Transforming silicon into a high performing integrated nonlinear photonics platform by integration with 2D graphene oxide films

Layered two-dimensional
(2D) GO films are integrated with silicon-on-insulator (SOI) nanowire
waveguides to experimentally demonstrate an enhanced Kerr nonlinearity,
observed through self-phase modulation (SPM). The GO films are integrated with
SOI nanowires using a large-area, transfer-free, layer-by-layer coating method
that yields precise control of the film thickness. The film placement and
coating length are controlled by opening windows in the silica cladding of the
SOI nanowires. Owing to the strong mode overlap between the SOI nanowires and
the highly nonlinear GO films, the Kerr nonlinearity of the hybrid waveguides
is significantly enhanced. Detailed SPM measurements using picosecond optical
pulses show significant spectral broadening enhancement for SOI nanowires
coated with 2.2-mm-long films of 1−3 layers of GO, and 0.4-mm-long films with
5−20 layers of GO. By fitting the experimental results with theory, the
dependence of GO’s n2 on
layer number and pulse energy is obtained, showing interesting physical
insights and trends of the layered GO films from 2D monolayers to quasi
bulk-like behavior. Finally, we show that by coating SOI nanowires with GO
films the effective nonlinear parameter of SOI nanowires is increased 16 fold,
with the effective nonlinear figure of merit (FOM) increasing by about 20 times
to FOM > 5. These results reveal the strong potential of using layered GO
films to improve the Kerr nonlinear optical performance of silicon photonic
devices.


Introduction
The 3 rd order nonlinear optical response has found wide ranging applications in telecommunications, metrology, astronomy, ultrafast optics, quantum photonics, and many other areas [1][2][3][4]. Nonlinear integrated photonic devices based on the Kerr (n2) effect in particular offer far superior processing speeds compared to electronic devices as well as the added benefits of compact footprint, low power consumption, high stability, and low-cost mass production, all of which are important for high-speed signal generation and processing in optical communication systems [5][6][7].
Nevertheless, the strong two-photon absorption (TPA) of silicon at near-infrared wavelengths poses a fundamental limitation to the performance of nonlinear photonic devices in the telecommunications band [5,6]. Other CMOS compatible platforms such as silicon nitride [19,20], high index doped silica glass [21,22], and silicon rich nitride [23,24], have a much weaker TPA and a higher nonlinear figure of merit (FOM), although they still face limitations in terms of nonlinear efficiency due to their lower intrinsic Kerr nonlinearity [5,25].
The need to improve the performance of nonlinear integrated photonic devices has motivated the on-chip integration of highly nonlinear materials such as polymers and two-dimensional (2D) materials [26,27]. The giant Kerr nonlinearity of 2D layered materials such as graphene, graphene oxide (GO), black phosphorus, and transition metal dichalcogenides (TMDCs) has been widely recognized and has enabled diverse nonlinear photonic devices with high performance and new functionalities [28][29][30][31][32]. In particular, enhanced spectral broadening of optical pulses has been reported for SOI nanowires with transferred MoS2 and graphene [33][34][35].
Among the various 2D materials, GO has received increasing interest due to its ease of preparation as well as the tunability of its material properties [36][37][38][39][40][41]. Previously, we reported GO films with a giant Kerr nonlinearity of about 4 orders of magnitude higher than that of silicon [40,42], and demonstrated significantly enhanced four-wave mixing (FWM) in doped silica waveguides and microring resonators integrated with layered GO films [43,44].
Moreover, GO has a material absorption that is over 2 orders of magnitude lower than undoped graphene as well as a large bandgap (2.1−2.4 eV) that yields a low TPA in the telecommunications band [45,46]. By using a large-area, transfer-free, layer-by-layer GO coating method, we also achieved highly precise control of the GO film thickness on integrated devices [45,47]. This overcomes critical fabrication limitations in terms of layer transfer for 2D materials and represents a significant improvement for the eventual manufacturing of integrated photonic devices incorporated with 2D layered GO films.
In this paper, we use our GO fabrication technique to demonstrate a significantly enhanced Kerr nonlinearity in silicon-on-insulator (SOI) nanowires integrated with 2D layered GO films.
Self-phase modulation (SPM) measurements are performed at different pulse energies for the SOI nanowires integrated with different numbers of GO layers (2.2-mm-long with 1−3 layers of GO and 0.4-mm-long with 5−20 layers of GO). Benefiting from the strong light-matter interaction between the SOI nanowires and the highly nonlinear GO films, we observe significant spectral broadening for the GO-coated SOI nanowires as compared with the uncoated SOI nanowires, achieving a high broadening factor (BF) of 3.75 for an SOI nanowire with 2 layers of GO and 4.34 for a device with 10 layers of GO. We also fit the SPM experimental results to theory and obtain the dependence of the Kerr nonlinearity of the GO films on the GO layer number and pulse energy, showing interesting physical insights and trends of the layered GO films in evolving from 2D monolayers to quasi bulk-like behavior. Finally, we obtain the effective nonlinearity (n2), nonlinear parameter (γ) and nonlinear FOM of the hybrid waveguides, showing that the GO films can enhance γ of SOI nanowires by up to 16 folds and the nonlinear FOM by almost 20 times. These results verify the effectiveness of integrating 2D layered GO films with silicon photonic devices to improve the performance of Kerr nonlinear optical processes. Figure 1(a) shows a schematic of an SOI nanowire waveguide integrated with a GO film while the fabrication process flow is given in Figure 1(b). SOI nanowires with a cross section of 500 nm × 220 nm were fabricated on an SOI wafer with a 220-nm-thick top silicon layer and a 2μm-thick buried oxide (BOX) layer via CMOS-compatible fabrication processes. Deep ultraviolet photolithography (248 nm) was used to define the device layout, followed by inductively coupled plasma etching of the top silicon layer. After that, a 1.5-μm thick silica layer was deposited by plasma enhanced chemical vapor deposition as an upper cladding layer.

