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Several models have been used to calculate optical forces since the beginning of optical trapping in the 1970´s to the Optical Tweezers (OT) in 1986 and are still under discussion these days. These models range from ray tracing geometrical optics to full electromagnetic Maxwell stress tensor formalisms, for very small particles in the Rayleigh regimen to tens of micron size particles in the Mie regime, where Mie resonances also appear. There is also a large effort to distinguish gradient vs scattering forces, which are clearly distinguished the geometrical optics frame, by reflected vs refracted beams, but not so easily distinguished in the full electromagnetic formalism. Moreover, Mie formalism was developed for an incident plane wave, which is far from the high numerical aperture (NA) beams used in OT. Even though there are models for high NA axial beams but most optical tweezers systems today use several OT points with inclined beams. Furthermore, the development of Bessel beams and other beams, also require a much more general calculation of the optical forces, as well as a theory for the forces in waveguides and photonic bandgap fibers in which is impossible to speak in terms of ray optics. One of the main difficult to calculate the optical forces in all these systems is the vector spherical wave decomposition of the incident beam. We develop a very general theory to perform this expansion for any beam which allowed us to calculate the forces for any beam and any particle size, and show a criteria to distinguish gradient from scattering forces, and the role of the Mie resonances in these cases. Dependence of the forces on the size of the particles is an important result for the development of optical chromatography. Experimental results in suspended microspheres allow us to compare the results with theory.
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