1. Introduction

Lithium niobate (LN) exhibits outstanding material properties that have been applied for a variety of applications [1–3]. Recent advance in LN integrated photonics on chip-scale platforms has shown significant advantages in device engineering and functionality innovation compared with conventional approaches [4–33]. For integrated photonic devices and circuits, high optical quality and low propagation loss is crucial for most applications, which has been demonstrated in LN whispering-gallery microresonators [10, 11, 13, 19, 27], LN microring resonators [29, 31], LN waveguides [32], LN photonic crystal nanoresonators [28], and hybrid waveguides and resonators [16,21,25].

Among various device geometries, microring is of great interest since it exhibits superior characteristics such as flexibility in dispersion engineering, capability of electrical integration, resilience to mechanical perturbation, and potential for large-scale integration. Precise engineering of group-velocity dispersion (GVD) underlies crucially many nonlinear photonic applications such as optical parametric oscillation [34], soliton formation [34], supercontinuum generation [35], Kerr frequency comb generation [36], etc., and significant efforts have been carried out in the past few years for dispersion engineering on a variety of device platforms [37–42]. For LN nanophotonic devices, however, current attentions primarily focus on nonlinear effects such as frequency conversion [10, 12, 17, 18, 22, 23, 27, 29, 30, 32], optomechanics [19, 28], photorefraction [26,28], and electro-optics [4,5,8,9,13,16,20,25,33]. Engineering of GVD has not yet been reported for LN nanophotonic devices.

On the other hand, microring resonators with only single-mode or few-mode families are crucial for many important applications, since intermodal interactions in these devices are dramatically reduced, which is critical for nonlinear photonic applications [43, 44]. However, such type of microring resonators require small waveguide dimensions and are more susceptible to waveguide sidewall roughness induced by fabrication imperfection. In this paper, we report dispersion-engineered LN microring resonators whose GVD can be precisely controlled in the normal and anomalous dispersion regimes, while simultaneously exhibiting high optical Qs greater than 1 million. The capability of precise GVD engineering in high-Q LN microresonators paves a critical step towards various nonlinear photonic applications on this promising device platform.

2. Devices and characterization

Figure 1(a) shows a typical LN microring resonator, fabricated on a 600-nm-thick x-cut LN-on-insulator wafer. The LN microring has a thickness of 490 nm and waveguide width of 1.2 μm, with a radius of 60 μm, sitting on a 2-μm-thick buried silicon oxide layer. The microring resonator is side coupled to a LN waveguide with a width of 800 nm, separated by a gap of 1 μm, which were optimized for good external coupling. The device structure was patterned by electron-beam lithography and etched by argon-ion milling process, whose detail can be found from our previous publication [19]. The plasma etching process produced a slant angle on the device sidewall, resulting in a trapezoid-like shaped cross section, as shown clearly in Fig. 1(b).

 

Fig. 1 (a) Scanning electron microscopic (SEM) image of a LN microring resonator with a radius of 60 μm, waveguide thickness of 490 nm, and waveguide width of 1.2 μm. (b) SEM image of the cross section of a waveguide. That of the microring is similar except with a larger waveguide width.

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To characterize the optical properties of the microring resonator, we launched a continuous-wave laser via an optical fiber taper to the on-chip LN waveguide which coupled the light into the microring resonator whose output was collected by the same LN waveguide and delivered to another fiber taper for detection. Figure 2 shows the detailed schematic of the experimental testing setup. The polarization state of the laser was controlled by a polarization controller for optimal coupling to the cavity modes. To characterize the linear optical properties of the device, the optical power of the laser was maintained low enough, around 5 μW, to prevent potential nonlinear optical effects. The laser wavelength was calibrated by a Mach-Zehnder interferometer.

 

Fig. 2 Schematic of the experimental setup. The inset shows an optical image of a device.

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3. Optical properties

By scanning the laser wavelength and recording the device transmission, we obtained the transmission spectrum of the microring resonator, as shown in Fig. 3. Figure 3(a) shows clearly that the device exhibits four mode families, as indicated as Family I – IV on Fig. 3(a), with free-spectral ranges in the range of ∼ 2.5 nm. Detailed analysis shows that the mode family I, II, and III correspond to the fundamental, second-order, and third-order quasi-transverse electric cavity modes, respectively. Each mode family exhibits nearly uniform coupling depth across a broad spectrum, indicating uniform efficiency of external coupling to the coupling waveguide.

