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Analytical expressions of the elements of a cross spectral density matrix are derived to describe the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis. The intensity and degree of polarization for the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis are also presented. The evolution properties of the partially coherent Lorentz-Gauss beam are numerically demonstrated. The influences of the uniaxial crystal and coherence length on the propagation properties of the partially coherent Lorentz-Gauss beam in uniaxial crystals orthogonal to the x-axis are examined. The uniaxial crystal considered here has the property of the extraordinary refractive index being larger than the ordinary refractive index. The partially coherent Lorentz-Gauss beam in the direction along the x-axis spreads more rapidly than that in the direction along the y-axis. With increasing the ratio of the extraordinary refractive index to the ordinary refractive index, the spreading of the partially coherent Lorentz-Gauss beam increases in the direction along the x-axis, but decreases in the direction along the y-axis. Meanwhile, the degree of polarization in the edges of the long and short axes of the beam spot increases. With increasing the coherence length, the beam spot of the partially coherent Lorentz-Gauss beam uniformly becomes less, and the maximum degree of polarization in the edge of the beam spot decreases.

PROPAGATION PROPERTIES OF PARTIALLY COHERENT LORENTZ-GAUSS BEAMS IN UNIAXIAL CRYSTALS ORTHOGONAL TO THE X-AXIS