Generation of dark hollow beam by use of phase-only filtering

A simple but effective scheme to generate dark hollow beams is proposed by use of phase-only filtering and optical Fourier transform. A Gaussian beam of fundamental mode is modulated by a pre-designed phase mask, which is a piecewise modification of an axicon lens, and followed by a Fourier transform to generate an ideal dark hollow beam at the focal plane. This method has an advantage that the total energy of the beam is conserved under paraxial approximation. Numerical calculations are provided to show the validity of the proposed scheme.