Propagation of electromagnetic wave through a vortex

Abstract

In this paper, we discuss in detail the propagation of electromagnetic waves through a vortex. The velocity profile of the vortex is represented by the cylindrical symmetry vortex which is nothing but the Burgers vortex in cylindrical coordinates. To obtain the equations for the electromagnetic field in a vortex in the cylindrical coordinates, we have used the Minkowski constitutive relations. To relax the complexity of the equations, we have used some constraints and the eikonal approximation. As a result of the constraints, we establish the dispersion relation of the vortex for the electromagnetic wave in terms of a sixth order algebraic equation. Besides, we also performed numerical calculations to study the dispersion relatioin and studied the incident cylindrical and plane waves. For the incident cylindrical wave, we observed that within a certain frequency range multiple propagation modes exist along the radial direction. We also noticed that the electromagnetic field attenuates along the radial direction for certain range of frequencies. Below the critical value of frequency, the wave propagation in the vortex along the radial direction stops. In the case of incident plane wave, we noticed that birefringence can be achieved in the vortex under special conditions. The observed birefringence depends on the incident angle, the frequency of the wave, and on the distance to the center of the vortex. Further, if the vortex is divided into layers along the radial direction, different layers have different equivalent refractive indexes, and different incident angle of the same layer has different equivalent refractive index. Lastly, we propose that for certain incident angle, surface wave may be seen on the layer.