## Abstract

A simple technique for *in situ* measurements of pulsed Gaussian-beam spot sizes is reported. This technique is particularly useful for measurements on highly focused beam spots. It can also be used for absolute calibration of the threshold-energy fluences for pulsed-laser-induced effects. The thresholds for several effects in picosecond-laser-induced phase transformation on silicon-crystal surfaces are calibrated with this technique.

© 1982 Optical Society of America

Full Article |

PDF Article
### Equations (6)

Equations on this page are rendered with MathJax. Learn more.

(1)
$$I\left(r,t\right)={I}_{0}\phantom{\rule{0.2em}{0ex}}\text{exp}\left(-{r}^{2}/{\rho}^{2}\right)\phantom{\rule{0.2em}{0ex}}\text{exp}\left(-{t}^{2}/{\tau}^{2}\right),$$
(2)
$$E\left(r\right)={\displaystyle {\int}_{-\infty}^{\infty}\mathrm{d}\mathit{\text{tI}}\left(r,t\right)}={E}_{0}\phantom{\rule{0.2em}{0ex}}\text{exp}\left(-{r}^{2}/{\rho}^{2}\right),$$
(3)
$$E\left({r}_{a}\right)={E}_{0}\phantom{\rule{0.2em}{0ex}}\text{exp}\left(-{{r}_{a}}^{2}/{\rho}^{2}\right)={E}_{a},$$
(4)
$$E\left({r}_{c}\right)={E}_{0}\phantom{\rule{0.2em}{0ex}}\text{exp}\left(-{{r}_{c}}^{2}/{\rho}^{2}\right)={E}_{c}.$$
(5)
$${{r}_{a}}^{2}={\rho}^{2}\left(\text{ln}\phantom{\rule{0.2em}{0ex}}{E}_{0}-\text{ln}\phantom{\rule{0.2em}{0ex}}{E}_{a}\right),$$
(6)
$${{r}_{c}}^{2}={\rho}^{2}\left(\text{ln}\phantom{\rule{0.2em}{0ex}}{E}_{0}-\text{ln}\phantom{\rule{0.2em}{0ex}}{E}_{c}\right).$$