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Four-wave mixing in high-Q tellurium-oxide-coated silicon nitride microring resonators

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Abstract

We report the first-time observation, to the best of our knowledge, of four-wave mixing (FWM) in hybrid tellurium oxide coated silicon nitride ring resonators with internal Q factors of 1.7 × 105 to 1.0 × 106. We show oscillation at NIR wavelengths ranging from 1020 nm to 2530 nm under 1590 nm pumping. The FWM process has been investigated for TeO2-coated Si3N4 ring resonators with a 600 µm radius and FWM is observed for threshold launched pump powers as low as 25 mW with normal group velocity dispersion (GVD). With the potential for engineering of the GVD to the anomalous regime, a phase-matched and more efficient FWM process can be realized, which can pave the way for broadband frequency comb generation in this platform. These results suggest further promise of higher performance and lower threshold power nonlinear devices on a low-loss CMOS compatible platform with the possibility of co-integration of active functionalities due to high solubility of rare earth dopants in tellurium oxide.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The field of nonlinear optics has continued to grow at a tremendous rate and has proven to be a nearly inexhaustible source of new phenomena and optical techniques for its wide range of applications including quantum photonics, optical switching, and optical signal processing [1]. Nonlinear optical frequency conversion is in the center of attention due to many applications, including all optical switching, correlated photon pair generation, and narrow linewidth or multiwavelength sources [2].

Silicon nitride has emerged as a high performance integrated photonic medium for linear and nonlinear optical devices due to its high refractive index contrast, nanoscale feature resolution, and mature fabrication methods which allow for low loss and compact waveguides [37]. Silicon nitride waveguides and devices can be included in 3D-integrated active silicon photonics platforms because it is a complementary metal oxide semiconductor (CMOS)-compatible material. More recently it has evolved as a high-performance medium for nonlinear optical devices, quantum microsystems, and monolithic and hybrid on-chip lasers [37]. Si3N4 exhibits a third-order nonlinearity, n2, of 2.4 × 10−19 m2/W, which is approximately one order of magnitude larger than that of silica or crystalline materials such as CaF2 or MgF2 [8,9]. Also, its ultra-low linear and nonlinear losses due to its wide transparency range and negligible two photon absorption, respectively, allows for realizing highly efficient nonlinear devices [10,11]. Despite the success of Si3N4 as a leading platform for on-chip nonlinear devices, it has relatively lower nonlinear refractive index compared to other materials of interest such as silicon-on-insulator (SOI) or silicon-rich silicon nitride [11], which raises the need for tight confinement of light within waveguides in order to enhance optical intensity and therefore increase the nonlinear coefficient.

Low dispersion, high refractive index, low optical attenuation, and high thermal and chemical stability motivate tellurite glass as another highly promising material for nonlinear integrated photonics. Tellurium oxide has one of the highest nonlinearities of all oxide glasses of n2 = 1.3 × 10−18 m2/W at 1900 nm enabling efficient nonlinear processes [12]. It has a significantly higher nonlinearity and higher Raman gain than Si3N4, as well as negligible two-photon absorption at telecommunications wavelengths [12,13]. TeO2 also has a slightly higher linear refractive index than Si3N4, thus also enabling highly compact waveguides and devices. In addition, tellurite glass has high rare earth solubility, allowing for monolithic rare-earth-doped devices such as amplifiers and lasers, and potentially active, linear and nonlinear functionality in one integrated platform [1417].

Optical microring resonators are important photonic structures because of the number of applications including nonlinear optical devices, low-threshold microlasers, switches, light emitters, and efficient optical sensors [18,19]. On-chip photonic platforms have allowed for exploration of novel classical and quantum nonlinear phenomena in highly controlled environments [18,19]. Frequency conversion via four-wave mixing (FWM) and optical frequency combs based on high quality factor (Q) ring resonators have received quite some attention due to their wide-ranging applications and compact, chip-scale integration [9].

We have recently shown low loss waveguides, high Q ring resonators, and optical amplifiers in a tellurite glass on silicon nitride platform using straightforward fabrication steps and applying a conventional low-confinement, single-mode Si3N4 thin stripe waveguide geometry [1417]. Besides passive and active devices, nonlinear integrated optical devices [13] can also be considered promising on this platform but have yet to be explored experimentally. The capability to fabricate high-Q resonators can now enable exploration of nonlinear optical phenomena in a compact device structure in the hybrid TeO2-Si3N4 platform.

