[Paper Review] Design of microring resonators integrated with 2D graphene oxide films for four-wave mixing

Yuning Zhang, Jiayang Wu+4 more|arXiv (Cornell University)|Jul 30, 2021

Photonic and Optical Devices40 references151 citations

TL;DR

This paper proposes a theoretical optimization of four-wave mixing (FWM) in microring resonators (MRRs) integrated with 2D graphene oxide (GO) films, leveraging resonant enhancement and tailored GO film parameters. By balancing Kerr nonlinearity and propagation loss, the authors achieve a 18.6 dB enhancement in FWM conversion efficiency—8.3 dB higher than prior experiments—demonstrating significant performance gains for nonlinear photonic devices.

ABSTRACT

We theoretically investigate and optimize the performance of four-wave mixing (FWM) in microring resonators (MRRs) integrated with two-dimensional (2D) layered graphene oxide (GO) films. Owing to the interaction between the MRRs and the highly nonlinear GO films as well as to the resonant enhancement effect, the FWM efficiency in GO-coated MRRs can be significantly improved. Based on previous experiments, we perform detailed analysis for the influence of the GO film parameters and MRR coupling strength on the FWM conversion efficiency (CE) of the hybrid MRRs. By optimizing the device parameters to balance the trade-off between the Kerr nonlinearity and loss, we achieve a high CE enhancement of ~18.6 dB relative to the uncoated MRR, which is ~8.3 dB higher than previous experimental results. The influence of photo-thermal changes in the GO films as well as variations in the MRR parameters such as the ring radius and waveguide dispersion on the FWM performance is also discussed. These results highlight the significantly improved FWM performance that can be achieved in MRRs incorporating GO films and provide a guide for optimizing their FWM performance.

Motivation & Objective

• To theoretically investigate and optimize four-wave mixing (FWM) performance in microring resonators (MRRs) integrated with 2D graphene oxide (GO) films.
• To analyze the influence of GO film thickness, number of layers, and MRR coupling strength on FWM conversion efficiency (CE).
• To address the trade-off between Kerr nonlinearity and propagation loss in GO-coated MRRs for optimal FWM performance.
• To evaluate the impact of photo-thermal effects and waveguide dispersion on FWM efficiency in hybrid GO-MRR devices.
• To provide a design roadmap for achieving higher FWM efficiency in CMOS-compatible integrated photonic devices using GO films.

Proposed method

• The study uses a theoretical model based on experimentally measured material parameters of GO films (refractive index, extinction coefficient, Kerr nonlinearity) and doped silica MRRs.
• The FWM conversion efficiency is calculated using coupled-mode theory and nonlinear Schrödinger equations, incorporating resonant enhancement and power-dependent losses.
• Parametric optimization is performed by varying GO film thickness (1 layer = 2 nm), number of layers (N = 1 to 50), ring radius (R), and coupling strength (t) to balance nonlinearity and loss.
• Photo-thermal effects are modeled by introducing power-dependent loss variations in the GO film, particularly for thicker films.
• Group-velocity dispersion (β₂) is computed for hybrid MRRs with different GO layer counts to assess phase-matching conditions for broadband FWM.
• Performance is compared against uncoated MRRs and GO-coated waveguides to isolate the resonant enhancement effect.

Experimental results

Research questions

• RQ1 How does the number of GO layers and film thickness affect the FWM conversion efficiency in GO-coated MRRs?
• RQ2 What is the optimal trade-off between Kerr nonlinearity and propagation loss in GO-coated MRRs for maximizing FWM efficiency?
• RQ3 How do photo-thermal effects in GO films influence FWM performance, especially in thicker films?
• RQ4 To what extent does the ring radius and coupling strength of the MRR impact the FWM efficiency and extinction ratio?
• RQ5 How does the inclusion of GO films alter the group-velocity dispersion and phase-matching bandwidth in MRRs?

Key findings

• A maximum FWM conversion efficiency (CE) enhancement of ~18.6 dB is achieved in GO-coated MRRs compared to uncoated MRRs, surpassing previous experimental results by ~8.3 dB.
• For a 1-layer GO film, the maximum CE enhancement of 14.6 dB is achieved at a ring radius of 135 µm and coupling strength of 0.812, highlighting the trade-off between absolute CE and relative enhancement.
• The FWM CE in GO-coated MRRs is significantly higher than in comparable GO-coated waveguides due to resonant intensity enhancement, with gains exceeding 20 dB in some configurations.
• Thicker GO films (e.g., 50 layers) lead to higher losses and reduced CE, but also induce stronger anomalous group-velocity dispersion, improving phase-matching for broadband FWM.
• Photo-thermal effects degrade FWM performance more significantly in thicker GO films due to increased defect density and thermal dissipation, limiting practical thickness limits.
• The hybrid MRRs with 1 layer of GO exhibit a group-velocity dispersion (β₂) that is slightly reduced compared to uncoated MRRs, enabling better phase matching and broadband FWM with < 2 dB degradation over Δλ/FSR = 30.