Talk:Longitudinal mode

Untitled

English needs some improvement — Preceding unsigned comment added by 90.128.64.101 (talk) 16:43, 6 February 2007 (UTC)

I have suggested some improvement as detailed below (mostly highlighted by italic font). 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 waves of wavelength that are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces. All other waves of wavelengths undergoing destructive interference are suppressed.

A longitudinal mode pattern has its nodes located axially along the length of the cavity. Transverse modes, with nodes located perpendicular to the axis of the cavity, may also exist.

A common example of longitudinal modes are the light waves inside a laser cavity. In the simplest case, the laser's optical cavity is formed by two parallel plane (flat) mirrors with gain medium between them (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:

$L=q{\frac {\lambda }{2n}}$

where q is an integer known as the mode order and n is the refractive index of the gain medium.WingkeeLEE 07:21, 9 June 2007 (UTC)

Corrected composite-cavity equation

I have just changed the equation for the longitudinal mode-spacing in a composite cavity from this:

$\Delta \nu =\sum _{i}{\frac {c}{2n_{i}L_{i}}}={\frac {c}{2}}\left[{\frac {1}{n_{1}L_{1}}}+{\frac {1}{n_{2}L_{2}}}+{\frac {1}{n_{3}L_{3}}}+\cdots \right]$,

to this:

$\Delta \nu ={\frac {c}{2\sum _{i}n_{i}L_{i}}}={\frac {c}{2}}\left[{\frac {1}{n_{1}L_{1}+n_{2}L_{2}+n_{3}L_{3}+\ldots }}\right]$.

To see why the second version is correct just consider an evacuated cavity (n = 1) as being composed of two sections, each of length L/2. The first equation gives a mode-spacing of 2c/L, while the second gives the correct value, c/2L.

--DJIndica (talk) 18:26, 29 January 2011 (UTC)