Zeroth-order continuous vector frozen waves for light scattering: exact multipole expansion in the generalized Lorenz–Mie theory

In this paper we theoretically investigate the exact beam shape coefficients (BSCs) of a specific and promising class of nondiffracting light waves for optical trapping and micro-manipulation known as continuous vector frozen waves (CVFWs). CVFWs are constructed from vector Bessel beams in terms of a continuous superposition (integral) over the longitudinal wavenumber, the final longitudinal intensity pattern being determined through the specification of a given spectrum S(kz). The incorporation of such highly confined and micro-structured fields into the theoretical framework of the generalized Lorenz–Mie theory (GLMT) is a first step toward the integration of such beams with optical tweezers systems as potential laser beams for the multiple manipulation of micro-particles and nano-particles along their optical axis and in multiple transverse planes. Linear, azimuthal, and radial polarizations are considered, the BSCs being calculated using three distinct approaches. The results extend and complete previous works on discrete frozen waves for light scattering problems with the aid of the GLMT.