Interferometer

An interferometer divides a beam, sends the parts along different paths, and brings them back together. When two beams of intensities $I_1$ and $I_2$ recombine with a phase difference $\phi$, the output is $I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$, so the output swings between bright and dark as the path difference changes by one wavelength. Because the wavelength is a fraction of a micrometer, an interferometer converts tiny changes in length, refractive index or frequency into large changes in intensity. Fringes appear only while the path difference is shorter than the source's coherence length, and their contrast, the visibility, falls as the two beams become unequal in power, polarization or coherence.

The common configurations differ in how the paths are arranged. In a Michelson interferometer a beam splitter sends light to two mirrors and recombines the reflections; because each arm is traversed twice, moving a mirror by half a wavelength, 316.4 nm for a 632.8 nm helium-neon laser, shifts the output by one full fringe, which is how displacement-measuring interferometers count distance. The Twyman-Green and Fizeau interferometers are its variants for testing optical surfaces. A Mach-Zehnder interferometer uses separate splitting and combining elements, so the two outputs are accessible and each path is traversed once; it is the structure of most integrated modulators and switches. A Fabry-Perot interferometer, or etalon, recirculates light between two mirrors and interferes many beams rather than two, which sharpens the fringes into narrow transmission peaks.

A Sagnac interferometer sends two beams around the same loop in opposite directions. At rest the paths are identical; rotation at rate $\Omega$ lengthens one relative to the other and produces a phase difference $\Delta\phi = 2\pi L D \Omega/(\lambda c)$ for a fiber coil of length $L$ and diameter $D$. For 1 km of fiber on a 10 cm coil at 1550 nm, the Earth's rotation produces 98.6 µrad, a signal that fiber-optic gyroscopes resolve for navigation.

Interferometers appear in the lab in several other forms: the delayed self-heterodyne linewidth measurement, the unbalanced interferometers that demodulate phase-coded signals, the optical coherence tomography scanner, and the wavemeter. The largest are the gravitational-wave detectors, Michelson interferometers with 4 km arms and resonant cavities in each arm, whose sensitivity at high frequencies is limited by shot noise and improved with squeezed light.

References: M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), Ch. 7; H. C. Lefèvre, The Fiber-Optic Gyroscope, 2nd ed. (Artech House, 2014).