In this work, we report on FWM in tellurium-oxide-coated silicon nitride microring resonators pumped at 1590 nm. Four-wave mixing has been measured in microring resonators with 600 μm radius, different TeO2 coating thicknesses and quality factors ranging from 1.7 × 105 to 1.0 × 106 for pump powers of tens of milliwatts. These results suggest further research on tellurium-oxide-coated silicon nitride ring resonators for low-power nonlinear optics is of interest. With optimized TeO2-coated Si3N4 waveguide designs and by increasing the Si3N4 strip height to the maximum crack free thickness in the next fabrication run, we expect to obtain higher nonlinear coefficient and anomalous GVD, which will result in lower threshold power [20]. Importantly, the materials and fabrication methods are compatible with standard silicon manufacturing methods, enabling the integration of tellurium oxide, and potentially other novel materials using a similar approach, in mass-producible nonlinear photonic integrated circuits.

2. Fabrication and design

In previous works we presented a detailed report of the design, fabrication and linear characterization of TeO2-Si3N4 waveguides [1417]. A brief description is provided here for completeness. A standard wafer-scale process was used to fabricate the silicon nitride strip waveguides. We first deposited a 0.2-µm thick Si3N4 film onto a 100-mm diameter silicon wafer with 8-µm-thick wet thermal SiO2 layer via low-pressure chemical vapor deposition (LPCVD). The Si3N4 layer thickness was chosen as a standard nitride thickness to achieve low-loss single-mode waveguides and to avoid film cracking due to stress difference with the silicon substrate. Microring resonators with 1.2-μm wide waveguides and 600-μm radii, and gaps varying from 1.0 to 3.0 μm between the outer walls of the ring and bus waveguide were defined by stepper lithography and reactive ion etching through the Si3N4 layer. The wafers were then annealed at high temperature in N2 to drive out hydrogen from the Si3N4 waveguides and reduce absorption at wavelengths around 1.5 µm. The wafers were diced into chips to form facets and transferred from the foundry. Then 0.26 µm, and 0.38 µm thick TeO2 coating layers were deposited onto the individual chips using a reactive radio frequency (RF) sputtering process with 145 W of tellurium target sputtering power, 2.8 mTorr pressure, and 12 and 7.6 sccm of argon and oxygen flow, respectively, at 20°C. A 2 µm thick Cytop top-cladding layer was then spin coated onto the chips.

Figures 1(a) and 1(b) show a cross section diagram and 3D drawing and of the TeO2-coated Si3N4 ring resonator structure, respectively. A scanning electron microscope (SEM) image of the top view of the ring resonator and its bus waveguide is shown in Fig. 1(c). The calculated electric field profiles of the transverse-electric- (TE-) polarized fundamental modes for uncoated Si3N4, 260 nm-TeO2-coated Si3N4, 380 nm-TeO2-coated Si3N4 waveguides at 1590 nm wavelength are displayed in Figs. 1(d), 1(e), and 1(f) respectively. Figure 1(g) summarizes the properties of the fabricated chips, including the TeO2 coating thickness, calculated fractional optical intensity overlap of the fundamental TE-polarized mode with the Si3N4 and TeO2, and effective mode area (Aeff) of each waveguide. The theoretical properties of uncoated and TeO2-coated Si3N4 ring resonators were investigated using a finite element method (FEM) mode solver. The waveguides were designed to be single mode at 1590 nm wavelength. Due to the asymmetry of the waveguide structure, simulations show that they only support the TE-polarized mode. As shown in Fig. 1(g), the fractions of 1590-nm optical mode power confined in the Si3N4 strip and TeO2 coating, are, 27% and 0%, 26% and 49%, and 18% and 65% for 0, 260 and 380-nm thick coatings, respectively. The rest of the optical power is confined in the upper and lower cladding materials.

 figure: Fig. 1.

Fig. 1. (a) Cross-section profile of the TeO2-coated Si3N4 waveguide structure (x = TeO2 thickness). (b) 3D drawing of the TeO2-coated ring resonator integrated with Si3N4 bus waveguide. (c) Top-view SEM image of a TeO2-coated Si3N4 ring resonator. (d), (e) and (f) Calculated electric field profile of the fundamental TE-polarized mode for an uncoated silicon nitride strip width and height of 1.2 and 0.2 µm, 260 nm coated TeO2, and 380 nm coated TeO2 respectively. (g) Samples with different TeO2 coating thicknesses fabricated for FWM experiments, calculated fractional optical intensity overlap of the fundamental TE mode with Si3N4 and TeO2, and their respective mode areas (Aeff).

