Gain-loss engineering of bound states in the continuum for enhanced nonlinear response in dielectric nanocavities.

We reveal the potential of bound states in the continuum (BIC) to enhance the nonlinear response in specialty optical resonators in the presence of gain and loss. We demonstrate this phenomenon in a square core-shell AlGaAs nanowire having a proper engineered spatial variation of gain and loss to sustain quasi-BICs. The presence of these high-quality modes at both fundamental and second-harmonic wavelengths leads to an extremely high enhancement in second harmonic generation, thus preluding a framework to fabricate composite media with high effective nonlinearity.