The resonant nonlinear scattering theory with bound states in the radiation continuum and the second harmonic generation

Abstract

A nonlinear electromagnetic scattering problem is studied in the presence of bound states in the radiation continuum (or resonances with the vanishing width). It is shown that the solution is not analytic in the nonlinear susceptibility and the conventional perturbation theory fails due to strong evanescent fields that necessarily occur if the scattering system has resonances with the vanishing width. A non-perturbative approach is developed. It is then applied to the system of two parallel periodic subwavelength arrays of dielectric cylinders with a second order nonlinear susceptibility. This scattering system is known to have bound states in the radiation continuum. In particular, it is demonstrated that, for a wide range of values of the nonlinear susceptibility, the structure converts over 40% of the incident fundamental harmonic flux into the outgoing second harmonic flux when the distance between the arrays is as low as a half of the incident radiation wavelength. The effect is non-perturbative and solely attributed to the presence of bound states in the radiation continuum. The example demonstrates that bounds states in the radiation continuum can be used to substantially enhance and control optically nonlinear effects in nanophotonic devices.