Microring resonators (MRRs) are indispensable and may be the most versatile elements in photonic integrated circuits (PICs) for applications ranging from conventional optical signal processing [1] and optical sensors [2] to emerging quantum information processing [3] and optical computing [4]. MRRs with an ultracompact footprint, e.g.,  radius <10μm will not only benefit the integration density of PICs, but also provide large nonlinear field enhancement (FE2) and large Purcell factors (Fp), which are of great importance for the nonlinear devices [5] and light sources [6], respectively. Waveguides with high linear refractive index (RI) are essential for ultracompact MRRs; otherwise, it may lead to excessive leakage loss from the sharp bends. While III-V compounds like the AlGaAs are very attractive for ultracompact MRRs for their large linear and nonlinear indices, this superiority is usually offset by the complex and demanding fabrication processes [7,8]. Hence, the MRRs are preferred to be fabricated using the silicon (Si)-based CMOS technologies for the sake of the most mature and scalable manufacturing and integration with the electronic ICs.

Table 1 gives a brief summary of the properties of the typical dielectrics in Si-based CMOS technologies, which have been utilized for MRRs. Their linear RIs (n0), nonlinear RIs (n2) and bandgaps (Eg) as well as the transparency windows (λw) are given. Here, only the dielectrics are listed because metals inherently introduce extremely large loss to a waveguide despite enabling super-small MRRs, i.e., plasmonic waveguide, which may lead to losses of ∼1000dB/cm for copper-capped waveguides [17] or only a quality factor of ∼90 for a 0.5-μm-radius MRR on gold [18]. While Si possesses the highest n0 among these dielectrics, allowing for a Si MRR with a radius as small as 1.5 μm [19], the Si waveguide is still suffering from the nonlinear losses due to the small bandgap of Si (1.12 eV) [9,20]. The large-bandgap materials such as the silicon nitride (SiN_x) [11], silica (SiO2) [21], tantalum pentoxide (Ta2O5) [14], and titanium dioxide (TiO2) [15] can avoid nonlinear losses in the telecommunication wavelengths and empower key nonlinear effects including the frequency comb generation (FCG) in MRRs with radii from several tens of microns to milimeters [22–24]. However, to the best of our knowledge, MRRs with none of these materials have been reported to show a radius <10μm. Fortunately, TiO2 has both the highest n0 and the highest n2 among these large-bandgap dielectrics in Table 1, making it attractive for nonlinear applications based on ultracompact MRRs.Table 1.

Properties of Si-Based CMOS-Compatible Dielectrics^a

Besides, the emerging demand for on-chip lasers with monolithic integration is in urgent need of better waveguides and MRRs, which are usually cladded with a rare-earth-doped film and pumped around 980 nm [25,26]. Though waveguides can be sourced with hybrid integration [27], monolithic integration still has its specific advantages [25], where Si waveguides are apparently not suitable because of absorbing the pumping lights (see λw in Table 1). SiN_x MRRs cladded with erbium- or ytterbium-doped aluminum oxide (Al2O3:Er3+ or Al2O3:Yb3+ [12]) or ytterbium-doped silica (SiO2:Yb3+ [28]) have been demonstrated for on-chip lasers. However, the radii were indeed very large, e.g., 80 μm [12] and even 1.59 mm [28] due to the small index contrast of the waveguide core to the claddings. Significantly, a large Purcell factor is of great importance for suppressing the spontaneous emission and reducing the threshold of on-chip lasers, while a large MRR most likely shows a small Purcell factor (e.g., 9 at maximum in Ref. [28]). With large n0 and transparency window until visible lights, the ultracompact TiO2 MRRs will be a promising platform for efficient on-chip lasers with the monolithic integration.

In this work, we experimentally demonstrate the TiO2 MRRs with sub-10-μm radii (e.g., 10 and 6 μm), for which quality factors (Q) of ∼7.9×104 and Purcell factors of 59 can be attained. Four-wave mixing (FWM) experiments are carried out and a conversion efficiency (CE) of −25dB is achieved to greatly outperform a large TiO2 MRR reported previously (i.e., a CE of −31dB for a racetrack MRR with the equivalent radius of 136.37 μm [29]), exemplifying the promising advantages of the ultracompact TiO2 MRRs. More comparisons between this work and other MRR platforms are given in Section 5, which further unfold the potentials of the TiO2 waveguide platform for more efficient integrated photonics.Table 2.

