GiresTournois etalon

The Gires–Tournois etalon is a transparent optical device with two reflecting surfaces, one highly reflective. It causes nearly complete reflection of incident light due to multiple-beam interference, introducing an effective phase shift dependent on wavelength. The complex amplitude reflectivity \( r \) is given by:

\[ r = -{\frac {r_{1}-e^{-i\delta }}{1-r_{1}e^{-i\delta }}} \]

where \( r_1 \) is the reflectivity of the first surface, and \( \delta \), the phase shift, is:

\[ \delta = {\frac {4\pi }{\lambda }}nt\cos \theta _{t} \]

with \( n \) as the refractive index, \( t \) as thickness, \( \theta_t \) as the refraction angle, and \( \lambda \) as wavelength.

When \( r_1 \) is real, all incident energy is reflected uniformly, but multiple reflections cause a nonlinear phase shift \( \Phi \). For small reflectivity (\( R = 0 \)), the phase shift equals the round-trip phase change (\( \Phi = \delta \)). However, as \( R \) increases, the phase shift becomes nonlinear and exhibits step-like behavior. This property is used in applications like laser pulse compression and nonlinear Michelson interferometers.

The Gires–Tournois etalon is closely related to Fabry–Pérot etalons. When the second surface's reflectivity drops below 1, the system transitions to resonant behavior typical of Fabry-Pérot etalons.