ABSTRACT

When non-paraxial light fields with different polarization states propagate in space, local areas can appear in their cross-sections, where the flux of light energy has a reversed direction, i.e. the longitudinal component of the Poynting vector in such areas has a negative value. Earlier, reversed energy flux in light fields was investigated in References [6, 362–372]. It has been shown in Reference [6] that when a linearly polarized plane wave is focused by an aplanatic system, in the first dark ring of the intensity distribution in the focal plane there is an area where the flux of light energy is directed in the opposite direction to the propagation direction of the incident plane wave. For a superposition of two mth-order Bessel beams with tranverse electric (TE) and transverse magnetic (TM) polarizations, the possibility of a negative value of the longitudinal component of the Poynting vector on the optical axis has been shown theoretically [362]. The practically realizable case (focusing by an aplanatic system) has been considered in Reference [364] and it has been shown both theoretically and numerically that when a Laguerre–Gaussian mode of the order (0, m) = (0, 2) with left circular polarization (σ = –1) is focused, then on the optical axis in the focus there are negative values of the longitudinal component of the Poynting vector. Strongly divergent vector spherical vortex beams, which are the exact solutions of the Maxwell’s equations, were considered in Reference [367]. In Reference [363], a superposition is studied of two arbitrary light fields with the different axial components of the wave vector. It has been shown that there are local areas in such light fields where the longitudinal component of the force acting on a microparticle is directed opposite to the wave vector of the light beam. In Reference [368], an optical spin torque induced by vector Bessel beams on a light-absorptive sphere of arbitrary size was calculated. It is shown that at different polarization states the sphere can rotate in opposite directions. Reverse flux on the optical axis in the focus of a vortex metalens is numerically shown in Reference [369]. The reversed propagation of energy in a vectorial Bessel beam with a fractional topological charge has been numerically shown in Reference [370]. Actually, such a light beam is a superposition of a countable number of the conventional Bessel modes. It was shown in Reference [371] that the axial component of linear momentum density flux can be negative in counterpropagating non-diffracting vortex Bessel beams. Expressions for the Poynting vector density for the vectorial X-beams were theoretically obtained in Reference [372] and the necessary conditions for the reversed energy flux were derived. In Reference [365], the reversed flux of energy was numerically shown for a non-paraxial accelerating 2D Airy beam. In Reference [366], a local wave vector is 246theoretically studied and conditions are considered that must be fulfilled for a light field so that it had locally backward propagation (i.e. the reversed flux of energy).