Editing Ring laser gyroscope (section)

==Principle of operation==
According to the [[Sagnac effect]], rotation induces a small difference between the time it takes light to traverse the ring in the two directions. This introduces a tiny separation between the frequencies of the counter-propagating beams, a motion of the [[standing wave]] pattern within the ring, and thus a beat pattern when those two beams interfere outside the ring. Therefore, the net shift of that interference pattern follows the rotation of the unit in the plane of the ring.

RLGs, while more accurate than mechanical gyroscopes, suffer from an effect known as "lock-in" at very slow rotation rates. When the ring laser is hardly rotating, the frequencies of the counter-propagating laser modes become almost identical. In this case, crosstalk between the counter-propagating beams can allow for [[injection locking]], so that the standing wave "gets stuck" in a preferred phase, thus locking the frequency of each beam to that of the other, rather than responding to gradual rotation.

Forced [[dithering]] can largely overcome this problem. The ring laser cavity is rotated clockwise and anti-clockwise about its axis using a mechanical spring driven at its resonance frequency. This ensures that the angular velocity of the system is usually far from the lock-in threshold.  Typical rates are 400&nbsp;Hz, with a peak dither velocity on the order of 1 degree per second. Dither does not fix the lock-in problem completely, as each time the direction of rotation is reversed, a short time interval exists in which the rotation rate is near zero and lock-in briefly can occur. If a pure frequency oscillation is maintained, these small lock-in intervals can accumulate. This was remedied by introducing noise to the 400&nbsp;Hz vibration.<ref name="MacKenzie">''Knowing Machines'', Donald MacKenzie, The MIT Press, (1991).</ref>

A different approach to avoiding lock-in is embodied in the Multioscillator Ring Laser Gyroscope,<ref>{{cite book |author1=Statz, Hermann |author2=Dorschner, T. A. |author3=Holz, M. |author4=Smith, I. W. |editor1-last=Stich |editor1-first=M.L. |editor2-last=Bass |editor2-first=M. |title=Laser handbook. |date=1985 |publisher=Elsevier (North-Holland Pub. Co) |isbn=0444869271 |pages=[https://archive.org/details/laserhandbook0001arec/page/229 229-332] |language=en |chapter=3. The multioscillator ring laser gyroscope |chapter-url=https://archive.org/details/laserhandbook0001arec/page/229 }}</ref><ref>Volk, C. H. et al., ''Multioscillator Ring Laser Gyroscopes and their applications'', in ''Optical Gyros and their Applications (NATO RTO-AG-339 AC/323(SCI)TP/9)'', Loukianov, D et al. (eds.) [http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.856.5890&rep=rep1&type=pdf#page=70] Retrieved 23 October 2019</ref> wherein what is effectively two independent ring lasers (each having two counterpropagating beams) of opposite circular polarization coexist in the same ring resonator. The resonator incorporates polarization rotation (via a nonplanar geometry) which splits the fourfold-degenerate cavity mode (two directions, two polarizations each) into right- and left-circular-polarized modes separated by many hundreds of MHz, each having two counterpropagating beams. Nonreciprocal bias via the [[Faraday effect]], either in a special thin Faraday rotator, or via a longitudinal magnetic field on the gain medium, then further splits each circular polarization by typically a few hundred kHz, thus causing each ring laser to have a static output beat frequency of hundreds of kHz. One frequency increases and one decreases, when inertial rotation is present; the two frequencies are measured and then digitally subtracted to finally yield the net Sagnac-effect frequency splitting and thus determine the rotation rate. The Faraday bias frequency is chosen to be higher than any anticipated rotation-induced frequency difference, so the two counterpropagating waves have no opportunity to lock-in.