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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 7 — Mar. 1, 2011
  • pp: 1023–1033

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

Lars Boyde, Kevin J. Chalut, and Jochen Guck  »View Author Affiliations

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

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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 10 3 ). In practice, the analytical approach presented in this study has numerous applications, reaching from multiparticle scattering problems in atmospheric physics and climatology to optical trapping, sorting, and sizing techniques.

© 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

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

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)

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