Quasinormal-mode modeling and design in nonlinear nano-optics

Based on quasinormal-mode theory, we propose a novel approach enabling a deep analytical insight into the multi-parameter design and optimization of nonlinear photonic structures at subwavelength scale. A key distinction of our method from previous formulations relying on multipolar Mie-scattering expansions is that it directly exploits the natural resonant modes of the nanostructures, which provide the field enhancement to achieve significant nonlinear efficiency. Thanks to closed-form expression for the nonlinear overlap integral between the interacting modes, we illustrate the potential of our method with a two-order-of-magnitude boost of second harmonic generation in a semiconductor nanostructure, by engineering both the sign of $\chi^{(2)}$ at subwavelength scale and the structure of the pump beam.