Backscattering in nonlinear microring resonators via a Gaussian treatment of coupled cavity modes

Abstract

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.

Backscattering and Hong-Ou-Mandel manifolds in microring resonators

“…A very commonly reported effect of backscattering in MRRs is resonance splitting. 10,11,13 A simple test of our model that demonstrates that it does capture the resonance splitting phenomena is shown in the normalized transmission plots in Fig. 2) that the MRR is resonant at θ = 0, 2π, 4π .…”

“…Keep in mind that we expect normal levels of backscattering to be around or less than 1%. 10,12,13 The amount of backscattering required in this section to detect the HOM effect for different input/output combinations is far beyond what we would reasonably expect to see in a normally fabricated MRR, as shown in Fig. (8).…”

“…We will now show probability and contour plots for a single MRR across a range of γ values: 1, 0.99, 0.95, and 0.9. A realistic level of backscattering is around or less than 1%, 10,12,13 but we have also included 5% and 10% backscattering as extreme examples to show the robustness of the HOMM in MRRs. Notice in Fig.…”

“…In this work, we investigate the HOMM in MRRs subject to backscattering which allows photons circulating in one direction, to back scatter into a counter circulating mode. Backscattering is commonly investigated in MRRs using a temporal coupled mode theory [9][10][11][12][13][14] and backscattering in MRRs is modeled from two main sources: either (1) "sidewall roughness" inside the MRR or (2) backscattering at the directional couplers. In this paper corresponding author: Peter Kaulfuss.…”

Interferometric cavity ringdown technique for ultrahigh Q-factor microresonators

“…This last causes surfacewall roughness that induces backscattering of light and, therefore, a simultaneous excitation of clockwise (CW) and counterclockwise (CCW) modes [6]. As a result, the system does not exhibit a Lorentzian-shaped spectral response but a resonant doublet [8,9]. In this case, the usual estimate of Q by the measure of the Full-Width at Half Maximum (FWHM) is inaccurate.…”