Graphene Oxide for Nonlinear Integrated Photonics

Integrated photonic devices operating via optical nonlinearities offer a powerful solution for all‐optical information processing, yielding processing speeds that are well beyond that of electronic processing as well as providing the added benefits of compact footprint, high stability, high scalability, and small power consumption. The increasing demand for high‐performance nonlinear integrated photonic devices has facilitated the hybrid integration of novel materials to address the limitations of existing integrated photonic platforms. Recently, graphene oxide (GO), with its large optical nonlinearity, high flexibility in altering its properties, and facile fabrication processes, has attracted significant attention, enabling many hybrid nonlinear integrated photonic devices with improved performance and novel capabilities. This paper reviews the applications of GO to nonlinear integrated photonics. First, an overview of GO's optical properties and the fabrication technologies needed for its on‐chip integration is provided. Next, the state‐of‐the‐art GO nonlinear integrated photonic devices are reviewed, followed by comparisons of the nonlinear optical performance of different integrated platforms incorporating GO as well as hybrid integrated devices including different kinds of 2D materials. Finally, the current challenges and future opportunities in this field are discussed.


Introduction
By avoiding the inefficient opticalelectrical-optical conversion, all-optical signal generation, amplification, and processing based on optical nonlinearities offers processing speed that far exceed that of electrical devices, [1][2][3] underpinning a variety of applications in many fields such as optical communications, [4][5][6][7] photonic computing, [8,9] optical manipulation, [10,11] specialized optical sources, [12,13] microscopy, [14,15] metrology, [16,17] spectroscopy, [18,19] optical cloaking, [20,21] and quantum information processing. [22,23] Compared to bulky discrete off-chip devices, photonic integrated circuits fabricated by wellestablished complementary metal-oxide semiconductor (CMOS) technologies provide an attractive solution to implement compact nonlinear optical devices on a chip scale, thus harvesting great dividends for integrated devices such as high stability and scalability, low power consumption, and large-scale manufacturing. [24][25][26] Although silicon-on-insulator (SOI) has been the dominant platform for photonic integrated circuits, its indirect bandgap is a significant handicap for optical sources, and its centrosymmetric crystal structure poses an intrinsic limitation for secondorder nonlinear optical applications. Furthermore, its strong twophoton absorption (TPA) at near-infrared wavelengths limits its third-order nonlinear optical response in the telecom band. [2,27] Other CMOS compatible platforms such as silicon nitride [5,28,29] and doped silica [30,31] have a much lower TPA, although they still face the limitation of having a much smaller third-order optical nonlinearity than silicon. To address these issues, the onchip integration of novel materials has opened up promising avenues to overcome the limitations of these existing integrated platforms. Many hybrid nonlinear integrated photonic devices incorporating polymers, [32,33] carbon nanotubes, [34,35] and 2D materials [36][37][38] have been reported, showing significantly improved performance and offering new capabilities beyond those of conventional integrated photonic devices.
2D materials, such as graphene, black phosphorus (BP), transition metal dichalcogenides (TMDCs), hexagonal boron nitride (hBN), and graphene oxide (GO), have motivated a huge upsurge in activity since the discovery of graphene in 2004. [39] With Laser Photonics Rev. 2023, 17,2200512 www.advancedsciencenews.com www.lpr-journal.org atomically thin and layered structures, they have exhibited many remarkable optical properties that are intrinsically different from those of conventional bulk materials. [40][41][42][43][44][45][46] Recently, there has been increasing interest in the nonlinear optical properties of 2D materials, which are not only fascinating in terms of laboratory research but also intriguing for potential practical and industrial applications. [47][48][49][50][51][52][53][54] Among the different 2D materials, GO has shown many advantages for implementing hybrid integrated photonic devices with superior nonlinear optical performance. [41,[55][56][57][58][59][60][61] It has been reported that GO has a large third-order optical nonlinearity (n 2 ) that is over 4 orders of magnitude higher than silicon [62,63] as well as a linear absorption that is over 2 orders of magnitude lower than graphene in the infrared region. [56,64] The former is critical for improving the efficiency of nonlinear wavelength conversion, whereas the latter allows for a low film loss, which is beneficial for enhancing the nonlinear optical response that scales nonlinearly with light power. In addition, GO has a heterogenous atomic structure that exhibits noncentrosymmetry, yielding a large second-order optical nonlinearity that is absent in pristine graphene that has a centrosymmetric structure. The bandgap and defects in GO can also be engineered to facilitate diverse linear and nonlinear optical processes. These material