Representation theory for vector electromagnetic beams

Abstract

A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a 3×2 mapping matrix and a 2-component Joneslike vector. The mapping matrix has one degree of freedom that can be described by the azimuthal angle of a fixed unit vector with respect to the wave vector. This degree of freedom allows us to find out such a beam solution in which every plane-wave component is specified by the same fixed unit vector I and has the same normalized Jones-like vector. The angle θ I between the fixed unit vector and the propagation axis acts as a parameter that describes the vectorial property of the beam. The impact of θ I is investigated on a beam of angular-spectrum field scalar that is independent of the azimuthal angle. The field vector in position space is calculated in the first-order approximation under the paraxial condition. A transverse effect is found that a beam of ellipticallypolarized angular spectrum is displaced from the center in the direction that is perpendicular to the plane formed by the fixed unit vector and the propagation axis. The expression of the transverse displacement is obtained. Its paraxial approximation is also given.

Improved theory for the polarization-dependent transverse shift of a paraxial light beam in free space

“…However, a similar effect may take place with freely propagating optical fields (in particular, upon tight focusing of a perturbed Gaussian beam [11]). Then it cannot be attributed to a certain beam section and relates to the whole length of the beam [14], i.e. is non-local.…”

“…This assertion evidently contradicts the known fact that the beam CG propagates along the geometric-optics trajectory, which is a straight line in the free space after the focusing lens. In fact, exhaustive description of the beam behaviour in this situation must rely on non-paraxial models recently developed basing on the plane-wave expansion of the light field [14,16]. However, following Ref.…”

Polarization-dependent transformation of a paraxial beam upon reflection and refraction: A real-space approach

“…In particular, the developed approach promotes better understanding of some features of the models and approximations usually employed in the beam shift theories [4][5][6][7][8][9][10][11]. One can easily verify that the paraxial beam model of Eqs.…”

“…To demonstrate equivalence of the presented approach and the previously developed models [4][5][6][7][8][9][10], let us determine the lateral shift of the refracted beam described by Eqs. (25), (29), and (31).…”

“…[1,2]). The most impressive and intensively studied manifestation is associated with lateral (out of the incidence plane) shifts of reflected and refracted beams occurring when a circularly polarized beam falls onto a plane boundary between two homogeneous media (Imbert-Fedorov shift) [3][4][5][6][7][8][9][10][11].…”