Fractional Fourier transform for incoherent one-dimensional off-axis Gaussian beams

Based on the Huygens-Fresnel principle,the analytical expression for the far-field divergence angle of one-dimensional off-axis Gaussian beams propagating in free space was derived using the integral transform technique to study the properties of the far-field divergence angle and the directionality.

Influence of turbulence on the coherent and incoherent combinations of off-axis Gaussian beams;

Starting from the Collins formula, the analytical equation for the off-axis Gaussian beam propagating through a paraxial ABCD optical system with hard-edged aperture is derived.

Starting from the Collins formula, the properties of the off-axis Gaussian beam (OAGB) propagating through a paraxial ABCD optical system with an aperture are studied in detail.

The closed-form expressions for the intensity of resulting beam for the coherent and incoherent combinations of non-paraxial off-axis Gaussian beams have been derived with some interesting special cases,such as the far-field expressions,on-axis intensity,paraxial approximation expressions for coherent and incoherent combinations of non-paraxial off-axis Gaussian beams.