properties of GO, together with its facile synthesis processes and high compatibility with integrated platforms, [64,65] have enabled a series of high-performance nonlinear integrated photonic devices. Here, we provide a systematic review of these devices, highlighting their capabilities in a range of nonlinear optical processes (Figure 1a) as well as a comparison of different integrated platforms. Figure 1b summarizes the typical applications of the nonlinear optical processes in Figure 1a, which cover a broad scope including all-optical wavelength conversion, [33,66] alloptical switching and modulation, [10,11] all-optical sampling and characterization, [67,68] laser mode locking, [69,70] Kerr frequency combs, [71,72] broadband optical sources, [12,13] nonlinear optical imaging, [14,15] optical parametric amplifiers, [4,73] and quantum optics. [22,23] This review paper is organized as follows. In Section 2, the optical properties of GO, including both the linear and nonlinear properties, are introduced, particularly in the context of integrated photonic devices. Next, the fabrication technologies for integrating GO films on chips are summarized in Section 3, which are classified into GO synthesis, film coating on chips, and device patterning. In Section 4, we review the state-of-the-art nonlinear integrated photonic devices incorporating GO. In Section 5, detailed comparison for the nonlinear optical performance of different integrated platforms incorporating GO is presented and discussed. The comparison of nonlinear integrated photonic devices incorporating different 2D materials is provided in Section 6. The current challenges and future perspectives are discussed in Section 7. Finally, the conclusions are provided in Section 8.

Optical Properties of GO
GO, which contains various oxygen-containing functional groups (OCFGs) such as epoxide, hydroxyl, and carboxylic, all attached on a graphene-like carbon network, is one of the most common derivatives of graphene. [74][75][76][77] The heterogeneous atomic structure including both sp 2 carbon sites with -states and sp 3 -bonded carbons with -states makes GO exhibit a series of distinctive material properties, particularly in its 2D form. In this section, we briefly introduce GO's optical properties, including both the linear and nonlinear properties and focusing on the near-infrared telecom band (around 1550 nm). Table 1 provides a comparison of the basic optical properties of GO with typical 2D materials such as graphene, TMDCs, and BP as well as bulk materials such as silicon (Si), silica (SiO 2 ), silicon nitride (Si 3 N 4 ), and high index doped silica glass (Hydex) used for implementing integrated photonic devices. In the following, we provide detailed introduction of GO's optical properties based on Table 1.

Linear Optical Properties
In contrast to graphene that has a bandgap of zero, [40] GO has a typical bandgap between 2.1 and 3.6 eV, [74,78] which yields low linear light absorption in the telecom band. Although in Table 1 the optical extinction coefficient k of GO (0.005-0.01) is not as low as for Si, Si 3 N 4 , and SiO 2 , it is nonetheless still much lower than the other 2D materials, particularly graphene with a k that is over 100 times higher than GO. This property of GO is highly attractive for nonlinear optical applications such as self-phase modulation (SPM) and four-wave mixing (FWM) that require high power to drive the nonlinear processes. On the other hand, GO has a refractive index n that is around 2 across a broad optical band from near-infrared to mid-infrared regions. [57,62,77,79] This results in a low material dispersion, which is critical for implementing devices with broad operation bandwidths, e.g., broadband FWM or SPM devices based on phase matching. [2,4] The bandgap of GO can be engineered by using different reduction methods to change the ratio of the sp 2 and sp 3 fractions, [104,105] thus yielding a variation in its material properties. Figure 2a compares the atomic structures of graphene, GO, reduced GO (rGO), and totally reduced GO (trGO). As can be seen, with the continued removal of the OCFGs, GO gradually reduces and finally converts to trGO. As compared with graphene, trGO has a similar carbon network but with more defects. The differences in the properties of trGO and graphene mainly come from these defects, which can form not only during the reduction process but also the oxidation process associated with the conversion from graphene to GO. [106,107] Figure 2b) compares the measured n, k of GO, rGO, trGO, and graphene. [79,108] As the degree of reduction increases, both n and k of rGO increase and show a trend towards graphene, with the n and k of trGO being extremely close to those of graphene. In contrast to bulk materials that have limited tuning ranges with respect to n and k (e.g., typically on the order of 10 −4 -10 −3 for n of Si [24] ), GO has a very wide tuning range for both n (from ≈2 to ≈2.7) and k (from < 0.01 to ≈2), which underpins many photonic devices that have excellent phase and amplitude tuning capabilities. [79,108] Similar to graphene and TMDCs, [109][110][111] GO films exhibit strong anisotropy in its optical absorption in a broad band from the visible to the infrared regions. [64,112] This property is useful for implementing polarization selective devices with wide operation bandwidths.