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The calculated nonlinear parameter (γ) and group velocity dispersion (GVD) parameters of uncoated and 260-nm- and 380-nm-thick TeO2-coated Si3N4 ring resonators are displayed in Fig. 2. The GVD parameter (D) of a waveguide is calculated by the formula

$$D = \displaystyle{\lambda \over c}\left( {\displaystyle{{d^2n_{eff}} \over {d\lambda ^2}}} \right)$$
where λ is the wavelength and neff is the effective refractive index calculated with the FEM mode solver [21,22] and c is the speed of light in free space. We calculated a negligible difference in dispersion for bent vs. straight waveguides due to the large bend radius of the Si3N4 and TeO2-coated Si3N4 ring resonators (600 μm). As shown in Fig. 2(a) the fabricated devices are in the normal dispersion regime and the tellurium oxide coating significantly reduces the magnitude of the dispersion. The nonlinear parameter of
$$\gamma = \frac{{\omega .{n_2}}}{{c.{A_{eff}}}}$$
where Aeff is the effective mode area of the waveguide, c is the speed of light, n2 is the Kerr coefficient of the material, and ω is the pump angular frequency) quantifies the effects of the Kerr index in a waveguide [22,23] and is shown in Fig. 2(b). In our calculation we take into account the contribution of the different materials to γ by applying the overlap integral in [24] as described in [20]. The enhancement of the nonlinear parameter is evident, where a Si3N4 strip with 1.2 µm width and 0.2 µm height gives a γ of 0.24 W−1m−1 without TeO2 coating whereas adding 0.26- and 0.38-µm-thick TeO2 coatings give a γ of 2.73 and 2.92 W−1m−1, respectively, at 1590 nm. The plot shows that the Si3N4 stripe height of 0.2 µm has near optimal effective nonlinearity for this waveguide structure. All calculations for refractive indices of the waveguide core and cladding materials are based on the material dispersion relations which were obtained from [25] and [26] for Si3N4 and SiO2, respectively, whereas for TeO2 were obtained from spectroscopic ellipsometry measurements fitted to a 2-term Sellmeier model given by the formula; ${n^2} = \varepsilon (\infty )+ \frac{{{B_1}{\lambda ^2}}}{{{\lambda ^2} - {C_1}^2}} - E{\lambda ^2} = 2.399 + \frac{{1.834{\lambda ^2}}}{{{\lambda ^2} - {{0.23617}^2}}} - 0.00515{\lambda ^2}\; $where ɛ(∞) is the index offset, B1 and C1 are the experimentally determined Sellmeier coefficients and E is the position of the pole in the infrared.

 figure: Fig. 2.

Fig. 2. (a) Calculated GVD parameter for hybrid TeO2-Si3N4 waveguides with coating thicknesses of 0, 260 and 380 nm. (b) Calculated nonlinear coefficient for hybrid TeO2-Si3N4 waveguides with coating thicknesses of 0, 260 and 380 nm, for varying Si3N4 strip waveguide height. The data shows higher effective nonlinearity in TeO2-Si3N4 hybrid waveguides than uncoated Si3N4 waveguides up to the typical maximum crack-free height for conventional LPCVD Si3N4 strip waveguides of ∼0.4 µm [27]. The dashed line indicates the Si3N4 strip height of 0.2 µm applied in this work.

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3. Experimental characterization and results

The experimental setup used in the demonstration of FWM in the TeO2-coated Si3N4 ring resonators is illustrated in Fig. 3. We characterized the linear and nonlinear microring resonator transmission properties by coupling TE-polarized 1550 to 1620 nm tunable laser light to and from the bus waveguide. For nonlinear measurements, the pump light was amplified by a high-power erbium-ytterbium co-doped fiber amplifier (EYDFA), then coupled to a polarization controller (PC) to adjust the state of polarization to select TE polarization for maximum transmission through the waveguide. The light was coupled into the bus waveguide via a 2-µm spot size tapered fiber at 1590-nm wavelength mounted on an xyz stage. Light at the output end of the waveguide was collected by a second lensed fiber and xyz stage where it was coupled through a 50/50 splitter connected to a photodetector and an optical spectrum analyzer (OSA).

 figure: Fig. 3.

Fig. 3. Experimental setup for generating and measuring nonlinear optical response from ring resonators.

