Elegant super Lorentz–Gaussian beams

A novel kind of rectangular symmetric optical beams is represented. These beams are called as elegant super Lorentz–Gaussian (eSLG) beams. Closed-form expression of free-space propagation under paraxial limit is derived. Multiplied by a family of orthogonal polynomials, eSLG beams can be used as basis field for the newly introduced class. The analytical formulae of first two modes of the corresponding fields are given. Moreover, the comparison between these modes and elegant Hermite–Gaussian (eHG) modes has been analyzed and presented graphically.