1.60 μm × 0.66 μm, and 2.00 μm × 1.50 μm, respectively. Figure 3a shows schematics of the hybrid waveguides. For comparison, we choose integrated waveguides with planarized top surfaces with each waveguide coated with 1 layer of GO film (≈2 nm in thickness [56,57] ). Unless elsewhere specified, the bare integrated waveguides in our following discussions are the same as those in Figure 3a. Figure 3b shows the transverse electric (TE) mode profiles for the hybrid waveguides, which were simulated via commercial mode solving software using the measured n of 2D layered GO films at 1550 nm in refs. [79,108]. Due to the significant anisotropy of 2D materials, the in-plane lightmatter interaction is normally much stronger than the out-of- plane interaction. [64,110] Therefore, in nonlinear integrated photonic devices incorporating 2D materials, the TE polarization is usually chosen to support the in-plane interaction between the 2D films and the evanescent field leaking from the waveguides. Figure 3c compares the refractive indices of GO, Si, Si 3 N 4 , Hydex, and SiO 2 over a wavelength range of 1500-1600 nm measured by spectral ellipsometry. GO has a refractive index that is higher than either Hydex or SiO 2 , but lower than Si 3 N 4 and Si. Si has the highest refractive index amongst the three waveguide materials, which results in the tightest light confinement in the waveguide and hence the smallest waveguide geometry. It should also be noted that the refractive index n of GO in Figure 3c only shows results for a film with 5 GO layers. For practical GO films, both their linear and nonlinear optical properties slightly change with layer number (i.e., film thickness), mainly due to the scattering loss stemming from film unevenness and imperfect contact between adjacent layers as well as the defects, impurities, and thermal dissipation in the multi-layered film structure. [41] The trends of the properties of layered GO films in evolving from 2D monolayers to quasi bulk-like behavior have been observed in refs. [58] and [64]. In our following theoretical analysis, we use the experimentally measured material property parameters and account for the dependence of GO film's properties on the layer number. Figure 3d shows the dispersion of the bare Si, Si 3 N 4 , and Hydex waveguides without GO films. The dispersion of the GOcoated Si waveguide is also shown for comparison. All the dispersions were simulated using the refractive indices in Figure 3c. The bare Si waveguide has normal dispersion, whereas the bare Si 3 N 4 and Hydex waveguides have slight anomalous dispersion. After coating with GO films, the GO-Si hybrid waveguide has a slightly reduced normal dispersion, while the GO-Si 3 N 4 and GO-Hydex waveguides exhibit slightly enhanced anomalous dispersion (not shown in Figure 3d) since the curves for these wavegudies almost overlap with those of the uncoated waveguides), indicating that incorporating GO films could benefit phase matching for FWM or SPM in these waveguides.
Figures 3e,f show the ratios of power in GO relative to the power in the waveguide core for different numbers of GO layers N, respectively, which were calculated based on the simulated TE mode files for the hybrid waveguides, assuming that the GO film thickness is proportional to N. The thickness of the GO film was assumed to be proportional to N in the simulation. For the hybrid waveguides with the same GO layer number, GO-Si waveguide has the strongest evanescent field leakage and mode overlap with the GO film, mainly a result of its smaller waveguide geometry. All the hybrid waveguides show an increased mode overlap with the GO films as N increases, reflecting the fact that the increase of GO film thickness can enhance the interaction between light and GO.
In Figure 4a, we compare the linear propagation loss of the hybrid waveguides versus GO layer number N, which was calculated by commercial mode solving software using the measured k of 2D layered GO films at 1550 nm in refs. [79,108]. For practical GO films, the value of k slightly increases with N, which mainly results from the accumulated film imperfections induced by film unevenness, stacking of multiple layers, and localized defects. [57,64] As can be seen, the GO-Si waveguide has a much higher propagation loss than comparable GO-Si 3 N 4 and GO-Hydex waveguides, and all of these waveguides show an increased propagation loss with increasing N. This is similar to the results shown in Figure 3e, indicating that an enhanced GO mode overlap results in increased linear propagation loss. Mode overlap plays an important role in balancing the trade-off between enhancing the third-order optical nonlinearity while minimizing linear loss to achieve the optimized performance for the GO hybrid waveguides, which has been discussed in detail in refs. [113,114].
