**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,

^{*}Department of Physics,

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**