With examples of two parallel dielectric gratings and two arrays of thin parallel dielectric cylinders, it is shown that the interaction between trapped electromagnetic modes can lead to scattering resonances with practically zero width. Such resonances are the bound states in the radiation continuum first discovered in quantum systems by von Neumann and Wigner. Potential applications of such photonic systems include: large amplification of electromagnetic fields within photonic structures and, hence, enhancement of nonlinear phenomena, biosensing, as well as perfect filters and waveguides for a particular frequency, and impurity detection.

A fully quantum mechanical investigation using time-dependent density functional theory reveals that the field enhancement in a coupled nanoparticle dimer can be strongly affected by nonlinear effects. We show that both classical as well as linear quantum mechanical descriptions of the system fail even for moderate incident light intensities. An interparticle current resulting from the strong field photoemission tends to neutralize the plasmon-induced surface charge densities on the opposite sides of the nanoparticle junction. Thus, the coupling between the two nanoparticles and the field enhancement is reduced as compared to linear theory. A substantial nonlinear effect is revealed already at incident powers of 10(9) W/cm(2) for interparticle separation distances as large as 1 nm and down to the touching limit.