 The first six longitudinal modes of a plane-parallel cavity. A longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces. All other wavelengths undergo destructive interference and are surpressed. A cavity resonator uses resonance to amplify a wave. ...
A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ...
Jump to: navigation, search A wave is a disturbance that propagates in a periodically repeating fashion, often transferring energy. ...
Jump to: navigation, search The wavelength is the distance between repeating units of a wave pattern. ...
Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...
A common example of longitudinal modes are the light wavelengths produced by a laser. In the simplest case, the laser's optical cavity is formed by two opposed plane (flat) mirrors surrounding the gain medium (a plane-parallel or Fabry-Perot cavity). The allowed modes of the cavity are those where the mirror separation distance L is equal to an exact multiple of half the wavelength, λ: Jump to: navigation, search Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific setting, electromagnetic radiation of any wavelength. ...
Jump to: navigation, search The range of sizes in which lasers exist is immense, extending from microscopic diode lasers (top) to football field sized neodymium glass lasers (bottom) used for inertial confinement fusion. ...
A cavity resonator uses resonance to amplify a wave. ...
Jump to: navigation, search A mirror is a surface with good specular reflection that is smooth enough to form an image. ...
Jump to: navigation, search A laser system generally consists of three important parts: An energy source (usually referred to as the pump or pump source); A gain medium or laser medium; A mirror, or system of mirrors, forming an optical resonator. ...
In optics, a Fabry-Perot interferometer or etalon is typically made of a transparent plate with two reflecting surfaces, or two parallel highly-reflecting mirrors. ...
 where q is an integer known as the mode order.
In practice, the separation distance of the mirrors L is usually much greater than the wavelength of light λ, so the relevant values of q are large (around 105 to 106). The frequency separation between any two adjacent modes q and q+1 are given (for an empty linear resonator of length L) by Δν:
 where c is the speed of light.
If the cavity is non-empty (i.e. contains one or more elements with a non-unity refractive index), the values of L used are the optical path lengths of varying refractive indices. This is given by: Jump to: navigation, search The refractive index of a material is the factor by which the phase velocity of electromagnetic radiation is slowed relative to vacuum. ...
In optics and telecommunication, the term optical path length has the following meanings: In a medium of constant refractive index, n , the product of the geometric distance and the refractive index. ...
![Delta nu = sum_i frac{c}{2 n_i L_i} = frac{c}{2}left[ frac{1}{n_1 L_1} + frac{1}{n_2 L_2} + frac{1}{n_3 L_3} + cdots right]](http://en.wikipedia.org/math/a/b/b/abb3a8b68a5817f691bde0ab65fe02be.png) where ni is the refractive index of the i'th element of length Li.
More generally, the longitudinal modes may be found for any type of wave in a cavity by solving the relevant wave equation with the appropriate boundary conditions. The wave equation is an important partial differential equation which generally describes all kinds of waves, such as sound waves, light waves and water waves. ...
In mathematics, boundary conditions are imposed on the solutions of ordinary differential equations and partial differential equations, to fit the solutions to the actual problem. ...
Both transverse and longitudinal waves may have longitudinal modes when confined to a cavity. Jump to: navigation, search A light wave is an example of a transverse wave. ...
Longitudinal waves, also referred to as compressional waves or pressure waves, are waves that have vibrations along or parallel to their direction of travel. ...
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