Metal Optics

a branch of optics concerned with the study of the interactions of metals with electromagnetic waves. The main optical features of metals are a large coefficient of reflection R (for example, for the alkali metals R ~ 99 percent) over a wide range of wavelengths, and also a large coefficient of absorption (an electromagnetic wave in the interior of metals is attenuated after passing through a layer of thickness δ ~ 0.1 1 X 10^-5 cm). These special features are related to the high concentration of the conduction electrons in metals.

As the conduction electrons interact with an electromagnetic wave incident on the surface of a metal, they also interact simultaneously with the vibrating lattice ions. Most of the energy they acquire from the electromagnetic field is radiated in the form of secondary waves, which combine to give the reflected wave. Part of the energy imparted to the lattice leads to the attenuation of the wave in the interior of the metal. The conduction electrons are capable of absorbing quanta of electromagnetic energy hω (h is Planck’s constant, and ω is the frequency of the radiation), no matter how small they are. For this reason, the electrons contribute to the optical properties of metals at all frequencies. Their contribution is especially great in the radio-frequency and infrared regions of the spectrum. With increasing ω, the contribution of the conduction electrons to the optical properties of metals decreases and the differences between metals and dielectrics become smaller.

The remaining valence electrons exert an effect on the optical properties of metals only when the electrons participate in the internal photoelectric effect, which occurs at hω ≧ Δε (Δε is the energy gap between the ground and excited states of the electrons). Excitation of the electrons leads to anomalous dispersion of the waves and to an absorption band with a maximum in the vicinity of the resonance absorption frequency. The absorption bands in metals are significantly broader than in dielectrics because of the strong electron-electron and electron-ion interactions. The metals usually exhibit several bands, which are located mainly in the visible and near-ultraviolet regions of the spectrum. However, a number of polyvalent metals also have absorption bands in the infrared region. At frequencies ω ≧ ωp, where ωp is the plasma frequency of the valence electrons, plasma vibrations of electrons are excited in the metal. They lead to the appearance of a region of transparency at ω ≈ ωp

The coefficient of reflection R decreases in the ultraviolet region, and the properties of metals approach those of dielectrics. At higher frequences (X-ray region), the optical properties are determined by the electrons of the inner shells of atoms, and metals no longer differ from dielectrics in optical properties.

The optical properties of metals are described by the complex dielectric constant ∑ (ω) = ∑’ (ω) − (i 4Π/ω) σ(ω), where ω’ is the real dielectric constant and σ is the conductivity of the metal, or by the complex index of refraction:

(K is the coefficient of absorption). The complex nature of the index of refraction expresses the exponential attenuation of the wave in the metal. If a plane wave is incident on the surface of a metal at an angle Ф ₋ 0, the wave will be inhomogeneous inside the metal. The plane of equal amplitudes is parallel to the metal surface, whereas the plane of equal phases is inclined toward the surface at an angle whose magnitude depends on f>. The waves reflected from the surface of the metal, which are polarized in the plane of incidence and perpendicular to it, have a phase difference. This causes plane-polarized light to become elliptically polarized after reflection. The coefficient of reflection R of the waves polarized in the plane of incidence is always nonzero in metals (in contrast to dielectrics) and has a minimum only at a certain value of Ф.

The mean free path / of the electrons becomes greater than δ in pure metals at low temperatures in the long-wavelength region of the spectrum. The attenuation of the wave ceases to be exponential, although it remains very strong (the anomalous skin effect). In this case the complex index of refraction becomes meaningless and the relationship between the incident and refracted waves becomes more complicated. However, the properties of reflected light at any ratio of / to δ are completely determined by the surface impedance Z, which is related to the effective complex indexes of absorption and refraction as follows:

For l < τ, the quantities n and K in the equations are replaced by n_eff and K_eff, respectively.

To measure n and K of a massive metal specimen, the light reflected from its surface is studied by polarization methods (the characteristics of the elliptical polarization of the reflected light are measured) or by methods based on measurements of R over a wide region of the spectrum during normal incidence of light on the surface of the metal. Such methods make possible measurement of the optical characteristics in the infrared, visible, and ultraviolet regions with an error of the order of 0.5-2.0 percent. Measurements of the fine structure of absorption bands are performed using methods based on modulation of the properties of the metal, which leads to modulation of the reflected light, which is what is measured (thermoreflection, piezoreflection, and so on). The methods mentioned above make possible determination of R with a high degree of accuracy upon temperature changes and deformation and under other conditions (see Table 1), and also the study of the fine structure of absorption bands. Special attention is paid to the preparation of the surfaces of the specimens under investigation. Surfaces of the required quality are produced by electric polishing or by vaporization of metal in a vacuum, with subsequent deposition on a polished substrate.

Metal optics uses optical characteristics, measured over a wide spectral range, to determine the basic characteristics of conduction electrons and electrons that participate in the internal

photoelectric effect. Metal optics is also of practical importance. Various instruments use metal mirrors, which must be constructed from materials with known values of R, n, and χ in various regions of the spectrum. The determination of n and χ also makes possible establishment of the presence of thin films on the surface of a metal (such as oxide films) and determination of their properties.