An electric field induced delocalization transition in second-harmonic generation effect

The emergence of second-harmonic generation (SHG) is a pivotal issue to the development of nano-optical devices and interfaces. Here, we perform a quantum analysis of the spectral statistics of the SHG resonances with the aim of determining the instability of this process. We compute different independent statistical properties to being chaotic. We find that the short-range fluctuations of the resonances at electric fields with different intensities are in agreement with random matrix theory (RMT) predictions. We conclude that although in low intensities of electric field the SHG dynamics follows Poisson statistics, in high intensities the dynamics is chaotic (ergodic). On the other hand, a study of the singularity spectrum of eigenstates provides additional evidence supporting RMT predictions. We also analyze the inverse participation ratio of eigenstates and find that it equals similar to 0.5 in localized phase, and approaches to 1/dimd(H) in delocalized (chaotic) phase.