## Abstract

Optical breakdown has been generated by focusing YAG laser
radiation in the air. The laser radiation itself was scattered due
to laser-induced air optical breakdown. Angular distributions of
scattered radiation at 1064, 532, and 355 nm were
measured. Analysis of the distributions has been performed in terms
of Mie scattering. It has been assumed that scattering of laser
radiation is due mainly to highly ionized plasma balls in the initial
phase of air optical breakdown. The wavelength-dependent angular
distribution has been analyzed with two parameters. The mean radius
and the plasma frequency of the plasma balls have been determined by a
least-squares fit procedure. Observed wavelength-dependent angular
distributions are in good agreement with ones calculated by Mie
theory.

© 1998 Optical Society of America

Full Article |

PDF Article
### Equations (11)

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

(1)
$${I}_{\perp}\left(\mathrm{\theta},\mathrm{\lambda}\right)=\frac{{\mathrm{\lambda}}^{2}}{4{\mathrm{\pi}}^{2}{r}^{2}}|\sum _{l=1}^{\infty}{\left(-i\right)}^{l}\left[{}^{e}{B}_{l}\frac{{P}_{l}^{\left(1\right)}\left(cos\mathrm{\theta}\right)}{sin\mathrm{\theta}}{-}^{m}{B}_{l}{P}_{l}^{\left(1\right)\prime}\left(cos\mathrm{\theta}\right)sin\mathrm{\theta}\right]{|}^{2},$$
(2)
$${I}_{|\phantom{\rule{0.2em}{0ex}}|}\left(\mathrm{\theta},\mathrm{\lambda}\right)=\frac{{\mathrm{\lambda}}^{2}}{4{\mathrm{\pi}}^{2}{r}^{2}}|\sum _{l=1}^{\infty}{\left(-i\right)}^{l}\left[{}^{e}{B}_{l}{P}_{l}^{\left(1\right)\prime}\left(cos\mathrm{\theta}\right)sin\mathrm{\theta}{-}^{m}{B}_{l}\frac{{P}_{l}^{\left(1\right)}\left(cos\mathrm{\theta}\right)}{sin\mathrm{\theta}}\right]{|}^{2},$$
(3)
$${}^{e}{B}_{l}={i}^{l+1}\frac{\left(2l+1\right)}{l\left(l+1\right)}\frac{n{\mathrm{\Psi}}_{l}^{\prime}\left(q\right){\mathrm{\Psi}}_{l}\left(\mathit{nq}\right)-{\mathrm{\Psi}}_{l}\left(q\right){\mathrm{\Psi}}_{l}^{\prime}\left(\mathit{nq}\right)}{n{\mathrm{\zeta}}_{l}^{\prime}\left(q\right){\mathrm{\Psi}}_{l}\left(\mathit{nq}\right)-{\mathrm{\zeta}}_{l}\left(q\right){\mathrm{\Psi}}_{l}\left(\mathit{nq}\right)},$$
(4)
$${}^{m}{B}_{l}={i}^{l+1}\frac{2l+1}{l\left(l+1\right)}\frac{n{\mathrm{\Psi}}_{l}\left(q\right){\mathrm{\Psi}}_{l}^{\prime}\left(\mathit{nq}\right)-{\mathrm{\Psi}}_{l}^{\prime}\left(q\right){\mathrm{\Psi}}_{l}\left(\mathit{nq}\right)}{n{\mathrm{\zeta}}_{l}\left(q\right){\mathrm{\Psi}}_{l}^{\prime}\left(\mathit{nq}\right)-{\mathrm{\zeta}}_{l}^{\prime}\left(q\right){\mathrm{\Psi}}_{l}\left(\mathit{nq}\right)},$$
(5)
$$q=\frac{2\mathrm{\pi}}{\mathrm{\lambda}}a,\hspace{1em}{\mathrm{\Psi}}_{l}\left(q\right)=\sqrt{\frac{\mathrm{\pi}q}{2}}{J}_{l+1/2},\hspace{1em}{\mathrm{\zeta}}_{l}\left(q\right)=\sqrt{\frac{\mathrm{\pi}q}{2}}{H}_{l+1/2}^{\left(1\right)}\left(q\right),$$
(6)
$${n}^{2}=1-\frac{\mathrm{\omega}_{p}{}^{2}}{\mathrm{\omega}\left(\mathrm{\omega}-i\mathrm{\beta}\right)},$$
(7)
$$f\left(R\right)=Aexp\left[-\frac{{\left(R-{a}_{0}\right)}^{2}}{\mathrm{\Delta}{a}^{2}}\right],$$
(8)
$$y\left(\mathrm{\theta},\mathrm{\lambda}\right)={\int}_{0}^{\infty}{I}_{\mathrm{\alpha}}\left(R,\mathrm{\theta},\mathrm{\lambda}\right)f\left(R\right)\mathrm{d}R+\mathrm{\Delta}\left(\mathrm{\theta},\mathrm{\lambda}\right),$$
(9)
$${\mathrm{\delta}}_{i}=\mathrm{\Delta}\left(\mathrm{\theta},\mathrm{\lambda}\right)/y\left(\mathrm{\theta},\mathrm{\lambda}\right),$$
(10)
$$\sum _{i=1}^{M}\mathrm{\delta}_{i}{}^{2},$$
(11)
$$f=\frac{\mathit{nr}}{2{\left(n-1\right)}^{2}},$$