Frequency Locking by Analysis of Orthogonal Modes

We describe a method for frequency locking a laser and a cavity. Orthogonal modes from the laser are incident on a cavity such that only one mode is resonant at the desired frequency. The polarisation or spatial phase distribution of the light reflected from the cavity is analysed, yielding the phase between the modes - this is the locking signal. We compare this method with other locking techniques, and show this to be a natural progression from these. Simulations are presented for applications of interest, e.g., gravity wave interferometry (an empty cavity) and optical frequency conversion (a polarisation dependent cavity)