The linear propagation loss of practical GO hybrid waveguides exposed to air can change with input light power, especially at high average powers. [55,58] Such power-dependent linear loss (PDLL) results from power-sensitive photo-thermal changes in the GO films, including a range of effects such as photothermal reduction, thermal dissipation, and self-heating in the  GO layers. [55,58,115] The photo-thermal changes arising from these sources show some interesting features. First, in a certain power range where the light power is not sufficiently high to induce permanent changes in the films, the changes can recover back when the light power is turned off. Second, their time responses (typically on the order of 10 −3 s [55] ) are much slower than those of the ultrafast third-order nonlinear optical processes (typically on the order of 10 −15 s [11,38] ). Finally, these changes are sensitive to the average light power in the GO films, and so are easily triggered by continuous-wave (CW) light with high average power. In contrast, for optical pulses with a high peak power but a low average power, the PDLL induced by these changes is not obvious. [55,58] Figures 4b-d compare the excess linear propagation loss induced by the PDLL (∆PL PDLL , after excluding the corresponding linear propagation loss in Figure 4a) versus average power of input CW light for the hybrid GO-Si, GO-Si 3 N 4 , and GO-Hydex waveguides, respectively. The ∆PL PDLL increases with both the GO film thickness and the average power for all the hybrid waveguides, reflecting the fact that there are more significant photo-thermal changes in thicker GO films, and particularly at higher average powers. The GO-Si waveguide shows much higher ∆PL PDLL than the GO-Si 3 N 4 and GO-Hydex waveguides with the same GO layer number-a result also arising from its stronger GO mode overlap that allows for a higher power in the GO film.

Nonlinear Optical Properties
Upon interaction with an external optical electric field having a high intensity, on the order of interatomic fields (i.e., 10 5 -10 8 V m -1 [49] ), materials can exhibit nonlinear optical responses accompanied by novel phenomena such as the generation of new frequencies, or with their linear optical parameters such as n and k becoming field-dependent. [116] In the past decade, the superior nonlinear optical properties of 2D materials have been widely investigated and recognized. [48,49,52,117] For GO, its heterogeneous structure and tunable bandgap enable distinctive nonlinear optical properties for a diverse range of nonlinear optical processes. [55,56,58,64] Generally, the nonlinear response of a material excited by an external optical field (E(t), scalar) can be expressed as (in scalar form for brevity, and in the dipole approximation) [2,48] where P(t) (scalar) is the light induced polarization, 0 is the vacuum permittivity, and (i) (i = 1, 2, 3, …) are the i th -order optical susceptibilities, which generally are tensors of rank (i + 1).
In Equation (1), (1) describes the linear optical properties such as n and k, while the material's nonlinear optical properties including the second-order, third-order, and higher-order nonlinear responses are described by (2) , (3) , and (n) (n ≥ 4), respectively. Since the value of (i) normally decreases rapidly with i, the efficiency of (n) (n ≥ 4) processes is much lower than that of (2) and (3) processes which dominate applications based on the materials' optical nonlinearities. Note that the susceptibilities in Equation (1) are complex, with the real and imaginary parts corresponding to the changes of the refractive index and optical absorption, respectively.
In this paper, we focus on GO's third-order optical nonlinearity, highlighting the on-chip integration of GO films for both enhanced Re ( (3) ) and Im ( (3) ) processes. For the second-order optical nonlinearity, we note that large (2) values of GO arising from its noncentrosymmetric atomic structure have been reported recently, [118,119] but its application to chip-scale devices is still in its infancy. Therefore, we provide a discussion on the future perspectives for this in Section 7.
