Virtual Critical Coupling

Younes Ra'Di, Alex Krasnok, Andrea Alù

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Electromagnetic resonators are a versatile platform to harvest, filter, and trap electromagnetic energy, at the basis of many applications from microwaves to optics. Resonators with a large intrinsic quality factor (Q) are highly desirable, since they can store a large amount of energy, leading to sharp filtering and low loss. However, exciting high-Q cavities with monochromatic signals suffer from poor excitation efficiency, i.e., most of the impinging energy is lost in the form of reflection, since high-Q resonators are weakly coupled to external radiation. Although critical coupling eliminates reflections in steady state by matching the intrinsic and coupling decay rates, this approach requires the introduction of loss in the resonator, causing dissipation and lowering the overall Q-factor. Here, we extend the notion of critical coupling to high-Q lossless resonators, based on tailoring the temporal profile of the excitation wave. Utilizing coupled-mode theory, we demonstrate an effect analogous to critical coupling by mimicking loss with nonmonochromatic excitations at complex frequencies. Remarkably, we show that this approach enables unitary excitation efficiency in open systems, even in the limit of extreme quality factors in the regime of quasi-bound states in the continuum.

Original languageEnglish (US)
Pages (from-to)1468-1475
Number of pages8
JournalACS Photonics
Issue number6
StatePublished - Jun 17 2020
Externally publishedYes


  • critical coupling
  • high-Q resonators
  • transient response
  • virtual absorption

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Electrical and Electronic Engineering
  • Biotechnology


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