Comparison of MRRs on Different Material Platforms

To design the ultracompact MRRs, we first use a finite-difference method in a commercial software (MODE Solutions, Lumerical Inc.) to calculate the fundamental transverse-electric (TE0) modes for bend waveguides with a fixed width of 3 μm and height of 0.46 μm at the wavelength 1550 nm, to directly extract the bend losses. Figure 1(a) shows the obtained losses with respect to various radius and RI of the bend waveguides. Because no sidewall roughness or material absorption is taken into consideration, the calculated losses mainly derive from the leakage of a sharp bend. As shown in Fig. 1(a), the leakage loss nearly exponentially increases as the radius decreases for any RI. However, for a small RI, the leakage loss itself is no way to be underestimated even at a relatively large bend radius, e.g., 1 dB/cm for a radius of 10 μm at RI = 2.0 (i.e., close to the RI of SiN_x). Figure 1(b) shows more details of the relationship between the leakage loss and the RI when fixing the bend radius to 6 μm. The inset in Fig. 1(b) is a close-up view of the relationship for RIs from 2.0 to 2.3. It is found that the bend loss is significantly alleviated by increasing the RI, e.g., from 45 dB/cm for RI = 2.0 to 8.9×10−2dB/m for RI = 2.3 (i.e., close to the RI of TiO2), which suggests that the TiO2 MRR can be bent to at least 6 μm and meanwhile sustains a negligible leakage loss.

On a 460-nm-thick TiO2 film deposited on a Si wafer with a 2.4-μm-thick oxidized layer as the insulator, the ultracompact MRRs with radii of 6, 10, and 15 μm are fabricated. The fabrication details are found in our previous work [29], in which the electron beam lithography (EBL) and the inductively coupled plasma (ICP) are used to pattern and etch the waveguides, with chromium (Cr) serving as the hard mask. The TiO2 waveguides are finalized with air as the top cladding after residual Cr stripping.

Figures 2(a) and 2(b) show the measured transmissions of the fabricated TiO2 MRRs with the ring waveguide width of 1170 nm and radii of 15 and 10 μm, respectively. Insets in the figures are scanning electron microscopy (SEM) images of the rings. A straight bus waveguide with a width of 620 nm is used to couple with each ring with a separation of 270 nm. Because higher-order modes can also be excited, we have used circles to mark the resonances of the TE0 modes on the transmission curves. By calculating the coupling efficiencies from the bus waveguide to the MRRs, i.e., 0.129–0.173 for the 15-μm-radius one and 0.117–0.16 for the 10-μm-radius one, respectively, we have determined the two MRRs to be over-coupled in the measured wavelength range from 1500 to 1600 nm. Figure 2(c) shows the SEM image of the fabricated TiO2 MRR with the radius R=6μm. Because it is expected to have a larger bend loss, to ensure enough light coupling, a pulley-type coupler is used to lengthen the coupling area, which has the same configuration for the waveguide widths and the separation as the point-type couplers of the large MRRs (i.e., W₁ = 620, W₂ = 1170 nm, gap = 270) and has a bending angle θ=45° for each bend in the two s-bends. Figure 2(d) shows the measured transmission (blue line) of this MRR, and a free-spectral range (FSR) larger than 25 nm is found. Meanwhile, the coupling efficiency of the pulley-type coupler is calculated and shown as the red line in Fig. 2(d), by which one determines the coupling status at each resonance, i.e., under coupling at the resonance of 1508.171 nm and over coupling at all the other resonances [30]. Lorentzian curves are applied to fit the transmission spectrum around each resonance of all the MRRs, and Fig. 2(e) shows an example for the resonance at 1531.93 nm of the 6-μm-radius MRR. With the fittings, one can extract the intrinsic Q (Q0) at each resonance by using Q0=2QL/(1±T0), where QL is the loaded Q, and T0 is the transmission at the resonant wavelength. Here, the plus sign is for the under coupling, while the minus sign is for the over coupling. The extracted values of Q0 are summarized in Fig. 2(f) and distributed around 8.3×104 (blue dashed line), 7.9×104 (green dashed line), and 4.4×104 (red dashed line) for the TiO2 MRRs with radii of 15, 10, and 6 μm, respectively.

