title: Exact analytical expansion of an off-axis Gaussian laser beam using the translation theorems for the vector spherical harmonics.
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)] 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.
authors.affiliation: Sector for Biological and Soft Systems, Department of Physics, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, UK. lb339@cam.ac.uk
authors.forename: Lars
authors.initials: L
authors.lastname: Boyde
authors.forename: Kevin J
authors.initials: KJ
authors.lastname: Chalut
authors.forename: Jochen
authors.initials: J
authors.lastname: Guck
mesh_terms: D007834:Lasers; D008962:Models, Theoretical; D016011:Normal Distribution