Propagation of doughnut-shaped super-Gaussian beams, convolution theorem and Hankel transform

Abstract

The most direct and simple method to calculate analytically the propagation in the far field of a coherent beam with a rectangular symmetry and a super-Gaussian-like irradiance profile involves the use of the convolution theorem. In this paper we extend this method to a circularly symmetric beam, and hence from the Fourier transform to the zero-order Hankel transform. Then, we examine the more complex case of super-Gaussian-like beam irradiance shapes with an axial shadow, as those emitted by unstable resonators with diffraction output coupling or with a variable-reflectivity mirror. The analytical results obtained by approximating the super-Gaussian-like beam with a convolution function and applying the Hankel transform are in excellent agreement with those obtained by numerical simulations.

Acknowledgements

One of the authors (S. B.) acknowledges stimulating discussions with Professor S. Ruschin.