Twin Bound States in the Continuum in a Waveguide Fabry–Pérot Resonator

We study bound states in the continuum (BICs) in a Fabry–Pérot (FP) resonator within a quantum-mechanical waveguide. We show that besides typical FP BICs corresponding to a discrete set of cavity lengths, there is a pair of symmetric and antisymmetric twin BICs (TBICs) if isolated mirrors possess BIC themselves. In contrast to the FP BIC, the TBIC does not require the formation of standing waves of the FP resonance between the mirrors. Therefore, the energy and parameters of TBICs are almost independent of the length of the FP resonator, and their wavefunctions have an exponentially small amplitude between the mirrors. Results of the numerical simulation of the 2D quantum-mechanical waveguide with attractive potentials (“impurities”) playing the role of mirrors of an FP resonator are supported by the illustrative analytical model.