Deeply penetrating waves in lossy media

Abstract

The incidence of an inhomogeneous plane wave on the interface between two lossy media is analyzed. The analytical expressions of the incidence angle of the phase vector, for which the transmitted wave has the phase or the attenuation vector parallel to the interface, are obtained. The transmitted wave with the attenuation vector parallel to the interface is physically interpreted, finding a wave in a lossy medium without attenuation away from the interface. The same effect appears at the interface between a lossless medium and a lossy one.

Analytical Investigation on a New Approach for Achieving Deep Penetration in a Lossy Medium: The Lossy Prism

“…Let us now define with ξ 1 the angle that the phase vector of the incident wave β 1 forms with the normal to the interface between air and lossy medium. The theory developed in [4], [6] demonstrates that, when ξ 1 is smaller than or equal to 45 • it is possible to find a critical value β 1c for the amplitude of β 1 such that the angle ζ 2 formed by α 2 with the normal to the separation surface is 90…”

“…This value, according to Eqs. (12)- (13) of [4] allowed the deep-penetration condition on a medium with conductivity σ 2 = 0.05 S/m. While we cannot exclude the possibility of realizing a conventional LWA [8], [17] that may provide even higher amplitudes of attenuation and phase vectors, the design proposed in [13] shows evident limits in the deep penetration achievable by means of a uniform LWA.…”

“…The amplitudes of phase and attenuation vectors achievable employing this structure will then be compared against the corresponding values that can be obtained employing conventional LWAs. We know that, to obtain deep penetration, the amplitude of the attenuation vector needs to be greater than a minimum value [4], but LWAs are usually designed to produce efficient beams with a negligible amplitude of the attenuation vector (α 1 << k 0 [8], [17]), this makes the design of a deeply penetrating antenna by means of commonly used LWAs very challenging, while the structure proposed here shows better results. The first consideration that needs to be exposed when comparing the lossy prism and the LWA is that in the former losses are present in the material, while in the latter losses are mainly due to radiation (LWAs do not require a lossy medium), and only a small quantity of energy is really dissipated (usually through a matched load posed at the end of the antenna).…”

“…Equations (12)- (13) of [4] provide requirements in terms of amplitude of both phase vector and incident angle of an inhomogeneous wave incoming from a lossless medium to guarantee deep penetration on a lossy medium with given electromagnetic characteristics. An antenna designed for the deep-penetration condition needs to be able to radiate an inhomogeneous wave in a lossless medium, for instance a vacuum (air), such that the mentioned equations are satisfied.…”

“…The proposed structure is therefore a preliminary input for the development of an air-coupled antenna, which increases the penetration depth without the need of reducing the operating frequency. The deep-penetration condition was first defined in [4] for a plane wave incoming from a lossless medium and impinging on a separation surface with a lossy medium. This condition occurs when the attenuation vector of the transmitted wave in the lossy medium is parallel to the separation surface between lossless and lossy media.…”