Critical Angle Formulation of Nonuniform Plane Waves for Determining Correct Refraction Angles at Planar Interface

Optimized Leaky-Wave Antenna for Hyperthermia in Biological Tissue Theoretical Model

“…It has been demonstrated in the literature that the incidence of an inhomogeneous wave incoming from a non-dissipative medium on a lossy medium may produce a transmitted wave that can penetrate deeper than the one produced by the incidence of a more conventional homogeneous wave, both numerically [2] and analytically [3][4][5][6]. In order to obtain a deep-penetration effect, the incoming wave must fulfill some conditions that bind the minimum attenuation vector to the electromagnetic characteristics of the medium and the incidence angle [5].…”

“…depending on the characteristics of the media involved, where ξ is the angle formed by the phase vector with the normal to the interface between the air and the lossy medium and the subscript "c" stands for "critical", meaning that ξ c is the minimum value of ξ that assures the deep-penetration phenomenon, i.e., ζ 2 = 90 • , ζ 2 being the angle formed by the attenuation vector of the wave inside the lossy medium with the normal to the interface with the air [5]. Moreover, in [6], an alternative and equivalent description, more suitable for ray tracing techniques, has been developed, and, among the results, it is demonstrated that the deep-penetration effect can be achieved at the interface between two lossy media. The deep-penetration phenomenon requires an incidence angle different from 0 • , and in any case, the presence of an attenuation vector in the incidence wave constitutes a sufficient condition for a possible enhancement of the penetration in a lossy medium, i.e., even in case of normal incidence, an inhomogeneous wave may allow deeper penetration [2].…”