Exact theory of optical forces of mie scatterers exposed to high numerical aperture beams examined with 3D photonic force measurements - art. no. 648309
Antonio A R Neves, Adriana Fontes, Wendel L Moreira, Andre A de Thomaz, Diogo B de Almelda, Luiz C Barbosa, Carlos L Cesar
One very important contribution of the Optical Tweezers technique is its ability to extract the missing mechanical measurements in the world of microorganisms and cells that could be correlated to biochemical information. A microsphere displacement is the preferential force transducer for this kind of measurement. However, the typical conditions used in Optical Tweezers with very high numerical aperture beams and microspheres with diameters up to ten wavelengths, requires a full vectorial description of the incident beam in partial waves with the origin of coordinate system at the center of the microsphere and not at the focus of the beam. Using the Angular Spectrum Representation of the incident beam and an analytical expression for integrals involving associated Legendre Polynomials, Bessel functions and plane waves we have been able to obtain a closed expression, without any approximation, for the beam shape coefficients of any orthogonally incident beam. The theoretical prediction of the theory agrees well with the experimental results performed on a 3D positioned dual trap in an upright standard optical microscope, thus obtaining the whole optical force curves as a function of the microsphere center for different wavelengths.