# Optical medium

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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 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:[1]

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

For a general introduction, see Serway[2] For a discussion of man-made media, see Joannopoulus.[3]

## Notes and references

1. ^ With ISO 31-5, NIST and the BIPM have adopted the notation c0.
2. ^ Raymond Serway & Jewett J (2003). Physics for scientists and engineers (6th Edition ed.). Belmont CA: Thomson-Brooks/Cole. ISBN 0-534-40842-7.
3. ^ John D Joannopouluos, Johnson SG, Winn JN & Meade RD (2008). Photonic crystals : molding the flow of light (2nd Edition ed.). Princeton NJ: Princeton University Press. ISBN 978-0-691-12456-8.