en>HuffTheWeevil: cleanup

2014-09-11T05:02:25Z

cleanup

← Older revision		Revision as of 07:02, 11 September 2014
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	~~{{unreferenced\|date=October 2011}}~~		The title of [http://vip.akwacity.com/oxwall/blogs/post/10278 at home std test] the over the counter [http://www.ddhelicam.com/board_Kurr59/59568 at home std testing] std test writer is Numbers but it's not the most masucline title out there. For many years he's been operating as a receptionist. One of the things she loves most is to read comics and she'll be beginning something else alongside with it. California is exactly where her home is but she requirements to move simply because home std test kit of her family.<br><br>Feel free to visit my [http://medweb.mit.edu/wellness/programs/herpes.html blog post] :: std testing at home - [http://test.ithink-now.org/content/think-f83d96d08fe71e25bf80a6cb59048a18 she said] -
	~~''For the longitudinal mode~~ of ~~conduction of electric currents, see [[Common mode]]''~~
	[[~~Image~~:~~longitudinal mode v2~~.~~svg\|200px\|thumb\|right\|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 [[wave]]s confined in~~ the ~~cavity. The longitudinal modes correspond to~~ the [~~[wavelength]]s of the wave which are reinforced by constructive [[Interference (wave propagation)\|interference]] after many reflections from the cavity's reflecting surfaces~~. ~~All other wavelengths are suppressed by destructive interference~~.

	~~A longitudinal mode pattern has its [[Node (physics)\|nodes]] located axially along the length of the cavity. [[Transverse mode]~~]s~~, with nodes located perpendicular to the axis of~~ the ~~cavity, may also exist~~.

	~~==Simple cavity==~~
	~~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) [[mirror]]s surrounding the [[gain medium]] (~~a ~~plane-parallel or [[Fabry–Pérot]] 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'':~~
	~~:<math> L = q \frac{\lambda}{2} </math>~~
	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 10~~<~~sup~~>5<~~/sup~~> to ~~10<sup>6<~~/sup>). The frequency separation between any two adjacent modes, ''q'' and ''q''+1, in a material that is transparent at the laser wavelength, are given (for an empty linear resonator of length ''L'') by Δ''ν'':
	~~:<math>\Delta\nu = \frac{c}{2nL} <~~/~~math>~~
	~~where ''c'' is the speed of light and n is the refractive index of the material (note: n≈1 in air)~~.

	~~==Composite cavity==~~
	~~If the cavity is non-empty (i~~.e. ~~contains one or more elements with different values of [[refractive index]]), the values of ''L'' used are the [[optical path length~~]~~]s for each element. The frequency spacing of longitudinal modes in the cavity is then given by~~:
	:~~<math>\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]</math>~~
	~~where ''n''<sub>i<~~/~~sub> is the refractive index of the i'th element of length ''L''<sub>i<~~/~~sub>~~.

	~~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]]~~.

	~~Both [[transverse wave\|transverse]] and [[longitudinal wave]]s may have longitudinal modes when confined to a cavity.~~

	~~The analysis of longitudinal modes is especially important in lasers with single transversal mode, for example, in single~~-~~mode [[fiber laser]]s. The number of longitudinal modes of such a laser can be estimated as ratio of the spectral width of gain to the spectral separation of longitudinal modes.~~

	~~==Power per longitudinal mode==~~
	~~For lasers with single transversal mode, the power per one longitudinal mode can be significantly increased by the [[coherent addition]~~] ~~of lasers. Such addition allows one to both scale~~-up the output power of a single-transverse-mode laser and reduce number of longitudinal modes; because the system chooses automatically only the modes which are common for all the combined lasers. The reduction of the number of longitudinal modes determines the limits of the [[coherent addition]]. The ability to coherently add one additional laser is exhausted when one longitudinal mode, common for the combined lasers, lies within the spectral width of the gain; a subsequent addition will lead to loss of efficiency of the coherent combination and will not increase the power per ''longitudinal mode'' of such a laser.

	~~==See also==~~
	*[[Modelocking]]
	*[[Normal mode]]

	~~[[Category:Wave mechanics]]~~

203.116.198.67: /* Surge line */

2013-09-26T06:29:04Z

Surge line

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en>Mrblain123: added link to main compressor article, reformatted the formula for surge margin

2011-11-23T22:53:11Z

added link to main compressor article, reformatted the formula for surge margin

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Compressor map - Revision history

en>HuffTheWeevil: cleanup

203.116.198.67: /* Surge line */

en>Mrblain123: added link to main compressor article, reformatted the formula for surge margin