As shown in Fig. 2(f), the more compact an MRR is, the lower Q0 (i.e., higher loss) it exhibits, which is usually an inevitable trade-off for a dielectric cavity. Two figures of merit (FOMs) can be applied to evaluate the overall performance of an MRR: power enhancement factor [5] and Purcell factor [31]. The former is mainly used for MRR-based nonlinear devices, and the latter can be utilized for characterizing MRR-based light source devices. The loss α of a bend waveguide as a function of the bend radius R generally follows the relationship [32]: α=a·R−b+c,(1)where a, b, and c can be extracted by fitting the measured α at different radii. According to α=λ/(Q0·R·FSR) [33], the bend waveguide losses are calculated to be 5.3, 5.6, and 10.2 dB/cm for the fabricated TiO2 MRRs with radii of 15, 10, and 6 μm, respectively. Figure 3(a) shows the measured bend losses (open diamond) with respect to the bend radius and the fitted curves (dashed lines). The best fitting happens, as shown by curve α2 (green dashed line), when a=44770, b=−5.098, and c=5.283, which implies that the loss of a straight TiO2 waveguide with the same width (i.e., 1170 nm) is 5.283 dB/cm. Meanwhile, we also add two fitting curves with the same a and c but different b in Fig. 3(a) to mimic the bend waveguide losses as a function of the RI of the waveguide, e.g., α1 for a larger RI (red dashed line) and α3 for a smaller RI (blue dashed line).

The power enhancement factor (FE2) of an MRR is a ratio of the power in the ring (Pring) to the power in the bus waveguide (Pbus) and can be expressed as follows [34]: FE2=PringPbus=4Qc/ω0(1+Qc/Q0)2vgL,(2)where Qc, ω0, vg, and L are the coupled Q, the resonant frequency, the group velocity, and the cavity length, respectively. When Qc=Q0, which happens at the critical coupling of the MRR, the power enhancement factor can attain the highest value: FEcritical2=Q0vgω0L=1αL.(3)

Here, Q0=ω0/(αvg) has been used in the derivation of Eq. (3). It is clearly shown that the FEcritical2 for an MRR is inversely proportional to both the bend waveguide loss and the cavity length. Figure 3(b) shows the calculated FEcritical2 for MRRs with different radii based on the measured and fitted losses in Fig. 3(a). An optimal radius is found to exist where FEcritical2 reaches the maximum. Meanwhile, when the RI increases, this optimal radius decreases, while the maximal FEcritical2 increases. For the TiO2 MRRs, the maximal FEcritical2 is 135 at the optimal radius of 8 μm, and FEcritical2 is 122 and 113 for the measured MRRs with radii of 10 and 6 μm, respectively.

The Purcell factor (FP) can be calculated by [35] Fp=34π2(λ0n0)3(Q0Veff),(4)where n0 is the RI of the waveguide, and the effective mode volume Veff of the MRR can be simply calculated by Veff=2πRAeff [36]. Here, Aeff is the effective mode area of a bend waveguide. Figure 3(c) shows the calculated FP for MRRs with different radii based on the measured and fitted losses in Fig. 3(a). The Q0 values are calculated by Q0=2πng/(λα), where ng is the group index of the bend waveguide. Similarly, the optimal radius also stands for a maximal FP, and such an optimal radius decreases as the RI of the MRR waveguide increases. In addition, the maximal FP also becomes larger for a larger RI. For the TiO2 MRRs, FP attains the maximum value of 65 at the optimal radius R=8μm, while 59 and 56 for R=10 and R=6μm, respectively. These results clearly indicate the benefits of ultracompact TiO2 MRRs for improving the nonlinear efficiency and the Purcell factor.

