Enhanced third-order optical Kerr nonlinearity in SiN nanowires with integrated 2D graphene oxide lms

Layered 2D graphene oxide (GO) lms are integrated with silicon nitride (SiN) waveguides to experimentally demonstrate an enhanced Kerr nonlinearity via four-wave mixing (FWM). Owing to the strong light–matter interaction between the SiN waveguides and the highly nonlinear GO lms, the FWM performance of the hybrid waveguides is signicantly improved. SiN waveguides with both uniformly coated and patterned GO lms are fabricated based on a transfer-free, layer-by-layer GO coating method together with standard photolithography and lift-off processes, yielding precise control of the lm thickness, placement and coating length. Detailed FWM measurements are carried out for the fabricated devices with different numbers of GO layers and at different pump powers. By optimizing the trade-off between the nonlinearity and loss, we obtain a signicant improvement in the FWM conversion eciency of ≈ 7.3 dB for a uniformly coated device with 1 layer of GO and ≈ 9.1 dB for a patterned device with 5 layers of GO. We also obtain a signicant increase in FWM bandwidth for the patterned devices. A detailed analysis of the inuence of pattern length and position on the FWM performance is performed. Based on the FWM measurements, the dependence of GO’s third-order nonlinearity on layer number and pump power is also extracted, revealing interesting physical insights about the 2D layered GO lms. Finally, we obtain an enhancement in the effective nonlinear parameter of the hybrid waveguides by over a factor of 100. These results verify the enhanced nonlinear optical performance of SiN waveguides achievable by incorporating 2D layered GO lms.

Owing to its ease of preparation and the tunability of its material properties, GO has received increasing interest as a promising member of the 2D material family [41][42][43][44][45][46]. Previously, we reported GO lms with a giant Kerr nonlinearity (n 2 ) of about 5 orders of magnitude higher than SiN [42], and demonstrated enhanced FWM in doped silica waveguides and microring resonators (MRRs) integrated with GO lms [32,47]. Unlike graphene, which has a metallic behavior with zero bandgap, GO is a dielectric with a distinct bandgap of 2.1−2.4 eV [41,48]. This results in material absorption that is over 2 orders of magnitude lower than graphene [32] as well as negligible TPA in the telecommunications band [48,49], both of which are highly desired for many nonlinear applications such as FWM. Moreover, by using a large-area, transfer-free, layer-by-layer GO coating method along with standard lithography and lift-off processes, we achieved GO lm coating on integrated photonic devices with highly precise control of lm thickness, placement and coating length [50]. This overcomes a critical fabrication bottleneck in terms of layer transfer for 2D materials [51] and marks an important step towards the eventual manufacturing of integrated photonic devices incorporated with 2D layered GO lms.
In this paper, we report the integration of 2D layered GO lms onto SiN waveguides − a CMOS-compatible platform that has been widely used for integrated nonlinear optics [2]. By using our GO fabrication techniques, both uniformly coated and patterned GO lms are integrated on SiN waveguides with precise control of the lm thickness, placement and coating length. Bene ting from the strong light-matter interaction between the SiN waveguides and the GO lms with an ultrahigh Kerr nonlinearity and a relatively low loss, signi cantly improved FWM performance of the hybrid waveguides is achieved. We perform FWM measurements for different numbers of GO layers and at different pump powers, achieving a FWM conversion e ciency (CE) enhancement of ≈7.3 dB for a uniformly coated device with 1 layer of GO and ≈9.1 dB for a patterned device with 5 layers of GO. Both an improved FWM CE and bandwidth are achieved for the patterned devices compared to the uniformly coated devices. The in uence of pattern length and position on FWM performance is also analysed. By tting the experimental results with theory, the dependence of the n 2 of the GO lm on layer number and pump power is extracted, showing interesting physical insights about the evolution of the layered GO lms from 2D monolayers towards quasi bulk-like behavior. Finally, we obtain an improvement in the effective nonlinear parameter (γ) of the hybrid waveguides by over a factor of 100. These results reveal the strong potential of integrating 2D layered GO lms on SiN devices to improve the nonlinear optical performance. Figure 1a shows the SiN waveguide integrated with a GO lm, along with a schematic showing atomic structure of GO with different oxygen functional groups (OFGs) such as hydroxyl, epoxide and carboxylic groups. The fabrication process ow for the device in Figure 1a is provided in Figure 1b.

