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 non-negligible intrinsic loss remains unclear. In this work we develop a general theory of VCC for chains of generally lossy 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 to a two-resonator chain enables an energy-efficient active optical delay beyond the delay-bandwidth limit. These results should prove useful in engineering integrated photonics systems for optical processes such as nonlinear wave mixing, adiabatic frequency tuning, optical buffering, optical synchronization, and quantum repeating.

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• Integrated optics
• Photonics
• Optical microcavities
• Waveguides
• Coupled mode theory