Analytical solution of the thermal effects in a high-power slab Tm:YLF laser with dual-end pumping

The thermal effects model of the anisotropic slab crystal was built based on the practical operation condition of the solid-state laser. A full analytical solution of the heat equation for an anisotropic cubic cross-section, solid-state crystal is presented. We can conclude that the analytical solution carries a very considerable reliability level when it was compared with the numerical solution and experimental measurements. The expressions that are reported here were applied to a slab Tm:YLF crystal, and the results showed that the thermal lens effect was enhanced with the increase of the pump power density. Thermal deformation produced by thermal lens effect plays a leading role in the Tm:YLF crystal at this time. When the product of crystal length and doping concentration was a constant value, the thermal focal length remained basically consistent. However, the slab laser crystal should have decreased doping concentration and a moderately increased crystal length in order to relieve the thermal effects.

Figure 1

The thermal model of an anisotropic slab crystal.

Figure 2

(a,b) 2D temperature distribution computed in the X-Y plane at $Z=0$. (c,d) 2D (3D) temperature distribution computed in the Y-Z plane at $X=a/2$. Thicknesses given in the legend from top to bottom correspond to curves shown in figure from bottom to top.

Figure 3

(a) Temperature distribution at $Z=0$ and $Z=L/2$ planes along $Y$ axis. (b) Temperature distribution along the crystal axis at $X=a/2$ and $Y=b/2$. Solid curves show our analytical solution; dotted curves show the numerical solution.

Figure 4

Thermal focal length under different pump powers. Solid curves show our analytical solution; points show experimental results.

Figure 5

Temperature distribution along the crystal center axis under the different crystal thicknesses. The thicknesses given in the legend from top to bottom correspond to curves shown in the figure from bottom to top.

Figure 6

Temperature distribution along the crystal center axis under the different pump powers. The thicknesses given in the legend from top to bottom correspond to curves shown in the figure from bottom to top.

Figure 7

Temperature distribution along the crystal center axis under the different waist radii. The thicknesses given in the legend from top to bottom correspond to curves shown in the figure from bottom to top.

Figure 8

Thermal focal length under different waist radii with the change of pump power (a) along the $a$ axis, (b) along the $c$ axis. The thicknesses given in the legend from top to bottom correspond to curves shown in the figure from bottom to top.

Figure 9

Thermal focal length along the $c$ and $a$ axes under different pump powers (the product of crystal length and doping concentration is constant). The thicknesses given in the legend from top to bottom correspond to curves shown in the figure from bottom to top.

Figure 10

Temperature distribution at $Z=0$ and $X=a/2$ planes along $Y$ axis (the product of crystal length and doping concentration is constant). The thicknesses given in the legend from top to bottom correspond to curves shown in the figure from bottom to top.