Device fabrication
Windows with two different lengths of 0.4 mm and 2.2 mm were then opened down to the BOX layer via photolithography and reactive ion etching, so as to enable GO film coating onto the SOI nanowire. Finally, the coating of 2D layered GO films was achieved by a solution-based method that yielded layer-by-layer GO film deposition, as reported previously [43,45,47].
Four steps for the in-situ assembly of monolayer GO films were repeated to construct multilayer films on the SOI nanowire. Our GO coating approach, unlike the sophisticated transfer processes employed for coating other 2D materials such as graphene and TMDCs [33,34], enables transfer-free GO film coating on integrated photonic devices, with highly scalable fabrication processes and precise control of the number of GO layers (i.e., GO film thickness). Apart from allowing precise control of the placement and coating length of the GO films that are in contact with the SOI nanowires, the opened windows also enabled us to test the performance of devices having a shorter length of GO film but with higher film thicknesses (up to 20 layers). This provided more flexibility to optimize the device performance with respect to SPM spectral broadening.   [43,47]. As compared with doped silica waveguides, the SOI nanowires allow much stronger light-material interaction between the evanescent field leaking from the waveguide and the GO film, which is critical to enhance nonlinear optical processes such as SPM and FWM.

Linear loss measurement
We fabricated and tested two types of GO-coated SOI nanowires with (i) 2.  This is about 2 orders of magnitude smaller than SOI nanowires coated with graphene [48], indicating the low material absorption of GO and its strong potential for the implementation of high-performance nonlinear photonic devices. The propagation loss increased with GO layer number − a combined result of increased mode overlap and several other possible effects such as increased scattering loss and absorption induced by imperfect contact between the multiple GO layers as well as interaction between the GO layers, as reported previously [43,47].
Unlike graphene that has a metallic behavior (e.g., high electrical and thermal conductivity) with a zero bandgap, GO is a dielectric that has a large bandgap of 2.1−2.4 eV [36,45], 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 for light 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.

