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
 * $$\eta = {E_x \over H_y}$$

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:


 * $$\eta = \sqrt{\mu \over \varepsilon}\ .$$

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


 * $$Z_0 = \sqrt{\mu_0 \over \varepsilon_0}\ .$$

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
 * $$ c_w = {\omega \over k}\ ,$$

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:
 * $$c_0 = {1 \over \sqrt{\varepsilon_0 \mu_0}}\ ,$$
 * 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.