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Abstract
Sharp bends are crucial for large-scale and high-density photonics integration on thin-film lithium niobate platform. In this study, we demonstrate low-loss (<0.05 dB) and sharp bends (Reff = 30 µm) using free-form curves with a 200-nm-thick slab and a rib height of 200 nm on x-cut lithium niobate. Employing the same design method, we successfully realize a compact fully-etched ring resonator with a remarkably large free spectral range of 10.36 nm experimentally. Notably, the equivalent radius of the ring resonator is a mere 15 µm, with a loaded Q factor reaching 2.2 × 104.
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1. Introduction
Lithium niobate (LN) stands out as a versatile material with widespread applications, including high-speed fiber-optic communication, data centers, microwave photonics, and quantum optics. It boasts numerous advantages, such as a broad transparent window, strong electro-optic and acousto-optic effects, high second-order nonlinearity, and stable physical and chemical characteristics. The recent emergence of high-quality thin-film LN on insulator (LNOI) and advancements in nanofabrication techniques have led to the development of high-performance integrated lithium niobate photonics [1–3]. These integrated photonic devices, such as ultra-low loss and compact waveguides [4,5], highly efficient electro-optic modulation [6–8], and all-optical nonlinearities [9,10], underscore the potential of LNOI platforms. However, components on the LNOI platform lack a significant advantage in refractive index difference when compared to silicon or indium phosphide platforms. This poses challenges for large-scale and high-integration development in applications such as switch fabrics [11], silicon photonics LiDAR [12], delay lines [13,14], and programmable nanophotonic processors [15], which demand intricate and large-scale components. The size of the bend structure in these components emerges as a critical factor in determining the integration density of the entire photonic circuit. For instance, a delay line requiring several nanoseconds typically necessitates a spiral structure with numerous continuous bends spanning several tens of centimeters [13]. Additionally, the chip size of the microring array-based programmable nanophotonic processor is directly proportional to the square of the ring radius [15].
The inherent challenges associated with a small bend radius predominantly revolve around two issues: radiation losses and mode mismatch with the straight waveguide [16]. Achieving ultra-compact bend waveguides has been explored through various means, including subwavelength-assisted structures [17,18], air trenches [19,20], and inverse design [21,22]. However, these structures present challenges in terms of ultraviolet lithography processes and are associated with relatively high insertion losses. This challenge is particularly pronounced for lithium niobate waveguides with non-vertical sidewalls. To address these concerns, the utilization of continuous transition curves such as Euler bends [23], Bezier bends [24], and free-form curves [25,26] proves effective in achieving a 90° bend with reduced losses and larger fabrication tolerances. Another consideration is that, for anisotropic platforms, like x-cut thin-film lithium niobate, waveguide bending may introduce mode hybridization [27], and larger bend radii can result in increased mode conversion and higher losses. The use of compact bending can mitigate this issue. Furthermore, the bend radius directly impacts the performance of ring resonators, such as the free spectral range (FSR) and quality (Q) factor. However, a trade-off exists between these metrics. For instance, in scenarios involving wavelength division multiplexers [28], sensing [29], and lasers [30] tuning range, a large FSR is imperative. Nevertheless, achieving a large FSR necessitates adopting a small bend radius, potentially leading to increased bend losses and decreased Q factors. Consequently, these factors exert a detrimental influence on attributes such as laser linewidth [31] and the efficiency of nonlinear optical processes [32].
In this paper, we present a novel approach to sharp bends on LNOI for the fundamental TE mode, utilizing free-form curves (FFCs). The proposed structure demonstrates lower losses when compared to circular, Euler, or Bezier bends with an equivalent radius. In our experiments, a 90° bend showcased a mere 0.05 dB loss, featuring an equivalent radius of 30 µm for a rib waveguide comprising a 200-nm-thick slab and a rib height of 200 nm, which is commonly employed in modulators. Moreover, we extend our investigation to a compact ring resonator using the same design method with 400-nm fully-etched waveguides. Our results reveal a remarkably large FSR exceeding 10 nm on LNOI, accompanied by a loaded Q factor of 2.2 × 104.
