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

Failed to parse (Missing texvc executable; please see math/README to configure.): \eta = {E_x \over H_y}

where Failed to parse (Missing texvc executable; please see math/README to configure.): E_x

and Failed to parse (Missing texvc executable; please see math/README to configure.): H_y
are the electric field and magnetic field, respectively.

In a region is with no electrical conductivity, the expression simplifies to:

Failed to parse (Missing texvc executable; please see math/README to configure.): \eta = \sqrt{\mu \over \varepsilon}\ .

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

Failed to parse (Missing texvc executable; please see math/README to configure.): Z_0 = \sqrt{\mu_0 \over \varepsilon_0}\ .

Waves propagate through a medium with velocity Failed to parse (Missing texvc executable; please see math/README to configure.): c_w = \nu \lambda , where Failed to parse (Missing texvc executable; please see math/README to configure.): \nu

 is the frequency and Failed to parse (Missing texvc executable; please see math/README to configure.): \lambda
is the wavelength of the electromagnetic waves. This equation also may be put in the form

Failed to parse (Missing texvc executable; please see math/README to configure.): c_w = {\omega \over k}\ ,

where Failed to parse (Missing texvc executable; please see math/README to configure.): \omega

is the angular frequency of the wave and Failed to parse (Missing texvc executable; please see math/README to configure.): k
is the wavenumber of the wave. In electrical engineering, the symbol Failed to parse (Missing texvc executable; please see math/README to configure.): \beta

, called the phase constant, is often used instead of Failed to parse (Missing texvc executable; please see math/README to configure.): 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]

Failed to parse (Missing texvc executable; please see math/README to configure.): c_0 = {1 \over \sqrt{\varepsilon_0 \mu_0}}\ ,

where Failed to parse (Missing texvc executable; please see math/README to configure.): \varepsilon_0

is the electric constant and Failed to parse (Missing texvc executable; please see math/README to configure.): ~ \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, 6^th Edition, 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, 2^nd Edition, Princeton NJ: Princeton University Press. ISBN 978-0-691-12456-8. 

See also

• Electromagnetic spectrum
• Electromagnetic radiation
• Optics
• SI units
• Free space
• Photonic crystal
• Photonic crystal fiber
• Čerenkov radiationcs:Optické prostředí

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