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

Abstract

Spatial distribution of longitudinal field component of circularly polarised optical beam depends on the polarization handedness, which causes a lateral shift of "centre of gravity" of the beam when its polarization toggles. We present generalised theory of this effect, which demonstrates relation of the latter with angular irradiance moments of the beam. The theory is applicable to arbitrary paraxial beams and shows that the lateral shift is the same for the all cross sections of the beam.

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

“…(13) would provide the second-order corrections and are thus neglected in the derivatives in Eqs. (19) and (20).…”

“…(19) and (20) must have contained the complex amplitude derivatives taken at points of the boundary, i.e., with corrections for the propagation distances between the reference plane and the boundary, see Eq. (13).…”

“…which, together with (15)- (20), yield four equations to determine the four unknowns u R X,Y (x R ,y) and u T X,Y (x T ,y) for given complex amplitudes of the incident beam u I X,Y (x I ,y). Note that in Eqs.…”

“…(5) and (6), corresponding contribution proportional to |E z | 2 + |H z | 2 ∼ γ 2 should be discarded in the first-order paraxial approximation [15,17]. But the very existence of the components (11), that explicitly change forms with switching the circular polarization sign, qualitatively affirms that polarization influences the beam spatial characteristics [19,20]. In fact, the longitudinal components, Eqs.…”

Giant spin hall effect of light in an exotic optical system

“…From another view point one can say, if light propagates in one particular direction, energy flow is in that direction only, but if due to some modification in the system some part of energy is flowing in the transverse direction (to propagation), that is associated with shift of beam in that transverse direction [11][12] [13] . Now, transverse component of Poynting vector arises due to the presence of longitudinal component of Electric and Magnetic field ( and ) which justifies our use of the three dimensional Jones matrix.…”