Interplay between diffraction and the Pancharatnam-Berry phase in inhomogeneously twisted anisotropic media

Abstract

We discuss the propagation of an electromagnetic field in an inhomogeneously anisotropic material where the optic axis is rotated in the transverse plane but is invariant along the propagation direction. In such a configuration, the evolution of an electromagnetic wave packet is governed by the Pancharatnam-Berry phase (PBP), which is responsible for the appearance of an effective photonic potential. In a recent paper [ACS Photon. 3, 2249 (2016)] we demonstrated that the effective potential supports transverse confinement. Here we find the profile of the quasimodes and show that the photonic potential arises from the Kapitza effect of light. The theoretical results are confirmed by numerical simulations, accounting for the medium birefringence. Finally, we analyze in detail a configuration able to support nonleaky guided modes

Q-plate technology: a progress review [Invited]

“…If successful, this is one area in which the chances of getting into real-world applications are high. The recently demonstrated waveguiding principle based on geometrical phases [107,112,113] could soon be demonstrated in continuous systems and applications based on it are likely to emerge.…”

Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

“…Let us now focus on the case when the twisting angle is independent from the propagation coordinate , a problem studied in refs. [209, 210]. Above we stated that in this case there is no accumulated gradient index, thus no guiding.…”

Spin-optical solitons in liquid crystals

“…In the linear regime, these eigenwaves acquire an additional phase term ∆φ = ∆k z when propagating along z, yielding a polarization state transformation from, e.g., linear to elliptical, circular, elliptical to linear etc., with a beat length l b = 2π/∆k [56]. When reorientation of the symmetry axis occurs in the transverse plane (x, y) owing to the electric field distribution across the beam profile, the point dependent coupling between eigenwaves translates to a geometric phase as the latter depends on the spin evolution across the wavepacket, i.e., it is non-transitive [49]. The PB phase needs to be larger on beam axis (than in its outskirts) while monotonically accumulating retardation along z in order to balance out diffraction [47].…”

“…Most recent optical manifestations have been associated with dielectric anisotropy in 2D metasurfaces and birefringent crystals [41,[43][44][45], entailing several applications in photonics [46]. When the spin transformation is a pointwise function of the anisotropic distribution across the beam profile, the PB phase can alter the phasefront of a propagating wavepacket and yield transverse confinement, leading to novel waveguiding approaches which do not rely on total internal reflection [47][48][49]. Furthermore, in bulk anisotropic dielectrics, such as homogeneously aligned nematic liquid crystals, the modulation of the optic axis distribution can be nonlinearly induced through all-optical reorientation, as mentioned above.…”