# 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.

## 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. 