Exact partial wave expansion of optical beams with respect to arbitrary origin

Abstract

Using an analytical expression for an integral involving Bessel and Legendre functions, we succeed in obtaining the partial wave decomposition of a general optical beam at an arbitrary location relative to the origin. We also showed that solid angle integration will eliminate the radial dependence of the expansion coefficients. The beam shape coefficients obtained are given by an exact expression in terms of single or double integrals. These integrals can be evaluated numerically on a short time scale. We present the results for the case of a linear-polarized Gaussian beam.

Electromagnetic forces for an arbitrary optical trapping of a spherical dielectric

“…This distance is determined by finding the position where the axial force is zero by varying the beam axial position only. Afterwards we simulate the optical forces in the radial direction for different polarization, wavelength and microsphere sizes using the theory presented in Section 2, the numerical convergence is determined by the maximum angular momentum chosen in the expansion, o r k n = max [2]. Note that all force components are considered since as the beam focuses at the edge, the contribution z force component becomes more significant and reaches the same order of the x and y force components.…”

“…(3) of Ref. [2]) was fundamental for this development that dramatically simplifies the BSC calculation for an arbitrary translation. We remark that no assumption has been made for the size of the scatterer, thus making it adequate for the most general case of the Mie regime and readily applicable (in the case of optics).…”

“…The main effort in the last few years is to have a proper description of the incident EM fields in a highly focused system. This is treated in more detail in a recent publication [2], with a use of a special integral [3], in terms of partial wave expansion coefficients, or beam shape coefficients (BSC), and can be readily applied to Eq. (1).…”

“…[2] for the case of an incident linear x -polarized truncated TEM 00 Gaussian beam, by the expression: …”

“…The beam focus is generally no longer at the origin of the coordinate system, so all of the beam azimuthal symmetry is lost, this important fact is also taken into account. In this theory the electromagnetic field in an optical trap uses a paraxial Gaussian beam before the objective lens (fulfilling the sine condition) and applying the Angular Spectrum Representation which describes correctly the electromagnetic fields and polarization of a high numerical aperture (NA) objective [2]. …”