Nonlinear loss measurement
We measured the nonlinear loss of the GO-coated SOI nanowires using a pulsed fiber laser (PriTel, repetition rate: ~60 MHz, pulse duration: ~3.9 ps). The experimental setup is shown in are also shown for comparison, where the EIL increased with pulse energy primarily due to TPA and free carrier absorption of silicon [49]. For the GO-coated SOI nanowires, on the other hand, the measured EIL was slightly lower than that for the bare SOI nanowire, with the difference increasing with GO layer number. This reflects the power-dependent loss of the GO layers (see Section 4 for detailed discussion). Figure 4(c) shows the ΔEIL for the hybrid waveguides extracted from Figure 4(b) after excluding the EIL induced by the bare SOI nanowire, which reflects the power dependent loss due solely to the GO films. The ΔEIL decreased as the pulse energy was increased -a trend that is consistent with saturable absorption (SA) [50,51] (see Section 4 for detailed discussion). We also note that these changes were not permanent -the measured insertion loss recovered to those in Figures 3(a-i) and (a-ii) when the pulse energy was reduced, with the measured EIL in Figures 4(b-i) and (b-ii) being repeatable.

SPM experiments
We used the experimental setup shown in Figure 5 to perform SPM measurements on the GOcoated SOI nanowires. Picosecond optical pulses generated by a pulsed fiber laser (the same as in Section 2.3) were delivered into the hybrid waveguides, with a VOA to tune the input pulse energy. An optical isolator was inserted before the device under test (DUT) to prevent the reflected light from damaging the laser source and a polarization controller (PC) was used to set the input light to TE-polarization. The signal output from the DUT was split by a 90:10 coupler -10% sent into an optical power meter (OPM) for power monitoring and the other 90% into an optical spectrum analyzer (OSA, Yokogawa AQ6370D) to observe the spectral broadening.   Figure 6(a-i) shows the normalized spectra of the optical pulses before and after transmission through the SOI nanowires with 2.2mm-long, 1−3 layers of GO, together with the output optical spectrum for the bare SOI nanowire, all taken with the same pulse energy of ~51.5 pJ (i.e., ~13.2 W peak power, excluding coupling loss) coupled into the SOI nanowires. As compared with the input pulse spectrum, the output spectrum after transmission through the bare SOI nanowire exhibited measurable spectral broadening. This is expected and can be attributed to the high Kerr nonlinearity of silicon. The GO-coated SOI nanowires, on the other hand, show much more significantly broadened spectra as compared with the bare SOI nanowire, clearly reflecting the improved Kerr nonlinearity of the hybrid waveguides. Figure 6(a-ii) shows the corresponding results for the SOI nanowires with 0.4-mm-long, 5−20 layers of GO, taken with the same coupled pulse energy as in Figure 6(a-i). The SOI nanowires with a shorter GO coating length but higher film thicknesses also clearly show more significant spectral broadening as compared with the bare SOI nanowire. We also note that in either Figure 6(a-i) or 6(a-ii), the maximum spectral broadening is achieved for a device with an intermediate number of GO layers (i.e., 2 and 10 layers of GO in (a-i) and (a-ii), respectively). This could reflect the trade-off between the Kerr nonlinearity enhancement (which dominates for the device with a relatively short GO coating length) and loss increase (which dominates for the device with a relatively long GO coating length) for the SOI nanowires with different numbers of GO layers (see Section 4 for detailed discussion).

Figures 6(b-i) and (b-ii)
show the power-dependent output spectra after going through the SOI nanowires with (i) 2 layers and (ii) 10 layers of GO films. We measured the output spectra at 10 different coupled pulse energies ranging from ~8.2 pJ to ~51.5 pJ (i.e., coupled peak power from ~2.1 W to ~13.2 W). As the coupled pulse energy was increased, the output spectra showed increasing spectral broadening as expected. We also note that the broadened spectra exhibited a slight asymmetry. This was a combined result of both the asymmetry of the input pulse spectrum and the free-carrier dispersion of silicon [49] (see Section 4).
To quantitively analyze the spectral broadening of the output spectra, we introduce the concept of a broadening factor (BF) [52,53]. The width of the optical spectra is described by the root-mean-square (RMS) width, defined as [52] ∆ω rms 2 =〈(ω-ω 0 ) 2 〉-〈(ω-ω 0 )〉 2 (1) where the angle brackets denote the average over the spectrum given by where S(ω) is the spectrum intensity. The BF is therefore defined as: where ∆ω0 is the RMS spectral width of the input optical pulses.