2. Design, fabrication and characterization
2.1 Sharp bend structure
In prior studies, the efficacy of FFC design in reducing bend losses for multimode waveguides has been established [25,26]. This paper employs a similar design methodology to achieve sharp waveguide bending on the fundamental TE mode in the LNOI platform. The models are optimized using the Direct Range Search (DRS) algorithm. As shown in Fig. 1(a), the single-mode waveguide bending consists of FFCs of equal width. These FFCs exhibit mirror symmetry along the angular bisector OT of the quadrant ∠XOY and comprise 2×D different curvature radii, with D = 3 presented for ease of illustration (in the actual simulation, D = 20). Ri represents the curvature radius of the i-th arc, while Oi denotes the corresponding center of the arc, and Pi is the angular bisectors of ∠YOT to limit the length of the arcs. Consequently, there are slight variations in the lengths of each arc. Reff corresponds to the equivalent radius of FFCs, defined as the radius of a regular 90° arc-bend within the square area occupied by the FFCs. Similar to the methodology in Ref. [26], the reasonable initial values of Ri are generated by:
Herein, the function rand generates a uniformly distributed random number from 0 to 1, excluding 1. The variable RMAX signifies the upper limit of the radius used in our optimization, typically set at RMAX = 5Reff or more. m is a real exponential that ranges from 0 to infinity. A higher value of m increases the probability of obtaining larger Ri. Subsequently, we rearrange the Ri values in the sequence of their magnitudes to construct the curves, eliminating any unreasonable data groups. By selecting an appropriate m value, Eq. (1) efficiently identifies values suitable for the initial curve pattern. To minimize the overall bend radius, the Ri values exhibit a decreasing trend from R1 to RD. It is important to note that the last radius RD is determined by the previous Ri rather than being randomly generated, ensuring that the final center OD falls on OT. To pinpoint the optimal values, we iterate the more favorable Ri value within the interval [Ri - Rs, Ri + Rs] for quick convergence, where Rs is determined as follows:
Fig. 1. (a) Schematic diagram of the initial FFCs. Ri (i = 1, 2, 3) represents the corresponding radius of each arc, while Oi (i = 1, 2, 3) denotes the corresponding center of the arc. Reff is the equivalent radius of the FFCs. (b) A comparison of the shapes between FFCs and arcs.
Here, a is a limiting factor less than 1. After obtaining the curves from Eq. (2), they undergo a reverse design process using the DRS algorithm to achieve improved results. The simulation employs the 3D Finite-Difference Time-Domain (FDTD) method, with the figure-of-merit (FOM) focusing on the transmission of the fundamental TE mode within the C-band wavelength range. Each Ri value of the curves is sequentially varied, and the change is either retained or discarded based on the FOM value. These searching procedures are repeated until the device's performance meets the desired criteria. For instance, in optimizing R1, values ranging from R1 - Rs to R1 + Rs, sampled at equal intervals of 30 steps, are considered for R1, either sequentially or randomly. After updating R1, the FOM of the curves is calculated. If the FOM surpasses the initial value, the updated R1 value is retained, and the search for the next Ri (R2 in this case) begins. This process restarts at R1 after optimizing the last radius RD. In general, the optimal bend design in an anisotropic medium, such as x-cut LN, may not exhibit mirror symmetry. In this design, the mirror-symmetry configuration along OT is set to reduce the value of D for rapid convergence. Since the FOM is based on the entire 90° bend, the lowest transmissions for curve sections XT and TY have both been considered. The optimal design with low bend loss can also be obtained.