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Figures 4(a), (b), and (c) show the resonance spectra for Si3N4 ring resonators with a gap of 1.8 µm and 0, 260, 380 nm TeO2 coating thicknesses respectively. We observed narrow resonances associated with the TE mode in the resonators. The relative transmission data and fitted Lorentzian function at 1590 nm wavelength with internal and loaded quality factors (Qi and Ql, respectively) are displayed in Figs. 4 (d), (e), and (f). We performed a best fit of each resonance, assuming a Lorentzian shape of the transmission dip. The quality factor is intrinsically limited by losses, whose main contribution in our rings is given by the propagation losses in the ridge waveguide [14]. The background losses are as low as 0.30, 0.33, 0.61 dB/cm at 1590nm wavelength for the undercoupled Si3N4 ring resonator and 260 nm and 380 nm thick TeO2-coated Si3N4 ring resonators linked to internal quality factors of 1.0×106, 8.9×105, and 6.0×105 respectively. The different internal Q factors can be attributed to changes in the mode properties and material overlaps and slight variations in the TeO2 coating properties from run to run. The insertion losses, evaluated by measuring the total transmission through the bus waveguide, were found to be ${{-}22\; \pm \; 0}{.5,\; {-}17\; \pm \; 0}{.5,\; {\textrm{and}}\; {-}20\; \pm \; 0}{.5}$ dB at 1590 nm for the chips with TeO2 coating thicknesses of 0, 260, and 380 nm, respectively. These relatively high insertion losses are mainly due to the reduced coupling efficiency between the tapered fiber and the bus waveguide due to diced facets, which we have shown can be improved in other works by focused ion beam (FIB) facet milling [15].

 figure: Fig. 4.

Fig. 4. Measured transmission spectra for Si3N4 ring resonators with 1.8-µm coupling gap and 600-µm radius around 1590 nm at the resonances chosen for the FWM experiment for (a) no TeO2 coating and (b) 260 nm and (c) 380 nm thick TeO2 coatings. Zoomed in view of resonance and fitted Lorentzian function at 1590 nm wavelength for (d) no coating and (e) 260 nm and (f) 380 nm thick TeO2 coatings.

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We pumped the uncoated Si3N4 and hybrid TeO2-Si3N4 ring resonators to investigate their potential nonlinear responses. The four-wave mixing process occurs due to the intensity-dependent refractive index, $n = {n_0} + I \times {n_2}$, where n0 denotes the linear refractive index, and I is the laser intensity. By pumping the ring resonator which consists of isotropic third-order nonlinear materials, frequency conversion can occur including two pump photons annihilating with frequency ${\omega _p}$ and generating a new pair of photons including an up-converted signal photon ${\omega _s}$, and a down-converted idler photon ${\omega _i}$, which means the frequencies of the signal and idler photons are equal to two times the pump frequency (i.e., ${\omega _s} + {\omega _i} = 2{\omega _p}$ or ${E_i} + {E_s} = 2 \times {E_p}$). In this parametric four-wave mixing process, wavelength conversion is achieved.

Figure 5 shows the transmission spectra under 1590-nm pumping for uncoated and TeO2-coated Si3N4 microring resonators and launched pump powers of 65 ± 2 mW. The main peaks in the spectra shown in Fig. 5 correspond to the pump input and the smaller peaks on the right and left are the idler field and signal fields which are located at wavelengths which satisfy the energy conservation condition of the FWM process. As shown in Fig. 5(a), no FWM signal is observed in the uncoated nitride resonator. Several FWM peaks are observed in the TeO2-coated resonators. In Fig. 5 (b) the central wavelengths of the pump and strongest idler, and signal resonances for the 260-nm thick TeO2- coated Si3N4 ring resonator are λp = 1589.88 nm, λi= 1981.79 nm, and λs = 1327.39 nm respectively. The central wavelengths of the pump and strongest idler and signal resonances for 380-nm thick TeO2- coated Si3N4 ring resonator in Fig. 5 (c) are λp = 1590.81 nm, λi = 2042.68 nm, and λs = 1302.67 nm respectively.

 figure: Fig. 5.

Fig. 5. Output spectra from uncoated and TeO2-coated Si3N4 ring resonators with 1.8 µm gap and 600 µm radius, resulting from typical FWM measurements for (a) no coating and (b) 260- and (c) 380-nm thick TeO2 coatings for (65 ± 2) mW launched pump power at 1590 nm.

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We define the FWM launched threshold power as the minimum pump power in the bus waveguide required for FWM signal, accounting for fiber-chip coupling losses. To have the better evaluation of this work, we calculated the theoretical estimated threshold pump power Pth, according to Ref. [28] at the pump wavelength in vacuum for 260- and 380-nm thick TeO2 coated Si3N4 ring resonators. In the threshold power calculation, we assume that the quality factor of pump, signal and idler are equal, based on the low waveguide propagation losses measured across a wide wavelength range in [15]. In Fig. 6, we show the threshold FWM pump power as a function of internal and loaded quality factors of Si3N4 ring resonators and TeO2-Si3N4 ring resonators with gap varying from 1 µm to 3.0 µm. The initiation of parametric oscillation can be strongly reduced in ring resonators, implying that high Q can give a dramatic reduction in the required optical pump power. The high nonlinearity of tellurium oxide in comparison with silicon nitride, can cause the FWM and optical comb generation process to occur at lower threshold pump power in hybrid TeO2-Si3N4 resonators if similarly, high Q factors can be obtained in comparison to those demonstrated in Si3N4 [29].

 figure: Fig. 6.

