Partially coherent nonparaxial modified Bessel-Gauss beams

The concept of partially coherent nonparaxial modified Bessel-Gauss (MBG) beams is proposed. Based on the generalized Rayleigh-Sommerfeld diffraction integral, the analytical propagation equations of nonparaxial MBG beams in free space are derived and analysed, and some special cases are discussed. In particular, under the paraxial approximation our results reduce to the corresponding paraxial ones. Numerical calculation examples are given to illustrate the dependence of intensity and spectral degree of coherence on the beam order m, xi and f parameters, and to compare the difference between the paraxial and nonparaxial results.