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J. Eur. Opt. Society-Rapid Publ. 22, 16( 2026)
4.2 Optimization verification of electro-optical coupling efficiency
Fig. 9. Schematic diagram of the electric field coupling array between the electrode and modulation arm.
4 Simulation results and performance analysis
This study constructed a three-dimensional model of Si 3 N 4- TFLN heterostructure using COMSOL Multiphysics, with a mesh accuracy of 0.1 lm. Using finite element method to solve the electro-optic effect and second-order nonlinear effect. Lumerical FDTD is used to calculate waveguide loss and crosstalk, with boundary conditions set as perfectly matched layer. All simulation parameters are set based on the material manual and process feasibility, with simulation errors controlled within ± 5 %.
4.1
Electromagnetic simulation results of the TFLN device
Figure 10 presents the electromagnetic simulation results of the on-chip device, which directly verifies the excellent electro-optic coupling performance and low microwave leakage loss of the designed structure. Figure 10a illustrates the coupling distribution of the optical field and electric field, where the red-yellow regions represent the concentrated areas of optical field energy, corresponding to the waveguide core made of LN. The effective mode refractive index n eff is 1.8193, simulated via COMSOL Multiphysics with a mesh accuracy of 0.1 lm, error ± 0.0005, which reflects the equivalent refractive index of light propagating in the waveguide. The blue background in Figure 10a represents the weak optical field region, corresponding to the SiO 2 cladding outside the waveguide. This result indicates that the optical field is highly confined in the LN waveguide core with no obvious high-order mode leakage, and the electric field is precisely coupled to the optical field core area – these are the direct reason for the high electro-optic conversion efficiency of the device. Figure 10b shows the electric field is localized at the edge of the T-shaped electrode, which effectively reduces the microwave leakage loss and ensures the 50 X characteristic impedance matching of the electrode, laying the foundation for the device to achieve a modulation bandwidth of > 70 GHz.
Three dimensional electromagnetic field simulation was conducted using COMSOL Multiphysics to compare the C values of traditional straight electrodes and gradient transition electrodes in this study.
Compared to traditional straight electrodes, the signal electrode has a width of 6 lm and a ground spacing of 4 lm, with no taper [ 37 ]. The simulation shows C = 0.516, and the dispersion rate of the electric field at the edge of the waveguide reaches 35 %.
In this study, the T-shaped gradient transition electrode was simulated and found to have a C of 0.85, with an electric field dispersion rate being reduced to 22 % and a relative increase of 65 % in C value which was calculated as( 0.85 – 0.516)/ 0.516 100 % 65 %.
Based on the formula V p = k / 2n eff r 33 CL, we substitute the design parameters. Reduces V p from 6.4 V in traditional structures to 5.6 V, corresponding to a decrease in V p L from 3.2 V cm to 2.8 V cm, verifying the direct effect of structural optimization on reducing driving voltage.
At the structural level, the 30 lm gradient transition design of the T-shaped electrode breaks through the bottleneck of field matching caused by fixed electrode size. Traditional straight electrodes have difficulty breaking through the gamma value of 0.52 due to the spatial misalignment between the electric field and the light field; In this study, a gradient structure was used to achieve“ dynamic matching” between the two, increasing the C to 0.85 and reducing the half wave voltage by 12.5 % under the same modulation arm length, while avoiding the deterioration of crosstalk caused by simply reducing the electrode spacing.
4.3 Improvement of frequency doubling efficiency 4.3.1 FSR of the MRR
Considering that the modulation bandwidth f m of the device designed in this article is greater than 70 GHz, in order to avoid overlapping interference of different sideband components in MRR, the FSR of MRR needs to be greater than twice the modulation bandwidth, that is, FSR > 140 GHz. While to achieve FSR > 140 GHz, the MRR circumference needs to be reduced from the current 1.147 mm to about 900 lm, and the corresponding semicircle radius needs to be reduced from 80 lm to65lm. But a smaller radius will cause the bending loss of MRR to increase from 0.1 dB / cm to 0.3 dB / cm, resulting in a decrease in Quality-factor( Q-factor) and subsequently a decrease in frequency doubling. According to the optimized design, the FSR of the micro ring is approximately 120 GHz, as shown in Figure 11.
Figure 11 shows the transmission spectrum performance of the Si 3 N 4-TFLN heterogeneous integrated MRR, and the spectral characteristics directly reflect the device’ s excellent frequency selection and resonant enhancement capabilities, which are the core for achieving high-efficiency frequency doubling. The MRR achieves an FSR of 120 GHz and a narrow resonant peak width of 4.65 pm( far narrower than the 20 – 50 pm of traditional silicon-based MRR), which not only