Fig. 6. Threshold pump power coupled into the bus waveguide for FWM generation as a function of the internal and loaded Q factor, Qi and Ql, respectively, for 260- and 380-nm thick TeO2-coated Si3N4 microring resonators with gap varying from 1.0 to 3.0 µm and extinction ratios varying from 0.4 to 16 dB. The inset shows idler and signal power vs. pump power launched in the bus waveguide for the ring resonator with 260-nm thick TeO2 coating and 1.8 µm gap.

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According to the experimental results, we do not see any FWM in Si3N4 ring resonators even with an internal quality factor of 1.0 × 106 and 65 ± 2 mW pump power launched into the bus waveguide, which is due to the pump mode being close to the cutoff condition, highly normal dispersion, low mode overlap with the Si3N4, and low nonlinearity of the SiO2 and Cytop cladding materials compared to TeO2. By coating a 260-nm-thick layer of tellurium oxide on top of the Si3N4 ring resonator we observed FWM in ring resonators with quality factors ranging from 5.7×105 to 1.0×106 and launched pump powers of 25 mW to 42 mW. Furthermore, by increasing the thickness of TeO2 to 380 nm, we observe FWM, even for lower Q values of 1.7×105 to 6.0×105 at threshold powers ranging from 33 mW to 45 mW. The threshold powers follow the theoretically predicted trend of being inversely proportional to Qi. The inset of Fig. 6 shows the idler and signal power versus pump power launched in the bus waveguide for a 260 nm thick TeO2-coated Si3N4 ring resonator with 1.8 µm gap, which shows a threshold pump power of 28 mW.

The theoretical estimated FWM threshold power of a ring resonator with 2 µm gap, 260 nm thick TeO2 coating and Qi = 1.0×106 is 23 mW while in experimental observation it is 25 mW. As shown in Table 1, for different resonators we observe good agreement between the experimental and theoretical threshold power. Dispersion is usually described in terms of dispersion co-efficient (D) as shown in Eq. (1) which can also be expressed with β2 [3034]:

$$D = \frac{{ - 2\mathrm{\pi }\textrm{c}{\mathrm{\beta }_2}}}{{{\lambda ^2}}}$$

Tables Icon

Table 1. Comparison between experimental and calculated properties of uncoated Si3N4 and hybrid TeO2-Si3N4 microring resonators at 1590 nm

The velocity of light, c is constant and the λ is the wavelength in which we want to measure dispersion. The second order dispersion β2 can be measured based on variations of the ring resonator free-spectral range (FSR) vs. frequency [3034]. We calculated the dispersion according to the transmission spectra and the FSR for the uncoated Si3N4 and hybrid TeO2-Si3N4 ring resonators around the 1590 nm pump wavelength as summarized in Table 1. Despite some differences our experimental values show a similar trend to our simulated results, which validates our measurements. Variations in the waveguide dimensions, including Si3N4 strip height and width and TeO2 film height, and the TeO2 film and Cytop top-cladding optical properties from run to run might account for other differences in the calculated and experimental values.

We expect to obtain higher nonlinear coefficients, anomalous GVD, and higher quality factor resonators with optimized TeO2-coated Si3N4 waveguide designs which will result in lower FWM threshold power and improve the efficiency of nonlinear interactions in on-chip Kerr devices [20]. Anomalous dispersion can be engineered by increasing the Si3N4 strip thickness to the maximum crack free thickness. By adjusting the thickness of the TeO2 top coating layer and even its composition via doping [20] the nonlinear parameter and GVD can be widely tuned in hybrid TeO2-Si3N4 ring resonators.

4. Conclusion

In conclusion, four-wave mixing has been demonstrated in the near-and mid-infrared in low loss TeO2-Si3N4 ring resonators with Q factors ranging from 1.7 × 105 to 1.0 × 106. We propose that such TeO2-Si3N4 ring resonators will open up the possibility of compact and efficient nonlinear integrated optical devices such as parametric amplifiers, monolithic multi wavelength light sources, and quantum sources. Due to the high solubility rare-earth dopants in TeO2, monolithic integration of active rare-earth doped amplifiers and lasers with nonlinear optical devices in a single low loss CMOS compatible Si3N4 platform can be achieved.

Funding

Natural Sciences and Engineering Research Council of Canada (RGPIN-2017-06423, STPGP 494306); Canada Foundation for Innovation (35548); Ontario Ministry of Research and Innovation (ER17-13-077).