The Re ( (3) ) processes (also termed parametric processes [2,48] ), represented by four-wave mixing (FWM), self-/cross-phase modulation (SPM/XPM), and third harmonic generation (THG), play an integral role in all-optical signal generation and processing with an ultrafast time response on the order of femtoseconds. [6,120,121] In Table 1, the Kerr coefficients (n 2 ) of relevant materials are also compared. The absolute value of n 2 for GO is about 10 times lower than that of graphene but still much higher than those of MoS 2 , WSe 2 , and BP. On the other hand, the n 2 of GO is about 4-5 orders of magnitude higher than Si, Si 3 N 4 , and Hydex, and so this forms the motivation for the on-chip integration of GO to implement hybrid devices for third-order nonlinear optical applications. The performance of hybrid nonlinear optical devices is a combined result of several factors, including not only the materials' optical nonlinearity but also their loss, dispersion, and mode overlap. Detailed comparison of the nonlinear optical performance of the bare and GO-coated integrated waveguides will be provided in Section 5.
For many nonlinear optical processes, the terms arising from Im ( (3) ) involve nonlinear optical absorption such as two-photon absorption (TPA), saturable absorption (SA), or multi-photon absorption (MPA). [2,48] The relatively large bandgap of GO results in low TPA in the telecom band that is helpful for improving the efficiency for the Re ( (3) ) processes. [2,3] In contrast to the TPA process where the absorption increases with light intensity, SA exhibits the opposite trend, due to the saturation of excited electrons filling the conduction band and hence preventing further transitions due to Pauli blocking. [53,122] In Table 1, the negative for GO is induced by SA, which originates from the groundstate bleaching of the sp 2 domain. [63,123,124] The SA in GO is useful for applications such as mode-locked fiber lasers [125][126][127] and all-optical modulators. [11,128] The bleaching of light absorption at high intensities is also beneficial for boosting processes arising from the Re ( (3) ). Compared to the photothermal changes mentioned in Section 2.1, SA is an ultrafast third-order nonlinear op-tical process determined by the peak input light power, and so it is more easily triggered by optical pulses with high peak powers. In contrast, the SA-induced loss change is not as observable for CW light with relatively low peak powers. In a passively modelocked fiber laser, the saturable absorber in the fiber loop attenuates the low-intensity light but transmits the high-intensity light when the cavity oscillates, which allows for suppression of weaker pulses in addition to the continuous background light and selective amplification of the high-intensity spikes. GO and rGO featuring broadband absorption and ultrafast recovery times have been used as high-performance saturable absorbers in modelocked fiber lasers. [127,129,130] As mentioned in Section 2.1, the bandgap of GO can be changed by using different reduction methods. [104,105] By increasing the degree of reduction, a switch in sign for both n 2 and of GO films has been observed during the transition from GO to trGO. [62,63] The large dynamic tunable ranges for n 2 and provide high flexibility in tailoring the performance of nonlinear integrated photonic devices incorporating GO.
Figures 5a−c compare the excess propagation loss induced by GO's SA (∆PL SA , after excluding the corresponding linear propagation loss in Figure 4a) versus peak input power of the optical pulses (P pk ) for the hybrid GO-Si, GO-Si 3 N 4 , and GO-Hydex waveguides, respectively. These results were calculated based on the SA theory in refs. [70,131] using the measured SA parameters for practical GO films in ref. [56]. For all the hybrid waveguides, ∆PL SA becomes more significant for increasing number of layers and input peak power, reflecting more significant SA in thicker GO films and at higher peak powers. Similar to the trend seen in Figure 4, GO-Si waveguides with stronger mode overlap show higher ∆PL SA than the GO-Si 3 N 4 and GO-Hydex waveguides for the same number of GO layers.
Figures 6a-c compare the overall excess insertion loss induced by SA (∆SA), after excluding the corresponding linear insertion loss, as functions of P pk and waveguide length L for the uniformly coated GO-Si, GO-Si 3 N 4 , and GO-Hydex waveguides, respectively. In each figure, the results for five different GO layer numbers calculated based on the corresponding results in Figure 5  are provided. To highlight the difference, different ranges for the waveguide length were chosen in Figures 6a − 6c. It is seen that ∆SA increases with both GO layer number and input peak power, which is consistent with Figure 5. In addition, ∆SA also increases with waveguide length, reflecting a more significant SA-induced insertion loss difference for longer waveguides.

On-Chip Integration of GO Films
The distinctive material properties of GO have motivated its onchip integration for implementing functional hybrid integrated devices. [64,[132][133][134] The facile solution-based synthesis process of GO and its high compatibility with integrated device fabrication offer competitive advantages for industrial manufacturing beyond laboratory, which has thus far been a challenge for the majority of 2D materials. In this section, we review the fabrication techniques for integrating GO films on chips, which are divided into GO synthesis, film coating on chips, and device patterning.

