Gires-Tournois etalon

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

:$r=-frac\{r\_1-e^\{-idelta\{1-r\_1\; e^\{-idelta$

where "r"₁ is the complex amplitude reflectivity of the first surface,
:$delta=frac\{4\; pi\}\{lambda\}\; n\; t\; cos\; heta\_t$:"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.

Nonlinear phase shift

Note that $|r|\; =\; 1$, independent of $delta$. This indicates that all the incident energy is reflected and intensity is uniform. However, the multiple reflection causes a nonlinear phase shift $Phi$. 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 $Phi$ through

:$r=e^\{iPhi\}$

and yield

:$anleft(frac\{Phi\}\{2\}\; ight)=-frac\{1+sqrt\{R\{1-sqrt\{R\; anleft(frac\{delta\}\{2\}\; ight)$

For "R" = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change ($Phi\; =\; delta$) - linear response. However, as can be seen, when "R" is increased, the nonlinear phase shift $Phi$ gives the nonlinear response to $delta$ 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.

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".)

* [http://www.rp-photonics.com/gires_tournois_interferometers.html Gires-Tournois Interferometer] in "RP Photonics Encyclopedia of Laser Physics and Technology"