Lakhtakia Akhlesh - Electromagnetic surface waves a modern perspective

Uniform plane waves are the simplest (nontrivial) solutions of the Maxwell equations in the frequency domain. The components of the field phasors and their spatial variation along a fixed axis are described using a Cartesian coordinate system. In the simplest case, the medium of propagation is a linear and homogeneous material that extends to infinity in all directions. The mathematical apparatus needed here is quite elementary.

Plane waves in air (approximated as vacuum) and isotropic dielectric materials are sufficiently simple to be taught in an undergraduate course using the approach of separation of variables. Plane waves in uniaxial dielectric materials are typically introduced in a first-year graduate course. Plane waves in bianisotropic materials are taught, if at all, in a specialized graduate coursewith a convenient approach provided by the three-dimensional spatial Fourier transform.

Scattering of an incident electromagnetic field occurs at the planar boundary of two half-spaces occupied by dissimilar linear and homogeneous materials. If the incident field is a plane wave, analytical treatment of the reflected and refracted plane waves does not require additional skills beyond the ability to satisfy standard boundary conditions, in exactly the same way as in the undergraduate electromagnetics course. The representation of each plane wavewhether incident, reflected, or refractedinvolves just one material and is obtained after pretending that this material fills all space.

An electromagnetic surface wave, in sharp contrast, is a creature of two materials. The surface wave straddles the planar interface of two half-spaces each occupied by a different material; remove the interface by making the two partnering materials identical, and the surface wave vanishes. Moreover, there is no guarantee that, at a specific frequency, a chosen pair of partnering materials will necessarily support the existence of a surface wave. Thus, a surface wave is far more delicate than a plane wave.

Electromagnetic plane waves have been known in one form or another for several millenniums, but the history of electromagnetic surface waves spans slightly more than a century. Initial progress was sporadic and slow, but the discovery of optical means of launching surface plasmon-polariton waves reported in 1959 led to a quickened pace during the 1970s. At optical frequencies, a surface plasmon-polariton wave is guided by the interface of a metal and a dielectric material (which could be air). Thousands of research papers are published every year on applications of this type of surface wave nowadays, many of the authors having only a beginners knowledge of electromagnetics.

Inevitably, attention began to be paid during the last four decades to other types of electromagnetic surface waves as well. The complexity of partnering materials has increased from isotropic to anisotropic and even to bianisotropic in one sense, and from homogeneous to periodically nonhomogeneous (in the direction normal to the interface) in another sense. These new types of surface waves have not had the vogue experienced by surface plasmon-polariton waves yet, but the spectacular growth of nanotechnologies during the last two decades promises a very bright future for all types of surface waves.

The attraction of surface waves stems from most of the energy of a surface wave being confined to the close vicinity of the interface of the two partnering materials. Any change in the composition of either partnering material in that vicinity could altereven eliminatethe surface wave. Conversely, by engineering the composition close to the interface, a surface wave can be allowed to propagate. At optical frequencies, the close vicinity is often less than a few micrometers. Nanotechnologies allow engineering of composition with a precision of a few nanometers, enabling hitherto unrealizable geometries for field confinement.

From a modern perspective, it does not matter if a partnering material is homogeneous, isotropic, and dielectric or if it is bianisotropic and periodically nonhomogeneous in the direction normal to the interface. A 4 4 matrix formalism can be devised to solve a dispersion equation and then determine the field phasors on each side of the interface. The same formalism can be used to analyze and design a practical prism-coupled configuration for launching a surface wave, and an extension allows treatment of the practical grating-coupled configuration as well. In this way, simple and complex surface plasmon-polariton waves, Zenneck waves, Fano waves, Dyakonov waves, Tamm waves, and Dyakonov-Tamm waves can all be treated in a unified fashion.