GO Synthesis
Material synthesis is the first step before integrating GO films onto chips. In contrast to graphene that has very low solubil-ity in water, GO can be dispersed in aqueous and polar solvents, thus allowing for solution-based material synthesis. The Brodie method [135] and the Hummers method [136] are the two basic GO synthesis approaches, both of which have long histories and have been modified on the basis of the initially proposed methods. [65,137] Figures 7a,b show schematic illustrations of these two methods. For the Brodie method, graphite is treated with fuming nitric acid (HNO 3 ) and potassium chlorate (KClO 3 ) in order to attach the OCFGs (Figure 7a), whereas for the Hummers method, the oxidation of graphite is achieved via treatment with potassium permanganate (KMnO 4 ) and sulfuric acid (H 2 SO 4 ) (Figure 7b). Compared to the Brodie method, the Hummers method is more facile and shows better compatibility with CMOS fabrication technologies. Figures 7c,d show another two GO synthesis approaches that are well known for the GO community-the Staudenmaier method and the Hofmann method. Both of these are modifications of the Brodie method, with slight changes in the procedure intended to produce highly oxidized GO. [138,139] The former uses a mixture of concentrated fuming HNO 3 and H 2 SO 4 followed by adding KClO 3 , whereas the latter uses concentrated HNO 3 in combination with concentrated H 2 SO 4 and KClO 3 . Some modified Hummers methods have also been proposed, [65,140] where the amount of KMnO 4 and H 2 SO 4 were engineered to improve the oxidation efficiency and hence the oxidation degree.
The above methods can produce a large volume of exfoliated GO sheets with a high concentration of OCFGs, which are easily disintegrated into smaller flakes. The lateral size (typically varying from several tens of nanometers to several tens of microns) and thickness (typically on the order of nanometers) of the GO flakes can be controlled by varying the mixing or sonication parameters. GO films consisting of large-size (>10 μm) flakes show better performance in terms of electrical/thermal conductivity as well as mechanical/sieving capability, whereas GO films made from small-size flakes are advantageous in achieving conformal coating on substrates with complex structures, particularly for integrated devices having feature sizes on the micron or nanometer scale.

Film Coating on Chips
The second step is to coat GO films onto integrated chips. In contrast to sophisticated film transfer processes used for the on-chip integration of graphene and TMDCs, the coating of GO films can be realized using solution-based methods without any transfer processes. Figure 8 shows schematic illustrations of two typical GO film coating strategiessolution dropping and self-assembly. Both of these are compatible with the Brodie and the Hummers methods and are suited to large-scale fabrication, but they also show differences, particularly with respect to film uniformity and thickness.
Solution dropping methods, mainly including drop casting [142] and spin or spray coating, [143,144] are simple and rapid to directly coat GO films in large areas. The main steps in these methods include solution preparation, solution dropping, and drying (Figure 8a). The relatively low film uniformity and large film thicknesses are the main limitations for these methods, which make it challenging to achieve film conformal coating of integrated     [112] Copyright 2014, OSA Publishing, reproduced with permission. [146] Copyright 2018, Elsevier Ltd, and reproduced with permission. [144] Copyright 2010, American Chemical Society. The sample images in (b) are reproduced with permission. [79] Copyright 2019, American Chemical Society.
waveguides. The typical film unevenness that they produce is >10 nm, and the typical film thicknesses are >100 nm. [112,145] In contrast to solution dropping methods, self-assembly methods can achieve both high film uniformity (< 1 nm [79] ) and low film thickness (down to the thickness of 2D monolayers [64] ). Figure 8b shows the process flow for self-assembly. First, a GO solution composed of negatively charged 2D GO nanoflakes synthesized via the Brodie or the Hummers methods is prepared. Second, the target integrated chip with a negatively charged surface is immersed in a solution with positively charged aqueous polymers to obtain a polymer-coated integrated chip with a positively charged surface. Finally, the polymer-coated integrated chip is immersed in the prepared GO solution, where a GO monolayer is formed onto the top surface through electrostatic forces. By repeating the above steps, layer-by-layer coating of GO films on integrated chips can be realized, with high scalability and accurate control of the layer number or the film thickness. The strong electrostatic forces also enable conformal film coating of complex structures (e.g., wire waveguides and gratings) with high film uniformity. In addition, unlike film transfer approaches where the coating areas are limited by the lateral size of the exfoliated 2D films, [147,148] the film coating area for the self-assembled methods is limited only by the size of the substrate and the solution container, which makes them excel at large-area film coating. By using plasma oxidation, the removal of GO films coated from integrated devices can be easily achieved, allowing for the recycling of the integrated chips and recoating of new GO films.

