Circularly symmetric Hermite-Gaussian correlated Schell-model beam

We introduce a novel class of random stationary, scalar source for producing far field with ring-shaped intensity profile, named as circularly symmetric Hermite-Gaussian correlated Schell-model (CSHGCSM) source. The analytical expressions for the cross-spectral density (CSD) function of a CSHGCSM beam propagating in free space and in linear isotropic random media are derived, respectively. It is shown that the CSHGCSM beam exhibits a robust ring-shaped profile in far field, and three-dimensionally (3D) optical cage could be obtained when the CSHGCSM beam focused by a thin lens. The optical cage length is dependent on parameters of mode order n, transverse coherence width δ, focal length f, and beam wavelength λ. Furthermore, it is demonstrated that the CSHGCSM beam propagating in linear random media at small distance from the source exhibits annular profile, then converts into Gaussian beam as the propagation distance increases. There is a phenomenon of regenerative oscillation for the spectral degree of coherence (SDOC) of the CSHGCSM beam in the presence of random media.