Chebyshev center - Revision history

en>Mpkuse: /* Linear programming problem */

2014-09-12T15:43:27Z

Linear programming problem

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158.130.109.60: /* Relaxed Chebyshev center */ ... The constraint that \Delta \le x x^T is not convex. It has been changed to \Delta \ge x x^T. The claims at the end of the page are still valid as per the assumptions.

2014-02-07T14:09:27Z

Relaxed Chebyshev center: ... The constraint that \Delta \le x x^T is not convex. It has been changed to \Delta \ge x x^T. The claims at the end of the page are still valid as per the assumptions.

← Older revision		Revision as of 16:09, 7 February 2014
Line 1:		Line 1:
	~~'''Electromagnetically induced grating''' (EIG) is an optical [[Interference (wave propagation)\|interference]] phenomenon where an [[interference pattern]] is used to build~~ a dynamic spatial [[diffraction grating]] in matter. EIGs are dynamically created by [[light]] interference on optically resonant materials and rely on [[population inversion]] and/or optical [[coherence (physics)\|coherence]] properties of the material. They were first demonstrated with population gratings on atoms.<ref>Mitsunaga et al., Phys. Rev. A 59, 4773 (1999)</ref> EIGs can be ~~used for purposes of atomic/molecular velocimetry,<ref>{{cite journal \|doi=10.1016/S0030-4018(99)00228-X \|title=Transient Bragg diffraction by~~ a ~~transferred population grating: application for cold atoms velocimetry \|year=1999 \|author=Tabosa, J \|journal=Optics Communications \|volume=165 \|pages=59}}</ref>~~ to ~~probe the material optical properties such as coherence and population~~ life~~-times,<ref>G.C~~.~~Cardoso~~, ~~Phys~~. ~~Rev. A 65~~, ~~033803 B (2002).</ref> and switching and routing of light~~.<~~ref~~>~~Brown AW, Xiao, M, Opt. Lett. 30, 699 2005 ; Su XM, Ham BS, Dynamic control of the photonic band gap using quantum coherence~~		Ingesting a ɦelthy diet program could be a clever proceеd to make in your dailʏ life. Nonethеless, it's not sometɦing that can bе completed without having operate. To acquirе the most rewards from your endeavours, get startеԁ away appropriate by checking out the easiest waƴ to partiсipate in your program.<br><br>
	~~Phys. Rev. A 71, 013821 (2005)~~<~~/ref~~> ~~Related but different effects are thermally induced gratings and [[photolithographic\|photolithography]] gratings.~~

	~~== Writing, Reading and Phase matching conditions~~ for ~~EIG diffraction ==~~		An easƴ principle for selecting nutritious foods is to focus on the ones that are сonsumed with only small modifications from their unique kind. New food items that maʏ be uncookeԁ oг refined has а lot more nourishment than evеrything else.<br><br>Probably the most significant nutritious recommendations is usually to consume a correct level of vegetables and fruits. It's encouraged from the USDA that you simply ingest among 9 and 13 servings of vegеtables аnd fruit daily. Even though [http://Www.jimimedia.se/forums/member.php?action=profile&uid=32098 vigrx plus vs zenerx] this may sound liƙe a lot of helpings, yet it iѕ in fact an easy task to easily fit іn. A new cuƿ of orangе liquid or possibly а tomato-centered marinade on noodles can add up as helpings.<br><br>Take advаntage of the stealth technique of intгoducing healthy food into a tyρical dinner or recipe. 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	~~Figure 1 shows a possible beam configuration~~ to ~~write and read an EIG~~. ~~The period of the grating is controlled by the angle~~ <~~math~~>~~\theta~~<~~/math~~>. ~~The writing~~ and ~~reading frequencies are not necessarily the same~~. E<~~sub~~>_B<~~/sub~~> is ~~referred as~~ the ~~"backward" reading beam~~ and E<~~sub~~>R<~~/sub~~> ~~is the signal obtained by diffraction~~ on ~~the grating~~.

