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

${\displaystyle \eta ={E_{x} \over H_{y}}}$

where ${\displaystyle E_{x}}$ and ${\displaystyle H_{y}}$ are the electric field and magnetic field, respectively. In a region with no electrical conductivity, the expression simplifies to:

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

For example, in free space the intrinsic impedance is called the characteristic impedance of vacuum, denoted Z₀, and

${\displaystyle Z_{0}={\sqrt {\mu _{0} \over \varepsilon _{0}}}\ .}$

Waves propagate through a medium with velocity ${\displaystyle c_{w}=\nu \lambda }$, where ${\displaystyle \nu }$ is the frequency and ${\displaystyle \lambda }$ is the wavelength of the electromagnetic waves. This equation also may be put in the form

${\displaystyle c_{w}={\omega \over k}\ ,}$

where ${\displaystyle \omega }$ is the angular frequency of the wave and ${\displaystyle k}$ is the wavenumber of the wave. In electrical engineering, the symbol ${\displaystyle \beta }$, called the phase constant, is often used instead of ${\displaystyle k}$.

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]

${\displaystyle c_{0}={1 \over {\sqrt {\varepsilon _{0}\mu _{0}}}}\ ,}$

where ${\displaystyle \varepsilon _{0}}$ is the electric constant and ${\displaystyle ~\mu _{0}\ }$ is the magnetic constant.

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