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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 30 — Oct. 20, 2012
  • pp: 7150–7159

Analytical solutions for anisotropic time-dependent heat equations with Robin boundary condition for cubic-shaped solid-state laser crystals

Mohammad Sabaeian  »View Author Affiliations


Applied Optics, Vol. 51, Issue 30, pp. 7150-7159 (2012)
http://dx.doi.org/10.1364/AO.51.007150


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Abstract

The problem of finding analytical solutions for time-dependent or time-independent heat equations, especially for solid-state laser media, has required a lot of work in the field of thermal effects. However, to calculate the temperature distributions analytically, researchers often have to make some approximations or employ complex methods. In this work, we present full analytical solutions for anisotropic time-dependent heat equations in the Cartesian coordinates with various source terms corresponding to various pumping schemes. Moreover, the most general boundary condition of Robin (or impedance boundary condition), corresponding to the convection cooling mechanism, was applied. This general condition can be easily switched to constant temperature and thermal insulation as special cases. To this end, we first proposed a general approach to solving time-dependent heat equations with an arbitrary heat source. We then applied our approach to explore the temperature distribution for three cases: steady-state pumping or long transient, single-shot pumping or short transient, and repetitively pulsed pumping. Our results show the possibility of an easier and more accurate approach to analytical calculations of the thermal dispersion, thermal stresses (strains), thermal bending, thermal phase shift, and other thermal effects.

© 2012 Optical Society of America

OCIS Codes
(120.6780) Instrumentation, measurement, and metrology : Temperature
(120.6810) Instrumentation, measurement, and metrology : Thermal effects
(140.3480) Lasers and laser optics : Lasers, diode-pumped
(140.3580) Lasers and laser optics : Lasers, solid-state

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: July 11, 2012
Revised Manuscript: September 5, 2012
Manuscript Accepted: September 7, 2012
Published: October 11, 2012

Citation
Mohammad Sabaeian, "Analytical solutions for anisotropic time-dependent heat equations with Robin boundary condition for cubic-shaped solid-state laser crystals," Appl. Opt. 51, 7150-7159 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-30-7150

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