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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 47, Iss. 13 — May. 1, 2008
  • pp: 2317–2325

Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser

Mohammad Sabaeian, Hamid Nadgaran, and Laleh Mousave  »View Author Affiliations

Applied Optics, Vol. 47, Issue 13, pp. 2317-2325 (2008)

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Knowledge about the temperature distribution inside solid-state laser crystals is essential for calculation of thermal phase shift, thermal lensing, thermally induced birefringence, and heat-induced crystal bending. Solutions for the temperature distribution for the case of steady-state heat loading have appeared in the literature only for simple cylindrical crystal shapes and are usually based on numerical techniques. For the first time, to our knowledge, a full analytical solution of the heat equation for an anisotropic cubic cross-section solid-state crystal is presented. The crystal is assumed to be longitudinally pumped by a Gaussian pump profile. The pump power attenuation along the crystal and the real cooling mechanisms, such as convection, are considered in detail. A comparison between our analytical solutions and its numerical counterparts shows excellent agreement when just a few terms are employed in the series solutions.

© 2008 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

Original Manuscript: February 11, 2008
Manuscript Accepted: March 26, 2008
Published: April 28, 2008

Mohammad Sabaeian, Hamid Nadgaran, and Laleh Mousave, "Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser," Appl. Opt. 47, 2317-2325 (2008)

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