Abstract Sadreev:

Resonances are signatures of bound states which eventually decay into the continuum coupled to them. There are many examples of resonances in different branches of physics, but basically in the linear quantum systems they are classified as the symmetric Breit-Wigner or asymmetric Fano resonances. We predict a new type of resonance in nonlinear systems caused by the interaction of the transmitted wave with the bound state in the continuum (BSC).

Firstly, the BSC as discrete localized solutions of the single-particle Schroedinger equation embedded in the continuum of positive energy states were predicted in 1929 by Neumann and Wigner. For a long time their analysis was regarded as a mathematical curiosity because of certain spatially oscillating central symmetric potentials. Later in 1973 the predicted BICs in semiconductor heterostructure superlattices were observed by Capasso et al as the very narrow absorption peak.

In the last time the phenomenon of BSC was considered in different quantum and wave propagation systems. In linear systems the BSC displayes as a collaps of the Fano resonance. In nonlinear systems a direct coupling of propagating waves with the BSC induces the new resonance. The width of the new resonance depends on the nonlinear coefficients and is proportional to the incoming wave. We demonstrate the BSC induced resonance in the two simplest systems: the nonlinear two-level Fano-Anderson model and the Fabry-Perot resonator with nonlinear mirrors.