Gires-Tournois etalon

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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.

The complex amplitude reflectivity of a Gires-Tournois etalon is given by

$r=-\frac{r_1-e^{-i\delta}}{1-r_1 e^{-i\delta}}$

where r₁ is the complex amplitude reflectivity of the first surface,

$\delta=\frac{4 \pi}{\lambda} n t \cos \theta_t$

n is the index of refraction of the plate

t is the thickness of the plate

θ_t is the angle of refraction the light makes within the plate, and

λ is the wavelength of the light in vacuum.

[edit] Nonlinear phase shift

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.

Note that $| r | = 1$ , independent of $δ$ . This indicates that all the incident energy is reflected and intensity is uniform. However, the multiple reflection causes a nonlinear phase shift $Φ$ . To show this effect, we assume $r 1$ is real and $r_1=\sqrt{R}$ , where $R$ is the intensity reflectivity of the first surface.

Further, define the nonlinear phase shift $Φ$ through

r = e i Φ

and yield

$\tan\left(\frac{\Phi}{2}\right)=-\frac{1+\sqrt{R}}{1-\sqrt{R}}\tan\left(\frac{\delta}{2}\right)$

For R = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change ( $Φ = δ$ ) - linear response. However, as can be seen, when R is increased, the nonlinear phase shift $Φ$ gives the nonlinear response to $δ$ and shows step-like behavior. Gires-Tournois etalon has applications for laser pulse compression and nonlinear Michelson interferometer.

Gires-Tournois etalons are closely related to Fabry-Pérot etalons.

[edit] References

F. Gires, and P. Tournois (1964). "Interferometre utilisable pour la compression d'impulsions lumineuses modulees en frequence". C. R. Acad. Sci. Paris 258: 6112–6115. (An interferometer useful for pulse compression of a frequency modulated light pulse.)

Gires-Tournois Interferometer in RP Photonics Encyclopedia of Laser Physics and Technology

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Categories: Optics | Interferometers

Gires-Tournois etalon

From Wikipedia, the free encyclopedia

[edit] Nonlinear phase shift

[edit] References

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