Modeling, analysis, and loop optimization of the Pound-Drever-Hall loop for ultra-stable lasers

State-of-the-art ultra-stable lasers have achieved a fractional frequency stability at the 10^-17 level. Further advancement to the 10^-18 level requires frequency stabilization servo controllers with stronger noise suppression capabilities over a broader frequency band. For external-cavity semiconductor lasers, the prevailing stabilization approach utilizes a combination of current frequency modulation and PZT frequency modulation. In this study, we employed a dedicated loop analyzer and an IQ demodulation frequency measurement method to perform detailed measurements of the transfer functions of individual stages and the closed-loop system of this dual feedback loop, with particular focus on its performance limitations in the frequency range within 10 kHz. By optimizing the feedback path, we improved the laser noise suppression at 1 kHz by three orders of magnitude, thereby reducing the contribution of residual laser frequency noise below 10 kHz to the fractional frequency stability at one second to 4.4×10^-19. The proposed method not only provides significant value for achieving ultra-stable lasers at the 10^-18 level but is also applicable to newer types of semiconductor lasers that rely solely on current frequency modulation.