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This study presents solutions for heat diffusion in laser materials with absorbing centers. The ratio of specific heats dictates three distinct thermal behavior regions, with analytical solutions provided for various timescales.

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Area of Science:

  • Physics
  • Materials Science
  • Thermal Engineering

Background:

  • Understanding heat diffusion in laser materials is crucial for device performance and longevity.
  • Absorbing centers within laser hosts can significantly impact thermal profiles.
  • Previous models may lack detailed analysis across different thermal regimes.

Purpose of the Study:

  • To derive and present analytical solutions for the heat diffusion equation in laser materials containing spherical absorbing centers.
  • To investigate the influence of the volume specific heat ratio between the absorbing center and the laser host on thermal behavior.
  • To provide time-dependent solutions applicable to both short and long timescales.

Main Methods:

  • Solving the heat diffusion equation for a spherical absorbing center embedded in a host material.
  • Analyzing the behavior based on the ratio of volume specific heats (absorbing center to host).
  • Developing series expansions for small and large time regimes.
  • Utilizing rapidly converging representations for the complementary error function with complex arguments for numerical evaluation.

Main Results:

  • Identified three distinct regions of thermal behavior determined by the volume specific heat ratio.
  • Provided analytical series expansions for transient heat diffusion solutions in each region.
  • Developed numerical evaluation methods for the specific case where the volume specific heat ratio exceeds 3/4.

Conclusions:

  • The volume specific heat ratio is a critical parameter governing heat diffusion dynamics in laser materials with absorbing centers.
  • The presented solutions offer a comprehensive framework for analyzing thermal effects across different timescales and material property ratios.
  • The developed numerical techniques enable accurate assessment of thermal behavior in specific laser material configurations.