Statistical properties of circular and rectangular multi-sinc Schell-model beams propagating in uniaxial crystals

With the extended Huygens-Fresnel principle, we derive the expressions for the spectral intensity, coherence, and effective beam width of circular and rectangular multi-sinc Schell-model (MSSM) beams propagating through uniaxial crystals. Numerical simulations are employed to extensively explore how beam and crystal parameters modulate the optical field. The results reveal that the propagating field exhibits multiple ring-shaped and array-like intensity distributions, with adjustable features such as the number of concentric rings, central brightness, array dimensions, and the morphology and diversity of sub-beams. Additionally, the spectral coherence displays an oscillatory distribution that evolves into a Gaussian distribution as the transmission distance increases. The anisotropy of uniaxial crystals not only influences the morphology of intensity distribution but also affects the evolution rate of coherence and the expansion rate of effective beam width. Our work contributes to optimizing beam propagation through uniaxial crystals, potentially benefiting precision optical systems in laser technology.