Reflective Spin-Orbit Geometric Phase from Chiral Anisotropic Optical Media

Mushegh Rafayelyan, Georgiy Tkachenko, and Etienne Brasselet

Phys. Rev. Lett. 116, 253902 – Published 22 June 2016

Abstract

We report on highly reflective spin-orbit geometric phase optical elements based on a helicity-preserving circular Bragg-reflection phenomenon. First, we present a dynamical geometric phase experiment using a flat chiral Bragg mirror. Then, we show that shaping such a geometric phase allows the efficient spin-orbit tailoring of light fields without the need to fulfill any condition on birefringent phase retardation, in contrast to the case of transmission spin-orbit optical elements. This is illustrated by optical vortex generation from chiral liquid crystal droplets in the Bragg regime that unveils spin-orbit consequences of the droplet’s curvature. Our results thus introduce a novel class of geometric phase elements—“Bragg-Berry” optical elements.

Received 25 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.253902

Physics Subject Headings (PhySH)

Bragg structures Metamaterials Photonics

Atomic, Molecular & Optical

Authors & Affiliations

Mushegh Rafayelyan, Georgiy Tkachenko, and Etienne Brasselet^*

Université Bordeaux, LOMA, UMR 5798, F-33400 Talence, France
CNRS, LOMA, UMR 5798, F-33400 Talence, France

^*etienne.brasselet@u-bordeaux.fr

Polychromatic Optical Vortex Generation from Patterned Cholesteric Liquid Crystals

Junji Kobashi, Hiroyuki Yoshida, and Masanori Ozaki

Phys. Rev. Lett. 116, 253903 (2016)

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 116, Iss. 25 — 24 June 2016

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Side view of the supramolecular helical ordering of the chiral liquid crystal planar Bragg mirror and incident $(i)$ and reflected $(r)$ optical features associated with the circular Bragg reflection. The mirror is made of a right-handed ( $χ = + 1$ ) cholesteric film of thickness $L = 5 μ m$ and pitch $p = 347 nm$ (MDA-02-3211 from Merck [11]). (b) Dynamical geometric phase experiment setup. The slightly oblique incidence ( $α ≃ 4 °$ ) allows the analysis of raw reflected light. QWP, quarter-wave plate; $P$ , polarizer. The thin “Fresnel” arrow refers to incident light reflected at air-glass interfaces and the thick arrow labeled “Bragg” refers to circular Bragg reflection. The sample is rotated at an angular frequency $Ω = 20 ° / s$ . (c) Illustration of the rotation of the supramolecular helix at an angular frequency $Ω$ . (d) Power Fourier spectrum of the periodic signal (see inset) acquired by the photodetector PD shown in panel (b) over $≃ 40$ periods.
Reuse & Permissions
Figure 2
(a) Definition of the parameters involved in the parametrization of the 3D director field of a radial cholesteric droplet in the spherical coordinate system $(r, θ, ϕ)$ . The incidence plane and incident wave vector $k$ in the case of illumination towards $z < 0$ is also shown. (b) Incoherent white light imaging of a radial cholesteric droplet immersed in glycerol between crossed linear polarizers whose orientations are given by the white cross. (c) Transmission image of the droplet under circularly polarized incoherent illumination at 532 nm.
Reuse & Permissions
Figure 3
(a),(b) Calculated orientation angle of the projection of the 3D director field at the surface of the droplet in a plane perpendicular to $z$ , when looking at the droplet towards $z < 0$ (top view) and $z > 0$ (bottom view). (c),(d) Space-variant optical axis orientation angle of an effective flat inhomogeneous chiral Bragg mirror that takes account of the curvature of the droplet surface. Without lack of generality all plots are evaluated taking $2 π R / p + Ψ_{0} = 0$ modula $2 π$ , $R$ being the droplet radius.
Reuse & Permissions
Figure 4
Optical vortex levitation of Bragg radial cholesteric droplets. (a) Setup. QWP, quarter-wave plate; (N)PBS, (non)polarizing beam splitter; ${Obj i}_{(i = 1, 2)}$ , microscope objectives; ${Cam i}_{(i = 1, 2)}$ , CMOS cameras; WL, halogen white light illumination. Cholesteric droplets are prepared in milli-Q water within a sealed square ( $1 \times 1 {mm}^{2}$ ) glass capillary oriented along the $x$ axis. (b) Measured transverse intensity distribution of the incident vortex laser beam ( $λ_{0} = 532 nm$ ). (c) Sketch of a radial cholesteric droplet levitated by the vortex beam focused by the underfilled microscope objective Obj1 ( $\times 20$ , $NA = 0.4$ ) and characterized by a divergence angle $θ_{0} ≃ 6.3 °$ and beam waist radius $w_{0} ≃ 1.5 μ m$ . (d) Image of a steady levitated droplet captured by Cam2.
Reuse & Permissions
Figure 5
(a),(b) Intensity and phase profiles retrieval for a 2D chiral Bragg mirror for the incident vortex beam with $ℓ = + 1$ . (c),(d) Same as (a),(b) for $ℓ = - 1$ . (e),(f) Intensity and phase profile analysis for a spherical (3D) chiral Bragg mirror (radial cholesteric droplet) for incident vortex beam with $ℓ = + 1$ . (g),(h) Same as (e),(f) for $ℓ = - 1$ . Experimental parameters for the 3D case: levitator beam power $P = 17 mW$ , levitated droplet radius $R = 23 μ m$ , and equilibrium elevation $h = 240 μ m$ .
Reuse & Permissions

Physical Review Letters