Fabry–Pérot interferometer

In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces (i.e: thin mirrors). Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning 'measuring gauge' or 'standard'. In optics, a Fabry–Pérot interferometer (FPI) or etalon is an optical cavity made from two parallel reflecting surfaces (i.e: thin mirrors). Optical waves can pass through the optical cavity only when they are in resonance with it. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning 'measuring gauge' or 'standard'. Etalons are widely used in telecommunications, lasers and spectroscopy to control and measure the wavelengths of light. Recent advances in fabrication technique allow the creation of very precise tunable Fabry–Pérot interferometers. The device is called an interferometer when the distance between the two surfaces (and with it the resonance length) can be changed, and etalon when the distance is fixed (however, the two terms are often used interchangeably). The heart of the Fabry–Pérot interferometer is a pair of partially reflective glass optical flats spaced micrometers to centimeters apart, with the reflective surfaces facing each other. (Alternatively, a Fabry–Pérot etalon uses a single plate with two parallel reflecting surfaces.) The flats in an interferometer are often made in a wedge shape to prevent the rear surfaces from producing interference fringes; the rear surfaces often also have an anti-reflective coating. In a typical system, illumination is provided by a diffuse source set at the focal plane of a collimating lens. A focusing lens after the pair of flats would produce an inverted image of the source if the flats were not present; all light emitted from a point on the source is focused to a single point in the system's image plane. In the accompanying illustration, only one ray emitted from point A on the source is traced. As the ray passes through the paired flats, it is multiply reflected to produce multiple transmitted rays which are collected by the focusing lens and brought to point A' on the screen. The complete interference pattern takes the appearance of a set of concentric rings. The sharpness of the rings depends on the reflectivity of the flats. If the reflectivity is high, resulting in a high Q factor, monochromatic light produces a set of narrow bright rings against a dark background. A Fabry–Pérot interferometer with high Q is said to have high finesse. The spectral response of a Fabry-Pérot resonator is based on interference between the light launched into it and the light circulating in the resonator. Constructive interference occurs if the two beams are in phase, leading to resonant enhancement of light inside the resonator. If the two beams are out of phase, only a small portion of the launched light is stored inside the resonator. The stored, transmitted, and reflected light is spectrally modified compared to the incident light. Assume a two-mirror Fabry-Pérot resonator of geometrical length ℓ {displaystyle ell } , homogeneously filled with a medium of refractive index n {displaystyle n} . Light is launched into the resonator under normal incidence. The round-trip time t R T {displaystyle t_{ m {RT}}} of light travelling in the resonator with speed c = c 0 / n {displaystyle c=c_{0}/n} , where c 0 {displaystyle c_{0}} is the speed of light in vacuum, and the free spectral range Δ ν F S R {displaystyle Delta u _{ m {FSR}}} are given by The electric-field and intensity reflectivities r i {displaystyle r_{i}} and R i {displaystyle R_{i}} , respectively, at mirror i {displaystyle i} are If there are no other resonator losses, the decay of light intensity per round trip is quantified by the outcoupling decay-rate constant 1 / τ o u t , {displaystyle 1/ au _{ m {out}},} and the photon-decay time τ c {displaystyle au _{c}} of the resonator is then given by