Sagnac

The Sagnac effect is a phase shift observed for beams of light (or matter waves) that traverse a closed path in opposite directions on a rotating platform. It is named after Georges Sagnac, who reported in 1913 an interference fringe shift dependent on rotation, using a rotating interferometer. The effect is described within the framework of non-inertial rotating frames and is independent of the source's frame, making it a robust probe of rotation.

In a loop of area A, rotating with angular velocity Ω about an axis perpendicular to the plane, the two counter-propagating beams have different travel times. The time difference is Δt = 4 A Ω / c^2. The resulting phase difference is Δφ = ω Δt = (8 π A Ω) / (λ c), where λ is the light wavelength and c is the speed of light. The sign of the effect depends on the direction of rotation. For matter waves with de Broglie wavelength, a similar expression holds with λ replaced by the appropriate matter wavelength.

The Sagnac effect underlies several technologies: ring laser gyroscopes and fiber-optic gyroscopes measure rotation rates with high sensitivity and are used in navigation systems for aircraft, ships, spacecraft, and inertial guidance. The phenomenon has been observed with various carriers, including microwaves, visible light, neutrons, and atoms, highlighting its geometric origin.

Although associated with non-inertial frames, the Sagnac effect is consistent with special relativity and does not require general relativity. It is often discussed in the context of interferometry, metrology, and navigation.