The ring laser gyro had its beginning with the observation that rotation removed the degeneracy between the clockwise and the counterclockwise traveling waves in a resonant cavity, and that the frequency difference was directly proportional to the angular rotation rate l. The measurement of rotation by the interference of electromagnetic waves in non-resonant or non-reentrant structures was recognized more than a half century earlier in 1897 by Oliver Lodge2. His research apparatus which is shown in Figure 1 consisted of mirrors at the corners of a 1 m x 6 m rectangle, light source, semi-transparent plate, and telescope, and was used in his study of the drag of the ether by rotating steel discs. In his negative comments concerning ether drag, he included the following comment. "Hence if, --, the whole apparatus, lantern, optical frame, telescope, observer and all were mounted on a turntable and caused to rotate, a reversible shift of the bands should be seen. ----The effect would be of an aberrational kind, the opposite light beams being accelerated and retarded by the motion appropriately.----My present optical apparatus mounted on a turntable revolving 4 times a minute should show something, viz.: 1/100th band shift each way. A certain amount of discomfort during the accelerative stages of any speed could hardly be avoided, and even

A brief and simplified overview of optical gyroscopes is presented with emphasis on recent developments in passive approaches.

The semiclassical theory of a ring laser gyro is reviewed including discussion of the Sagnac effect, mode coupling, mode locking, dither, bias techniques, role of isotopes, and gaseous laser media. In addition a fully quantized theory for media with nonmoving atoms is used to examine the stability of unidirectional operation.

The paper gives an overview of multioscillator laser theory. As an example, we discuss the application of multioscillator laser theory in ZLAG (Zeeman laser gyro) investigations.

Several years ago Ezekiel proposed and built a passive ring laser gyroscope whereby laser light is injected into an optical cavity via an external source'. The passive approach has potentially several advantages over the active ring gyro, as has been pointed out by Ezekiel and others 2,3,4. Among them are elimination of Langmuir flow effects and elimination of magnetic field sensitivity. When considering the passive RLG it might appear that it should not exhibit the beat frequency locking phenomenons. We wish to point out that at least under some conditions, the passive gyro should show locking behavior.

In these notes the number-phase uncertainty relationship satisfied by laser light is derived and found to be very nearly AnAΦ = 1/2. This relation is of interest due to a calculation which relates the deviation of laser light from a minimum uncertainty state to the quantum noise limit on the performance of ring laser gyroscopes.

Measured power spectral densities SAf of ringlaser beat frequencies Af(t) consist mainly of 1) white noise 2) 1/f or flicker noise 3) 1/f2 noise. Consequently, experimental results can be represented by a power series of the Fourier frequency f, SAf(f) = ho + h_1 f-1+ h_2 f-2 where ho is found to be close to quantum noise, h_1 is usually somewhat above the Gagnepain-Uebersfeld limit, and h_2 appears to vary widely between devices. The most important 1/f noise mode determines the ultimate limit of ring laser performance. All analyzed noise follows the power laws above, independent of the magnitudes of the noise involved.

In a Ring Laser Gyro (RLG), because of coupling of the clockwise and counterclockwise rotating beams of light, at low input rotation rate, the frequencies of the two lock together causing the lock-in phenomenon. Both theory and experiments-have explained this lock-in phenomenon as due to mirror backscattering. Mirror backscattering comes mainly from mirror surface and coating imperfections. In RLG application, lock-in, characterized by SQL, the rotation rate below which the gyro output is locked, affects performance in several ways. First of all, it creates a dead band where the gyro does not operate, secondly, it affects scale factor linearity and stability; and thirdly, in a mechanically dithered RLG, it contributes directly to the increase in angular random walk noise in gyro output. The understanding and reduction of SQL is therefore very important in RLG technology.