Acknowledgments

We acknowledge the Centre for Emerging Device Technologies (CEDT) at McMaster University for the support with the reactive sputtering system, and CMC Microsystems for the provision of RSoft Component Design Suite.

Disclosures

The authors declare no conflicts of interest.

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31. D. Farnesi, F. Cosi, C. Trono, G. C. Righini, G. Nunzi Conti, and S. Soria, “Stimulated anti-Stokes Raman scattering resonantly enhanced in silica microspheres,” Opt. Lett. 39(20), 5993–5996 (2014). [CrossRef]  

32. S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017). [CrossRef]  

33. K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016). [CrossRef]  

34. S. Fujii and T. Tanabe, “Dispersion engineering and measurement of whispering gallery mode microresonator for Kerr frequency comb generation,” Nanophotonics 9(5), 1087–1104 (2020). [CrossRef]  

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2020 (4)

H. C. Frankis, H. M. Mbonde, D. B. Bonneville, C. Zhang, R. Mateman, A. Leinse, and J. D. B. Bradley, “Erbium-doped TeO2-coated Si3N4 waveguide amplifiers with 5 dB net gain,” Photonics Res. 8(2), 127–134 (2020).
[Crossref]

H. M. Mbonde, H. C. Frankis, and J. D. B. Bradley, “Enhanced nonlinearity and engineered anomalous dispersion in TeO2-coated Si3N4 waveguides,” IEEE Photonics J. 12(2), 1–10 (2020).
[Crossref]

G. Frigenti, D. Farnesi, G. Nunzi Conti, and S. Soria, “Nonlinear optics in microspherical resonators,” Micromachines 11(3), 303 (2020).
[Crossref]

S. Fujii and T. Tanabe, “Dispersion engineering and measurement of whispering gallery mode microresonator for Kerr frequency comb generation,” Nanophotonics 9(5), 1087–1104 (2020).
[Crossref]

2019 (4)

2018 (1)

D. T. H. Tan, K. J. A. Ooi, and D. K. T. Ng, “Nonlinear optics on silicon-rich nitride—a high nonlinear figure of merit CMOS platform [Invited],” Photonics Res. 6(5), B50–B66 (2018).
[Crossref]

2017 (3)

2016 (1)

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

2015 (1)

2014 (3)

2013 (3)

2011 (1)

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref]

2010 (1)

2009 (2)

2008 (1)

2007 (1)

2004 (1)

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref]

1993 (1)

S. H. Kim, T. Yoko, and S. Sakka, “Linear and nonlinear optical properties of TeO2 glass,” J. Am. Ceram. Soc. 76(10), 2486–2490 (1993).
[Crossref]

1965 (1)

Agrawal, G. P.

Alic, N.

Baets, R.

Bao, C.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Barbosa, F. A. S.

Bassim, N. D.

Beha, K.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

Bienstman, P.

Bonneville, D. B.

H. C. Frankis, H. M. Mbonde, D. B. Bonneville, C. Zhang, R. Mateman, A. Leinse, and J. D. B. Bradley, “Erbium-doped TeO2-coated Si3N4 waveguide amplifiers with 5 dB net gain,” Photonics Res. 8(2), 127–134 (2020).
[Crossref]

H. C. Frankis, K. Miarabbas Kiani, D. B. Bonneville, C. Zhang, S. Norris, R. Mateman, A. Leinse, N. D. Bassim, A. P. Knights, and J. D. B. Bradley, “TeO2 waveguides integrated on a low-loss Si3N4 platform for application in scalable photonic circuits,” Opt. Express 27(9), 12529–12540 (2019).
[Crossref]

Bradley, J. D. B.

Briles, T. C.

Bryant, A.

Camacho, R. M.

Cardenas, J.

Cheben, P.

Chu, S.

Clader, B. D.

Clemmen, S.

Cole, D. C.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

Cosi, F.

Dave, U.

Del’Haye, P.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

Dhakal, A.

Dhoore, S.

Diddams, S. A.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref]

Duchesne, D.

Dutt, A.

Epping, J.

J. Epping, “Dispersion engineering silicon nitride waveguides for broadband nonlinear frequency conversion,” Ph.D. dissertation, University of Twente, Enschede, Netherlands, (2015).

Fainman, Y.

Farnesi, D.

Ferrera, M.

Finkelstein, H.

Foster, A. C.

Foster, M. A.

Frankis, H. C.

Frigenti, G.

G. Frigenti, D. Farnesi, G. Nunzi Conti, and S. Soria, “Nonlinear optics in microspherical resonators,” Micromachines 11(3), 303 (2020).
[Crossref]

Fujii, S.

