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Backscatter and spontaneous four-wave mixing in micro-ring resonators

Jonte R. Hance, GF Sinclair, JG Rarity

Published Apr 8, 2021• 0 citations
Publisher

Abstract

We model backscatter for electric fields propagating through optical micro-ring resonators, as occurring both in-ring and in-coupler. These provide useful tools for modelling transmission and in-ring fields in these optical devices. We then discuss spontaneous four-wave mixing and use the models to obtain heralding efficiencies and rates. We observe a trade-off between these, which becomes more extreme as the rings become more strongly backscattered.

DOI
10.25405/ncl.34496412

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We model backscatter for electric fields propagating through optical micro-ring resonators, as occurring both in-ring and in-coupler. These provide useful tools for modelling transmission and in-ring fields in these optical devices. We then discuss spontaneous four-wave mixing and use the models to obtain heralding efficiencies and rates. We observe a trade-off between these, which becomes more extreme as the rings become more strongly backscattered.
Systems of coupled cavities have the potential to provide bright quantum optical states of light in a highly versatile manner. Micro-ring resonators for instance are highly scalable candidates for photon sources thanks to CMOS fabrication techniques and their small footprint, however, surface roughness of the wave-guides, and defects in the coupler geometry routinely induce splitting of the cavity modes due to back-scattering and back-coupling. The parasitic back-propagating mode in the micro-ring leads to hybridisation of the modes, altering the linear and nonlinear properties of this coupled cavity system, and ultimately constraining the fidelity of quantum light sources that can be produced. In this paper, we derive a comprehensive general model for Gaussian non-linear processes in coupled cavity systems, based on an effective field Hamiltonian and a dispersive input-output model. The resulting dynamics of the equations of motion are evaluated in a Gaussian process formalism via the symplectic transformations on the optical modes. We numerically model and explore the problem of back-scattering in micro-ring resonators in physically relevant parameter regimes, involving the splitting of various resonances, we calculate the consequent impurity and heralding efficiency of various heralded photon schemes, we explore a perturbative explanation of the observations and assess the correspondence between spontaneous and stimulated processes in these systems.
Systems of coupled cavity modes have the potential to provide bright quantum optical states of light in a highly versatile manner. Microring resonators, for instance, are highly scalable candidates for photon sources. Thanks to CMOS fabrication techniques for their small footprint and the relative ease of coupling many such microrings together. However, surface roughness of the waveguides and defects in the coupler geometry routinely induce splitting of the cavity modes due to backscattering and backcoupling. The parasitic back-propagating mode in a microring leads to hybridization of the modes, altering the linear and nonlinear properties of a system of coupled cavity modes and ultimately constraining the fidelity of quantum light sources that can be produced. In this paper, we derive a comprehensive general model for Gaussian nonlinear processes in systems of coupled cavity modes based on an effective field Hamiltonian and a dispersive input–output model. The resulting dynamics of the equations of motion are evaluated in a Gaussian process formalism via symplectic transformations on the optical modes. We then use this framework to numerically model and explore the problem of backscattering in microring resonators in physically relevant parameter regimes, involving the splitting of various resonances, and we calculate the consequent impurity and heralding efficiency of various heralded photon schemes. We provide a perturbative explanation of the observations and assess the correspondence between spontaneous and stimulated processes in these systems.
Efficient and bright single photon sources on photonic chips are key to scaling quantum technologies. Spontaneous four wave mixing in micro-ring resonators creates excellent narrowband and tunable photon sources. We experimentally demonstrate the optimization of heralding efficiency and brightness by tuning the coupling of the pump, signal and idler modes into the resonator whilst operating in a pulsed pump regime. We observe a maximum detected pair rate of over 93,000~coincidences per second in a moderately over-coupled regime, alongside a high intrinsic idler heralding efficiency of 97.87$\pm$8.97\% when operating close to maximal over-coupling. The measured dependence on coupling strength is in strong agreement with theoretical predictions, experimentally validating the predicted trade-off between brightness and heralding efficiency.