Device Patterning
Device patterning is critical for engineering functionalities of advanced integrated devices. In Figure 9, we summarize the typical methods used to pattern GO films, including inkjet printing, laser writing, lithography followed by lift-off, pre-patterning, and nanoimprinting. All of these methods have strong potential for Laser Photonics Rev. 2023, 17, 2200512 Figure 9. Schematic illustration of typical methods for patterning GO films: a) inkjet printing, b) laser writing, c) lithography & lift-off, d) pre-patterning, e) nanoimprinting, and f) scan-probe lithography. In a-f), the figure in the right side of each row shows an image for as-fabricated samples. The sample images in a-f) are reproduced with permission. [164] Copyright 2011, Springer Nature, reproduced with permission. [132] Copyright 2019, Springer Nature, reproduced with permission. [58] Copyright 2020, Wiley-VCH, reproduced with permission. [152] Copyright 2020, Springer Nature, reproduced with permission. [165] Copyright 2011 American Vacuum Society, and reproduced with permission. [154] Copyright 2020, Springer Nature, respectively.
industrial manufacturing, and each of them has advantages for specific applications. In Table 2, we compare the different GO film patterning methods.
Inkjet printing is a simple and rapid GO film patterning method that can simultaneously achieve film coating and patterning. It is compatible with solution dropping coating methods, and is usually employed to fabricate patterns over large areas, with relatively low resolution on the order of microns. [149,150] Figure 9a shows the process flow, where specialized ink solutions need to be prepared before printing. The printing processes involve forming a jet of single droplets, drop casting, and droplet drying, similar to solution dropping methods, with the pattern shape and position normally controlled via programs.
Laser writing is a one-step, noncontact, and mask-free film patterning method that has been widely used for patterning polymers, [156,157] metal surfaces, [158,159] and 2D materials. [160,161] Figure 9b illustrates the process flow for patterning GO films using laser writing. The laser source can consist either of CW or pulsed lasers, with an objective lens used to focus the laser beam. Laser writing involves complex processes such as photochemical reduction, thermal melting/sublimation, and structural reorganization, [162] ultimately resulting in localized thinning or ablation of GO films depending on the laser power. Laser writing can be used to pattern both thick films deposited by solution dropping and thin films coated via self-assembly, The patterning resolution is mainly determined by the spot size of the focused laser beam, which typically ranges from several microns to hundreds of nanometers. [163] One of the largest advantages of laser patterning is the flexibility. Because no mask is needed in the fabrication process, arbitrary patterns can be enabled by swiftly changing the controlling computer program, making this method perfect for pattern design and prototyping. Lithography followed by lift-off is another widely used GO film patterning method. [58,64] Unlike laser writing that performs patterning and etching simultaneously, for lithography the patterns are first formed on photoresist using well-developed techniques in the integrated circuit industry such as photolithography and electron beam lithography. The patterns on the photoresist are then transferred to GO films deposited on the photoresist via lift off processes that are common for fabricating integrated metal electrodes (Figure 9c). Compared to GO films coated via solution dropping, films formed by self-assembly show a better lift-off outcome owing to their strong adhesion to the substrates enabled by the electrostatic forces. The patterning resolution is determined by both the lithography resolution and the film property. For visible, ultraviolet, deep ultraviolet (DUV) photolithography, the patterning resolution is mainly limited by the lithography resolution (typically > 300 nm), which is much larger than the sizes of the exfoliated GO nanoflakes (typically ≈50 nm). For electron beam lithography with a higher patterning resolution (typically < 100 nm), the influence of the GO film thickness and flake size becomes more prominent, especially when the minimum feature size is < 150 nm. [64] Direct coating of GO films onto prepatterned structures, or prepatterning, is a simple method that can realize large-area GO film patterning. It relies on pre-fabrication to pattern the target substrates and conformal coating of GO films (Figure 9d), thus being suitable for the self-assembled GO films. [152] Prepatterning is normally used for mass producing repetitive patterns. Similar to lithography followed by lift off, the patterning resolution is mainly limited by the minimum gap width of the pre-patterned structure when it is >300 nm, and the GO film thickness and flake size when it is <150 nm.
