## Abstract

A large-core multimode optical fiber of a few meters length is studied as
a 10-MW beam delivery system for a 15-ns pulsed Nd:YAG laser. A laser-to-fiber
vacuum coupler is used to inhibit air breakdown and reduce the probability of
dielectric breakdown on the fiber front surface. Laser-induced damage inside
the fiber core is observed behind the fiber front surface. An explanation
based on a high power density is illustrated by a ray trace. Damaged spots and
measurements of fiber output energies are reported for two laser beam
distributions: a flat-hat type and a near-Gaussian type. Experiments have been
performed to deliver a 100-pulse mean energy between 100 and 230 mJ without
catastrophic damage.

© 1997 Optical Society of America

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### Equations (22)

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(1)
$$E={\int}_{0}^{\mathrm{\Delta}t}P\mathrm{d}t={\int}_{0}^{\mathrm{\Delta}t}{\int}^{{S}_{0}}I\left({r}_{0},\mathrm{\theta},0\right)\mathrm{d}s\mathrm{d}t,$$
(2)
$$P={\int}^{{S}_{0}}I\left(r,\mathrm{\theta},0\right)\mathrm{d}s.$$
(3)
$${P}_{a}\left({r}_{0},0\right)={\int}_{0}^{2\mathrm{\pi}}{\int}_{{r}_{0}}^{{r}_{0}+{l}_{0}}I\left(r,\mathrm{\theta},0\right)r\mathrm{d}r\mathrm{d}\mathrm{\theta},$$
(4)
$${P}_{a}\left({r}_{0},0\right)=S\left({r}_{0},0\right)I\left({r}_{0},0\right).$$
(5)
$$I\left({r}_{0},0\right)=\frac{{P}_{a}\left({r}_{0},0\right)}{S\left({r}_{0},0\right)}.$$
(6)
$$I\left(r,z\right)=\frac{{P}_{a}\left({r}_{0},0\right)}{S\left(r,z\right)}.$$
(7)
$$\frac{I\left(r,z\right)}{I\left({r}_{0},0\right)}=\frac{S\left({r}_{0},0\right)}{S\left(r,z\right)}$$
(8)
$$I\left(r,\mathrm{\theta},0\right)={I}_{0}.$$
(9)
$$\frac{{P}_{a}\left({r}_{0}\right)}{P}=\frac{2{l}_{0}}{R_{0}{}^{2}}{r}_{0}.$$
(10)
$$\frac{{P}_{a}\mathrm{Max}}{P}=\frac{{P}_{a}\left({R}_{0}\right)}{P}=2\frac{{l}_{0}}{{R}_{0}},{l}_{0}\ll {r}_{0}.$$
(11)
$$\frac{I\left(0;{n}_{1}d\right)}{I\left({R}_{0},0\right)}=\frac{S\left({R}_{0},0\right)}{S\left(0;{n}_{1}d\right)}$$
(12)
$$\frac{I\left(0;{n}_{1}d\right)}{I\left({R}_{0},0\right)}=\frac{\mathrm{\pi}\left[R_{0}{}^{2}-{\left({R}_{0}-{l}_{0}\right)}^{2}\right]}{\mathrm{\pi}l_{0}{}^{2}}\approx 2\frac{{R}_{0}}{{l}_{0}},{l}_{0}\ll {R}_{0}.$$
(13)
$$I\left({r}_{0},\mathrm{\theta}\right)={I}_{M}\left(1-\frac{r_{0}{}^{2}}{R_{0}{}^{2}}\right).$$
(14)
$$\frac{{P}_{a}\left({r}_{0}\right)}{P}=\frac{4{l}_{0}{r}_{0}}{R_{0}{}^{2}}\left(1-\frac{r_{0}{}^{2}}{R_{0}{}^{2}}\right).$$
(15)
$$\frac{{P}_{a}\mathrm{Max}}{P}=\frac{{P}_{a}\left({R}_{0}/\sqrt{3}\right)}{P}=\frac{8}{3\times \sqrt{3}}\frac{{l}_{0}}{{R}_{0}}.$$
(16)
$$\frac{I\left(0;2.48{n}_{1}d\right)}{I\left({R}_{0}/\sqrt{3};0\right)}=\frac{S\left({R}_{0}/\sqrt{3};0\right)}{S\left(0;2.48{n}_{1}d\right)}.$$
(17)
$$\frac{I\left(0;2.48{n}_{1}d\right)}{I\left({R}_{0}/\sqrt{3},0\right)}=\frac{2}{\sqrt{3}}\frac{{R}_{0}}{{l}_{0}}.$$
(18)
$$P_{a}{}^{\mathrm{Max}}\mathrm{paraboloid}={P}_{a}\left({R}_{0}/\sqrt{3}\right),$$
(19)
$$P_{a}{}^{\mathrm{Max}}\mathrm{paraboloid}=\frac{4}{3\sqrt{3}}\mathrm{\pi}{l}_{0}{I}_{M}{R}_{0},$$
(20)
$$P_{a}{}^{\mathrm{Max}}\mathrm{flat-hat}={P}_{a}\left({R}_{0}\right)=2\mathrm{\pi}{l}_{0}{I}_{0}{R}_{0}.$$
(21)
$$\frac{P_{a}{}^{\mathrm{Max}}\mathrm{paraboloid}}{P_{a}{}^{\mathrm{Max}}\mathrm{flat-hat}}=\frac{4}{3\times \sqrt{3}}\approx 0.77.$$
(22)
$$\frac{I\left(0;2.48{n}_{1}d\right)}{I\left(0;{n}_{1}d\right)}=\frac{4}{3\times \sqrt{3}}\times \frac{1}{\sqrt{3}}\approx 0.44.$$