Refractive index profiles with a local resonance based on Heun's equation


  • Cornelis A. van Duin,

  • Frans W. Sluijter


The propagation of electromagnetic waves in inhomogeneous magnetoactive plasmas is studied. In particular, the so-called extraordinary mode is considered. The starting point is the Fuchsian equation with four singular points: Heun's equation. Transformations are developed that transform Heun's equation into a Helmholtz equation. In this way, refractive index profiles accommodating a local resonance are generated. These refractive index profiles are connected with plasma density profiles through the dispersion relation for the extraordinary mode. The thus generated plasma density profiles contain a number of adjustable parameters.