Considering Photoinduced Second-Harmonic Generation as a dc Kerr Optical Parametric Oscillation or Amplification Process

Abstract

Photoinduced second-harmonic generation (SHG) in centrosymmetric materials like silica and silicon nitride has been commonly explained as an effective second-order (${\ensuremath{\chi}}^{(2)}$) process mediated by a dc electric field and the medium's third-order (${\ensuremath{\chi}}^{(3)}$) nonlinearity. In this explanation, the coherent photogalvanic effect is the source of a dc electric field whose spatial periodicity naturally enables quasi-phase-matching. While successful in explaining many observations from experiment, the behavior at low input powers, and in particular, the apparent existence of a threshold for efficient photoinduced SHG observed in some experiments has largely been overlooked theoretically. In this Paper, we reconsider photoinduced SHG within the framework of four-wave mixing (FWM), involving degenerate pump, second-harmonic signal, and dc electric field. We propose a hypothesis that photoinduced SHG is a FWM-mediated dc Kerr optical parametric oscillation or amplification process. This hypothesis can explain the threshold behavior, and moreover, predicts unconventional light amplification, both of which we verify by experiments in silicon-nitride microresonators. Finally, we discuss the physical implications of our work in various platforms and future directions.