Analysis and simulation of efficient electro-optic comb generation based on dual-ring detuning modulation

Integrated electro-optic (EO) frequency combs are pivotal components in a wide range of applications, including optical communications, spectroscopy, optical computing, precision timing, and frequency measurement. Although broadband on-chip EO combs are typically generated within resonators possessing high-quality factors, their relatively low conversion efficiency remains a significant constraint. By comparison, EO combs produced in dual rings exhibit enhanced conversion efficiencies, which generally necessitate satisfying a generalized critical coupling condition. In this work, we employ a virtual state model to successfully derive a generalized critical coupling condition for dual-ring modulators under detuning modulation. Based on this theory, we obtain an approximate analytical solution for the dual-ring detuning modulation, showing that it can be equated to phase modulation. In addition, this condition provides a direct guide for selecting modulation parameters of the dual ring, leading to more precise control and optimization. Utilizing this condition, we have designed an efficient and energy-concentrated EO comb generation system that permits a wide range of possibilities in the choice of driving frequency and modulation depth. Our theoretical approach provides an optimization strategy for efficient EO comb generation, offering more compact, high-performance, and flexible solutions for high-speed data transmission, sensing, and quantum optical computing systems.