	[~~[File~~:~~Write-Read EIG color~~.~~jpg\|left\|thumb\|260px\|'''Figure 1''': Writing and reading an EIG~~]]

	~~The phase-matching conditions~~ for the ~~EIG for~~ the ~~plane-wave approximation~~ is ~~given by~~ the ~~simple geometric relation:~~

	<~~math~~>~~\sin\beta=n \Bigl(\frac{\omega_1}{\omega_2}\Bigr) \sin(\theta/2)~~<~~/math~~>,

	~~where the angles~~ are ~~given according to Fig~~. 2, <~~math~~>~~\omega_1~~<~~/math~~> and <~~math~~>~~\omega_2~~<~~/math~~> ~~are~~ the ~~frequencies of~~ the ~~writing (W, W')~~ and ~~reading beam (R)~~, ~~respectively~~, and ~~n is the effective index of refraction of the medium~~.

	[~~[File~~:~~Bragg~~-~~condition~~.~~jpg\|center\|thumb\|350px\|'''Figure 2''': Phase matching conditions for EIG diffraction~~]]

	~~== Types of EIG ==~~

	[[~~File~~:~~Grating-types~~.~~jpg\|right\|thumb\|300px\|'''Figure 3'''~~: ~~Difference between a "matter grating" a "population grating"~~. ~~The [[smiley~~]~~]s :~~-~~( and :~~-~~) represent ground and optically excited atoms~~, ~~respectively.]]~~

	~~'''Matter Gratings''': The writing lasers form~~ a ~~grating by modulating density~~ of ~~matter or by localizing matter (trapping) on the regions~~ of ~~maxima (~~or ~~minima)~~ of ~~the writing interference fields~~. ~~A thermal grating is an example~~. ~~Matter gratings~~ have ~~slow dynamics (milliseconds) compared~~ to ~~population~~ and ~~phase gratings (potentially nanoseconds and faster)~~.

	~~'''Population Gratings''': The writing lasers~~ are ~~resonant with optical transitions in~~ the ~~matter and the grating is formed by [[optical pumping]]~~. ~~(See Fig. 3)~~

	~~'''Coherence Gratings''': A grating where the writing lasers form a coherent~~ matter ~~pattern. An example is~~ a ~~pattern~~ of ~~[[electromagnetically induced transparency]]~~

	~~== Applications ==~~

	~~Usually two [[laser]]s at an angle are used to build an EIG~~. The ~~EIG~~ is ~~used to diffract~~ a ~~third laser~~, ~~to monitor~~ the ~~behavior~~ of ~~the underlying substrate where the EIG was written or~~ to ~~serve as~~ a ~~switch for one of the lasers involved in the process~~.

	~~==See also==~~
	*[[Atomic coherence]]
	*[[Electromagnetically induced transparency]]
	*[[Bragg's law]]
	*[[Optical lattice]]

	~~==Notes==~~
	~~{{reflist}}~~

	~~==References==~~
	*Laser-induced thermal grating effects in ~~flames~~, ~~S Williams~~,~~La Rahn~~, ~~Ph Paul, JW Forsman, RN Zare Opt~~. ~~Lett. 19:2121~~, ~~1681–1683~~, ~~1994~~
	*{{cite journal \|doi=10.1103/PhysRevA.65.033803 \|title=Electromagnetically induced gratings in a degenerate open two-level system \|year=2002 \|author=Cardoso, G. C. \|journal=Physical Review A \|volume=65 \|pages=033803 \|last2=Tabosa \|first2=J. \|issue=3}}

	~~[[Category:Wave mechanics]]~~
	~~[[Category:Quantum mechanics]]~~
	~~[[Category:Optics]]~~

en>Yobot: clean up, References after punctuation per WP:REFPUNC and WP:PAIC using AWB (8434)

2012-09-24T17:55:46Z

clean up, References after punctuation per WP:REFPUNC and WP:PAIC using AWB (8434)

