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 }}nt\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

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