Systematic and quantitative analysis of residual amplitude modulation in Pound-Drever-Hall frequency stabilization

We theoretically analyze the effects of two primary mechanisms of residual amplitude modulation, estimate the resulting frequency instabilities, and discuss relevant experimental countermeasures, providing useful information that are beneficial for the development of ultrastable optical oscillators as well as many precision experiments relying on stable lasers. A Pound-Drever-Hall signal comprising contributions from the birefringence of the electro-optic crystal is derived and used to examine the birefringence-related amplitude modulation and the resultant frequency offset in terms of various experimental parameters. The combined effect of the crystal birefringence and pararsitic 'etalons is further investigated by dividing the etalons into three representative categories according to their locations in the optical path. The analysis shows that introducing a resonant optical cavity only scales the birefringence-generated amplitude modulation by a constant, thereby lending strong support to the active control scheme using a separate detection path. When a parasitic 'etalon is added, the active control scheme can still suppress the resultant instability except for the parasitic 'etalon that is located closely in front of the optical cavity. In this case the etalon produces rather large frequency instability and therefore should be avoided. In addition, numerical calculations are performed to assess the impact of a special situation where the front and end surfaces of an ultrastable optical cavity are potential sources of the parasitic etalon that can strongly couple with the cavity.