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 ). 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 AmericaFull Article | PDF Article
James A. Lock and Gérard Gouesbet
J. Opt. Soc. Am. A 11(9) 2503-2515 (1994)
Gérard Gouesbet and James A. Lock
J. Opt. Soc. Am. A 11(9) 2516-2525 (1994)
J. Opt. Soc. Am. A 16(7) 1641-1650 (1999)