Examining the theoretical basis for the analysis of surface plasmons in the microwave and terahertz regimes

Abstract

Surface electromagnetic modes guided by thin metal layers are usually called surface plasmons SP. SP were originally discovered by Ritchie in the fifties of the twentieth century in the optical regime. Then, surface plasmons found many applications in different areas of science including terahertz and microwave devices. Departing from optics to radio frequencies, an urgent need for a solid theoretical basis to analyze SP in those regimes has appeared. The only candidate was Sommerfeld's analysis for radiation of electromagnetic waves over imperfect ground planes, published in 1909. This kind of analysis has been used recently by many researches working on SP applications at radio frequencies. The main goal of this paper is to give a theoretical analysis which proves the unsuitability of Sommerfeld's analysis to the problem of SP. Index Terms -Schelkunoff Integrals, Sommerfeld Integrals, Surface Plasmons, Surface Waves, Terahertz Surface Plasmons, Zenneck Surface Waves. I. HISTORY OF SP AND ITS RELATION TO SURFACE WAVES SP's are coherent electron oscillations that exist at the interface between two materials where the real part of the permittivity changes sign across the interface. When a SP couples with a photon, the resulting hybrid excitation is called a surface plasmon polariton (SPP). Under the right conditions the photon can excite a longitudinal wave of electrons in the metal. This interaction of a photon with an electron can be considered as an inelastic scattering. This type of interaction can be used to enhance weak optical processes, such as generation of higher order harmonics and surface-enhanced Raman scattering [I]. Note that this kind of interaction is in contrast to Rayleigh scattering, which is elastic scattering, encountered in classical electromagnetics. This resulting electron/molecule oscillation, SPP, produces its own electromagnetic wave which is confmed to a very small region near the interface. This SPP can propagate along the metal dielectric interface at a wavelength which is shorter than that of incident light until its energy is lost either via absorption in the conductivity of the metal or through radiation in free space. One of the earliest papers in the history of SP is Ritchie's paper published in 1957 [2]. Ritchie presented SP as the response of electrons in thin metal layers to fast electron bombardment. Then in 1968, Otto showed the optical excitation of SP using the method ofJrustrated total reflection [7]. SP were never studied at radio frequencies and terahertz until the fIrst decade of the twenty fIrst century. The interest was due to the ability of SP to enable near fIeld imaging and bio-sensing with unprecedented sensitivity [8]. Departing from the optical regime to the microwave and terahertz regimes, SP started to be defIned as the same physical entity as SommerJeld-Zenneck waves, studied in the beginning of the twentieth century. Accordingly, Sommerfeld's analysis [9] gained a new interest and has been used extensively for the study of SP at radio frequencies [10-11]. ...