Singular beams with transverse electric and transverse magnetic fields

Abstract

We have obtained the solutions of the paraxial wave equation in free space and homogeneous media in the form of transverse electric (TE) and transverse magnetic (TM) fields with Laguerre-Gaussian (LG) and Hermite-Gaussian (HG) modulation functions. In contrast to the standard TE and TM beams we revealed that the axially symmetric field of LG mode beams have local elliptical polarization, while axial symmetry is totally broken down in the HG beams. The results obtained can be used for matching the fields inside the uniaxial crystal and free space.