The overall phase shift and lens effect calculation

using Gaussian boundary conditions and paraxial

ray approximation for an end-pumped solid-state laser

H NADGARAN and P ELAHI^*

Department of Physics, College of Science, Shiraz University, Shiraz 71454, Iran

^*Department of Physics, Payame Noor University, Shiraz 71365-944, Iran

E-mail: nadgaran@susc.ac.ir; phy1pe@yahoo.com; pelahi@spnu.ac.in

Abstract. In this work, the inhomogeneous equation of heat conduction was exactly solved by

applying inhomogeneous boundary conditions for laser crystals of

aspect ratio=1 (aspect ratio=radius of the laser rod/length of the

laser rod). We have shown that the paraxial ray

approximation leads the solution to be a function of $r^{2}$, that

is, the approximation is equivalent to a situation in which a

homogeneous pump source is used. The solution was then used to

derive expressions for the overall phase shift, focal length of

the thermal lens and the end effect induced curvature of the end face.

The expressions were then applied to Nd:YAG laser medium. The

result shows a meaningful correction of the order of 0.001 cm to

the focal length of Nd:YAG rod for 3 W source power and beam

waist of 100 $\mu$m.

Keywords. Thermal effects; thermal lensing; phase shift.

PACS No. 42.55.Xi