Analytical description of on-axis zero-order continuous frozen waves in the generalized Lorenz-Mie theory

This paper describes an analytical approach for the incorporation of a specific class of non-diffracting beams known as zero-order continuous frozen waves (FWs) within the context of the generalized Lorenz- Mie theory (GLMT). To do so, two main drawbacks observed in a previous work and related to the com-putation of the beam shape coefficients are resolved, viz., the determination of the Fourier coefficients of compositions of generalized Legendre functions and the exact solution to particular integrals involving Bessel functions, the latter being facilitated by the choice of an on-axis configuration. Examples are given for FWs with linear, circular and azimuth polarizations, together with field reconstructions in the GLMT. The approach here presented is important for the incorporation of continuous FWs as alternative laser beams and for the reliable calculation of their optical properties in the field of light scattering.(c) 2022 Elsevier Ltd. All rights reserved.