Virtual Fano resonances and multimirror Fabry-Pérot bound states in the continuum

The confinement of a standing wave between perfectly reflecting mirrors represents one of the archetypal mechanisms for the formation of bound states in the continuum (BICs), related to the corresponding Fabry-P & eacute;rot (FP) resonance. In the present paper, we study theoretically FP BICs in two-dimensional waveguides with two and three resonators playing the role of the mirrors. We provide an analytical description and numerical evidence for the formation of FP BICs in the waveguide with three mirrors, which do not exhibit Fano resonances in the transmission spectrum when considered separately. Conversely, FP BICs in the waveguide with two mirrors appear only in conjunction with the Fano resonance in the single mirror, as expected. We show that such a counterintuitive phenomenon, which can be related to the manifestation of a virtual (at complex energy) Fano resonance, is quite general and can be observed in both quantum-mechanical and optical waveguides.