SPM spectral broadening
We used the theory from Refs. [49,50,52] to model the SPM process in the GO-coated SOI nanowires. The evolution of an optical pulse going through the hybrid waveguides was simulated by using a split-step Fourier method to solve the nonlinear Schrödinger equation (NLSE) as follows [49]: where i = √1, A(z, t) is the slowly varying temporal envelope of the optical pulse along the z axis, which is the direction of light propagation, β2 is the second-order dispersion coefficient, γ is the waveguide nonlinear parameter, σ and µ are the free carrier absorption (FCA) and free carrier dispersion (FCD) coefficients of silicon, respectively, Nc is the free carrier density in silicon, and α is the total loss including both linear loss and nonlinear loss.
In Eq. (4), we retain only the second-order dispersion β2 since the dispersion length (> 1 m) is much longer than the physical length of the waveguides (i.e., the third-order nonlinearity dominates during the pulse propagation). The total loss α can be expressed as: where αL is the linear loss, αNL-SOI and αNL-GO are the nonlinear losses induced by the SOI nanowire and the GO film, respectively.
In Eq. (5), αNL-SOI includes the nonlinear losses induced by TPA and FCA of silicon, which are [49]: where βTPA, Si is the TPA coefficient of silicon and Aeff is the effective mode area of the waveguides. In Eqs. (4) and (6), Nc results from free carriers generated in silicon, given by [49]: where ℏ is the Planck's constant, ω is the angular frequency, τc = ~1 ns is the effective carrier lifetime. The τc term in Eq. (7) can be ignored since the pulse duration (~3.9 ps) is much less than τc so that the generated free carriers do not have time to recombine within the pulse duration [34,49]. The measured EIL of the bare SOI nanowire as a function of the coupled pulse energy is shown in Figure 7(a) along with the fit EIL calculated from Eqs. (6)−(7). The fit βTPA, Si and σ are 5.02 ×10 -12 m/W and 1.44×10 -21 m 2 , respectively, which agree well with the literature [49], confirming that the nonlinear loss of the bare SOI nanowire was mainly induced by TPA and FCA. We also note that FCD significantly affected the output spectral shapes, largely accounting for the significant asymmetry.
Since the TPA and FCA of the GO films is negligible in the telecommunications band [42,43], αNL-GO in Eq. (5) is mainly a result of SA in the GO films, as noted previously [40,42,51].
In Figure 7 (b), we exclude the nonlinear loss induced by the SOI nanowires before the GO  [56,57]. Note that the spectral broadening induced by SPM has negligible direct impact on the saturable absorption since the absorption induced by GO was wavelength independent in our model due to the broadband response of the 2D layered GO films [47]. In our calculations, we neglected any potential spectral/temporal coupling effects that could induce interplay between SA and SPM. This was because the length of the hybrid SOI nanowires was much shorter than the dispersion length for the picosecond pulses used, and so the change in the pulse spectrum due to SPM did not have a significant effect on the temporal shape of the pulse [50]. According to our simulations, the maximum difference induced by SPM on ΔEIL is < 1%. Based on Eqs. (4)−(8), we fit the experimentally measured spectra to obtain the effective nonlinear parameter γeff of the hybrid waveguides. In our calculations, the hybrid waveguides were divided into SOI (with silica cladding) and hybrid (with GO in opened windows) segments and the SPM differential equation in Eq. (4) was solved for each segment. Figure 8(a) shows the measured and fit optical spectra for the input pulses. We approximated the input pulse shape by a Gaussian profile as below: where P0 is the pulse peak power, C0 is the initial chirp, and T0 is se duration. The measured and fit optical spectra for the output signal after transmission through the bare SOI nanowire at a coupled pulse energy of 51.5 pJ are shown in Figure 8(b), showing good agreement between theory and experiment, with the discrepancy arising mainly from small imperfections in the input pulse spectrum. We obtain a γ of 288 W -1 m -1 for the bare SOI nanowire, in agreement with previous reports [6]. The measured and fit optical spectra for the output signals after transmission through the SOI nanowires with 2 and 10 layers of GO are shown in Figures 8(c) and (d), respectively, where the coupled pulse energy is the same as Figure 8(b). Here again, we obtain good agreement between theory and experiment, particularly for the BFs where the deviation is < 3.2 %. This small discrepancy is mainly due to slight differences between the measured and fit output spectra.

