The diode-pumped alkali laser (DPAL) is a new type of laser source which has been widely studied in the recent years. The temperature distribution of a sealed vapor cell, which is the crucial component in a DPAL system, produces an important effect on the output performance of a DPAL. In this paper, the strict solution of the heat conduction equation for a cesium vapor cell is obtained by using a finite difference procedure. The temperature distribution of a dummy open cell is first analyzed, and then the temperature distributions of two independent windows, regarded as the boundary conditions of solving a sealed cell, are evaluated in detail. By combining the results of the two steps together, we finally acquire the temperature distribution of a real sealed cesium vapor cell. The results reveal that the temperature gradients on both radial and longitudinal directions change with the pump power, cell radius, and absorption coefficient when the sealed cesium vapor cell is heated or pumped with the laser diodes. The conclusions are helpful for accurately evaluating the output characteristics of a DPAL.
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