Electromagnetic waves vacuum interface

Refractive index or index of refraction is the ratio of wavelength or phase velocity of an electromagnetic wave in a vacuum to that in the substance. It measures the amount of refraction a ray of light undergoes as it passes through a refraction interface. Refractive index is a useful physical property to identify a pure compound. 

The process of total reflection of an incident wave in an optically dense medium against the interface of an optically less dense medium turns out to be of particular and renewed interest with respect to the concepts of nontransverse and longitudinal waves. In certain cases this leads to questions not being fully understood in terms of classical electromagnetic field theory [26]. Two crucial problems that arise at a vacuum interface can be specified as follows ... 

Additional complications arise when the EM wave in a dissipative medium approaches a vacuum interface at an oblique angle [26]. The incident and reflected wave fields then become inhomogeneous (damped) in the direction of propagation. As a consequence the matching at the interface to a conventional undamped electromagnetic wave in vacuo becomes impossible. 

Surface electromagnetic waves (SEW) on a metal-vacuum interface (often called surface plasmons) are discussed to demonstrate the essential features of SEW. SEW are surface waves in the sense that the electric and magnetic fields decay exponentially as one moves away from the surface, either into the metal or into the vacuum. Figure 1 shows the coordinate system we shall use. The metal-vacuum interface is the z = 0 plane, and the metal occupies the z < 0 half-space. The direction of propagation is the positive x-directi on. The metal has a... 

Figure 5. Decay lengths for the electromagnetic field of a surface electromagnetic wave on a Cu-vacuum interface. The right-hand scale is for the decay length into the Cu and the left-hand scale for the decay length into vacuum.

Surface plasmons, or surface plasmon polaritons, are surface electromagnetic waves that propagate inside a metal along a metal/dielectric (or metal/ vacuum) interface their excitation by light is surface plasmon resonance (SPR) for planar surfaces or localized surface plasmon resonance (LSPR) for nanometer-sized metal particles. 

If an electromagnetic wave in a vacuum, is incident on a medium having a refractive index n and a plane interface, at an angle a to the normal, then the wave will be partly or wholly reflected at an angle a to ad on the opposite side of the normal, where a = a (Fig. 1). However, it is also possible that part of the light penetrates into the medium and while doing so is refracted towards the normal and at an angle to the normal. Thus the index of refraction... 

Figure 1.7 Normalized SPP dispersion relation for dielectric/ideal-free-electron-plasma interface for Sd = 1 and sa = 2. The straight dotted line represents the dispersion law of electromagnetic waves in a vacuum...

As an application relevant to the optical properties of solids we consider a situation where electromagnetic radiation is incident on a solid from the vacuum, with the wave-vector of the radiation at a 90° angle to the surface plane (this is called normal incidence). First, we review the relevant boundary conditions. We denote the vacuum side by the index 1 and the solid side by the index 2. For the first two Maxwell equations, (A.27) and (A.28), we take the volume of integration to consist of an infinitesimal volume element with two surfaces parallel to the interface and negligible extent in the perpendicular direction, which gives... 

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