Ray and wave optics in Bonnor-Melvin domain walls: Photon rings

Abstract

In this study, we examine the propagation of light rays and wave dynamics within the $(2+1)$-dimensional analogue of the Bonnor-Melvin magnetic (BMM) spacetime, which incorporates a nonzero cosmological constant. The BMM spacetime, characterized by cylindrical symmetry, maintains Lorentz invariance along the axial direction, facilitating a systematic investigation of ray trajectories and wave behavior in the corresponding $(2+1)$-dimensional magnetic background. This three-dimensional spacetime can be derived as a $(2+1+0)$-brane solution within the context of gravity coupled to nonlinear electrodynamics. Initially, we analyze general ray trajectories and derive exact solutions for the angular motion of light rays. Our findings reveal that light is confined to circular paths within a specific radial region, indicating the formation of light rings governed by the magnetic background. Extending this analysis to wave dynamics, we solve the Helmholtz equation analytically, identifying discrete wave modes with quantized frequencies. The background gravitational field induces oscillatory wave behavior, resulting in well-defined photonic states. These states are notably ring-shaped and rotate, resembling magnetic vortices.