Theory of generalized virtual critical coupling to resonator chains

Virtual critical coupling (VCC) optimizes coupling from a bus waveguide into a resonator by shaping the optical input into a truncated, increasing exponential pulse to excite the resonator’s complex transmission zero. This approach is challenging at optical frequencies due to broadband modulation requirements and strong sensitivity to dispersion. Moreover, its adaptation to resonators with intrinsic loss remains unclear. In this work, we develop a general theory of VCC for chains of coupled resonators to address these issues. First, we prove analytically that as the number of resonators increases, VCC can be achieved with smoother inputs and delayed outputs, improving ease of generation and robustness to dispersion. Second, we show that when intrinsic loss is significant, optimal coupling is no longer achieved by VCC but by a generalized matched-filter excitation. Third, we demonstrate that generalized VCC in a two-resonator chain enables an energy-efficient active optical delay beyond the delay–bandwidth limit. These results shall prove useful to engineer integrated photonics systems for optical processes such as nonlinear wave mixing, adiabatic frequency tuning, optical buffering, optical synchronization, and quantum repeating.