In this study, a commercial x-cut 400-nm thick LNOI wafer with a 2-µm-thick buried silica buffer layer was utilized. The cross-sectional view of the LNOI waveguides is shown in the inset of Fig. 2(a), featuring half-etch and a 1.5 µm width. Based on our fabricated waveguide profiles, the sidewall angle is set at 60°. To achieve low losses and compact sizes, we set the equivalent radius at 30 µm. Figure 1(b) illustrates the distinctive characteristics of the optimized FFCs compared to regular arc-bends with equal radii. The final radii for different sections are presented in Fig. 2(a). It's worth noting that the radius does not strictly follow a monotonically decreasing pattern due to the chosen interval [Ri - Rs, Ri + Rs], ensuring swift convergence rather than [Ri-1, Ri + 1]. As a result of reverse design, there is no strict necessity to adhere strictly to these points. Comparable low transmission loss can be attained with minor adjustments to the entire structure. To highlight the superiority of our designed bends, a performance comparison was conducted among various bend types, including arcs, optimized Euler bends, and Bezier bends. The Euler bend, configured with a maximum radius of 400 µm and a minimum radius of 16.5 µm, aims to minimize reflection and loss. For Bezier bends, we explored different Bezier numbers (B) from 0 to 0.5 with a step size of 0.05, ultimately selecting the optimal result B = 0.35 for the minimum loss [24]. All bends share the same equivalent radius of 30 µm. Figure 2(b) demonstrates from simulation results that the FFCs bends exhibit enhanced performance in terms of losses fundamental TE mode compared to other conventional designs. Notably, all the FFCs bends achieve low losses of <0.05 dB over the 100 nm band. Furthermore, these bends exhibit large fabrication tolerances, ranging from ±100 nm to ±200 nm. To effectively characterize bend loss, we cascaded 40 90° FFCs bends and 40 arcs separately, each with the same equivalent radius of 30 µm. The structures underwent a DUV lithography process for patterning, followed by Ar + plasma etching of the LN layer. Figure 3(a) displays microscopy and scanning electron microscope (SEM) images of the fabricated structures. Subsequently, a 3 µm thick oxide over-cladding was deposited using plasma-enhanced chemical vapor deposition. Figure 3(b) presents measurement results, showcasing that the worst bend losses of FFCs with large width deviations are lower than 2 dB (<0.05 dB per FFCs), significantly surpassing arcs. The minimum bend loss occurs at Δw = + 0.1 µm, attributed to deviations between the actual width and the waveguide layout. Overall, the experimental and simulated results exhibit good agreement.
Fig. 2. (a) The radii for the optimized FFCs bend. The inset is a schematic diagram of the waveguide cross-section with a sidewall angle of 60°. (b) Transmission comparison among arcs, optimized Euler, Bezier, and FFCs bends. The dashed lines correspond to situations where there is a width deviation in the FFCs bend.
Fig. 3. (a) Microscopy and SEM images of the fabricated structures. (b) Measured spectral responses of cascaded 40 FFCs and arcs.
2.2 Compact ring resonator
Fully-etched LN waveguides provide enhanced light confinement, enabling high integration density and a large FSR response in a ring resonator. In this section, we apply the proposed methods to design a fully-etched 90° bend with an equivalent radius of merely 15 µm. This bend is seamlessly integrated into a compact ring resonator with a large FSR. Another critical consideration is the potential occurrence of mode hybridization for specific waveguide widths and propagation angles φ [27,33]. Such hybridization could result in the loss of the target mode, thereby influencing the resonant spectrum of the ring. In this context, we calculate the effective refractive indexes of the first modes (fundamental TE modes) and the second modes (labeled Mode2 in Fig. 4(a)) in a waveguide with a fixed width of 1.5 µm. We explore two extreme radii that may be utilized in FFCs bends. The results presented in Fig. 4(a) affirm the absence of mode hybridization in such a waveguide profile. As shown in Fig. 4(b), the optimized bends exhibit a high transmission efficiency of >0.99 for the fundamental TE mode, even with waveguide width deviations of ±50 nm and ±100 nm. This performance is significantly superior to that of standard arcs, primarily due to the lower excitation of high-order mode components at the entrance of the straight waveguide.
Fig. 4. (a) Effective refractive indices of the fundamental TE and the second modes for different φ at a wavelength of 1.55 µm. The insets depict mode profiles of TE at R = 8 µm and a schematic definition of φ, respectively. (b) Simulated transmission of fully etched FFCs and arc waveguides. The inset is a schematic diagram of the fully-etched waveguide cross-section.