Device fabrication
SiN waveguides with a cross section of 1.6 μm × 0.66 μm were fabricated via annealing-free and crackfree processes that are compatible with CMOS fabrication [52,53]. First, a SiN layer was deposited via low-pressure chemical vapor deposition (LPCVD) in two steps, with a 370-nm-thick layer for each, so as to control strain and to prevent cracks. In order to produce high-quality lms, a tailored ultra-low deposition rate (< 2 nm/ min) was used. Waveguides were then formed via a combination of deep ultraviolet lithography and uorine-based dry etching that yielded exceptionally low surface roughness. Next, a 3-μm thick silica upper cladding layer was deposited via high-density plasma-enhanced chemical vapor deposition (HDP-PECVD) to avoid void formation. To enable the interaction between the GO lms and the evanescent eld leaking from the SiN waveguides, the silica upper cladding was removed using a perfectly selective chemical-mechanical planarization (CMP) that left the top surface of the SiN waveguides exposed in air, with no SiN consumption and no remaining topography.
Layered GO lms were coated on the top surface of the chip by a solution-based method that yielded layer-by-layer lm deposition, as reported previously [32,48,50]. Four steps for the in-situ assembly of monolayer GO lms were repeated to construct multilayer lms. Our GO coating approach, unlike the sophisticated transfer processes employed for coating other 2D materials such as graphene and TMDCs [36,54,55], enables transfer-free and high-uniformity GO lm coating over large areas (e.g., 4-inch wafers [48]), with highly scalable fabrication processes and precise control of the number of GO layers (i.e., GO lm thickness).
In addition to the uniformly coated devices, we selectively patterned GO lms on SiN waveguides using standard lithography and lift-off processes. The chip was rst spin-coated with photoresist and then patterned via photolithography to open a window on the SiN waveguides. Alignment markers, prepared by metal lift-off after photolithography and electron beam evaporation, were used for accurate placement of the opened windows on the SiN waveguides. Next, GO lms were coated on the chip using the coating method mentioned above and patterned via a lift-off process. As compared with the drop-casting method that produces a GO lm thickness of about 0.5 μm and a minimum size of about 1.3 mm for each step [49], the combination of our GO coating method with photolithography and lift-off allows precise control of the lm placement (deviation < 20 nm), size (down to 100 nm) and thickness (with an ultrahigh resolution of ≈2 nm). The precise deposition and patterning control, along with the large area coating capability, is critical for large-scale, highly precise and cost-effective integration of 2D layered GO lms on-chip. Apart from allowing precise control of the size and placement of the GO lms that are in contact with the SiN waveguides, the patterned GO lms also enabled us to test the performance of devices having a shorter length of GO lm but with higher lm thicknesses, which provides more exibility to optimize the device performance with respect to FWM CE and bandwidth. Figure 2a shows a microscope image of a SiN waveguide patterned with 10 layers of GO, which illustrates the high transmittance and good morphology of the GO lms. Figure 2b presents a scanning electron microscopy (SEM) image of a GO lm with up to 5 layers of GO monolayers, clearly showing the layered lm structure. Figure 2c shows the measured Raman spectra of a SiN chip without GO and with 10 layers of uniformly coated GO lms. The successful integration of GO lms is con rmed by the presence of the representative D (1345 cm -1 ) and G (1590 cm -1 ) peaks of GO [32,41]. Figure 2d plots the GO lm thickness as a function of GO layer number measured by atomic force microscopy. The plots show the average of measurements on three samples and the error bars re ect the variations. The GO lm thickness shows a nearly linear relationship with the layer number, with a thickness of ≈2 nm on average for each layer.

Device characterization
We fabricated and tested two types of GO-coated SiN waveguides: the rst with either 1 or 2 layers of uniformly coated GO lms and the second with 5 or 10 layers of patterned GO lms. The length of the SiN waveguides was 20 mm, which was the same as the GO coating length for the uniformly coated devices.
