User:Cleonis/Sandbox/Sagnac effect
Ring lasers[edit]
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 continuous 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.
schematic representation of the frequency shift when a ring laser interferometer is rotating. Both the counterpropagating light and the co-propagating light go through 12 cycles of their frequency.
The red and blue dots represent counter-propagating photons, the grey dots represent molecules in the laser cavity.
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 image 'frequency shift' illustrates the effect of the ring laser's rotation.
In a linear laser the laser light that is generated fits the length of the laser cavity exactly; an integer multiple of the wavelength fits the length of the laser cavity. This means that in traveling back and forth the laserlight goes through an integer number of cycles of its frequency. In the case of a ring laser the same applies: the number of cycles of the the laser light's frequency is the same in both directions. This quality of the same number of cycles in both directions is preserved when the ring laser setup is rotating. The image illustrates that there is wavelength shift (hence a frequency shift) in such a way that the number of cycles is the same in both directions of propagation.
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.
Lock-in[edit]
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.
Synchronisation procedures[edit]
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.