The surface quality of optics used in an extremely sensitive laser instrument, such as a Ring Laser Gyro (RLG), is critical. This has led to the development of a Variable Angle Scatterometer at the Air Force Wright Aeronautical Laboratories at Wright-Patterson Air Force Base, which can detect low level light scatter from the high quality optics used in RLG's, without first overcoating with metals. With this instrument we have been able to identify damage effects that occur during the typical processing and handling of optics which cause wide variation in subsequent measurements depending on when, in the process, one takes data. These measurements indicate that techniques such as a Total Integrated Scatter (TIS) may be inadequate for standards on extremely low scatter optics because of the lack of sensitivity of the method on such surfaces. The general term for optical surfaces better than the lowest level of the scratch-dig standards has become "supersmooth", and is seen in technical literature as well as in advertising. A performance number, such as Bidirectional Radiation Distribution Function (BRDF), which can be measured from the uncoated optical surface by equipment such as the Variable Angle Scatterometer (VAS) is proposed as a method of generating better optical surface specifications. Data show that surfaces of average BRDF values near 10 parts per billion per steriadian (0.010 PPM/Sr) for 0-(301 = 0.5, are now possible and measurable.

We report here the successful reduction of the lock-in band of a triangular ring laser gyro by dithering two flat diaphragm mirrors 180 degrees out of phase along their normals. This causes a frequency shift of the backscattered light of each beam out of the capture band of the counterpropagating beam. After properly matching the phase and amplitudes of the mirror drives we obtained a residual lock-in roughly two orders of magnitude below the undithered value. A quantitative explanation of this result is given.

The error angle created when an alternating bias is used to bias the laser gyre is given for different operating conditions. These conditions are defined by the time required to reverse the biase angle by one count. 1. Slow dither--where the time for reversal is long (i.e., greater than a "characteristic time" of the inverse of the lock-in frequency). 2. Fast dither--where the frequency and reversal rates of the gyro bias are very high (i.e., the time for reversal of a count is less than the "characteristic time"). 3. Very fast dither--where the reversal of the bias rate is virtually instantaneous (less than the time for one count, i.e., 1/F output). This is referred to as square wave dither.

A summary is given of the uses and calculation of modes and phase shifts in a non-planar ring laser cavity. The multioscillator ring gyro configuration is used as an example of an application of non-planar cavities. A discussion follows on how the possible bias magnetic sensitivity due to a slightly out-of-plane path in a nominally planar gyro may be dramatically reduced by proper control of mirror birefringences and differential reflectivities.

We consider two types of ring gyro operation which are designed to reduce the lock-in threshold and to bias the gyro away from the dead band, respectively. In the phase-conjugate ring gyro, the two lasing modes are coherently coupled and mutually phase-conjugated. The coherent phase relationship between the two modes provides the basis for resisting the frequency pulling due to backscattering. In the photorefractive-biased ring laser gyro, the nonreciprocal optical transmission leads to a split in both oscillation frequency and intensity. This splitting provides the bias for operation away from the dead zone.

Two types of effects are investigated as to their potential for calibrating a large ring and for introducing test signals of known magnitued: 1) tilting the base of the ring by a known angle and with known time evolution, and 2) utilizing Fresnel drag from a controlled flow of gas.

The Sagnac effect using matter (de Broglie) waves is considered for gyroscopic applications. Superfluid helium in a torus with a Josephson junction interupting it would be an embodiment of this idea. An optical analog of the Josephson junction is discussed. An experimental search for the Sagnac effect in superfluid helium (isotope 4) is presented.

All-fiber ring resonators using ultra low loss directional couplers have been fabricated with finesse as high as 500. Resonator finesse is no longer limited by coupler loss and can be increased by lowering fiber loop loss. New polarization effects in the resonator have been observed indicating polarization dependent coupling in the directional coupler.

The discovery of circularly polarized eigenmodes in ring resonators has suggested the possibility of enhanced precision measurements of optical rotation. We argue that, except for possible limitations from small scale birefringence, several orders of magnitude improvement can be made in these measurements. The enhancement is attributed to the multiple-pass properties of light in such a resonator.