Abstract
Despite recent progress in nonlinear optics in wavelength-scale resonators, there are still open questions on the possibility of parametric oscillation in such resonators. We present a general approach to predict the behavior and estimate the oscillation threshold of multi-mode subwavelength and 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 low- Q nature of multipolar modes in wavelength-scale resonators, there is a nonlinear interaction between these modes. As a result, the OPO threshold, compared to the single-mode case, can be reduced by a factor that is significantly larger than the number of interacting modes. The multi-mode interaction can also lead to a phase transition manifested through a sudden change in the parametric gain as well as the oscillation threshold, which can be utilized for enhanced sensing. 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 classes of resonators, such as bound states 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.
Highlights
Optical parametric oscillators (OPOs) have been widely used for may applications ranging from metrology and spectroscopy to quantum information science [1,2,3,4,5,6,7,8,9]
We establish a connection between up-conversion processes in nanostructures and parametric down-conversion. This allows us to explore the possibility of OPO in the existing structures which have been offered for sum-frequency/secondharmonic generation
To estimate the OPO threshold in multi-mode wavelength-scale resonators, we expand the field inside the cavity in terms of orthogonal eigenmodes (Fig. 1a), and we approximate the nonlinear dynamics of the electric field with a slowly varying envelope evolving in timedomain
Summary
Optical parametric oscillators (OPOs) have been widely used for may applications ranging from metrology and spectroscopy to quantum information science [1,2,3,4,5,6,7,8,9]. Miniaturized OPOs have recently been demonstrated in on-chip OPOs based on Kerr [5, 6, 20] and quadratic [21] nonlinearities as well as whispering-gallery resonators [22] The size of these resonators are still orders of magnitude larger than their operating wavelengths. In the low-Q regime of these resonators, multiple modes around the signal wavelength can spectrally and spatially overlap (Fig. 1) This allows them to nonlinearly interact with each other through the pump. We establish a connection between up-conversion processes in nanostructures and parametric down-conversion This allows us to explore the possibility of OPO in the existing structures which have been offered for sum-frequency/second-. Our approach is general and can predict optical parametric oscillation in a wide range of nanostructured resonators, such as bound state in continuum, photonic crystal, and inversely designed cavities
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