Circularly symmetric frozen waves: Vector approach for light scattering calculations

•A theoretical derivation of circularly symmetric generalized frozen waves for light scattering calculations is provided.•The beam shape coefficients are exactly derived, thus avoiding quadrature techniques or localized approximations.•The approach allows us to consider frozen waves in the generalized Lorenz-Mie theory beyond the paraxial approximation.•Examples are provided in terms of numerical calculation of radiation pressure force for specific frozen waves.•The beams may be incorporated in optical tweezers as structured light fields for simultaneous trapping at specific points.

This work introduces particular classes of vector wave fields for light scattering calculations, viz. structured light fields composed of specific superpositions of circularly symmetric Bessel beams of arbitrary order. Also known as generalized frozen waves, such beams carry all the non-diffracting properties of their constituents with the additional feature of allowing for an arbitrary design of the longitudinal intensity pattern along the surface of several cylinders of fixed radius, simultaneously. This feature makes the generalized frozen waves especially suitable for optical confinement and manipulation and atom guiding and selection. In the framework of the generalized Lorenz-Mie theory, the beam shape coefficients which describe such beams are evaluated in exact and analytic form, the resulting expressions being then applied in light scattering problems. Particular frozen waves are considered beyond the paraxial approximation, optical forces being calculated for specific dielectric Rayleigh particles.