User:Cleonis/Sandbox/Sagnac effect
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[edit] Ring lasers
The type of ring interferometer that was described in the opening section is sometimes called a 'passive ring interferometer'. A passive ring interferometer uses light entering the setup from outside. The interference pattern that is obtained is a fringe pattern, and what is measured is a phase shift.
It is also possible to construct a ring interferometer that is self-contained, based on a completely different arrangement. This is called a "ring laser". The light is generated and sustained by incorporating laser excitation in the path of the light.
To understand what happens in a ring laser cavity, it is helpful to discuss the physics of the laser process in a laser setup with continous generation of light. As the laser excitation is started, the molecules inside the cavity emit photons, but since the molecules have a thermal velocity, the light inside the laser cavity is at first a range of frequencies, corresponding to the statistical distribution of velocities. The process of stimulated emission makes one frequency quickly outcompete other frequencies, and after that the light is very close to monochromatic.
When a ring laser is rotating, the laser process generates two frequencies of laser light.
In every section of the ring laser cavity, the light propagates with the same velocity in either direction. For the sake of simplicity, assume that all emitted photons are emitted in a direction parallel to the ring. (That is in fact a huge simplification, but it does not affect the content of this exposition.) The molecules in the laser cavity, represented as grey dots in the animation, have a thermal velocity, and on average they have a velocity in counter-clockwise direction along the ring. The molecules in the laser cavity can be seen as resonators. A passing photon will stimulate emission of the excited molecule only if the frequency of the passing photon exactly matches the frequency of the photon that the molecule is ready to emit.
A photon that is emitted in counter-clockwise direction is on average Doppler-shifted to a higher frequency, a photon that is emitted in clockwise direction is on average Doppler-shifted to a lower frequency. The upwards Doppler-shifted photons are more likely to stimulate emission on interaction with molecules that they "catch up with", the downwards shifted photons are more likely to stimulate emission on interaction with molecules that they meet "head on". Seen in this way, the fact that the ring laser generates two frequencies of laserlight is a direct consequence of the fact that everywhere along the ring the velocity of light is the same in both directions. The constancy of the speed of light provides a constant background, and the molecules inside the laser cavity have a certain velocity with respect to that constant background. This constant background is referred to as inertial space.
By bringing the two frequencies of laserlight to interference a beat frequency can be obtained; the beat frequency is the difference between the two frequencies. This beat frequency can be thought of as an interference pattern in time. (The more familiar interference fringes of interferometry are a spatial pattern). The period of this beat frequency is linearly proportional to the angular velocity of the ring laser with respect to inertial space.
In the case of ring laser interferometry there is no need for calibration. (In a sense one might say that the process is self-calibrating). The beat frequency will be zero if and only if the ring laser setup is non-rotating with respect to inertial space.
[edit] Lock-in
Because of the way the laser light is generated, light in laser cavities has a strong tendency to be monochromatic (and usually that is precisely what laser apparatus designers want). This tendency to not split in two frequencies is called 'lock-in'. The ring laser devices incorporated in navigational instruments (to serve as a ring laser gyroscope) are generally too small to go out of lock spontaneously. By "dithering" the gyro through a small angle at a high audio frequency rate, going out of lock is ensured.
[edit] Synchronisation procedures
The procedures for synchronizing clocks all over the globe must take the rotation of Earth into account. The signals used for the synchronizing procedure can be in the form of electric pulses conducted in electic wires, they can be lightpulses conducted in fiber optic cables, or they can be radio signals.
If a number of stations, situated on the equator, relay pulses to one another, will the time-keeping still match after the relay has circumnavigated the globe? One condition for handling the relay correctly is that the time it takes the signal to travel from one station to the next is taken into account each time. On a non-rotating planet that ensures fidelity: two time-disseminating relays, going full circle in opposite directions around the globe, will still match when they are compared at the end. However, on a rotating planet, it must also be taken into account that the receiver moves during the transit time of the signal, shortening or lengthening the transit time compared to what it would be in the situation of a non-rotating planet.
It is recognized that the synchronisation of clocks and ring interferometry are related in a fundamental way. Therefore the necessity to take the rotation of Earth into account in sychronisation procedures is also called the Sagnac effect.
