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

Abstract

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 S i 3 N 4 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.

Optimization of Fiber Ring Resonator Transmission Spectrum Based on Multi-Beam Interference Theory and Transfer Matrix Theory

“…Wenya Liu, Jiubin Tan, and Jiwen Cui are with the Key Lab of Ultra-Precision Intelligent Instrumentation, Harbin Institute of Technology, Ministry of Industry and Information Technology, Harbin 150080, China, and also with Center of Ultra-Precision Optoelectronic Instrument, Harbin Institute of Technology, Harbin 150080, China(e-mail: 21B901002@stu.hit.edu.cn; jbtan@hit.edu.cn; cuijiwen@hit.edu.cn) explain the asymmetry of the resonance curve caused by the RPMF-FRR constructed as the angle is not equal to π/2, there remains a need of systemic studies to identify the mechanism of asymmetric resonance curve caused by orthogonal mode loss in coupler, and build a structure to enhance the robustness of FRR. In this paper, based on the multi-beam interference theory [14], [15], a model is established to analyze and simulate the asymmetry of the spectrum caused by difference of coupler orthogonal mode loss in the RPMF-FRR and a TPMF-FRR made up of 2 couplers is proposed, the asymmetric error improved from 11% of RPMF-FRR to 0.8% of TPMF-FRR. Furthermore, based on the transfer matrix theory [16], [17], we evaluate different construction methods of FRR using key parameters such as Free Spectrum Range(FSR), Full Width at Half Maximum(FWHM), Fineness(F), and resonant depth(h), both theory and experiment have depict that the fewer segments, the better performance, provided guidance for further optimizing the FRR.…”