Integral localized approximation description of ordinary Bessel beams and application to optical trapping forces.

Leonardo A Ambrosio,Hugo E Hernández-Figueroa

doi:10.1364/boe.2.001893

Leonardo A Ambrosio, Hugo E Hernández-Figueroa

Open Access

https://doi.org/10.1364/boe.2.001893

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Abstract

Ordinary Bessel beams are described in terms of the generalized Lorenz-Mie theory (GLMT) by adopting, for what is to our knowledge the first time in the literature, the integral localized approximation for computing their beam shape coefficients (BSCs) in the expansion of the electromagnetic fields. Numerical results reveal that the beam shape coefficients calculated in this way can adequately describe a zero-order Bessel beam with insignificant difference when compared to other relative time-consuming methods involving numerical integration over the spherical coordinates of the GLMT coordinate system, or quadratures. We show that this fast and efficient new numerical description of zero-order Bessel beams can be used with advantage, for example, in the analysis of optical forces in optical trapping systems for arbitrary optical regimes.

Highlights

The generalized Lorenz-Mie theory (GLMT) is an extension of the Lorenz-Mie theory [1] for describing the electromagnetic field components of an arbitrary laser beam in terms of spherical harmonic functions [2,3], the coefficients of which being called the beam shape coefficients (BSCs), responsible for correctly modeling the intensity profile of the beam [4]
Regardless of the scheme adopted for evaluating the BSCs, since the development of the GLMT plenty of applications have been benefited by this theoretical methodology
As we have shown that the ILA can furnish the values of the most significant BSCs with great accuracy, we turn our attention to the most outstanding advantage of using the integral localized approximation, viz., the computation time of these coefficients

Summary

Introduction

The generalized Lorenz-Mie theory (GLMT) is an extension of the Lorenz-Mie theory [1] for describing the electromagnetic field components of an arbitrary laser beam in terms of spherical harmonic functions [2,3], the coefficients of which being called the beam shape coefficients (BSCs), responsible for correctly modeling the intensity profile of the beam [4] Their numerical evaluation using quadratures [2] or finite series [4], can be a pretty time-consuming, lengthy or awkward task, first because of numerical integrations over the spherical coordinates of the adopted coordinate system, and second because of the inexistence of a single expression, in the latter case.

The GLMT and the ILA applied to ordinary Bessel beams

Numerical results for the BSC’s of an ordinary Bessel beam

Application to optical force calculations

Conclusions