Light drag in nonuniformly moving anisotropic media through the lens of gradient-index optics

TL;DR

The paper studies light propagation in nonuniformly moving anisotropic media by discretizing the velocity field into infinitesimal uniform drags and modeling the path with gradient-index (GRIN) optics, effectively treating motion-induced inhomogeneities as $n[\mathbf{\beta}(\mathbf{x})]$. It derives local refraction relations for dispersive anisotropic media in uniform motion, extends them to general velocity fields using Fermat's invariant and conformal mapping, and obtains analytic ray trajectories in symmetric flows. In the isotropic limit it reproduces Gordon's optical metric results and, for rotating and vortex motions, provides dispersive predictions that align with known non-dispersive analyses while highlighting new invariants and optical-Aharonov-Bohm-type effects. The magnetized plasma application demonstrates how dispersion and anisotropy interact with drag to alter O and X mode paths, illustrating practical implications for diagnostics and motivating future development of an optical metric for dispersive anisotropic media.

Abstract

The trajectory of light rays propagating through a nonuniformly moving anisotropic medium is determined by considering the Fresnel drag experienced by the wave at each point along the ray. By showing that symmetries in the velocity field manifest as symmetries in the effective wave index representing the moving medium, methods classically employed to model gradient index media are then used to obtain analytical forms for the ray trajectory. When applied to isotropic media, the results are verified to be consistent with those obtained using an optical (Gordon) metric. The potential of this method to model light rays in anisotropic media is finally demonstrated by considering waves in a nonuniformly moving magnetized plasma, exposing how nonuniform motion and anisotropy can compete with one another.

Figures (11)

• Figure 1: Sketch of the light-dragging effect observed in lab-frame as a result of propagation in a uniformly-moving (anisotropic) dielectric. The incidence angle, defined with respect to the velocity normal, is $\theta_i$. The refracted angle is $\theta_t$, whereas the refracted ray direction is $\vartheta$.
• Figure 2: Model for the ray trajectory in a nonuniform velocity field. The trajectory is obtained as the limit of successive uniform drags at the interface between two infinitesimally thin layers with different but constant velocity. Since layers are homogeneous, light travels in straight line across each layer. This is analogous to the stratification employed for inhomogeneous refractive indexes in GRIN media.
• Figure 3: (Left) Representation of the optical path of light in an isotropic GRIN medium, propagating in the direction of the wavefront defined by the wavevector angle $\theta$. (Right) Transformation of the physical plane and ray tracing by a conformal mapping $f$, recovering a medium gradient-index independent of $Y$-coordinate following the generalized Snell's law ${\mathfrak F=N\sin\theta=\mathrm{cst}}$. The angle $\theta$ is preserved through the transformation between the two spaces.
• Figure 4: Sketch of the curvilinear parameterization based on the streamlines of the moving medium.
• Figure 5: Light path in an isotropic dielectric in linear motion ${ \mathbf{\beta} = \alpha x \hat{\mathbf{e}} _y}$, for an incident ray at normal incidence. The solid and dashed red rays represent the path for two nondispersive media with different constant optical indices, highlighting the tendency of light to avoid high-index regions. The purple ray shows the path in a dispersive medium with anomalous dispersion. Since the transverse component of the wavevector is conserved, it remains, in this particular case of normal incidence, perpendicular to the velocity all along the path. Just like for conventional material-GRIN turning point, the wavevector flips sign at the turning point.