Geometric Phase in Optics: From Wavefront Manipulation to Waveguiding

Abstract

Geometric phase is a unifying and central concept in physics, including optics. As a matter of fact, optics played a pivotal role from the inception of this new paradigm, as some of the first experimental demonstrations have been carried out in optics. A specific type of geometric phase was first introduced by Pancharatnam while investigating interference effects between different polarizations. This specific type of geometric phase, nowadays called the Pancharatnam–Berry phase, is related to the variation of light polarization, encompassing exotic properties when compared with the dynamic phase associated with the optical path. The most widespread manifestation of the Pancharatnam–Berry phase occurs in the presence of a twisted anisotropic material, yielding a point‐wise phase modulation proportional to the local rotation angle of the material. Here the basic mechanism behind the Pancharatnam–Berry phase is discussed. The various applications of this relatively original concept in photonics are then reviewed, presenting both the most important results and manufactured devices reported in literature. The interplay between geometric phase and diffraction occurring in bulk structures is discussed in detail. In the latter case it is shown how geometric phase can be harnessed to generate a new kind of optical waveguide without the necessity of any index gradient.

3D Engineering of Orbital Angular Momentum Beams via Liquid‐Crystal Geometric Phase

“…When the quadratic phase of a Fresnel lens π r 2 /λ f ( r 2 = x 2 + y 2 , f denoting the focal length) is encoded with the same Dammann function, the so‐called DZP is formed to generate M equal‐energy focal points coaxially (see more details about Dammann encoding method in Note S1, Supporting Information). [ 36,37 ] Here, we imprint two binary and two continuous phase patterns of a 2D‐DG, a DZP, a q‐plate [ 38 ] and a PB‐lens [ 39 ] into a single LC GPOE, as shown in Figure a. Its LC orientation distribution is expressed as $$\begin{eqnarray} \alpha &=& {\alpha _{{\rm{2D - DG}}}} + {\alpha _{{\rm{DZP}}}} + {\alpha _{q{\rm{ - plate}}}} + {\alpha _{{\rm{PB - lens}}}}\nonumber\\ &=& \frac{1}{2}\left[ {{\psi _M}\left( {\frac{{2\pi x}}{{{\Lambda _x}}}} \right) + {\psi _N}\left( {\frac{{2\pi y}}{{{\Lambda _y}}}} \right)} \right]\nonumber\\ && +\, \frac{1}{2}{\psi _P}\left( {\frac{{\pi {r^2}}}{{\lambda f}}} \right) + q\phi + \frac{{\pi {r^2}}}{{2\lambda {f_{{\rm{PB}}}}}} \end{eqnarray}$$$${\psi _M}$$, $${\psi _N}$$ , and $${\psi _P}$$ are the Dammann functions corresponding to M , N and P equal‐energy orders.…”

“…When the quadratic phase of a Fresnel lens 𝜋r 2 /𝜆f (r 2 = x 2 + y 2 , f denoting the focal length) is encoded with the same Dammann function, the so-called DZP is formed to generate M equal-energy focal points coaxially (see more details about Dammann encoding method in Note S1, Supporting Information). [36,37] Here, we imprint two binary and two continuous phase patterns of a 2D-DG, a DZP, a q-plate [38] and a PBlens [39] into a single LC GPOE, as shown in Figure 1a. Its LC orientation distribution is expressed as…”

Mechanically reprogrammable Pancharatnam–Berry metasurface for microwaves

“…In this article, we propose and demonstrate a reprogrammable metasurface platform based on mechanical control for quasicontinuous Pancharatnam-Berry (PB) phase tunability operating at microwave frequencies. PB phase, 7,8,62,63 also known as geometric phase, is a robust control method for incident circularly polarized waves, which is determined by the rotation angle of meta-atoms and it is therefore decoupled from amplitude control. Figure 1(a) schematically shows our reprogrammable PB metasurface platform, which consists of 20 × 20 supercells covering an area of 870 mm × 870 mm.…”

Twisted Rainbow Light and Nature‐Inspired Generation of Vector Vortex Beams

“…The emerging technologies provide new possibilities for controlling light through the geometric phase discovered by Pancharatnam and Berry that is independent of the optical path. [22,23] The geometric-phase elements benefit from the broadband [24][25][26] or achromatic operation, [27,28] sensitivity to polarization states, [29][30][31] excellent integrability, [32,33] and the possibility of generating light fields with arbitrarily designed wavefront and controlled polarization. [34] Unique properties of the geometric-phase elements allow generation of vector vortex beams, [35,36] mutual conversion between spin and orbital angular momentum, [37][38][39] or preparation of structured vortex fields [40] and vortex arrays.…”