Vector beams in free space

Abstract

Introduction Higher-order modes of optical beams have been the subject of many studies over the past 20 years [1, 2]. Because laser resonators deliver in principle quite complex spatial patterns, spatial modes of beams were studied intensively when lasers were first developed [3]. Beams in higher-order spatial modes are solutions of the paraxial wave equation, with Hermite-Gauss and Laguerre-Gauss beams being the most important families of beams. These are solutions of the wave equation in Cartesian and cylindrical coordinates, respectively. The latter beams have been at the heart of a revival of research on higher-order modes due to the orbital angular momentum that they carry [4]. They have also received much attention due to the phase singularities present in their transverse amplitude [5]. Higher-order modes have stimulated much research in the application of forces and torques to objects in optical tweezers [1, 2]. Their usefulness has carried higher-order spatial modes further into new paths, in studies with non-classical sources of light and applications in quantum information [6]. The beams mentioned above are scalar solutions of the wave equation and thus independent of the polarization of the light. Vector beams are formed by the non-separable combinations of spatial and polarization modes. This enhanced modal space produces an interesting set of beams that offer new effects and applications. The origin of these beams is not recent either, as the possibility of combining higher-order spatial modes and polarization started with those early studies of modes as well.