For the patterned devices, the GO lms were coated at the beginning of the SiN waveguides and the coating length was 1.5 mm. Figure 3a depicts the insertion loss of the GO-coated SiN waveguides measured using a transverse electric (TE) polarized continuous-wave (CW) light with a power of 5 dBm. We employed lensed bers to butt couple the CW light into and out of the SiN waveguides with inversetaper couplers at both ends. The butt coupling loss was ≈5 dB per facet, corresponding to 0-dBm CW power coupled into the waveguides. The propagation loss of the SiN waveguides with a monolayer of GO was ≈6.1 dB/cm, corresponding to an excess propagation loss of ≈3.1 dB/cm induced by the GO lm. This is about a factor of 3 higher than reported for doped silica waveguides and mainly results from the higher mode overlap in the SiN waveguide reported here versus the much larger buried waveguides in doped silica [32,50]. The loss reported here is also about 2 orders of magnitude smaller than SiN waveguides coated with graphene [31], re ecting the low material absorption of GO and its strong potential for the implementation of highperformance nonlinear photonic devices. In contrast to graphene that has a metallic behavior (e.g., high electrical and thermal conductivity) with zero bandgap, GO is a dielectric that has a large bandgap of 2.1−2.4 eV [41,48], which results in low linear light absorption in spectral regions below the bandgap. In theory, GO lms with a bandgap > 2 eV should have negligible absorption at near-infrared wavelengths. We therefore infer that the linear loss of the GO lms is mainly due to light absorption from localized defects as well as scattering loss stemming from lm unevenness and imperfect contact between the different layers. We note that the linear loss of the GO lms is not a fundamental property. Therefore, by optimizing our GO synthesis and coating processes, such as using GO solutions with reduced ake sizes and increased purity, it is anticipated that the loss of our GO lms can be further reduced. In Figure 3b, we label the slope rates of the curve at 1, 5 and 10 layers of GO, where we see that the propagation loss of the hybrid waveguides increases with GO layer number super linearly. This is a result of an increase in the contributions just outlined, as reported previously [32,50]. Figure 4 shows the experimental setup used to measure FWM in the GO-coated SiN waveguides. Two CW tunable lasers separately ampli ed by erbium-doped ber ampli ers (EDFAs) were used as the pump and signal sources, respectively. In each path, there was a polarization controller (PC) to ensure that the input light was TE-polarized. The pump and signal were combined with a 3-dB ber coupler before being coupled into the hybrid waveguide as device under test (DUT). A charged-coupled device (CCD) camera was set above the DUT for coupling alignment. An optical isolator was employed to prevent the re ected light from damaging the laser source. The signal output from waveguide was sent to an optical spectrum analyzer (OSA) with a variable optical attenuator (VOA) to prevent high-power damage.

Fwm Experiment
Figure 5a-i shows the experimental FWM optical spectra for the SiN waveguides uniformly coated with 1 and 2 layers of GO, together with the FWM spectrum of the bare SiN waveguide. For comparison, we kept the same power of 23 dBm for both the pump and signal before the input of the waveguides, which corresponded to 18 dBm power for each coupled into the waveguides. The difference among the baselines of the spectra re ects the difference in waveguide propagation loss for different samples. It can be seen that although the hybrid waveguide with 1 layer of GO lm had an additional propagation loss of ≈7.1 dB, it clearly shows enhanced idler output powers as compared with the bare SiN waveguide. The CE (de ned as the ratio of the output power of the idler to the input power of the signal, i.e., P out, idler / P in, signal ) of the SiN waveguides without GO and with 1 layer of GO were ≈-65.7 dB and ≈-58.4 dB, respectively, corresponding to a CE enhancement of ≈7.3 dB for the hybrid waveguide. In contrast to the positive CE enhancement for the hybrid waveguide with 1 layer of GO, the change in CE for the hybrid waveguide with 2 layers of GO was negative. This mainly resulted from the increase in propagation loss with GO layer numbers, as noted in Figure 3b. there is a maximum CE enhancement of ≈9.1 dB for the SiN waveguide patterned with 5 layers of GO, which is even higher than that for the uniformly coated waveguide with 1 layer of GO. This re ects the trade-off between FWM enhancement (which dominates for the patterned devices with a short GO coating length) and loss (which dominates for the uniformly coated waveguides with a much longer GO coating length) in the GO-coated SiN waveguides (see Section 4). Figure 5b shows the measured CE versus pump power for the uniformly coated and patterned devices, respectively. The plots show the average of three measurements on the same samples and the error bars re ect the variations, showing that the measured CE is repeatable. As the pump power was increased, the measured CE increased linearly with no obvious saturation for the bare SiN waveguide and all the hybrid waveguides, indicating the low TPA of both the SiN waveguides and the GO lms. For the bare waveguide, the dependence of CE versus pump power shows a nearly linear relationship, with a slope rate of about 2 for the curve as expected from classical FWM theory [17]. For the GO-coated waveguides, the measured CE curves have shown slight deviations from the linear relationship with a slope rate of 2, particularly at high light powers. This is a re ection of the change in GO material properties with light power (see Section 4). Figure 5c shows the output signal/idler power versus wavelength detuning (i.e., wavelength spacing between pump and signal) for the uniformly coated device with 1 layer of GO and the patterned device with 5 layers of GO. The results for the bare SiN waveguide are also shown for comparison. The coupled pump power was 18 dBm, with the pump wavelength xed at 1550 nm and the signal wavelength detuned from 1540 nm to 1560 nm. For all devices the output signal powers decreased with increasing wavelength detuning, which was caused by gain roll-off of the EDFA. The output idler power, on the other hand, decreased even more rapidly with wavelength detuning, and this was predominantly a result of decreased phase-matching. As compared with the bare and uniformly coated SiN waveguides, the patterned devices showed a much broader FWM bandwidth with higher idler power on both edges, re ecting a wider FWM phase matching bandwidth for a shorter length of GO lms as expected.

