## Abstract

A previously developed theoretical procedure for determination of
electromagnetic fields associated with the interaction of a
higher-order Gaussian beam with a homogeneous spherical particle is
used to investigate the effects of incident beam type on far-field
scattering. Far-field scattering patterns are calculated for
(0,0), (0,1), and (1,1) mode Hermite–Gaussian beams and
for the helix doughnut mode beam. The effects of incident beam type
on the angular distribution of far-field scattering, for both
on-sphere-center and off-sphere-center focusing, are
examined.

© 1998 Optical Society of America

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### Equations (4)

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(1)
$${\mathrm{\xi}}_{l}^{\left(1\right)}\left(\mathrm{\alpha}\tilde{r}\right)={\mathrm{\psi}}_{l}\left(\mathrm{\alpha}\tilde{r}\right)-i{\mathrm{\chi}}_{l}\left(\mathrm{\alpha}\tilde{r}\right)\Rightarrow {\left(-i\right)}^{\left(l+1\right)}exp\left(i\mathrm{\alpha}\tilde{r}\right),$$
(2)
$${\mathrm{\xi}}_{l}^{\left(1\right)}\prime \left(\mathrm{\alpha}\tilde{r}\right)={\mathrm{\psi}}_{l}\prime \left(\mathrm{\alpha}\tilde{r}\right)-i{\mathrm{\chi}}_{l}\prime \left(\mathrm{\alpha}\tilde{r}\right)\Rightarrow {\left(-i\right)}^{\left(l\right)}exp\left(i\mathrm{\alpha}\tilde{r}\right),$$
(3)
$${S}_{r}\left(\mathrm{\theta},\mathrm{\varphi}\right)=\underset{r\to \infty}{\mathrm{lim}}\frac{{r}^{2}\u3008\mathbf{S}{\u3009}_{r}}{\frac{c}{8\mathrm{\pi}}E_{0}{}^{2}\mathrm{\pi}{a}^{2}}=\underset{\tilde{r}\to \infty}{\mathrm{lim}}\frac{{\tilde{r}}^{2}}{\mathrm{\pi}}\mathrm{Real}\left[{E}_{\mathrm{\theta}}^{\left(s\right)}{H}_{\mathrm{\varphi}}^{\left(s\right)}*-{E}_{\mathrm{\varphi}}^{\left(s\right)}{H}_{\mathrm{\theta}}^{\left(s\right)}*\right].$$
(4)
$${S}_{r}\left(\mathrm{\varphi}\right)={\int}_{{\mathrm{\theta}}_{0}}^{\mathrm{\pi}}{S}_{r}\left(\mathrm{\theta},\mathrm{\varphi}\right)sin\left(\mathrm{\theta}\right)d\mathrm{\theta},$$