Rectangular symmetrical mesa beams and their comparison with flattened Gaussian and multi-Gaussian beams

A two-component analytical model describing 1D, paraxial, rectangular symmetrical mesa beams of arbitrary fractional orders is proposed. Such beams possess a plane wavefront and flat-topped intensity profiles at their waists. It is shown that they are reasonably well matched with 1D flattened Gaussian and generalized multi-Gaussian beams described by more complicated models in the form of finite superpositions of an on-axis fundamental Gaussian mode mixed, respectively, either with on-axis, 1D, elegant Hermite-Gaussian modes of higher orders or with off-axis fundamental Gaussian modes. A procedure of exact optimization fitting, the main propagation characteristics and the modal content of all the above beams are considered in detail. The proposed model is shown to have the most compact and convenient mathematical description of the beams and their characteristics.