Theory of a dithered-ring-laser gyroscope. II. Cayley transformations and square-wave dithering.

Abstract

This paper reformulates the problem of a dithered-ring-laser gyroscope as a mapping of points on the unit circle onto other such points. These mappings are represented by Cayley matrices. The relationship to our earlier Floquet theory is established, and it is shown how the properties of the mapping determine the lock-in behavior and the dynamics of the system. With square-wave dithering the mapping can be calculated analytically, and the expression allows rapid numerical exploration of the behavior in various regimes of operation. The Cayley transformation method is found to offer a convenient and intuitively transparent way to handle the locking phenomenon in a dithered ring laser.