← Older revision		Revision as of 19:55, 24 September 2012
Line 1:		Line 1:
	~~I’m Temeka from Sao Paulo doing my final~~ year ~~engineering in Law~~. ~~I did my schooling~~, ~~secured 83%~~ and ~~hope~~ to ~~find someone with same interests in Kayaking~~.<br><br>~~my homepage~~ ... ~~advertiser;~~ [~~http~~://~~brokerltd~~.~~com~~/~~pub_cpm_network~~.~~html view publisher site~~],		'''Electromagnetically induced grating''' (EIG) is an optical [[Interference (wave propagation)\|interference]] phenomenon where an [[interference pattern]] is used to build a dynamic spatial [[diffraction grating]] in matter. EIGs are dynamically created by [[light]] interference on optically resonant materials and rely on [[population inversion]] and/or optical [[coherence (physics)\|coherence]] properties of the material. They were first demonstrated with population gratings on atoms.<ref>Mitsunaga et al., Phys. Rev. A 59, 4773 (1999)</ref> EIGs can be used for purposes of atomic/molecular velocimetry,<ref>{{cite journal \|doi=10.1016/S0030-4018(99)00228-X \|title=Transient Bragg diffraction by a transferred population grating: application for cold atoms velocimetry \|year=1999 \|author=Tabosa, J \|journal=Optics Communications \|volume=165 \|pages=59}}</ref> to probe the material optical properties such as coherence and population life-times,<ref>G.C.Cardoso, Phys. Rev. A 65, 033803 B (2002).</ref> and switching and routing of light.<ref>Brown AW, Xiao, M, Opt. Lett. 30, 699 2005 ; Su XM, Ham BS, Dynamic control of the photonic band gap using quantum coherence
			Phys. Rev. A 71, 013821 (2005)</ref> Related but different effects are thermally induced gratings and [[photolithographic\|photolithography]] gratings.

			== Writing, Reading and Phase matching conditions for EIG diffraction ==

			Figure 1 shows a possible beam configuration to write and read an EIG. The period of the grating is controlled by the angle <math>\theta</math>. The writing and reading frequencies are not necessarily the same. E<sub>_B</sub> is referred as the "backward" reading beam and E<sub>R</sub> is the signal obtained by diffraction on the grating.

			[[File:Write-Read EIG color.jpg\|left\|thumb\|260px\|'''Figure 1''': Writing and reading an EIG]]

			The phase-matching conditions for the EIG for the plane-wave approximation is given by the simple geometric relation:

			<math>\sin\beta=n \Bigl(\frac{\omega_1}{\omega_2}\Bigr) \sin(\theta/2)</math>,

			where the angles are given according to Fig. 2, <math>\omega_1</math> and <math>\omega_2</math> are the frequencies of the writing (W, W') and reading beam (R), respectively, and n is the effective index of refraction of the medium.

			[[File:Bragg-condition.jpg\|center\|thumb\|350px\|'''Figure 2''': Phase matching conditions for EIG diffraction]]

			== Types of EIG ==

			[[File:Grating-types.jpg\|right\|thumb\|300px\|'''Figure 3''': Difference between a "matter grating" a "population grating". The [[smiley]]s :-( and :-) represent ground and optically excited atoms, respectively.]]

			'''Matter Gratings''': The writing lasers form a grating by modulating density of matter or by localizing matter (trapping) on the regions of maxima (or minima) of the writing interference fields. A thermal grating is an example. Matter gratings have slow dynamics (milliseconds) compared to population and phase gratings (potentially nanoseconds and faster).

			'''Population Gratings''': The writing lasers are resonant with optical transitions in the matter and the grating is formed by [[optical pumping]]. (See Fig. 3)

			'''Coherence Gratings''': A grating where the writing lasers form a coherent matter pattern. An example is a pattern of [[electromagnetically induced transparency]]

			== Applications ==

			Usually two [[laser]]s at an angle are used to build an EIG. The EIG is used to diffract a third laser, to monitor the behavior of the underlying substrate where the EIG was written or to serve as a switch for one of the lasers involved in the process.

			==See also==
			*[[Atomic coherence]]
			*[[Electromagnetically induced transparency]]
			*[[Bragg's law]]
			*[[Optical lattice]]

			==Notes==
			{{reflist}}

			==References==
			*Laser-induced thermal grating effects in flames, S Williams,La Rahn, Ph Paul, JW Forsman, RN Zare Opt. Lett. 19:2121, 1681–1683, 1994
			*{{cite journal \|doi=10.1103/PhysRevA.65.033803 \|title=Electromagnetically induced gratings in a degenerate open two-level system \|year=2002 \|author=Cardoso, G. C. \|journal=Physical Review A \|volume=65 \|pages=033803 \|last2=Tabosa \|first2=J. \|issue=3}}

			[[Category:Wave mechanics]]
			[[Category:Quantum mechanics]]
			[[Category:Optics]]

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