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| In [[optics]], a '''Gires–Tournois etalon''' is a transparent plate with two reflecting surfaces, one of which has very high reflectivity. Due to [[multiple-beam interference]], light incident on the lower-reflectivity surface of a Gires–Tournois etalon is (almost) completely reflected, but has a phase shift that depends strongly on the [[wavelength]] of the light.
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| The complex amplitude reflectivity of a Gires–Tournois etalon is given by
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| :<math>r=-\frac{r_1-e^{-i\delta}}{1-r_1 e^{-i\delta}} </math>
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| where ''r''<sub>1</sub> is the complex amplitude reflectivity of the first surface,<br>
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| :<math>\delta=\frac{4 \pi}{\lambda} n t \cos \theta_t</math>
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| :''n'' is the [[index of refraction]] of the plate
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| :''t'' is the thickness of the plate | |
| :''θ<sub>t</sub>'' is the [[angle of refraction]] the light makes within the plate, and | |
| :''λ'' is the wavelength of the light in vacuum.
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| == Nonlinear phase shift == | |
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| [[Image:Phase Shift.gif|thumb|right|400px|Nonlinear phase shift ''Φ'' as a function of ''δ'' for different ''R'' values: (a) ''R'' = 0, (b) ''R'' = 0.1, (c) ''R'' = 0.5, and (d) ''R'' = 0.9.]]
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| Note that <math>|r| = 1</math>, independent of <math>\delta</math>. This indicates that all the incident energy is reflected and intensity is uniform. However, the multiple reflection causes a [[nonlinear]] [[phase shift]] <math>\Phi</math>. To show this effect, we assume <math>r_1</math> is real and <math>r_1=\sqrt{R}</math>, where <math>R</math> is the intensity reflectivity of the first surface.
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| Further, define the nonlinear phase shift <math>\Phi</math> through
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| :<math>r=e^{i\Phi} </math>
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| and yield
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| :<math>\tan\left(\frac{\Phi}{2}\right)=-\frac{1+\sqrt{R}}{1-\sqrt{R}}\tan\left(\frac{\delta}{2}\right) </math>
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| For ''R'' = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change (<math>\Phi = \delta</math>) – linear response. However, as can be seen, when ''R'' is increased, the nonlinear phase shift <math>\Phi</math> gives the nonlinear response to <math>\delta</math> and shows step-like behavior. Gires–Tournois etalon has applications for laser [[pulse compression]] and nonlinear [[Michelson interferometer]].
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| Gires–Tournois etalons are closely related to [[Fabry–Pérot etalon]]s.
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| ==References== | |
| *{{cite journal | author=F. Gires, and P. Tournois | title=Interferometre utilisable pour la compression d'impulsions lumineuses modulees en frequence | journal=C. R. Acad. Sci. Paris | year=1964 | volume=258 | pages= 6112–6115 | url= }} (''An interferometer useful for pulse compression of a frequency modulated light pulse''.)
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| *[http://www.rp-photonics.com/gires_tournois_interferometers.html Gires–Tournois Interferometer] in ''RP Photonics Encyclopedia of Laser Physics and Technology''
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| {{DEFAULTSORT:Gires-Tournois etalon}}
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| [[Category:Optics]]
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| [[Category:Interferometers]]
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