Modeling of Steady-State Temperature Distribution in Diode-Pumped Alkali Vapor Lasers: Analysis of the Experimental Results

Combining the first-order ordinary differential equations of pump and laser power and the second-order ordinary differential equation of temperature, an optical model for diode-pumped alkali vapor lasers in two pumped configurations, is reported. This model, taking into account the axial distributions of pump and laser beam radii and the radial distributions of intensities and temperature, shows good agreement between the calculated and experimental results. An observed maximum temperature rise of ~58 K corresponding to a pump power of 20 W is reproduced, and a wide region of heat source density of quenching is predicted by the model. The heat production of relaxation and of quenching are demonstrated to be within an order of magnitude, indicating that quenching is as important as relaxation in the temperature calculation. It can also be deduced that the peak of the temperature profile is mainly dominated by relaxation, whereas its width can be attributed to thermal diffusion and quenching. In addition, dependencies of laser and thermal power on the pump beam waist are calculated, and an optimal ratio of 0.7 between the pump and laser beam waist is obtained.