## Abstract

The use of the generalized Lorenz–Mie theory (GLMT) requires
knowledge of beam-shape coefficients (BSC’s) that describe the
beam illuminating a spherical scatterer. We theoretically
demonstrated that these BSC’s can be determined from an actual beam in
the laboratory. We demonstrate the effectiveness of our theoretical
proposal by determining BSC’s for a He–Ne laser beam focused to a
diameter of a few micrometers. Once these BSC’s are determined,
the electromagnetic fields of the illuminating beam may be
evaluated. By relying on the GLMT, we can also determine all
properties of the interaction between beam and scatterer, including
mechanical effects (radiation pressures and torques).

© 2001 Optical Society of America

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### Equations (5)

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(1)
$${S}_{z}=\mathrm{\u220a}\mathrm{Re}\sum _{n=1}^{\infty}\sum _{m=1}^{\infty}{a}_{\mathit{nm}}{g}_{n}{g}_{m}^{*},$$
(2)
$${a}_{\mathit{nm}}=\frac{1}{{k}^{2}{r}^{2}}{i}^{m-n}\left(n+\frac{1}{2}\right)\left(m+\frac{1}{2}\right)\left({\mathrm{\u220a}}^{n+m+1}{D}_{\mathit{nm}}^{1}+i{\mathrm{\u220a}}^{n+m}{D}_{\mathit{nm}}^{2}\right),$$
(3)
$${D}_{\mathit{nm}}^{1}=\frac{\mathrm{d}r{\mathrm{\Psi}}_{n}^{1}\left(\mathit{kr}\right)}{\mathrm{d}r}\frac{\mathrm{d}r{\mathrm{\Psi}}_{m}^{1}\left(\mathit{kr}\right)}{\mathrm{d}r}+{k}^{2}{r}^{2}{\mathrm{\Psi}}_{n}^{1}\left(\mathit{kr}\right){\mathrm{\Psi}}_{m}^{1}\left(\mathit{kr}\right),$$
(4)
$${D}_{\mathit{nm}}^{2}=\mathit{kr}\left[\frac{\mathrm{d}r{\mathrm{\Psi}}_{n}^{1}\left(\mathit{kr}\right)}{\mathrm{d}r}{\mathrm{\Psi}}_{m}^{1}\left(\mathit{kr}\right)-\frac{\mathrm{d}r{\mathrm{\Psi}}_{m}^{1}\left(\mathit{kr}\right)}{\mathrm{d}r}{\mathrm{\Psi}}_{n}^{1}\left(\mathit{kr}\right)\right],$$
(5)
$$\sqrt{\frac{{\mathrm{\u220a}}_{0}}{{\mathrm{\mu}}_{0}}}\frac{|{E}_{0}{|}^{2}}{2}=1,$$