S. Fujii and T. Tanabe, “Dispersion engineering and measurement of whispering gallery mode microresonator for Kerr frequency comb generation,” Nanophotonics 9(5), 1087–1104 (2020).
[Crossref]

Gaeta, A. L.

Garces, G. T.

G. T. Garces, “Classical and quantum applications of optical four wave mixing in an integrated silicon nitride platform,” Master dissertation, Universitat Politècnica de Catalunya, Spain (2014).

Han, K.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Helin, P.

Helt, L. G.

Hendrickson, S. M.

Hermans, A.

Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref]

Huang, Y.

Ikeda, K.

Janz, S.

Jaramillo-Villegas, J. A.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Ji, X.

Kim, S.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Kim, S. H.

S. H. Kim, T. Yoko, and S. Sakka, “Linear and nonlinear optical properties of TeO2 glass,” J. Am. Ceram. Soc. 76(10), 2486–2490 (1993).
[Crossref]

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332(6029), 555–559 (2011).
[Crossref]

Knights, A. P.

Krückel, C.

C. Krückel, “Integrated nonlinear optics in silicon nitride waveguides,” Ph.D. dissertation, Chalmers Univ of Tech. Sweden (2015).

Kuyken, B.

Lamont, M. R. E.

Le Thomas, N.

Leaird, D. E.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Lee, H.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

Leinse, A.

Li, J.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

Li, Q.

Li, Y.

Lin, Q.

Liow, T.-Y.

Lipson, M.

Liscidini, M.

Little, B. E.

Lo, G.-Q.

Lu, X.

Luke, K.

Luo, X.

Madden, S. J.

Malitson, I. H.

Mateman, R.

Mbonde, H. M.

H. C. Frankis, H. M. Mbonde, D. B. Bonneville, C. Zhang, R. Mateman, A. Leinse, and J. D. B. Bradley, “Erbium-doped TeO2-coated Si3N4 waveguide amplifiers with 5 dB net gain,” Photonics Res. 8(2), 127–134 (2020).
[Crossref]

H. M. Mbonde, H. C. Frankis, and J. D. B. Bradley, “Enhanced nonlinearity and engineered anomalous dispersion in TeO2-coated Si3N4 waveguides,” IEEE Photonics J. 12(2), 1–10 (2020).
[Crossref]

K. Miarabbas Kiani, H. C. Frankis, H. M. Mbonde, R. Mateman, A. Leinse, A. P. Knights, and J. D. B. Bradley, “Thulium-doped tellurium oxide waveguide amplifier with 7.6 dB net gain on a silicon nitride chip,” Opt. Lett. 44(23), 5788–5791 (2019).
[Crossref]

Merget, F.

Miarabbas Kiani, K.

Moille, G.

Moll, K. D.

Morandotti, R.

Moss, D. J.

Muneeb, M.

Ng, D. K. T.

D. T. H. Tan, K. J. A. Ooi, and D. K. T. Ng, “Nonlinear optics on silicon-rich nitride—a high nonlinear figure of merit CMOS platform [Invited],” Photonics Res. 6(5), B50–B66 (2018).
[Crossref]

Norris, S.

Nunzi Conti, G.

Oh, D. Y.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

Okawachi, Y.

Ooi, K. J. A.

D. T. H. Tan, K. J. A. Ooi, and D. K. T. Ng, “Nonlinear optics on silicon-rich nitride—a high nonlinear figure of merit CMOS platform [Invited],” Photonics Res. 6(5), B50–B66 (2018).
[Crossref]

Painter, O. J.

Papp, S. B.

X. Lu, G. Moille, A. Singh, Q. Li, D. A. Westly, A. Rao, S. Yu, T. C. Briles, S. B. Papp, and K. Srinivasan, “Milliwatt-threshold visible–telecom optical parametric oscillation using silicon nanophotonics,” Optica 6(12), 1535–1541 (2019).
[Crossref]

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

Peccianti, M.

Poitras, C. B.

Qi, M.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Rahim, A.

Rao, A.

Raza, A.

Razzari, L.

Righini, G. C.

Roberts, S. P.

Roelkens, G.

Romero-García, S.

Rottenberg, X.

Ryckeboer, E.

Sakka, S.

S. H. Kim, T. Yoko, and S. Sakka, “Linear and nonlinear optical properties of TeO2 glass,” J. Am. Ceram. Soc. 76(10), 2486–2490 (1993).
[Crossref]

Saperstein, R. E.

Severi, S.

Singh, A.

Sipe, J. E.

Song, J.

Soria, S.

Srinivasan, K.

Su, D.

Subramanian, A. Z.

Tan, D. T. H.

