Definitions

# Optical medium

An optical medium is material through which electromagnetic waves propagate. It is a form of transmission medium. The permittivity and permeability of the medium define how electromagnetic waves propagate in it. The medium has an intrinsic impedance, given by
$eta = \left\{E_x over H_y\right\}$
where $E_x$ and $H_y$ are the electric field and magnetic field, respectively. In a region with no electrical conductivity, the expression simplifies to:

$eta = sqrt\left\{mu over varepsilon\right\} .$

For example, in free space the intrinsic impedance is called the characteristic impedance of vacuum, denoted Z0, and

$Z_0 = sqrt\left\{mu_0 over varepsilon_0\right\} .$

Waves propagate through a medium with velocity $c_w = nu lambda$, where $nu$ is the frequency and $lambda$ is the wavelength of the electromagnetic waves. This equation also may be put in the form

$c_w = \left\{omega over k\right\} ,$
where $omega$ is the angular frequency of the wave and $k$ is the wavenumber of the wave. In electrical engineering, the symbol $beta$, called the phase constant, is often used instead of $k$.

The propagation velocity of electromagnetic waves in free space, an idealized standard reference state (like absolute zero for temperature), is conventionally denoted by c0:

$c_0 = \left\{1 over sqrt\left\{varepsilon_0 mu_0\right\}\right\} ,$
where $varepsilon_0$ is the electric constant and $~ mu_0$ is the magnetic constant.

For a general introduction, see Serway For a discussion of man-made media, see Joannopoulus.