 

Fig. 3 (a) Normalized laser-scanned transmission spectrum of a LN microring resonator with a radius of 60 μm, thickness of 490 nm, and a width of 1.2 μm. The insets show the mode field profiles of mode (b) and (c), respectively. (b)–(d) Detailed transmission spectra of a fundamental, a second-order, and a third-order cavity mode, respectively, with the experimental data shown in black and the theoretical fitting shown in red.

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Figures 3(b) and 3(c) show detailed characterizations of a fundamental mode at 1493.11 nm and a second-order mode at 1492.30 nm, respectively, whose mode field profiles are shown in the insets of Fig. 3(a). These two modes exhibit optical Q of as high as 1.3 × 10⁶ and 1.08 × 10⁶, respectively, which are comparable to those obtained in other on-chip LN microdisk and microring resonators [27,29,31], although our devices exhibit a much smaller waveguide cross section. The similarity of the optical Qs between the fundamental and second-order cavity modes indicates that the optical Q in our devices is still limited by device sidewall roughness. Therefore, further optimization of the fabrication process to improve the sidewall roughness is expected to further improve the optical quality. As shown in Fig. 3(d), even the third-order cavity modes exhibits high optical Q of 1.3 × 10⁵.

The high optical Q enables us to precisely map the dispersion properties of the devices. The dispersion of a cavity mode family can be characterized by the Taylor expression of the cavity resonance frequency ω_μ around a reference cavity resonance ω₀ [43, 44], ${\omega }_{\mu }={\omega }_0+\mu D_1+\frac{1}{2}{\mu }^2{D}_2+\frac{1}{6}{\mu }^3{D}_3+\cdots$, where μ is the relative mode number, D₁/(2π) represents the free-spectral range around ω₀, and the parameter D₂ is related to the GVD β₂ as $D_2=-\frac{c}{n}{D}_1^2{\beta }_2$.

To obtain the GVD for the device, we scanned the laser wavelength across a broad spectrum from 1480 nm to 1620 nm for the fundamental mode family and from 1480 nm to 1600 nm for the second-order mode family, and recorded the detailed resonance frequencies. Figures 4(a) and 4(b) show the dispersion of these two mode families, both of which show an overall quadratic dependence. By fitting the experimental data, we obtained that D₁/(2π) = 335.15 and 316.04 GHz for the fundamental and second-order mode family respectively, and correspondingly D₂/(2π) = 2.66 and 13.82 MHz. As a result, the fundamental cavity mode family exhibits a very small anomalous GVD in this spectral region, with a value of β₂ = −0.024 ps²/m which is as small as that of a silica optical fiber [34]. The second-order mode family is also in the anomalous dispersion regime over this spectral region, but with a slightly larger magnitude of β₂ = −0.128 ps²/m. On the other hand, Fig. 4(a) shows that, for the fundamental mode family, there exists two mode crossings over this broad spectral region, which originates from the mode hybridization with the second-order and a high-order mode. However, for the second-order mode family, the mode crossing is reduced to only one that is induced by the mode hybridization with the fundamental mode. These observations indicate that there are multiple high-Q mode families with anomalous dispersions that can potentially be employed for nonlinear photonic applications, depending on the specific mode crossing requirement.

 

Fig. 4 Recorded frequency dispersion of the fundamental (a) and second-order (b) mode family as a function of relative mode number μ, respectively, for the 1.2 μm wide ring. The black dots are experimental data, and the solid red lines are theoretical fittings. (a) μ = 0 is designated to be at around 1550 nm, and the scanned wavelength range is from 1480 nm to 1620 nm. (b) μ = 0 is around 1540 nm, and the scanned wavelength range is from 1480 nm to 1600 nm.

