Analytical description of on-axis zero-order continuous frozen waves in the generalized Lorenz–Mie theory. (February 2023) - Ambrosio, Leonardo André
Highlights: Continuous frozen waves are analytically described in the framework of the generalized Lorenz–Mie theory. In their simplest form, such waves are constructed from suitable continuous superpositions of zero-order Bessel beams. The beam shape coefficients are evaluated and described in terms of Beta and generalized hypergeometric functions. The analysis is restricted to the on-axis case. Examples of field reconstruction within the GLMT are provided for different polarizations and longitudinal intensity patterns. Abstract: 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 computation 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.