Wigner distribution function of the zero-order Bessel beam and superimposed zero-order Bessel beams

Abstract

We apply the Wigner function to analyze Bessel beams, a special class of propagating waves with properties that have been found useful in optical trapping and materials processing. In this paper, the analytical expressions of the Wigner distribution for the cases of a zero-order Bessel beam and superimposed zero-order Bessel beams are computed. Marginals are obtained from the Wigner distribution functions. Scalar optics and signal analysis are then used to interpret the resulting equations.