title: Analytical solution of the heat equation in a longitudinally pumped cubic solid-state laser.
abstract: 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.
authors.affiliation: Physics Department, College of Science, Shiraz University, Shiraz 71454, Iran. nadgaran@susc.ac.ir
authors.forename: Mohammad
authors.initials: M
authors.lastname: Sabaeian
authors.forename: Hamid
authors.initials: H
authors.lastname: Nadgaran
authors.forename: Laleh
authors.initials: L
authors.lastname: Mousave