Propagation properties of an orthogonal cosine-Gaussian Schell-model beam in uniaxial crystals orthogonal to the optical axis

Abstract

The analytical expressions for an orthogonal cosine-Gaussian Schell-model (OCGSM) beam propagating in uniaxial crystals orthogonal to the optical axis are derived. Based on the formulas derived, the propagation properties, such as the normalized spectral density, the spectral degree of coherence (SDOC), and the effective beam width of an OCGSM beam in uniaxial crystals are illustrated. Numerical results show that, by changing the beam mode order n and m, the OCGSM beam can split into two- or four-beamlet elliptical beams and keep invariant in uniaxial crystals during propagation, which is different from the conventional Gaussian Schell-model beam. The SDOC of the OCGSM beam will evolve into an elliptical shape and the effective beam width of the OCGSM beam will spread faster along the x direction than the y direction in uniaxial crystals. In addition, the significant influence of the beam mode order, the spatial coherence length and the ratio of the extraordinary refractive index to the ordinary refractive index of the uniaxial crystals on the evolution properties of an OCGSM beam is discussed in detail.