Steady-state frequency-tracking distortion in the digital Pound–Drever–Hall technique

We present here a general method for evaluating the steady-state frequency-tracking distortion in the digital Pound–Drever–Hall technique with modulation harmonic distortion. The theoretical tracking distortion model is established based on the multi-beam interference theory. The effects of the additional harmonic phase shift and the relative distortion ratio changes in the model are simulated by the Runge–Kutta method. Moreover, we demonstrate the steady-state frequency-tracking distortion caused by the modulation harmonic distortion in a resonant frequency tracking system with a 35 mm Si₃N₄ waveguide ring resonator. According to the measured and simulated results, we obtain the optimal modulation frequency and depth with minimal frequency-tracking distortion, which are 11.49 MHz and 3.96, respectively.