Quasi-Gaussian electromagnetic beams

Abstract

A class of Maxwellian beams, which is an exact solution of the vector wave equation (Helmholtz equation) and Maxwell's equations, is introduced. The solution, termed a quasi-Gaussian electromagnetic (EM) beam, is formed from a superposition of sources and sinks with complex coordinates, and is characterized by an arbitrary waist ${w}_{0}$ and a diffraction convergence length known as the Rayleigh range ${z}_{R}$. An attractive feature of this beam is the description of strongly focused (or strongly divergent) EM-optical wave fields for $k{w}_{0}\ensuremath{\le}1$, where $k$ is the wave number. A vector wave analysis is developed to determine and compute the spatial Cartesian components of the electric and magnetic fields (valid in the near field and the far field) stemming from Maxwell's vector equations and the Lorenz gauge condition, with particular emphasis on the parameter $k{w}_{0}$ and the polarization states of the vector potentials used to derive the EM field's components. The results are potentially useful in the study of the axial and/or arbitrary wave scattering, radiation force, and torque in lasers operating with strongly focused (or strongly divergent) beams for particle manipulation in optical tweezers and imaging applications.