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 a Gires–Tournois etalon is (almost) completely reflected, but has an effective 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.

Nonlinear effective 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.

Suppose that $r_1$ is real. Then $|r| = 1$, 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. Define the effective phase shift $\Phi$ through

$r=e^{i\Phi}.$

One obtains

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

For R = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change ($\Phi = \delta$) – 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

• 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