In optics, a Gires–Tournois etalon (also known as Gires–Tournois interferometer) is a transparent plate with two reflecting surfaces, one of which has very high reflectivity, ideally unity. 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=- |
| ||||||
1-r1e-i\delta |
where r1 is the complex amplitude reflectivity of the first surface,
\delta= | 4\pi |
λ |
nt\cos\thetat
n is the index of refraction of the plate
t is the thickness of the plate
θt is the angle of refraction the light makes within the plate, and
λ is the wavelength of the light in vacuum.
Suppose that
r1
|r|=1
\delta
\Phi
To show this effect, we assume
r1
r1=\sqrt{R}
R
\Phi
r=ei\Phi.
One obtains
\tan\left( | \Phi | \right)=- |
2 |
1+\sqrt{R | |
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
\Phi
\delta
Gires–Tournois etalons are closely related to Fabry–Pérot etalons. This can be seen by examining the total reflectivity of a Gires–Tournois etalon when the reflectivity of its second surface becomes smaller than 1. In these conditions the property
|r|=1