Intense Focusing of Light Using Metals

Abstract

At optical frequencies the dielectric response of metals is dominated by the plasma like behaviour of the electron gas:

$$ \varepsilon \left( \omega \right) = 1 - \frac{{\omega _p^2}}{{\omega \left( {\omega + i\gamma } \right)}}.$$

There is a characteristic plasma frequency which is the natural frequency of oscillation of the electron gas

$$ \omega _p^2 = \frac{{n{e^2}}}{{{\varepsilon _0}{m_e}}}.$$

Dissipation is introduced through the damping factor, γ, which in turn can be related to the conductivity of the metal if we assume that the same form persists to low frequencies,

$$ \gamma = {\sigma ^{ - 1}}{\varepsilon _0}.$$

It is customary to ignore the dependence of ε on wave vector, q, and this is a good approximation for many purposes. However in some circumstances, for example where we consider the response of nanostructures to light, we may have to worry about the short wavelength, large q behaviour of ε. One obvious cut-off length is the separation between electrons in the metal. Another might be the inelastic scattering length for electrons which is typically a few nanometres. The very short wavelength response of metals at optical frequencies has been studied in the electron microscope where losses at large momentum transfers can be measured.