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# 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 Ex and Hy are the electric field and magnetic field, respectively. In a region is with no electrical conductivity (e.g. free space), the expression simplifies to

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

Waves propagate through a medium with velocity cw = νλ, where ν is the frequency and λ is the wavelength of the electromagnetic waves. This can also be put in the form

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

where ω is the angular frequency of the wave and k is the wavenumber of the wave. In electrical engineering, the symbol β, called the phase constant, is often used instead of k.

The propagation velocity of electromagnetic waves in free space, i.e. the absence of a medium, is

$c_w = {1 \over \sqrt{\varepsilon_0 \mu_0}}\ ,$
where $\varepsilon_0$ is the permittivity of free space
$~ \mu_0 ~$ is the permeability of free space.