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4. Dispersion engineering

Flexible engineering and tuning of GVD is essential for many important applications [34]. In particular, realization of a small magnitude of GVD either in the normal or anomalous dispersion regime is crucial for controlling the nonlinear optical processes. In general, this can be achieved by tailoring the waveguide dimensions such that the waveguide dispersion compensates the material dispersion. To find the right waveguide dimension, we carried out numerical simulations by the finite element method, with the material dispersion taken into account [45], the detailed schematic is shown as Fig. 5(a) inset. The GVD can be tuned by changing h₁, H, θ, and W either separately or simultaneously. However, for the fabrication convenience, we only vary the width of the waveguide to approach suitable GVD. Figure 5(a) shows the GVD curves for LN waveguides with different widths. We use the GVD of a straight waveguide as a guidance here since it is generally fairly close to that of a microring resonator with the same cross section and a relatively large radius. Figure 5(a) shows that, in the telecom band, the GVD of the fundamental quasi-TE mode can be flexibly tuned from slightly anomalous regime to slightly normal dispersion regime by changing the waveguide width from 1.4 μm to 2.0 μm.

 

Fig. 5 (a) The simulated dispersion curves obtained by varying the width (W) of the straight waveguide. Blue line: W = 1.2 μm. Red line: W = 1.4 μm. Yellow line: W = 2.0 μm. The inset shows schematic of the straight waveguide, where H = 490 nm, h₁ = 210 nm, h₂ = 110 nm, and θ = 23°. (b) Recorded frequency dispersion of the ring with the width of (b) 1.4 μm and (c) 2.0 μm. The data was recorded from 1500 nm to 1600 nm. The black dots are experimental data, and the solid red lines are theoretical fittings.

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To confirm our simulations, we fabricated LN microring resonators with waveguide widths of 1.4 μm and 2.0 μm, whose other structure parameters are same to the ring of Fig. 3, and characterized their optical properties. Figure 5(b) shows the recorded dispersion profile of the fundamental quasi-TE cavity mode family inside a LN microring with a waveguide width of 1.4 μm, where the fitted D₁/(2π) = 335.67 GHz and D₂/(2π) = 1.67 MHz, corresponding to a GVD value of β₂ = −0.015 ps²/m in the telecom band, which is even smaller than that shown in Fig. 4(a). When the waveguide width increases to 2.0 μm, the GVD is shifted to slightly normal dispersion (Fig. 5(c)), with a value of β₂ = 0.043 ps²/m (the fitted D₁/(2π) = 336.55 GHz and D₂/(2π) = −4.80 MHz). The experiment results agree well with the theoretical expectation. A slightly discrepancy is likely due to the curvature of a microring which deviates slightly the GVD away from a straight waveguide and the variation of the angle between the optical axis of LN and propagation direction of light along the ring.

One interesting property of lithium niobate is that it exhibits considerable birefringence which provides another way to control the dispersion. To show this, we fabricated microring resonators on a z-cut LN-on-insulator wafer, whose geometry is the same as the microring used in Fig. 3. Figure 6(a) shows the experimentally recorded dispersion profile of the second-order quasi-TE mode inside a microresonator. The experimental result indicates a normal dispersion with a GVD value of β₂ = 0.040 ps²/m that is close to our theoretical expectation (Fig. 6(b)). This GVD is distinctive to that of Fig. 4(b) although the device geometries are identical, clearly showing the impact of material birefringence.

 

Fig. 6 (a) Recorded frequency dispersion of the ring on the z-cut LN with the same structure as Fig. 3, scanned from 1490 nm to 1570 nm. The black dots are experimental data, and the solid red line is theoretical fitting, with D₁/(2π) = 327.56 GHz, D₂/(2π) = −4.08 MHz. (b) The dispersion is simulated for the second-order mode, based on a z-cut LN straight waveguide with the width of 1.2 μm.

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5. Conclusion

In conclusion, we report high-Q LN microring resonators with optical Q above a million. In particular, we were able to precisely engineer the group-velocity dispersion of the microring resonators in both normal and anomalous dispersion regimes between −0.128 ps²/m and 0.043 ps²/m, by controlling the waveguide dimensions and by using the material birefringence. We achieved anomalous dispersion in the telecom band, with a value as small as β₂ = −0.015 ps²/m that is even smaller than that of a silica optical fiber. The flexible engineering of group-velocity dispersion now paves a critical step towards broad nonlinear photonic applications in LN microring resonators.