laser materials.

Main Methods:

• Developed a double-series mathematical expression for laser rod temperature as a function of time.
• Incorporated surface cooling rates, pump beam variations, and material properties (specific heat, thermal conductivity).
• Utilized an eigenfunction expansion representation for temperature prediction.

Main Results:

• The model accurately predicts spatial and time-dependent quasi-steady-state temperatures.
• Demonstrated the model's applicability to Ti:sapphire, Nd:YAG, and Cr:LiSAF laser rods.
• The mathematical framework accounts for complex thermal behaviors under multipulsed or continuous pumping.

Conclusions:

• The developed model provides critical insights into laser rod thermal management.
• This predictive capability is essential for optimizing laser performance and preventing material failure.
• The eigenfunction expansion method offers a robust approach for thermal analysis in laser materials.