Enhanced 3 order optical nonlinearity in silicon nitride nanowires integrated with 2D graphene oxide films

numbers of GO layers and at different pump powers. By optimizing the trade-off between the nonlinearity and loss, we obtain a significant improvement in the FWM conversion efficiency 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 significant increase in FWM bandwidth for the patterned devices. A detailed analysis of the influence 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 films. 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 films.

Other CMOS compatible platforms such as silicon nitride (SiN) and doped silica [2,28] have a much lower TPA, although they still suffer from intrinsic limitation arising from a much lower Kerr nonlinearity.
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 films with a giant Kerr nonlinearity (n2) 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 films [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 film coating on integrated photonic devices with highly precise control of film 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 films.
In this paper, we report the integration of 2D layered GO films 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 films are integrated on SiN waveguides with precise control of the film thickness, placement and coating length. Benefiting from the strong light-matter interaction between the SiN waveguides and the GO films with an ultrahigh Kerr nonlinearity and a relatively low loss, significantly 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 efficiency (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 influence of pattern length and position on FWM performance is also analysed. By fitting the experimental results with theory, the dependence of the n2 of the GO film on layer number and pump power is extracted, showing interesting physical insights about the evolution of the layered GO films 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 films on SiN devices to improve the nonlinear optical performance. SiN waveguides with a cross section of 1.6 μm × 0.66 μm were fabricated via annealing-free and crack-free 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 370nm-thick layer for each, so as to control strain and to prevent cracks. In order to produce highquality films, a tailored ultra-low deposition rate (< 2 nm/ min) was used. Waveguides were then formed via a combination of deep ultraviolet lithography and fluorine-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 films and the evanescent field 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.

Device fabrication
Layered GO films were coated on the top surface of the chip by a solution-based method that yielded layer-by-layer film deposition, as reported previously [32,48,50]. Four steps for the in-situ assembly of monolayer GO films were repeated to construct multilayer films. 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 film 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 film thickness). In addition to the uniformly coated devices, we selectively patterned GO films on SiN waveguides using standard lithography and lift-off processes. The chip was first 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 films 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 film 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 film 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 films on-chip. Apart from allowing precise control of the size and placement of the GO films that are in contact with the SiN waveguides, the patterned GO films also enabled us to test the performance of devices having a shorter length of GO film but with higher film thicknesses, which provides more flexibility to optimize the device performance with respect to FWM CE and bandwidth.     We fabricated and tested two types of GO-coated SiN waveguides: the first with either 1 or 2 layers of uniformly coated GO films and the second with 5 or 10 layers of patterned GO films.

Device characterization
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 films 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 fibers to butt couple the CW light into and out of the SiN waveguides with inverse-taper couplers at both ends. The butt coupling loss was ≈5 dB per facet, corresponding to 0-dBm CW power coupled into the waveguides.  ≈3.0 dB/cm, which was obtained from cutback measurements of SiN waveguides with the same geometry but different lengths. 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 film. 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], reflecting the low material absorption of GO and its strong potential for the implementation of high-performance 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 films with a bandgap > 2 eV should have negligible absorption at near-infrared wavelengths. We therefore infer that the linear loss of the GO films is mainly due to light absorption from localized defects as well as scattering loss stemming from film unevenness and imperfect contact between the different layers. We note that the linear loss of the GO films is not a fundamental property. Therefore, by optimizing our GO synthesis and coating processes, such as using GO solutions with reduced flake sizes and increased purity, it is anticipated that the loss of our GO films 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 amplified by erbium-doped fiber amplifiers (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 fiber 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 reflected 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.       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, reflecting a wider FWM phase matching bandwidth for a shorter length of GO films 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 that is opposite to TPA) for the GO films 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 films 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 films. 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 GO-coated doped silica waveguides and can be attributed to the photo-thermal changes of GO films [50,60]. The absorbed CW power generated heat and increased the temperature of the hybrid waveguides, which temporarily modified some OFGs in the GO films. The photo-thermal induced changes in the OFGs could modify both the linear loss and n2, and depend on the average CW power. This is distinct from TPA-induced loss that occurs instantaneously and depends on peak power. Since the time response for photo-thermal changes is slow, we    Based on the values for γ of the hybrid waveguides obtained from the FWM experiments, we calculated the Kerr coefficient (n2) of the layered GO films using [32,47]: (6) where λ is the pump wavelength, D is the integral of the optical fields over the material regions, Sz is the time-averaged Poynting vector calculated using COMSOL Multiphysics, n0 (x, y) and

