Wavelength-scale optical parametric oscillators

Abstract

Despite recent progress in nonlinear conversion in wavelength-scale resonators, there are still open questions on the possibility of parametric down-conversion and oscillation in such resonators. The existing theories have limitations in accurately predicting the behaviors of wavelength-scale nonlinear resonators, especially where multiple resonances are involved. We present a general approach to predict the behavior and estimate the oscillation threshold of multi-mode wavelength-scale optical parametric oscillators (OPOs). As an example, we propose an OPO based on Mie-type multipolar resonances, and we demonstrate that due to the nonlinear interaction between the multipolar modes, the OPO threshold, compared to the single-mode case, can be reduced by a factor which is significantly larger than the number of interacting modes. We compare the threshold for electric and magnetic mode excitations to emphasise the importance of the field overlap, the phase matching counterpart in wavelength-scale resonators. We establish an explicit connection between the second-harmonic generation efficiency and the OPO threshold. This allows us to estimate the OPO threshold based on measured or simulated second-harmonic generation in different class of resonators, such as bound-state in the continuum and inversely designed resonators. Our approach for analyzing and modeling miniaturized OPOs can open unprecedented opportunities for classical and quantum nonlinear photonics.

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