Engineering bound states in continuum via a nonlinearity-induced extra dimension

Bound states in continuum (BICs) are states of a system possessing significantly large lifetimes with applica-tions across various branches of science. In this work, we propose an expedient protocol to engineer BICs using the Kerr nonlinearities of a system which otherwise has no BICs. The generation of BICs is a direct artifact of the nonlinearity and the associated expansion in the dimensionality of the system. In particular, we consider single-and two-mode anharmonic systems and provide a number of solutions apposite for the creation of BICs. The nonlinearity-induced BICs can be controlled by external drive. In close vicinity to the BIC, the steady state response of the system is immensely sensitive to perturbations in natural frequencies of the system, and we illustrate its propitious sensing potential in the context of experimentally realizable setups for both optical and magnetic nonlinearities.