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

where <math>E_x</math> and <math>H_y</math> are the electric field and magnetic field, respectively. In a region is with no electrical conductivity (e.g. free space), the expression simplifies to

<math>\eta = \sqrt{\mu \over \varepsilon}.</math>

Waves propagate through a medium with velocity <math>c_w = \nu \lambda </math>, where <math>\nu</math> is the frequency and <math>\lambda</math> is the wavelength of the electromagnetic waves. This can also be put in the form

<math> c_w = {\omega \over k}\ ,</math>

where <math>\omega</math> is the angular frequency of the wave and <math>k</math> is the wavenumber of the wave. In electrical engineering, the symbol <math>\beta</math>, called the phase constant, is often used instead of <math>k</math>.

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

<math>c_w = {1 \over \sqrt{\varepsilon_0 \mu_0}}\ ,</math>

where <math>\varepsilon_0</math> is the permittivity of free space

<math>~ \mu_0 ~</math> is the permeability of free space.