Comparative studies of properties of standard and elegant Laguerre–Gaussian beams

The properties of standard Laguerre–Gaussian beam (sLGB) and elegant Laguerre–Gaussian beam (eLGB) through the misaligned complex hard edge apertures (MCHEAs) are investigated. Analytical formulae for the far field distributions of sLGBs and eLGBs through the different hard edge apertures are derived based on the generalized Huygens–Fresnel diffraction integral equation. The propagation properties and beam qualities of sLGBs and eLGBs are studied comparatively. It is shown that the divergence angle of sLGBs with the low order modes is less than that of eLGBs. However, the energy distributions of eLGBs with the high order modes after through the multiple hard edged apertures are more convergent in comparison with sLGBs, and eLGBs have the better beam quality than sLGBs. The study results are useful for the propagations and applications of sLGBs and eLGBs through the complex optical systems.