Exact Partial Wave Expansion for an Arbitrary Optical Beams

Optical tweezers have become an important tool for biological manipulations and cell mechanical properties measurements [1]. These measurements use the displacement from equilibrium position of a microsphere as the force transducer. Therefore, the calibration procedure requires the use of good models for the optical force in microspheres. Geometrical optics has been used when the particle dimensions are much greater than the light wavelength, and Rayleigh scattering theory for the opposite. However, when the particles are of the same order of the wavelength these approximations are no longer valid. Mie resonances are typical of this size regime. Classical Mie scattering theory was developed for plane waves and cannot explain the measurements obtained using a focus beam as we have in optical tweezers. In this case, it is necessary to decompose the incident beam in plane waves relative to the center of the microsphere. As the beam focus is no longer at the origin of the coordinate system all the beam azimuthal symmetry is lost. This can be a complicated problem, especially when a full vectorial diffraction description of the electromagnetic fields and highly focused laser beams are required. All sorts of approximations and tricks have been used to proceed forward to obtain numerical results [2].