FWM theory
We used the theory from Refs. [32,56,57] to model the FWM process in the GO-coated SiN waveguides.
Assuming negligible depletion of the pump and signal powers due to the generation of the idler, the coupled differential equations for the degenerate FWM process can be expressed as [58,59] where A p,s,i are the amplitudes of the pump, signal and idler waves along the z axis, which we de ne as the light propagation direction, α p,s,i are the linear losses, Δβ = β s + β i -2β p is the linear phase mismatch, with β p,s,i denoting the propagation constants of the pump, signal and idler waves, and γ p,s,i are the waveguide nonlinear parameters. In our case, where the wavelength detuning range was small (≤ 10 nm), we assumed that the linear loss and the nonlinear parameter are constant, i.e., α p = α s = α i = α, γ p = γ s = γ i = γ.
Since the bandgaps of SiN (5 eV [2]) and GO (2.1−2.4 eV [41,48]) are much larger than the TPA bandgap (1.6 eV) in the telecommunications band, we neglected nonlinear loss induced by TPA of SiN and GO in Eqs. (1) − (3). In our previous Z-scan measurements [42,46], we observed saturable absorption (SA) behavior (with loss decreasing with light power -a trend that is opposite to TPA) for the GO lms as a result of using optical pulses with higher peak powers (> 10 W). In our FWM experiment, we did not observe any SA phenomenon for the hybrid waveguides. This is probably because the peak powers of the CW light were much lower (< 0.15 W, the power in the GO lms was even lower given the mode overlap with GO).
Figures 6a, b depict the insertion loss of the GO-coated SiN waveguides versus input CW power (after excluding the butt coupling loss). There was small but observable increase in the insertion loss with input CW power for the GO-coated waveguides. In contrast, we could not observe any obvious changes for the bare (uncoated) waveguide. This indicates that the change in the insertion loss of the hybrid waveguides was induced by the GO lms. We also note that the power-induced loss changes were not permanentwhen the CW power was reduced the measured insertion loss recovered to that at low power in Figure 3a, with the measured insertion loss being repeatable. This phenomenon is similar to that observed from GOcoated doped silica waveguides and can be attributed to the photo-thermal changes of GO lms [50,60]. The absorbed CW power generated heat and increased the temperature of the hybrid waveguides, which temporarily modi ed some OFGs in the GO lms. The photo-thermal induced changes in the OFGs could modify both the linear loss and n 2 , and depend on the average CW power. This is distinct from TPAinduced loss that occurs instantaneously and depends on peak power. Since the time response for photothermal changes is slow, we accounted for the power-dependent loss of the GO lms by using the measured loss versus CW power in Figures 6a, b to calculate α of the hybrid waveguides in Eqs. (1) − (3). Note that there were the same overall CW powers coupled into the waveguides (assuming the idler power could be neglected) for a single CW light with 15−21 dBm power in Figures 6a, b and two CW lights (pump and signal with the same power) with 12−18 dBm power for each in Figures 5a, b. The dispersions β p,s,i in Eqs. (1) − (3) were calculated by Lumerical FDTD commercial mode solving software using the refractive index n and extinction coe cient k of layered GO lms measured by spectral ellipsometry. By numerically solving Eqs. (1) -(3), the FWM CE was calculated via where L is the length of the SiN waveguide (i.e., 20 mm). For the patterned devices, the waveguides were divided into bare SiN (without GO lms) and hybrid (with GO lms) segments with different α, γ and β p,s,i .
