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Bound states in the continuum are non-radiating solutions of the wave equation which are completely decoupled from the radiation continuum and therefore it is impossible to excite them from the far-field in linear systems. In this work, we develop a general theory of parametric excitation of BICs in nonlinear systems via spontaneous symmetry breaking, which results in a coupling between BIC and bright modes of the system. Using the temporal coupled-mode theory and perturbation analysis, we found the threshold intensity for excitation of BIC and study the possible stable solutions depending on the pump intensity and frequency detuning between the pump and BIC. We revealed that at some parameters of the pump beam, both BIC and the bright mode can have non-zero amplitudes forming a stable hybrid state. Also, at some parameters, there are no stable solutions and BIC can be used for frequency comb generation. Our findings can be very promising for use in nonlinear photonic devices and all-optical networks.
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