Kerr nonlinearity (n2) of the GO films
Based on γeff of the hybrid waveguides, we further extract the Kerr coefficient (n2) of the layered GO films using [43]: where λc is the pulse central wavelength, D is the integral of the optical fields over the material regions, Sz is the time-averaged Poynting vector calculated using Lumerical FDTD commercial mode solving software, and n2 (x, y) is the Kerr coefficient of the different material regions.
These calculations assumed picosecond optical pulses having a relatively small spectral width (< 10 nm). We therefore neglected any variation in n2 arising from its dispersion and used n2 instead of the more general third-order nonlinearity χ (3) in our subsequent analysis and discussion. The values of n2 for silica and silicon used in our calculation were 2.60 × 10 -20 m 2 /W [5] and 6.03 × 10 -18 m 2 /W, respectively, the latter obtained by fitting the experimental results for the bare SOI nanowire. Note that γ in Eq. (10) 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. [58,59].  The values of n2 are over 3 orders of magnitude higher than that of silicon and agree reasonably well with our previous waveguide FWM [43] and Z-scan measurements [42]. Note that the layer-by-layer characterization of n2 for GO is challenging for Z-scan measurements due to the weak response of extremely thin 2D films [40,42]. The high n2 of GO films highlights their strong Kerr nonlinearity for not only SPM but also other third-order (χ (3) ) nonlinear processes such as FWM, and possibly even enhancing χ (3) for third harmonic generation (THG) and stimulated Raman scattering, parametric gain, quantum optics, and other processes [60][61][62][63][64][65][66][67][68][69][70]. In Figure 9(b), n2 (both at 51.5 pJ and 8.2 pJ) decreases with GO layer number, showing a similar trend to WS2 measured by a spatial-light system [71]. This is probably due to increased inhomogeneous defects within the GO layers as well as imperfect contact between the different GO layers. At 51.5 pJ, n2 is slightly higher than at 8.2 pJ, indicating a more significant change in the GO optical properties with inceasing power. We also note that the decrease in n2 with GO layer number becomes more gradual for thicker GO films, possibly reflecting the transition of the GO film properties towards bulk material properties − with a thickness independent n2. with the coupled pulse energy. Note that the variation of n2 is much lower than in our previous FWM experiments using CW light [44], probably due to weaker photo thermal effects induced by picosecond optical pulses having much lower average powers compared to CW light. Since it was difficult to accurately measure the slight change in film thickness and refractive index of GO with the coupled pulse energy during the SPM, we neglected any changes in these parameters in our calculations. In principle, this approximation could lead to slight deviations in n2, possibly explaining the non-monotonic relationship between n2 and the coupled pulse energy. Despite this, the fit n2 can still be regarded as a parameter reflecting the overall Kerr nonlinear performance at different coupled pulse energies.
After our SPM experiment, we used low-power (0 dBm) CW light to retest the insertion loss of the GO-coated SOI nanowires. No significant change was observed, and the measured output SPM spectra in Figure 6 were repeatable when we reinjected the optical pulses, indicating that the optically induced changes (e.g., loss, n2) of the GO films were not permanent. Note that we previously showed that the material properties of GO can also be permanently changed by femtosecond laser pulses [38][39][40][41] with significantly higher peak powers. This is distinct from the reversible power-dependent changes observed here. The layer-number and power-dependent material properties of the layered GO films enable many new device features that are difficult to achieve for silicon photonic devices. We believe this could enable one to tailor the device performance for diverse applications beyond enhancing the Kerr nonlineary as reported here.

