Enhancing second harmonic generation by Q-boosting lossless cavities beyond the time bandwidth limit

Nanostructures proved to be versatile platforms to control the electromagnetic field at subwavelength scale. Indeed, high-quality-factors nanocavities have been used to boost and control nonlinear frequency generation by increasing the light-matter interaction. However, nonlinear processes are triggered by high-intensities, which are provided by ultrashort laser pulses with large bandwidth, that cannot be fully exploited in such devices. Time-varying optical systems allow one to overcome the time-bandwidth limit by modulating the cavity external coupling. Here we present a general treatment, based on coupled mode theory, to describe second harmonic generation in a doubly resonant cavity for which the quality-factor at the fundamental frequency is modulated in time. We identify the initial quality factor maximizing second harmonic efficiency when performing Q-boosting and we predict a theoretical conversion efficiency close to unity. Our results have direct impact on the design of next generation time-dependent metasurfaces to boost nonlinear frequency conversion of ultrashort laser pulses.