# Thermo-Optic Numerical Research on Segmented Circular LD Arrays Side-Pumping a Nd:YAG Laser Rod
## 1 Introduction  
For the side-pumping geometry of lasers, the liquid cooling systems are often designed to cool the laser rod and pump-source [1, 2], decrease the influence of thermo-optic effects [3], and ensure a stable laser output with high beam quality [4]. The laser rod, immersed in the fluid of the transparent coolant jacket, is pumped by the outside circular laser diode (LD) arrays; this arrangement effectively avoids the space conflict. The symmetrical annular pump leads to Gaussian gain distribution in the laser rod and thus to high-power laser output with high beam quality [1, 5]. Therefore, the annular liquid-cooling is the most commonly used method in side-pumping geometry, especially in high-powerapplications [2; 6]. However, the complex liquid cooling systems considerably increase the volume of lasers and decrease mobility.  
In conduction cooling side-pumped lasers, there are two typical geometries. One is the compensated semicircular LD array side-pumping arrangement, in which the two same semicircular LD structures are configured with each other in a compensated geometry [7]. In the semicircular LD side-pumping structure, the cylindrical half-surface of the laser rod is conductively cooled by a heat sink, and the other half-surface is arranged to absorb pump radiation. The asymmetrical pump geometry induces non-Gaussian gain distribution in the laser rod. However, the laser beam quality is improved to a certain extent by the compensated geometry of the two same semicircular LD structures. The other typical geometry is the segmented circular LD array side-pumping configuration, in which the multi-circular LD array and rod holders alternate periodically along the length of the laser rod [8; 9]. The symmetrical side-pumping structure directly induces heat flows to propagate along the axial of the laser rod rather than the radial direction to the surface of the laser rod, thereby avoiding a high radial temperature gradient. Finally, the heat is removed by the segmented holders. This scheme reduces the thermal lensing caused by the radial temperature gradient and has been demonstrated in applications of Q-switched neodymium-doped yttrium aluminum garnet (Nd:YAG) [10] and Raman [11; 12] lasers. However, no detailed comparative research has yet been conducted on the temperature distributions and thermo-optic effects in laser rods between this scheme and the other side-pumping schemes under the same cooling boundary conditions.  
The current work is an extension of our previous work [8], with our prime motivation being to provide a numerical analysis method as an efficient design tool for compact and miniature side-pumped lasers, especially for segmented circular LD array side pumping lasers. In this paper, the temperature distributions and thermo-optic effects of laser rods in these three different side-pumping schemes are comparatively analyzed under the same cooling boundary conditions. The relative merits are discussed. The numerical results reveal that the segmented side-pumping scheme is an effective method to decrease thermal lensing and to miniaturize laser systems, especially in medium-power applications.