FWM experiments in the fabricated ultracompact TiO2 MRRs have been performed by using the setup illustrated in Fig. 4. The signal light and the pump light are generated from two individual continuous-wave (CW) tunable lasers, polarization tuned by fiber polarization controllers (PCs) and power adjusted by erbium-doped fiber amplifiers (EDFAs) and variable optical attenuators (VOAs). Band-pass filters are applied after the EDFAs to reduce the out-of-band amplified spontaneous emission (ASE). The two lights are combined by a 3-dB coupler, polarization selected (here is TE) by a polarization beam splitter (PBS), and then injected into the waveguides by a tapered lensed fiber. The output beam is collected by another tapered lensed fiber and measured by an optical spectral analyzer (OSA).

Although intermodal four-wave mixing could happen within nonresonant structures [37,38], it is indeed hard to align all the four waves to the resonances at different modes which usually exhibit different resonance spacing (i.e., the free-spectral range or FSR). Hence, here we only focus on the FWM experiments for the TE0 mode in this work despite existing resonances at other modes. For the TiO2 MRRs with R=6μm and R=10μm, Figs. 5(a) and 5(b) show the measured output FWM spectra for on-resonances (red lines) and off-resonances (blue lines) under input pump power (i.e., power in the bus waveguide) of 13 and 16 dBm, respectively. For the MRR with R=6μm, we pump it around the resonance of 1531.93 nm while 1558.72 nm for R=10μm. The input signal wavelengths have one FSR separation from the pump wavelengths for both the MRRs, i.e., 1556.45 and 1543.72 nm for that with R=6μm and R=10μm, respectively. The input signal power is fixed to −0.81 dBm (far smaller than the pump powers) during all the measurements, while the input pump power is variable. The measured spectra show CEs of −36dB and −25dB for the MRRs with R=6μm and R=10μm, respectively, in which CE is defined as the ratio of the output idler power for on-resonance cases to the output signal power for off-resonance case. Here, CE represents how efficiently the MRR transfers the photon energy of the pump light to the idler light via the Kerr nonlinear process. The CEs with respect to different input pump powers are also measured and shown in Fig. 5(c). Linear fittings (red) are applied to the measured data and both show slopes of ∼2, which not only implies that the lights can be stably coupled into the MRRs, but also verifies an absent nonlinear loss of the TiO2 waveguide under the current coupled powers.

Figure 6(a) shows the calculated dispersions (D) of a TiO2 waveguide with the width of 1170 nm and the height of 460 nm when it is straight (purple), 10-μm-radius bend (green), and 6-μm-radius bend (red), respectively. Usually, anomalous dispersions are preferred to cancel out the nonlinear phase shifts in a waveguide to achieve broadband FWM wavelength conversion [39], but the absolute values of the anomalous dispersions should not be too large. The 10-μm-radius TiO2 bend waveguide exhibits anomalous dispersions with absolute values of D<10ps/(nm⋅km) in the wavelength range from 1575 to 1732 nm as shown in the inset of Figure 6(a). Note that if the bend is even sharper, e.g.,  with a radius of 6 μm, the dispersions may change to be normal. To verify the broadband operation of the fabricated 10-μm-radius TiO2 MRR, we tune the signal light wavelength to be around the resonance of 1589.6 nm, i.e., two FSRs separation from the pump. Figure 6(b) shows the measured output FWM spectra for on-resonances (red) and off-resonances (blue), respectively. A CE of −26.5dB is achieved, only 1.5 dB degraded compared with the one-FSR separation case and suggesting a 3-dB FWM conversion bandwidth to be at least 61.8 nm.

