Scientific review on the Complex Eikonal, and research perspectives for the Ionospheric Ray-tracing and Absorption

Abstract

Scientific review on the Complex Eikonal, and research perspectives for the Ionospheric Ray-tracing and Absorption he present paper conducts a scientific review on the complex eikonal, extrapolating the research perspectives on the ionospheric ray-tracing and absorption. As regards the scientific review, the eikonal equation is expressed, and some complex-valued solutions are defined corresponding to complex rays and caustics. Moreover, the geometrical optics is compared to the beam tracing method, introducing the limit of the quasi-isotropic and paraxial complex optics approximations. Finally, the quasi-optical beam tracing is defined as the complex eikonal method applied to ray-tracing, discussing the beam propagation in a cold magnetized plasma. As regards the research perspectives, this paper proposes to address the following scientific problem: in absence of electromagnetic (e.m.) sources, consider a material medium which is time invariant, linear, optically isotropic, generally dispersive in frequency and inhomogeneous in space, with the additional condition that the refractive index is assumed varying even strongly in space. The paper continues the topics discussed by Bianchi et al. [2009], proposing a novelty with respect to the other referenced bibliography: indeed, the Joule’s effect is assumed non negligible, so the medium is dissipative, and its electrical conductivity is not identically zero. In mathematical terms, the refractive index belongs to the field of complex numbers. The dissipation plays a significant role, and even the eikonal function belongs to the complex numbers field. Under these conditions, for the first time to the best of our knowledge, suitable generalized complex eikonal and transport...