Medium (optics)

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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 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 $c w = νλ$ , 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.