## Exact analytical expansion of an off-axis Gaussian laser beam using the translation theorems for the vector spherical harmonics |

Applied Optics, Vol. 50, Issue 7, pp. 1023-1033 (2011)

http://dx.doi.org/10.1364/AO.50.001023

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### Abstract

The interaction of a Gaussian laser beam with a particle that is located off axis is a fundamental problem encountered across many scientific fields, including biological physics, chemistry, and medicine. For spherical geometries, generalized Lorenz–Mie theory affords a solution of Maxwell’s equations for the scattering from such a particle. The solution can be obtained by expanding the laser fields in terms of vector spherical harmonics (VSHs). However, the computation of the VSH expansion coefficients for off-axis beams has proven challenging. In the present study, we provide a very viable, theoretical framework to efficiently compute the sought-after expansion coefficients with high numerical accuracy. We use the existing theory for the expansion of an on-axis laser beam and employ Cruzan’s translation theorems [
Q. Appl. Math.
20, 33 (1962)QAMAAY0033-569X] for the VSHs to obtain a description for more general off-axis beams. The expansion coefficients for the off-axis laser beam are presented in an analytical form in terms of an infinite series over the underlying translation coefficients. A direct comparison of the electromagnetic fields of such a beam expansion with the original laser fields and with results obtained using numerical quadratures shows excellent agreement (relative errors are on the order of

© 2011 Optical Society of America

**OCIS Codes**

(140.3430) Lasers and laser optics : Laser theory

(140.7010) Lasers and laser optics : Laser trapping

(290.4020) Scattering : Mie theory

(140.3295) Lasers and laser optics : Laser beam characterization

**ToC Category:**

Lasers and Laser Optics

**History**

Original Manuscript: October 11, 2010

Revised Manuscript: December 21, 2010

Manuscript Accepted: December 21, 2010

Published: February 25, 2011

**Virtual Issues**

Vol. 6, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Lars Boyde, Kevin J. Chalut, and Jochen Guck, "Exact analytical expansion of an off-axis Gaussian laser beam using the translation theorems for the vector spherical harmonics," Appl. Opt. **50**, 1023-1033 (2011)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-7-1023

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