Nonlinear parameter ( γ ) of the hybrid waveguides and n2 of the GO films
n2 (x, y) are the linear refractive index and n2 profiles 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 n2 [32].
We therefore used n2 instead of the more general third-order nonlinearity (χ (3) ) in our analysis.
The values of n2 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 fitting the experimental results for the bare SiN waveguide. Note that γ in Eq. (6) is an effective nonlinear parameter weighted not only by n2 (x, y) but also by n0 (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   9b, which was calculated by integrating the time-averaged Poynting vectors for different material regions. Most of the power is confined to the SiN waveguide (88.3% and is constant within 0.2%) and the mode overlap with the GO films is small (< 1%). This is not surprising given the difference in volume between the bulk SiN waveguide and the ultrathin 2D GO film.
The mode overlap with GO film increases with GO layer number, leading to an increased loss and γ for the hybrid waveguide with thicker GO films.

Figure 9c
shows n2 versus layer number for the GO films at fixed pump powers of 12 dBm and 18 dBm. The n2 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 n2 for the GO films highlights their strong Kerr nonlinearity not only for FWM but also other third-order ( (3) ) nonlinear processes such as SPM and cross phase modulation (XPM), and possibly even enhancing  (3) for THG and stimulated Raman scattering [13,24,46,64]. We observe that n2 (both at 12 dBm and 18 dBm) decreases with GO layer number, similar to the trend observed for layered WS2 films 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 n2 with GO layer number decreases for thicker GO films, reflecting the transition of the GO film properties towards bulk properties, with a thickness independent n2.
In Figure 9d, we plot n2 for the GO films as a function of pump power coupled into the hybrid waveguides, which shows a very slight change in n2 with power that is reversible. Unlike the monotonic decrease in n2 with GO layer number that we observe, the power dependent change in n2 shows very slight oscillations. This is similar to that observed from FWM in GOcoated MRRs [47], and can be attributed to the power-sensitive (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 n2 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 field.
We verified that all measurements (insertion loss and CE) were repeatable, reflecting the fact that no permanent changes in the material properties of the GO films occured. Previously [42,43,67,68], we demonstrated that the material properties of GO can be permanently modified by direct laser writing with high power femtosecond laser pulses. This is distinct from the nonpermanent 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 films [32]. Table I compares relevant parameters for doped silica and SiN waveguides incorporated with 2D GO films, 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 film was much higher due to the significantly increased mode overlap with the GO film. On the other hand, this also resulted in a significantly increased γ for the GO-SiN hybrid waveguides. Mode overlap is an important factor for optimizing the tradeoff in nonlinear optical performance between the Kerr nonlinearity and loss when integrating 2D layered GO films 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 film thickness) of < 400 nm. This is significant, given the stress-induced cracking observed for thick SiN films [69]. In contrast to the doped silica waveguides that employed only uniformly coated GO films, here we find that the use of patterned GO films can result in a more significant improvement in FWM CE due to a better balance between loss and Kerr nonlinearity as well as a much broader FWM bandwidth. Finally, there is significant potential to reduce the intrinsic linear loss of the GO films, which is not fundamental as it is for graphene, and this represents the greatest opportunity to improve the nonlinear device performance.

Conclusion
We demonstrate improved FWM efficiency in SiN waveguides integrated with 2D layered GO SiN into a viable and highly performing nonlinear photonic platform, which we believe could play an important role in integrated nonlinear optics well beyond the FWM process studied here.