Propagation properties of partially coherent super-Lorentz–Gauss modes through a paraxial and real ABCD optical system

Based on the generalized Huygens–Fresnel integral and the Hermite–Gaussian expansion of a Lorentzian distribution, analytical expressions for the mutual coherence functions and the spatial complex degrees of coherence of the partially coherent super-Lorentz–Gauss (SLG) modes SLG01 and SLG11 through a paraxial and real ABCD optical system are derived. As a numerical example, the focusing of the partially coherent SLG01 and SLG11 modes is illustrated, and the influence of the spatial correlation length on the normalized intensity distributions and the spatial complex degrees of coherence is examined. The analytical formulae of the beam propagation factors of the partially coherent SLG01 and SLG11 modes are also presented. The effects of the beam parameter and the coherent parameter on the beam propagation factors are numerically investigated