Berry Phase of Light under Bragg Reflection by Chiral Liquid-Crystal Media

A Berry phase is revealed for circularly polarized light when it is Bragg reflected by a chiral liquid-crystal medium of the same handedness. By using a chiral nematic layer we demonstrate that if the input plane of the layer is rotated with respect to a fixed reference frame, a geometric phase effect occurs for the circularly polarized light reflected by the periodic helical structure of the medium. Theory and numerical simulations are supported by an experimental observation, disclosing novel applications in the field of optical manipulation and fundamental optical phenomena.

Figure 1

Reflection from (a) a conventional mirror and (b) a chiral liquid-crystal (CLC) medium. The red arches depict the cholesteric helix; while the mirror reverses the polarization of the reflected light, a circularly polarized beam matching the handedness of the chiral helix maintains the same polarization when reflected.

Figure 2

Modes of light propagation in the CLC layer. Only the Bragg regime is considered. The (red) curved arrows indicate the Bragg-reflected beams to which a Berry phase is associated.

Figure 3

Numerically calculated Berry phase versus the angle $\theta$ of the molecular alignment at the input plane of the CLC cell. The results (dots) match their corresponding (lines) analytical prediction ${\mathrm{\Phi }}_B(\theta )=2\sigma \theta$, where $\sigma =\pm 1$ is the handedness of the cholesteric helix and of the input polarization.

Figure 4

Experimental setup. A diode pumped solid-state (DPSS) laser at 532 nm is divided into a reference and a probe beam by the beam splitter (BS), then recombined in a Michelson-type interferometer onto a CCD camera; while the reference is reflected by an ordinary mirror, the probe beam is reflected by a CLC cell that has two regions of planar alignment in its entrance plane (anchoring angles ${\theta }_{\mathrm{I}}=0$ and ${\theta }_{\mathrm{II}}=\pi /2$), as shown in the inset. The red helical arches depict the cholesteric helix for a better clarity on the handedness. OBJ, objective; PH, pinhole; L, lens; QWP, quarter-wave plate.

Figure 5

(a) Instantaneous snapshot of the CLC cell showing the interface between regions I and II corresponding to the orthogonal anchoring ${\theta }_I=0$ and ${\theta }_{II}=\pi /2$. (b) Interference pattern recorded for a probe beam hitting the cell across the interface; dislocation lines evidence the $\pi$ phase shift between regions I and II. (c) One-dimensional intensity profiles taken on the interference pattern in regions I and II, respectively.