Enhancing Nonlinear Wave Phenomena by Bound States in the Continuum

A bound state in the continuum (BIC) is a trapped or guided mode with a frequency in the radiation continuum. It corresponds to a discrete eigenvalue embedded in the continuous spectrum of a linear operator, and it is where a related boundary value problem loses uniqueness. On open structures, a resonant state is a complex-frequency solution that radiates power to infinity. Near a BIC, resonant states with arbitrarily large quality factors can be created by changing the structure or varying a physical parameter slightly, and they can be used to enhance nonlinear wave phenomena. In this project, we study a number of applications of BICs in nonlinear optics, including harmonic generation, optical bistability and symmetry breaking. Harmonic generation is a process that converts power from an incident wave of a fixed frequency to higher harmonic waves. Optical bistability is the case where two stable solutions exist for identical incident waves. Symmetry breaking refers to the situation where asymmetric solutions exist on symmetric structures with symmetric incident waves. We aim to realize these nonlinear wave phenomena in tiny structures (of wavelength size at least in onedirection) consisting of ordinary nonlinear materials. For harmonic generation, we aim to increase the percentage of power converted to higher harmonic waves. For optical bistability and symmetry breaking, we aim to reduce the intensity of the incident waves and minimize the energy needed to switch from one solution to another. The realization of these nonlinear optical phenomena may lead to practical applications as light sources and optical switches.