## Abstract

There has been an interest to understand the trapping performance produced by a laser beam with a complex wavefront structure because the current methods for calculating trapping force
ignore the effect of diffraction by a vectorial electromagnetic wave. In this letter, we present a method for determining radiation trapping force on a micro-particle, based on the
vectorial diffraction theory and the Maxwell stress tensor approach. This exact method enables one to deal with not only complex apodization, phase, and polarization structures of
trapping laser beams but also the effect of spherical aberration present in the trapping system.

© 2004 Optical Society of America

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### Equations (3)

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(1)
$${\mathbf{E}}_{2}\left({\mathbf{r}}_{p},-d\right)=-\frac{i{k}_{1}}{2\pi}\underset{{\Omega}_{1}}{\iint}\mathbf{c}({\varphi}_{1},{\varphi}_{2},\theta )\mathrm{exp}\left\{i{k}_{0}\left[{r}_{p}\kappa +\Psi \left({\varphi}_{1},{\varphi}_{2},-d\right)\right]\right\}\mathrm{sin}{\varphi}_{1}d{\varphi}_{1}d\theta $$
(2)
$${\mathbf{H}}_{2}\left({\mathbf{r}}_{p},-d\right)=-\frac{i{k}_{1}}{2\pi}\underset{{\Omega}_{1}}{\iint}\mathbf{d}({\varphi}_{1},{\varphi}_{2},\theta )\mathrm{exp}\left\{i{k}_{0}\left[{r}_{p}\kappa +\Psi \left({\varphi}_{1},{\varphi}_{2},-d\right)\right]\right\}\mathrm{sin}{\varphi}_{1}d{\varphi}_{1}d\theta .$$
(3)
$$\u3008\mathbf{F}\u3009=\frac{1}{4\pi}\underset{0}{\overset{2\pi}{\int}}\underset{0}{\overset{\pi}{\int}}\u3008\left({\epsilon}_{2}{E}_{r}\mathbf{E}+{H}_{r}\mathbf{H}-\frac{1}{2}\left({\epsilon}_{2}{E}^{2}+{H}^{2}\right)\hat{r}\right)\u3009{r}^{2}\mathrm{sin}\varphi d\varphi d\theta ,$$