## Abstract

We built a 32-laser-diode-formed virtual point source pumping
system and achieved different pump light distributions from central intense to
central uniform and central depressed. Continuous wave
TEM_{00} operations of a Nd:YAG laser were performed under
these pump light distributions and their thermal lensing effects were
estimated. Results show that the operation under central depressed pump light
distribution has the lowest thermal lensing effect and can provide the highest
output power, which agrees with the results derived from the theoretical
calculation with the heat conduction equation.

© 1997 Optical Society of America

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### Equations (10)

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(1)
$${f}_{T}=\frac{1}{{A}_{T}{P}_{\mathrm{in}}},$$
(2)
$$n\left(r\right)={n}_{0}+\mathrm{\Delta}n{\left(r\right)}_{T},$$
(3)
$$n\left(r\right)={n}_{0}\left(1-\frac{2{r}^{2}}{{b}^{2}}\right),$$
(4)
$$f\cong \frac{{b}^{2}}{4{n}_{0}L},$$
(5)
$$T\left(r\right)={T}_{0}+{T}_{2}{r}^{2},$$
(6)
$$n\left(r\right)={n}_{0}+{T}_{2}{r}^{2}\left(\frac{\mathrm{d}n}{\mathrm{d}T}\right).$$
(7)
$${f}_{T}=-\frac{1}{2{\mathit{LT}}_{2}\left(\mathrm{d}n/\mathrm{d}T\right)}.$$
(8)
$$\left[\frac{{\partial}^{2}}{\partial {r}^{2}}+\frac{1}{r}\frac{\partial}{\partial r}+\frac{{\partial}^{2}}{\partial {z}^{2}}\right]T\left(r,z\right)+\frac{Q\left(r,z\right)}{k}=0,$$
(9)
$$Q\left(r\right)=\mathrm{\eta}\frac{{P}_{\mathrm{in}}}{\mathrm{\pi}r_{\mathrm{rod}}{}^{2}L}\mathrm{\rho}\left(r\right),$$
(10)
$$\mathrm{\rho}\left(r\right)=\frac{1}{C}\mathrm{\sum}_{n=0}^{N}{c}_{n}{r}^{n},$$