The FWM differential equations in Eqs. (1) -(3) were solved for each segment, with the output from the previous segment as the input for the subsequent segment. Figure 7a shows the experimental and theoretically calculated CE as a function of wavelength detuning for the bare SiN waveguide, the uniformly coated device with 1 layer of GO and the patterned device with 5 layers of GO. The measured CE values, obtained from the raw experimental results in Figure 5c after accounting for the EDFA gain roll-off, show good agreement with theory from Eqs. (1) − (4). The patterned device has not only a higher CE, but also a broader FWM bandwidth. According to Ref. [16], the FWM bandwidth can be approximated by where β 2 is group-velocity dispersion (GVD) and L is the interaction length. In Eq. (5), the FWM bandwidth is inversely proportional to the square root of the product of β 2 and L, i.e., reducing β 2 or L increases the FWM bandwidth. The increased bandwidth for the patterned device resulted mainly from the shorter GO coating length. A small contribution arose from better phase matching due to a slightly enhanced anomalous dispersion for the hybrid waveguides (with β 2 ≈ −1.05 × 10 −25 s 2 m −1 for the hybrid waveguide with 10 layers of GO calculated by FDTD simulations) versus the uncoated SiN waveguide (with β 2 ≈ −1.0 × 10 −25 s 2 m −1 ). These effects complement the strong Kerr nonlinearity of the layered GO lms, which is the dominant cause of enhanced FWM in the hybrid waveguides.

Figures 7b−d show the CE of the hybrid waveguides calculated from Eqs. (1) − (4). We compared the CE
performance of the hybrid waveguides while varying three parameters of the GO lms including the layer number, coating length and coating position. In each sub gure, we only changed one parameter, keeping the other two constant. Figure 7b compares the CE of the hybrid waveguides with four different numbers of GO layers (i.e., 1, 2, 5, 10), where we see that the hybrid waveguide with an intermediate number of GO layers has the maximum CE. This re ects the trade-off between γ and loss in the hybrid waveguides, which both increase with GO layer number. Figure 7c plots the CE of the hybrid waveguides as a function of GO coating length. Similar to the trend with GO layer number, the maximum CE is obtained for intermediate GO coating lengths, re ecting a trade-off where the Kerr nonlinearity enhancement dominates for short GO coating lengths while the loss increase dominates for longer lengths. Figure 7d shows the CE of the hybrid waveguides as a function of GO coating position. In contrast to the trend in Figures 7b, c, the hybrid waveguide with GO lms at the beginning (i.e., pattern position = 0) has the greatest CE. This is expected since the pump power in the GO lm is highest at the start of the waveguide and decreases as the GO segment moves further along the waveguide. Clearly this effect gets smaller with decreasing propagation loss of the bare waveguide, being much lower (< 0.5 dB) for doped silica waveguides (with a propagation loss of 0.24 dB/cm [32] ) versus the SiN waveguides (with a propagation loss of ≈3 dB/cm) studied here. Figure 8 shows the nonlinear parameter γ of the hyrbid waveguides with different numbers of GO layers obtained from tting theory to experiment, both at high (18 dBm) and low (12 dBm) pump powers. As expected, γ increases with the GO layer number. In particular, for the SiN waveguides with 10 layers of GO, γ is about two orders of magnitude higher than the bare SiN waveguide. The very small change in γ with power mainly arises from a corresponding change in n 2 of the GO lms.