D. T. H. Tan, K. J. A. Ooi, and D. K. T. Ng, “Nonlinear optics on silicon-rich nitride—a high nonlinear figure of merit CMOS platform [Invited],” Photonics Res. 6(5), B50–B66 (2018).
[Crossref]

Tanabe, T.

S. Fujii and T. Tanabe, “Dispersion engineering and measurement of whispering gallery mode microresonator for Kerr frequency comb generation,” Nanophotonics 9(5), 1087–1104 (2020).
[Crossref]

Trono, C.

Vahala, K. J.

K. Y. Yang, K. Beha, D. C. Cole, X. Yi, P. Del’Haye, H. Lee, J. Li, D. Y. Oh, S. A. Diddams, S. B. Papp, and K. J. Vahala, “Broadband dispersion-engineered microresonator on a chip,” Nat. Photonics 10(5), 316–320 (2016).
[Crossref]

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[Crossref]

Van Thourhout, D.

Vu, K. T.

Wang, C.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Weiner, A. M.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
[Crossref]

Westly, D. A.

Witzens, J.

Xu, D.-X.

Xuan, Y.

S. Kim, K. Han, C. Wang, J. A. Jaramillo-Villegas, X. Xue, C. Bao, Y. Xuan, D. E. Leaird, A. M. Weiner, and M. Qi, “Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators,” Nat. Commun. 8(1), 372 (2017).
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Supplementary Material (1)

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Figures (6)

Fig. 1.
Fig. 1. (a) Cross-section profile of the TeO2-coated Si3N4 waveguide structure (x = TeO2 thickness). (b) 3D drawing of the TeO2-coated ring resonator integrated with Si3N4 bus waveguide. (c) Top-view SEM image of a TeO2-coated Si3N4 ring resonator. (d), (e) and (f) Calculated electric field profile of the fundamental TE-polarized mode for an uncoated silicon nitride strip width and height of 1.2 and 0.2 µm, 260 nm coated TeO2, and 380 nm coated TeO2 respectively. (g) Samples with different TeO2 coating thicknesses fabricated for FWM experiments, calculated fractional optical intensity overlap of the fundamental TE mode with Si3N4 and TeO2, and their respective mode areas (Aeff).
Fig. 2.
Fig. 2. (a) Calculated GVD parameter for hybrid TeO2-Si3N4 waveguides with coating thicknesses of 0, 260 and 380 nm. (b) Calculated nonlinear coefficient for hybrid TeO2-Si3N4 waveguides with coating thicknesses of 0, 260 and 380 nm, for varying Si3N4 strip waveguide height. The data shows higher effective nonlinearity in TeO2-Si3N4 hybrid waveguides than uncoated Si3N4 waveguides up to the typical maximum crack-free height for conventional LPCVD Si3N4 strip waveguides of ∼0.4 µm [27]. The dashed line indicates the Si3N4 strip height of 0.2 µm applied in this work.
Fig. 3.
Fig. 3. Experimental setup for generating and measuring nonlinear optical response from ring resonators.
Fig. 4.
Fig. 4. Measured transmission spectra for Si3N4 ring resonators with 1.8-µm coupling gap and 600-µm radius around 1590 nm at the resonances chosen for the FWM experiment for (a) no TeO2 coating and (b) 260 nm and (c) 380 nm thick TeO2 coatings. Zoomed in view of resonance and fitted Lorentzian function at 1590 nm wavelength for (d) no coating and (e) 260 nm and (f) 380 nm thick TeO2 coatings.
Fig. 5.
Fig. 5. Output spectra from uncoated and TeO2-coated Si3N4 ring resonators with 1.8 µm gap and 600 µm radius, resulting from typical FWM measurements for (a) no coating and (b) 260- and (c) 380-nm thick TeO2 coatings for (65 ± 2) mW launched pump power at 1590 nm.
Fig. 6.
Fig. 6. Threshold pump power coupled into the bus waveguide for FWM generation as a function of the internal and loaded Q factor, Qi and Ql, respectively, for 260- and 380-nm thick TeO2-coated Si3N4 microring resonators with gap varying from 1.0 to 3.0 µm and extinction ratios varying from 0.4 to 16 dB. The inset shows idler and signal power vs. pump power launched in the bus waveguide for the ring resonator with 260-nm thick TeO2 coating and 1.8 µm gap.

Tables (1)

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Table 1. Comparison between experimental and calculated properties of uncoated Si3N4 and hybrid TeO2-Si3N4 microring resonators at 1590 nm

Equations (3)

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D = λ c ( d 2 n e f f d λ 2 )
γ = ω . n 2 c . A e f f
D = 2 π c β 2 λ 2
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