We review the properties of the surface waves that are scattered by two-dimensional sub-wavelength indentations on metallic surfaces. We show that two distinct waves are involved, a surface plasmon polariton (SPP) and a quasi-cylindrical wave (quasi-CW). We discuss the main characteristics of these waves, their damping characteristic lengths and their relative excitation weights as a function of the separation distance from the indentation and as a function of the metal conductivity. In particular we show that derive a closed-form expression for the quasi-CW, which clarifies its physical origin and its main properties. We further present an intuitive microscopic model, which explains how the elementary SPPs and quasi-CWs exchange their energies by multiple-scattering to build up a rich variety of near- and far-field optical effects.

A microscopic view of the electromagnetic properties of sub-wavelength metallic surfaces

A microscopic view of the electromagnetic properties of sub-λ metallic surfaces

The theory of propagating waves near a surface is reviewed with an eye to gain insight into the mechanisms involved, and to provide analytical-based models, for power-efficient on-body propagation. The Zenneck wave, and in particular the Norton wave, are appraised as candidate mechanisms for the propagation. For flush-mounted (ldquoband aidrdquo) antennas, desired for on-body sensors, the Norton wave is the only direct propagation mechanism between the sensors. The Norton wave fits very well to simulation results presented here, and comparisons are also made with available published physical experiments, although these measurements typically feature the optical paths of elevated, or non-flush, antennas.

Propagation Between On-Body Antennas

A reference model for the electrical conductivity structure beneath the deep seafloor is proposed and justified using a variety of geophysical evidence. The model consists of relatively conductive sediment and crustal layers of 6.5 km extent overlying a resistive (≈10−5 S/m) subcrustal channel of 30 km thickness and terminated in a deeper conductive layer and half-space. Its seafloor-to-seafloor response to a horizontal electric dipole source is explored as a function of frequency and range, showing that, compared with the response for a half-space with the lowest conductivity in the reference model, significant enhancement of the field amplitude can occur at long ranges (>100 km) and low frequencies (<1 Hz). At the same time, marked attenuation relative to the half-space response is seen at higher frequencies. The field enhancement is due to trapping of electromagnetic energy in a leaky subcrustal waveguide, as demonstrated by computing the complex Poynting vector. The attenuation occurs in the relatively conductive sedimentary and crustal layers overlying the lithospheric waveguide when their electrical thickness exceeds a skin depth. The results indicate that attempts either to model controlled electromagnetic sources or to interpret controlled source data using half-space models for the Earth can be badly misleading. The practicality of lithospheric communications in the real Earth is also investigated. Using measured receiver noise figures and the reference model, the receiver bandwidth necessary to achieve a given signal-to-noise ratio as a function of range and frequency is estimated for a seafloor horizontal source of strength 105 A-m. The results indicate that significant (≈100 km) ranges can be achieved only around 1 Hz with a bandwidth of ≈1 Hz at a SNR of 10, yielding a very low data rate of <3.5 bits/s. Longer ranges and higher frequencies are precluded by attenuation in the sediment and crustal layers and because the conductivity in the resistive channel is too large.

Some comments on seabed propagation of ULF/ELF electromagnetic fields

Electromagnetic surface waves

Lateral electromagnetic waves along a plane boundary between homogeneous half-spaces are reviewed. The electromagnetic fields generated by vertical and horizontal electric dipoles near the boundary between air and the earth (salt or fresh water, soil, ice, etc.) are summarized in terms of a new unified theory of lateral-wave propagation. Complete theoretically determined fields are displayed and compared with measured fields at f = 601 MHz relative to the boundary between air and salt water (σ = 3.5 S/m, e r = 80). Near, intermediate, and asymptotic fields are related graphically to the new general theory and to the approximate and restricted formulas of Norton and Banos as well as to the Zenneck wave. Application is made to the specific problem of communication with submerged submarines by means of transmitters consisting of electrically short monopoles in air and horizontal traveling-wave antennas and directional arrays in sea water. The properties of the antennas are evaluated in the frequency range 10 ≤ f ≤ 30 kHz which is optimum for receiver depths near 10 m, and at f = 1 kHz which is optimum for depths up to 50 m. The effects of reflections from the ionosphere and of the earth's curvature are not included.

M.F. Brown

Papers

Lateral electromagnetic waves along plane boundaries: A summarizing approach