FOM of the hybrid waveguides
To quantitively analyze the improvement in the nonlinear performance of the GO-coated SOI nanowires, we calculated the effective nonlinear FOM defined as [5,6]: where βTPA, eff is the effective TPA coefficient obtained by fitting the results in Figure 4(b) and n2, eff is the effective Kerr coefficient calculated by [6,27]: where we see that n2,eff increases with GO layer number. In particular, for the hybrid waveguides with 10 or more GO layers, n2,eff is an order of magnitude higher than the bare SOI nanowire. is shown in Figure 10(b) where we see that a very high FOMeff of 19 times that of silicon is achieved for the hybrid SOI nanowires with 20 layers of GO. This is remarkable since it indicates that by coating SOI nanowires with GO films, not only can the nonlinearity be significantly enhanced but the relative effect of nonlinear absorption can be greatly reduced as well. This is interesting given that the GO films themselves cannot be described by a nonlinear FOM since the nonlinear absorption displays SA rather than TPA, and yet nonetheless the GO films still are able to reduce the βTPA, eff of the hybrid waveguides, thus improving the overall nonlinear performance. Aside from the Kerr nonlinearity (n2, γ) and the nonlinear FOM (FOMeff), the other remaining key factor affecting nonlinear performance is the linear loss. As mentioned the loss of our hybrid waveguides is about 2 orders of magnitude lower than comparable devices integrated with graphene [48], and this played a key role for achieving high BFs in our SPM experiments.
Nonetheless, the linear loss did pose a limitation for our devices -otherwise the maximum performance would have been achieved for the thickest films where γeff was the greatest.
Reducing the linear loss of the GO films further will significantly improve our device performance even more. We note that the linear loss of the GO films is not a fundamental property − in theory, GO films with a bandgap > 2 eV should have negligible linear loss in spectral regions below the bandgap. 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 significantly reduced.
Finally, we contrast these results with our previous demonstration of enhanced FWM in doped silica devices integrated with layered GO films [43,44]. In that work the waveguides were very different, having negligible nonlinear absorption and comparatively weak nonlinearity, and so it was perhaps not surprising that the GO layers had a dramatic impact on the nonlinear performance. In contrast, silicon already has a very large Kerr nonlinearity − about twenty times higher than doped silica -and so it is perhaps not obvious that integrating 2D layered GO films would significantly enhance the effective nonlinearity. Even more remarkably, by coating SOI nanowires with GO, the very low nonlinear FOM of silicon of about 0.3, which has posed significant limitations for its nonlinear optical performance [6], can be dramatically improved by almost 20 times. Thus, coating SOI nanowires with GO films can effectively transform silicon into a viable and highly performing nonlinear optical platform.
This is can be attributed to the ultrahigh Kerr nonlinearity of the GO films (about 4 orders of magnitude higher than silicon) as well as the significantly enhanced mode overlap between GO and the SOI nanowires, having much smaller dimensions (500 nm × 220 nm in contrast to 2 µm × 1.5 µm for doped silica waveguides). Mode overlap is important for optimizing the tradeoff between Kerr nonlinearity enhancement and loss increase when introducing 2D layered GO films onto different integrated platforms to enhance the nonlinear optical performance. By redesigning the waveguide cross section to optimize the mode overlap, the nonlinear performance such as SPM spectral broadening and FWM conversion efficiency can be further improved. Considering the wide use of SOI devices for diverse applications based on the Kerr nonlinearity, GO-silicon hybrid devices that provide a significantly improved Kerr nonlinearity and nonlinear FOM could play an important role in nonlinear integrated photonic devices well beyond the SPM spectral broadening enhancement reported here.

Conclusion
We demonstrate an enhanced Kerr nonlinearity in SOI nanowires integrated with 2D layered GO films. The GO films are integrated onto CMOS-compatible SOI nanowires with different lengths over opened windows based on a large-area, transfer-free, layer-by-layer GO coating method. This yields precise control of the film thickness, placement and coating length. We perform detailed SPM measurements in the SOI nanowires with GO films and achieve significant spectral broadening enhancement for the hybrid waveguides. By fitting the experimental results with theory, we obtained the change of GO's third-order nonlinearity with layer number and pulse energy. We observe an enhancement in the nonlinear parameter of up to 16 times and an improved nonlinear FOM of up to a factor of 19. These results highlight the extremely powerful approach of incorporating layered GO films into SOI nanowires to greatly enhance their Kerr nonlinear optical performance, thus transforming silicon into a highly performing nonlinear optical platform.