J. Eur. Opt. Society-Rapid Publ. 22, 16( 2026) 159
Fig. 10. Electromagnetic simulation results of on-chip multifunctional devices.
Fig
. 11. Performance of MRR.
ensures the accurate filtering of the optical carrier and the enhancement of the sideband optical field, but also avoids the overlapping interference of sideband components. Based on the spectral parameters, the MRR Q-factor is calculated to be 3.2 10 5, which is 50 % higher than that of the single TFLN material MRR, and this high Q-factor significantly improves the optical field energy accumulation in the cavity, laying the foundation for the device to achieve a theoretical frequency doubling efficiency of 15 %.
4.3.2 Quantitative calculation of MRR Q-factor and loss correlation analysis
The MRR Q-factor designed in this paper is 3.2 10 5, representing a 50 % improvement over the MRR fabricated from single TFLN material. This Q-factor is quantitatively calculated based on the transmission spectral characteristics of MRR, combined with the waveguide intrinsic loss mechanism. The specific process is as follows.
The Q-factor of a MRR is defined as the ratio of the resonant wavelength( k₀) to the full width at half maximum D k FWHM of the resonant peak, and the calculation formula is as follows [ 30, 34 ]: k 0
Q ¼: ð29Þ
k FWHM
The transmission spectrum of the MRR was simulated using Lumerical FDTD Solutions, with a grid resolution set to 0.05 lm. PML boundary conditions were employed to eliminate boundary reflections. The simulation results are presented in Figure 8. The full width at half maximum of the resonance peak at k₀ = 1550nmis4.65pm.
Substituting the Q-factor calculation formula, we obtain Q = 3.33 10 5.
The above formula is based on the theoretical calculation of the full width at half maximum of the transmission spectral resonance peak. We should also consider the actual impact of waveguide sidewall roughness and interface scattering loss.
The interface scattering loss of the Si 3 N 4-LN heterojunction is a key factor affecting the MRR Q-factor and frequency doubling efficiency. This loss is quantitatively calculated based on the Rayleigh scattering model, which is suitable for describing the scattering loss caused by small-scale interface inhomogeneities( roughness < k / 10) [ 33 – 35 ]. The specific calculation is as follows:
For optical waveguides with smooth interfaces( root mean square roughness r < k / 10), the calculation formula for interface scattering loss( a scatter) is:
a scatter ¼ 8p2 r 2 n 3 eff k 4 cos h; ð30Þ
where r = 0.3 nm, representing the root-mean-square roughness of the Si 3 N 4-LN interface, measured through Atomic Force Microscopy( AFM) within a 5 5 lm scanning area; n eff = 1.99768, indicating the effective refractive index of the Si 3 N 4 waveguide, obtained from COMSOL Multiphysics simulation; k = 1550nm, h = 0 °. Thisisthe incident angle of the light field relative to the interface, assuming normal incidence within the waveguide core. Substituting the above parameters into the Rayleigh scattering formula yields, we obtain a 0.2 dB / cm.
This low interfacial scattering loss, combined with the low intrinsic transmission loss of Si 3 N 4( 0.15 dB / cm), results in a total MRR loss of 0.35 dB / cm. After introducing the correction factor, the Q-factor under actual working conditions is 3.2 10 5, which is consistent with the experimental test results.
The achievement of a high Q-factor benefits from the synergistic effect of two key factors:( 1) the intrinsic transmission loss of the Si 3 N 4 waveguide layer is as low as 0.15 dB / cm, significantly lower than that of a single TFLN waveguide( 0.5 dB / cm [ 13 ]);( 2) by optimizing the Si 3 N 4- LN heterojunction interface through improved bonding processes, the interface roughness is reduced to < 0.5 nm. According to Rayleigh scattering theory, the scattering loss