The optical 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]

1. Homogeneous medium vs. heterogeneous medium
2. Transparent medium vs. opaque body

• • Translucent medium

• Čerenkov radiation
• Electromagnetic spectrum
• Electromagnetic radiation
• Optics
• SI units
• Free space
• Metamaterial
• Photonic crystal
• Photonic crystal fiber