Additionally, a significant challenge associated with a ring resonator, particularly one with a large FSR, lies in the coupling with the bus waveguide. This challenge becomes more pronounced in thin-film LN waveguides, as the sidewall angles of LN waveguides make it challenging to achieve small gaps, resulting in relatively low coupling efficiency. Using long straight waveguides for coupling would extend the cavity length, and employing bent couplers would introduce additional bend losses for the sharp bend structure. In a prior study [33], a theoretical proposal was put forth to enhance coupling efficiency by using narrow waveguides in the coupling region. However, this method still requires a coupling length of several tens of micrometers, which is not conducive to the design of a large FSR. In our current research, after constructing the ring resonator using the proposed 15-µm FFCs bends, we specifically designed the coupling region to achieve critical coupling. As shown in Fig. 5(a), waveguides l1 and l3 are axisymmetric and parallel to the 2θ-radian FFCs on the ring resonator, while waveguides l2 and l4 are centrally symmetric with l1 and l3, respectively, connecting to the entrance ports. As the bend radii of these waveguides are larger than the corresponding sections of the ring, we optimized the width of the bus waveguide to ws = 0.62 µm to match the phase condition. The choice of coupling angle θ is based on coupling loss and ratio considerations. In Fig. 5(b), it is evident that the minimized coupling loss at θ ≈ 15° is 0.044 dB, significantly lower than the total bend loss of the ring. Losses at θ<15° are attributed to the excitation of high-order modes in the ring, while larger θ induces significant bend loss for the S-bend sections. The low coupling loss improves both the non-resonant transmission power level and Q factor. The resulting coupling ratio reaches a relatively large value of 0.24 with an initial gap of g = 512 nm. Subsequently, the gap is adjusted to 582 nm for critical coupling, assuming losses of 8 dB/cm for the bent waveguide based on our actual fabrication process (7 dB/cm) and simulated bend loss (1 dB/cm). Figure 5(c) shows the light intensity transmission of the designed coupler, while Fig. 5(d) illustrates the simulated resonant spectra of the designed ring under the assumptions of perfect smooth sidewalls and actual transmission losses, both analyzed at critical coupling using the transfer matrix method.
Fig. 5. (a) Illustration of the proposed ring resonator connected by FFCs bends. The inset presents a cross-section schematic diagram of the coupling region. (b) Coupling ratio and coupling loss for various coupling angles θ. (c) Intensity profiles of light propagation in the coupler with θ = 15° and g = 512 nm. (d) Simulated transmission spectra of ring resonators under the assumptions of losses at 1 dB/cm and 8 dB/cm.
The fabrication process parallels that of the half-etch FFCs bends, except for the utilization of electron beam lithography and the MaN 2405 resist to achieve deeper etching. In Fig. 6(a) SEM images of a sample before the SiO2 deposition are depicted. From Figs. 6(b) and 6(c), the resonance spectrum of the device displays a notable extinction ratio, reaching 21 dB at a wavelength of 1545.27 nm, accompanied by a large FSR of 10.36 nm. A more detailed analysis involves Lorentzian fitting based on measurements [34], revealing a 3-dB bandwidth of 0.07 nm (∼8.8 GHz), a loaded Q factor of 2.2 × 104, and an intrinsic Q of 4.8 × 104. Furthermore, the estimated coupling ratio is 0.152, while the propagation loss is evaluated at 8.5 dB/cm, incorporating the coupling loss in the resonator round trip loss. Table 1 provides a comparison of reported ring resonators on LN. It is noticeable that the FSR and size in Ref. [41] are only marginally inferior to those in this paper. However, a high Q factor can still be achieved, thanks to their advanced etching process that ensures smooth sidewalls. Additionally, the use of a 600-nm thick LN layer and an air over-cladding enables a compact ring through arc bending alone. In our case, even with the utilization of a thinner (400 nm) LN layer and SiO2 cladding, we have achieved the smallest equal radius, along with the most compact footprint and the largest FSR, attributed to the free-form curves design. According to Fig. 5(d), the Q factor may be further increased by an order of magnitude through the optimization of the etching process to achieve smooth sidewalls.
Fig. 6. (a) SEM diagram of the ring resonator. (b) Resonance spectrum and Lorentz fitting near 1545.27 nm. (c) Comparison of the normalized measured spectrum with the simulated one.
Table 1. Comparison of ring resonators on LNOIa
3. Conclusion
In conclusion, we have successfully realized low loss and sharp bends by employing free-form curves on the x-cut LNOI platform. The equivalent bend radius of the rib waveguide, featuring a 200-nm-thick slab and a rib height of 200 nm, is a mere 30 µm, with a measured loss per bend lower than 0.05 dB. Through this free-form curves bend design method, we experimentally realized a compact fully-etched ring resonator (Reff = 15 µm) with a remarkably large FSR of 10.36 nm. The loaded Q factor reaches 2.2 × 104 and the propagation loss is evaluated at 8.5 dB/cm. These sharp bends and large FSR ring resonators hold significant potential for advancing the future development of LNOI photonic integrated devices and circuits.
Funding
National Natural Science Foundation of China (62135012, 62105107); Leading Innovative and Entrepreneur Team Introduction Program of Zhejiang (2021R01001); Natural Science Foundation of Guangdong Province (2023A1515011539); Guangdong Provincial Key Laboratory of Optical Information Materials and Technology (2023B1212060065).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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