Beam propagation factor and the kurtosis parameter of flattened gaussian beams

Abstract

The characterization of flattened Gaussian beams is extended to cartesian coordinates. The representation and the propagation formula contain only even Hermite-Gauss modes. The beam propagation factor and the kurtosis parameter dependences of the beam order N have been evaluated using the mode coefficients of the representation. The flattened Gaussian beams could be classified into two types according to the evolution of the kurtosis parameter in the free space (apart from the case N = 0, the ordinary Gaussian beam for which the kurtosis is constant): (i) for N ≤, 3 they have either two maxima and one minimum, or two minima and one maximum; and (ii) for N > 3 they exhibit either a unique maximum or a unique minimum.