Degree of paraxiality of cylindrical vector partially coherent Laguerre-Gaussian beams

We derive the analytical expression for the degree of paraxiality of cylindrical vector (CV) partially coherent Laguerre-Gaussian (LG) beams based on the definition of the degree of paraxiality. Numerical results show that the degree of paraxiality of the CV partially coherent LG beams does not always increase with the increase of the initial beam waist, but oscillates when the initial beam waist and wavelength are comparable. The degree of paraxiality also depends on the beam orders and the initial coherence length of the CV partially coherent LG beams. Our results are useful for determining whether the CV partially coherent LG beams are paraxial or nonparaxial. It may be useful in some applications such as atomic trapping, tight focusing and micro-lithography.