## Abstract

The correct formula of the thermal focal length in a side-pumped Nd:YAG laser rod is discussed and confirmed by experimental results. It is shown that thermally induced stresses that cause a distortion of flatness occur within the region of the whole rod. The presented calculations are in agreement with the experimental observations. The results reveal that the temperature-dependent variation of the refractive index and the distortion caused by the thermally induced stresses constitute the major contributions to thermal lensing.

© 2007 Optical Society of America

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### Equations (42)

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(1)
{\text{Nd}}^{\text{3}+}
(2)
{\text{Nd}}^{\text{3}+}
(3)
$$f=\frac{KA}{{P}_{a}}{\left[\frac{1}{2}\text{\hspace{0.17em}}\frac{\mathrm{d}n}{\mathrm{d}T}+\alpha {C}_{r\text{,}\varphi}{{n}_{0}}^{3}+\frac{\alpha {r}_{0}\left({n}_{0}-1\right)}{L}\right]}^{-1}\text{,}$$
(7)
{C}_{r\mathrm{,}\varphi}
(8)
$$f=\frac{KA}{{P}_{a}}{\left(\frac{1}{2}\text{\hspace{0.17em}}\frac{\mathrm{d}n}{\mathrm{d}T}+\alpha {C}_{r\mathrm{,}\varphi}{{n}_{0}}^{3}+\alpha \left({n}_{0}-1\right)\right)}^{-1}\text{.}$$
(9)
{\text{Nd}}^{\text{3}+}
(10)
0.6328\text{\hspace{0.17em} \mu m}
(11)
{\mathrm{T}\mathrm{E}\mathrm{M}}_{00}
(12)
632.8\text{\hspace{0.17em} nm}
(13)
\text{105 \hspace{0.17em} mm}
(16)
102.02\text{\hspace{0.17em} mm}
(17)
{C}_{r\text{,}\varphi}
(18)
0.808\text{\hspace{0.17em} \mu m}
(19)
1.064\text{\hspace{0.17em} \mu m}
(20)
\text{0 .6328 \hspace{0.17em} \mu m}
(21)
\text{56 \hspace{0.17em} cm}
(22)
\text{4 \hspace{0.17em} cm}
(26)
50\text{\hspace{0.17em} cm}
(27)
\text{460 \hspace{0.17em} \mu s}
(28)
\text{10 \hspace{0.17em} Hz}
(29)
\text{256}\times \text{256}
(30)
\text{16}\times \text{16}
(31)
\text{1 .5 \hspace{0.17em} kHz}
(32)
\text{3 \hspace{0.17em} cm}
(33)
\text{0 .6328 \hspace{0.17em} \mu m}
(34)
{\mathrm{T}\mathrm{E}\mathrm{M}}_{00}
(35)
\text{632 .8 \hspace{0.17em} nm}
(36)
\text{100 \hspace{0.17em} Hz}
(37)
\text{0 .32 \hspace{0.17em} cm}
(38)
\text{2 \hspace{0.17em} cm}
(39)
\frac{\mathrm{d}n}{\mathrm{d}T}
(40)
\frac{\mathrm{d}n}{\mathrm{d}T}
(42)
-4.3\times {10}^{-6}