Performance analysis of Drever-Hall laser frequency stabilization using a proportional+integral servo

In this paper, we derive analytical expressions for finite gain, finite bandwidth laser frequency locking systems. The common case of Drever-Hall (FM sideband) locking to a Fabry-Perot cavity is discussed, using a proportional+integral (PI) controller as an example. The effects of nonnegligible loop time-delay on stability are discussed, and an optimal design procedure for a frequency locking system is given.