Nonlinear parameter ( γ ) of the hybrid waveguides and n 2 of the GO lms
Based on the values for γ of the hybrid waveguides obtained from the FWM experiments, we calculated the Kerr coe cient (n 2 ) of the layered GO lms using [32,47]: where λ is the pump wavelength, D is the integral of the optical elds over the material regions, S z is the time-averaged Poynting vector calculated using COMSOL Multiphysics, n 0 (x, y) and n 2 (x, y) are the linear refractive index and n 2 pro les over the waveguide cross section, respectively. This work was performed in the regime close to degeneracy where the three FWM frequencies (pump, signal, idler) were close together compared with any dispersion in n 2 [32]. We therefore used n 2 instead of the more general thirdorder nonlinearity (χ (3) ) in our analysis. The values of n 2 for silica and silicon nitride used in our calculations were 2.60 × 10 -20 m 2 /W [2] and 2.61 × 10 -19 m 2 /W, respectively, the latter obtained by tting the experimental results for the bare SiN waveguide. Note that γ in Eq. (6) is an effective nonlinear parameter weighted not only by n 2 (x, y) but also by n 0 (x, y) in the different material regions, which is more accurate for high-index-contrast hybrid waveguides studied here as compared with the theory in Refs. [32,61]. Figure 9a shows the TE mode pro les for the SiN waveguides without GO and with 10 layers of GO. The mode overlap with GO lms versus GO layer number is shown in Figure 9b, which was calculated by integrating the time-averaged Poynting vectors for different material regions. Most of the power is con ned to the SiN waveguide (88.3% and is constant within 0.2%) and the mode overlap with the GO lms is small (< 1%). This is not surprising given the difference in volume between the bulk SiN waveguide and the ultrathin 2D GO lm. The mode overlap with GO lm increases with GO layer number, leading to an increased loss and γ for the hybrid waveguide with thicker GO lms. The n 2 values, although slightly lower than graphene [62,63], are nonetheless over four orders of magnitude higher than SiN and agree reasonably well with our previous measurements [32,42,46,47].
Such a high n 2 for the GO lms highlights their strong Kerr nonlinearity not only for FWM but also other third-order (c (3) ) nonlinear processes such as SPM and cross phase modulation (XPM), and possibly even enhancing c (3) for THG and stimulated Raman scattering [13,24,46,64]. We observe that n 2 (both at 12 dBm and 18 dBm) decreases with GO layer number, similar to the trend observed for layered WS 2 lms measured by a spatial-light system [65]. In our case, this was probably a result of an increase in inhomogeneous defects within the GO layers as well as imperfect contact between the multiple GO layers. We also note that the rate of decrease in n 2 with GO layer number decreases for thicker GO lms, re ecting the transition of the GO lm properties towards bulk properties, with a thickness independent n 2 .
In Figure 9d, we plot n 2 for the GO lms as a function of pump power coupled into the hybrid waveguides, which shows a very slight change in n 2 with power that is reversible. Unlike the monotonic decrease in n 2 with GO layer number that we observe, the power dependent change in n 2 shows very slight oscillations.
This is similar to that observed from FWM in GO-coated MRRs [47], and can be attributed to the powersensitive (reversible) photo-thermal changes of GO [50,66] as well as self-heating and thermal dissipation in the multiple GO layers. The power-dependent change in n 2 we obtained here is much smaller than that from GO-coated MRRs [47], which is perhaps not surprising since the light intensity in MRRs is much higher due to the resonant enhancement of the optical eld.
We veri ed that all measurements (insertion loss and CE) were repeatable, re ecting the fact that no permanent changes in the material properties of the GO lms occured. Previously [42,43,67,68], we demonstrated that the material properties of GO can be permanently modi ed by direct laser writing with high power femtosecond laser pulses. This is distinct from the non-permanent photo-thermal changes we observe here.  Finally, we compare these results with a previous demonstration of enhanced FWM in doped silica waveguides integrated with layered GO lms [32]. Table I compares relevant parameters for doped silica and SiN waveguides incorporated with 2D GO lms, where we see that the two waveguides were quite different. For this work, the excess propagation loss in the hybrid SiN waveguides induced by the GO lm was much higher due to the signi cantly increased mode overlap with the GO lm. On the other hand, this also resulted in a signi cantly increased γ for the GO-SiN hybrid waveguides. Mode overlap is an important factor for optimizing the trade-off in nonlinear optical performance between the Kerr nonlinearity and loss when integrating 2D layered GO lms onto integrated photonic devices. According to our simulations, the FWM CE can be further improved by redesigning the cross section of the SiN waveguide to optimize the mode overlap, particularly for SiN waveguides having a lower height (i.e., SiN lm thickness) of < 400 nm. This is signi cant, given the stress-induced cracking observed for thick SiN lms [69]. In contrast to the doped silica waveguides that employed only uniformly coated GO lms, here we nd that the use of patterned GO lms can result in a more signi cant improvement in FWM CE due to a better balance between loss and Kerr nonlinearity as well as a much broader FWM bandwidth. There is signi cant potential to reduce the intrinsic linear loss of the GO lms, which is not fundamental as it is for graphene, and this represents the greatest opportunity to improve the nonlinear device performance. Finally, graphene oxide also has signi cant potential for the mid-IR wavelength range [70][71][72][73][74][75][76] as well as for advanced photonic integrated circuits in silicon [77][78][79][80][81][82].

Conclusion
We