Vector analysis of the interference of paired coplanar beams with linear or circular polarization

In this work, using a focusing formalism based on Richards–Wolf theory, the multi-beam interference of two and four light beams with linear or circular polarization with different orthogonality and orientation of the polarization vector is numerically studied. The possibility of forming light fields with a periodic polarization structure is demonstrated. In particular, it is established that when focusing four beams equidistant from the optical axis with changing linear polarization orientation, which mimics a change in the polarization vector of a single radially or azimuthally polarized beam, periodic light fields are formed. The polarization distribution of such fields is actually a set of polarization singularities corresponding to radially and azimuthally polarized beams. The proposed approach does not require the manufacture of complex subwavelength gratings, grating-based elements, or modal superposition of light fields with the aid of diffractive optical elements or spatial light modulators. The generated light fields make it possible to significantly speed up the process of laser processing of light-sensitive thin-film materials aimed at creating arrays of various ordered nano- and microstructures.