Gires-Tournois etalon
Encyclopedia
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
where r1 is the complex amplitude reflectivity of the first surface,
, independent of 
. This indicates that all the incident energy is reflected and intensity is uniform. However, the multiple reflection causes a nonlinear phase shift 
. To show this effect, we assume 
is real and 
, where 
is the intensity reflectivity of the first surface.
Further, define the nonlinear phase shift
through
and yield
For R = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change (
) – linear response. However, as can be seen, when R is increased, the nonlinear phase shift 
gives the nonlinear response to 
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.
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
, 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
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
of the light.
The complex amplitude reflectivity of a Gires–Tournois etalon is given by
where r1 is the complex amplitude reflectivity of the first surface,
- 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.
Nonlinear phase shift
Note that, independent of . This indicates that all the incident energy is reflected and intensity is uniform. However, the multiple reflection causes a nonlinear phase shift . To show this effect, we assume is real and , where is the intensity reflectivity of the first surface.Further, define the nonlinear phase shift
throughand yield
For R = 0, no reflection from the first surface and the resultant nonlinear phase shift is equal to the round-trip phase change (
) – linear response. However, as can be seen, when R is increased, the nonlinear phase shift gives the nonlinear response to and shows step-like behavior. Gires–Tournois etalon has applications for laser pulse compressionPulse compression
Pulse compression is a signal processing technique mainly used in radar, sonar and echography to increase the range resolution as well as the signal to noise ratio...
and nonlinear Michelson interferometer
Michelson interferometer
The Michelson interferometer is the most common configuration for optical interferometry and was invented by Albert Abraham Michelson. An interference pattern is produced by splitting a beam of light into two paths, bouncing the beams back and recombining them...
.
Gires–Tournois etalons are closely related to Fabry–Pérot etalons.