What is Sagnac Effect?

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- GoPhotonics

Jan 31, 2023

The Sagnac effect is a phase shift that can be seen when two light beams go around a spinning object in opposite directions over the same closed route. This phenomenon was discovered in 1913 by French physicist Georges Sagnac. He constructed an interferometer where the two beams follow the same optical path but move in opposing directions. It is an important concept in the field of physics, as it is a key component of the development of modern navigation technology. 

Working Principle of Sagnac Effect

The Sagnac effect, also known as Sagnac interference, is encountered in a setup called ring interferometer or Sagnac interferometer that is brought on by rotation. This phenomenon occurs when a beam of light is split and the two beams are made to travel in opposite directions around a closed path. When the two beams are recombined, they will interfere with each other, resulting in a shift in the interference pattern.  

The Sagnac effect is based on the concept of the relative velocity of light. When the light travels in opposite directions in a closed loop, the time it takes for each path is slightly different due to the rotational movement of the interferometer as the light traveling in one direction will appear to be moving faster to an observer on the loop, while the light traveling in the opposite direction will appear to be moving slower. This difference in the relative velocities of the light waves results in a phase shift between the two light beams, which can be measured as a shift in the interference pattern of the light. The difference in travel time can then be used to measure the rotation of the observer. Sagnac effect is independent of the refractive index of the medium in which the light propagates.

Sagnac Interferometer

Figure 1: Schematic of a sagnac interferometer

The interferometric setup has a beam splitter (half-silvered mirror), three corner mirrors, a light source and a fringe detector.  The light from the light source is split into two beams by the beam splitter. These counter-propagating waves then circulate the interferometer and interfere on the beam splitter and interference fringes are observed by the detector. A small angular misalignment of the mirrors in the ring will alter the fringe pattern and result in a parallel fringe pattern. This makes the output fringe pattern of this interferometer sensitive to any phase change between the two counter-propagating beams. Figure 1 shows the schematic of a sagnac interferometer.

Glass fibers are commonly used in modern version of the Sagnac interferometer to direct the light in a circle.

When the entire interferometer, including the light source and the fringe detector, is rotated at an angular velocity of Ω rad/sec, a fringe shift Δφ with respect to the fringe position for the stationary interferometer is observed, which is given by the formula

where A is the area enclosed by the light path, λ0 is the vacuum wavelength and the free space velocity is c. 

Applications of Sagnac Effect

The Sagnac Effect has been used in a variety of scientific applications, from measuring the rotation of the Earth to determining the speed of light. It is commonly used in modern navigation systems, including GPS and inertial navigation systems such as those found in aircraft and spacecraft, to measure rotational movement. It is also used in the design of interferometers, instruments that rely on the precise measurement of light and in fiber optic gyroscopes, which are used to measure angular velocity. It can be also used in the production of extremely precise clocks. The Sagnac effect can be observed in both Sagnac and Mach-Zehnder interferometers.