Scattering is one of the simplest light mater interactions possible. For spherical particles, this process can be described using the Lorenz-Mie theory, which makes use of vector spherical harmonic solutions of Maxwell’s equations to represent the fields involved. Using these solutions it is possible to describe the light field scattered from microscopic spherical particles and thus represent the field around a scattering object as a function of the incident fields. These solutions also allow us to determine the optical momentum transfer to the scattering object. This can be calculated using Maxwell stress tensor. Here, we use this approach to calculate the quadratic relationship between the incident field and the optical forces acting on the scattering objects. This relationship defines also a set of orthogonal optical eigenmodes, which delivers a natural basis to describe momentum transfer in light-matter interactions. Using this natural description of the momentum transfer it is possible to define, for each numerical aperture, particle size or geometry the optimal trapping beam in 1, 2 or 3 dimensions. We present a study as a function of the particle parameter and conclude on the maximum achievable trapping stiffness enhancement factor as a function of these parameters.
Michael Mazilu, "Optimal trapping beam for spherical micro-particles (Conference Presentation)," Proc. SPIE 10347, Optical Trapping and Optical Micromanipulation XIV, 103470M (Presented at SPIE Nanoscience + Engineering: August 06, 2017; Published: 19 September 2017); https://doi.org/10.1117/12.2271741.5581158750001.
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