Super Lorentz-Gauss modes and their paraxial propagation properties.

An orthonormal family of super Lorentz-Gauss (SLG) modes is proposed to describe the highly divergent higher-order modes. The first-order and the second-order SLG modes SLG(01) and SLG(11) are illustrated as examples. Analytical propagation formulas of the SLG(01) and SLG(11) modes through a paraxial ABCD optical system are derived, and analytical beam propagation factors of the SLG(01) and SLG(11) modes are presented. The paraxial propagation properties of the SLG(01) and SLG(11) modes in free space are also compared with those of the corresponding Hermite-Gaussian (HG) HG(01) and HG(11) modes, respectively. This research indicates that SLG modes are more appropriate than HG modes to describe the highly divergent higher-order modes.