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Fabry-Perot Interferometers

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Definition: interferometers consisting of two highly reflecting mirrors, forming a standing-wave resonator

A Fabry-Perot interferometer (actually Fabry-Pérot interferometer, also called Fabry-Pérot resonator or cavity) is a linear optical resonator (or cavity) which consists of two highly reflecting mirrors (with some small transmittivity) and is often used as a high-resolution optical spectrometer. One exploits the fact that the transmission through such a resonator exhibits sharp resonances and is very small between those.

Fabry-Perot interferometer

Figure 1: Fabry-Perot interferometer

Strictly, a Fabry-Perot interferometer by definition consists of two planar mirrors, but the term is very frequently also used for resonators with curved mirrors. From a theoretical viewpoint, plane-plane optical resonators are special in the sense that their resonator modes extend up to the edges of the mirrors and experience some diffraction losses. However, Fabry-Perot interferometers are usually used with input beams of much smaller diameter, which are actually not really matched to the resonator modes. For the usually small mirror spacings, where diffraction within a round trip is rather weak, this deviation is not very important.

For optical spectrum analysis, the Fabry-Perot interferometer is often made short enough to achieve a sufficiently large free spectral range; the bandwidth of the resonances is then the free spectral range divided by the finesse. Due to the high reflectivities, the finesse can be rather high (well above 1000, and with supermirrors even much higher). For a given finesse, the wavelength resolution can be improved by increasing the mirror distance, but only at the cost of reducing the free spectral range, i.e., the range within which unique spectral assignment is possible.

transmission of Fabry-Perot resonator

Figure 2: Frequency-dependent transmission of a linear Fabry-Pérot cavity with mirror reflectivities of 90%.

The resonance frequencies can often be tuned by changing the cavity length (mirror distance) with a piezo actuator. When the voltage applied to the piezo is periodically varied, e.g. with a triangular temporal shape, and the transmitted power versus time is monitored with a photodetector and an oscilloscope, the latter can directly display the optical spectrum of the incident light, provided that the spectral width is smaller than the free spectral range.

Fabry-Perot cavity, animated graphs

Figure 3: Animated graphs, showing the reflected and transmitted complex amplitudes and the power transmission while the round-trip phase shift is varied. Both mirrors are assumed to have a reflectivity of 80%. In this symmetric situation, total transmission and zero reflection are obtained in resonance.

Fabry-Perot cavity, animated graphs

Figure 4: Same as above, but with mirror reflectivities of 80% and 50%. In this asymmetric situation, the reflection does no more go to zero in resonance.

A typical application of a Fabry-Perot interferometer is to check whether a laser operates on a single mode or on multiple modes. High-finesse Fabry-Perot interferometers are also used as reference cavities.

A special kind of Fabry-Perot interferometer is the Gires-Tournois interferometer. Tgus is used not for spectral analysis, but for generating chromatic dispersion.

See also: interferometers, etalons, Gires-Tournois interferometers, optical resonators, resonator modes, mode matching, reference cavities, free spectral range, finesse, supermirrors

Category: resonators

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