Spin-redirection Berry phase with planar rays

Abstract

Geometric or Berry phases are fundamental manifestations that appear in many areas of physics. They arise from the geometry of the space describing the properties of multi-component wave fields. An important example for electromagnetic waves is the spin-redirection Berry phase associated with the evolution of the spin direction. Because this effect has traditionally been studied in isotropic media where the spin is aligned with the ray trajectory, it has become commonly assumed that this spin-redirection Berry phase requires nonplanar rays. Here we show that a spin-redirection phase can in fact arise along a planar ray if the spin evolves along the ray. We expose this effect through the singular example of a moving unmagnetized plasma, and demonstrate how this behavior can more generally arise from a finite transverse spin. In identifying this new spin-redirection mechanism our work not only provides the tools to discover additional manifestations of SOIs in nature, but also uncovers supplemental degrees of freedom to harness SOIs to control light.

Figures (3)

• Figure 1: (a) Ray trajectory (orange) and polarization plane (grey plane) of a wave in a moving (blue arrows) unmagnetized plasma. The trajectory, which is not affected by motion, remains straight. On the other hand, since the vector $\hat{\boldsymbol{w}}$ (red) which is parallel to the electric spin density $\boldsymbol{\mathsf{s}}_e$ is redirected by motion, the polarization plane orientation varies along the ray. (b) The same polarization plane redirection is obtained when associating with this ray a nonplanar virtual trajectory (green) defined by the tangent vector $\hat{\boldsymbol{w}}$.
• Figure 2: (a) Cyclic evolution of the velocity ($\boldsymbol{0}\rightarrow\hat{\boldsymbol{x}}\rightarrow\hat{\boldsymbol{y}}\rightarrow \boldsymbol{0}$) along a straight ray and associated rotation of the wave polarization $\hat{\boldsymbol{e}}$ from $\hat{\boldsymbol{e}}_i$ to $\hat{\boldsymbol{e}}_f$. (b) The polarization rotation angle $\Theta$, given by the accumulated spin-deviation-redirection Berry phase $\psi_B$, is equal to the solid angle enclosed by the closed contour described by $\hat{\boldsymbol{w}}$ around $\boldsymbol{v}_g$, analogously to the polarization rotation typical of a redirection of $\boldsymbol{k}$.
• Figure 3: (a) Rotation of polarization due to a rotation of the velocity along the ray. (b) Cone described by $\hat{\boldsymbol{w}}$ around $\boldsymbol{v}_g\parallel \boldsymbol{k}$ during the cycle. (c) Associated helix virtual trajectory. The solid angle described by $\hat{\boldsymbol{w}}$ grows with $\mathcal{N} \beta$ (darker to lighter colors), leading to significant polarization rotation for $\mathcal{N}\beta=\mathcal{O}(1)$.