The comparison of overall performances of MRRs on different material platforms is shown in Table 2. First of all, although supercompact MRRs can be achieved in a plasmonic waveguide [18] or a Si waveguide [19], the Purcell factors are actually, not pronouncedly superior to the TiO2 MRRs due to the large losses (i.e., small quality factors). Meanwhile, the extremely large loss of a plasmonic waveguide and the presence of nonlinear losses of a silicon waveguide inevitably limit their applications in nonlinear photonic devices. Among all the reported MRRs on various material platforms, the stoichiometric silicon nitride (Si3N4) MRRs may have the highest Q up to 3.7×107 [40]. This extremely high Q can considerably enhance the nonlinear interactions yielding an FE2 tens of times larger than all the other MRR platforms, which finally allows for FCGs with ultralow sub-μW thresholds. However, though the FP also exhibits an outstanding value, it was indeed achieved in a thick (730 nm) and very wide (2.3 μm) Si3N4 waveguide, probably making it unsuitable for monolithic integration where a large amount of light should be decoupled into the rare-earth-doped cladding. Contrarily, light can be efficiently decoupled into the SiO2:Yb3+ cladding of a thin (100 nm) Si3N4 MRR, which, however, has a super-large radius of 1.59 mm and hence a very small maximal FP∼9 [28]. Anyway, the Si3N4 MRRs were usually quite large due to a small RI of the Si3N4. Recently, silicon-rich nitride (SRN) has been attracting much attention as the engineered RI can be as large as 3.1 [44,45]. Unfortunately, the high loss (Q<19,000) of such an SRN MRR and its relatively large footprint (R=50μm) still give a low FE2 and Fp.

High Q have been demonstrated with TiO2 MRRs but they again have large radii (150 μm [42] and 136.37 μm [29]) and consequently lower FE2 and FP than that of the ultracompact TiO2 MRRs demonstrated here. The benefits of a large FE2 are pronounced, regarding that an FWM CE of −25dB can be achieved here with a pump power of 16 dBm, while that is only −31dB for the 136.37-μm-radius TiO2 MRR under the same pump power. Previously, we have achieved Q∼1.0×105 in a racetrack-type TiO2 MRR with R=10μm and straight regions being 40 μm long in total (corresponding to an effective radius of 16.37 μm of a ring-type MRR [43]), which is calculated to exhibit comparable FE2 and FP with the present results. Nevertheless, the bottom-up fabrication method for that TiO2 MRRs may be limited by its poor scalability. Overall, compared with TiO2 MRRs reported previously and MRRs in other materials, the TiO2 MRRs presented here show significantly large FE2 and FP and the capability for scalable fabrication as well.

In conclusion, we have theoretically and experimentally investigated the way to achieve high figures of merit of an MRR. By taking advantages of the large RI of TiO2, we have demonstrated ultra-compact TiO2 MRRs with the smallest radius so far, i.e., down to 6 μm. The benefits of considerably decreasing the footprints but sustaining moderately high Q are verified by FWM experiments, e.g.,  a CE of −25dB in a 10-μm-radius TiO2 MRR presented here versus a CE of −31dB in a 136.37-μm-radius reported previously under the same pump powers, because the smaller one possesses a larger power enhancement factor (122 versus 15). Meanwhile, the thicker (460 nm) TiO2 waveguide here can keep a small anomalous dispersion for broadband wavelength conversion, which has also been verified experimentally. Note that the loss of the 460-nm-thick TiO2 waveguides shown here (5.283 dB/cmfor the straight ones) is larger than that (3.1 dB/cm) of the 360-nm-thick ones reported in our previous work [29]. It is because a longer deposition could heat the sample to a higher temperature and thus more easily allow the scattering clusters to form in the TiO2 film. Apart from the losses arising from the film (i.e., absorption loss and scattering loss due to the clusters inside), the thicker waveguide may also suffer from a higher scattering loss due to the sidewall roughness. To decrease these losses and finally achieve efficient optical parametric oscillation or frequency combs in the ultracompact TiO2 MRRs, both the deposition and etching processes are required to be optimized, e.g.,  depositing the film for several times to ensure sufficient heat dissipation to alleviate cluster formation or etching the waveguides with advanced hard mask like the hydrogen silsesquioxane (HSQ) to obtain smoother sidewalls. Besides nonlinear devices, as the ultracompact TiO2 MRRs can provide large Purcell factors (>56) as well, various light source devices may also be favored. In addition, TiO2 can also be directly doped with rare-earth ions [46,47], which may further improve the emission efficiency of on-chip light sources. We believe these results shed lights on various applications which require highly efficient and ultracompact on-chip devices for the integrated photonics.

Acknowledgment. The authors thank DTU Nano-lab for the support of the fabrication facilities and technologies.