Propagation of partially coherent modified Bessel-Gaussian beams beyond the paraxial approximation

By using the generalized Rayleigh diffraction integral formulation and theory of partially coherent light,the closed-form propagation expression for nonparaxial partially coherent modified Bessel-Gaussian beams of any order in free space is derived.The far-field expression of nonparaxial partially coherent modified Bessel-Gaussian beams and the propagation equation of paraxial partially coherent modified Bessel-Gaussian beams are presented as special cases of nonparaxial partially coherent modified Bessel-Gaussian beams.Numerical calculations and analysis show that,the f parameter plays an important role in deter- mining the beam nonparaxiality,in addition,the spectral degree of coherence also affects the nonparaxial behavior of partially coherent modified Bessel-Gaussian beams.