Nanoimprinting is a film patterning method that can achieve a very high patterning resolution (e.g., down to ≈10 nm [166] ). Similar to lithography followed by lift off, it also needs to pattern photoresist before transferring the patterns onto the GO films. Instead of using photolithography or electron beam lithography, prefabricated imprint molds are employed to pattern the photoresist (Figure 9e). To fabricate different patterns, different molds are required, therefore this approach is mainly used for fabricating relatively simple and repetitive patterns. [153] Scanning probe lithography (SPL) is another technique that has been employed to directly pattern GO films, [154,155] where the patterning was realized by using a scanning probe tip to induce localized reduction, thinning, or ablation of GO films (Figure 9f). Similar to laser writing, the SPL process does not need any mask or photoresist, and the pattern can be controlled via computer program. Unlike laser writing that normally has a patterning resoultion >300 nm, the patterning resolution of SPL can reach below 100 nm (e.g., ≈12 nm [154] ), which is mainly limited by the size of the employed probe tip.
Finally, it is worth mentioning that the fabrication techniques used to incorporate GO films in Figures 7-9 are not limited to nonlinear integrated photonic devices. Rather, they are universal and can be used to fabricate other integrated photonic devices such as polarizers, [64,167] lenses, [108,168] and sensors, [169,170] and also integrated electronic devices such as field-effect transistors, [169,171] supercapacitors, [172,173] and solar cells. [174,175] For nonlinear integrated photonic devices, selfassembly methods are more widely used than solution dropping methods, mainly due to the high film uniformity and low film thickness they can achieve, which result in low film loss that is desirable for boosting nonlinear optical processes such as FWM and SPM. It should also be noted that the properties of GO and rGO films are affected by the fabrication methods. As a result, the quality and consistency of synthesized materials in practical settings vary widely. For practical GO and rGO films, their linear optical properties can be quantified by refractive index n and extinction coefficient k measured via spectral ellipsometry, [79] and their nonlinear optical properties can be quantified by Kerr coefficient n 2 and nonlinear absorption coefficient characterized via Z-scan measurements. [63,176,177] The reduction degree of GO can be quantified by a few parameters such as the C-O ratio, the I D /I G ratio, and the I 2D /I G ratio. [178,179] The first one can be mea-Laser Photonics Rev. 2023, 17, 2200512 www.advancedsciencenews.com www.lpr-journal.org sured via the X-ray photoelectron spectroscopy, whereas the last two can be obtained from Raman spectroscopy.

Enhanced Nonlinear Optics in GO Hybrid Integrated Devices
The large optical nonlinearity and low loss of GO, along with its facile fabrication processes for large-scale and highly precise onchip integration, have enabled many hybrid integrated devices with superior nonlinear optical performance. [55][56][57][58]119,129] In this section, we summarize the state-of-the-art nonlinear integrated photonic devices incorporating GO.
As a typical third-order process, FWM has been widely exploited for all-optical signal generation, amplification, and processing. [4,28,33,67,180] Enhanced FWM in GO hybrid integrated devices was first demonstrated using Hydex waveguides, [57] where FWM measurements were performed for 1.5 cm long waveguides uniformly coated with 1-5 layers of GO. A maximum conversion efficiency (CE) of ≈-47.1 dB that corresponded to a net CE enhancement of ≈6.9 dB was achieved for the device with 2 layers of GO (Figure 10a).
Enhanced FWM in Hydex microring resonators (MRRs) with patterned GO films was subsequently demonstrated. [58] Benefitting from the resonant enhancement in the MRRs, a maximum CE of ≈-38.1 dB that corresponded to a CE enhancement of ≈10.3 dB was achieved for a MRR with a patterned film including 50 GO layers (Figure 10b). Based on the FWM measurements, the change in n 2 of GO films as a function of the layer number and light power was also analyzed, showing interesting trends in evolving from 2D materials to bulk-like behavior. Following the experimental demonstration, detailed theoretical analyses and optimization were performed in ref. [114] showing that CE enhancement up to ≈18.6 dB can be achieved by optimizing the GO coating length and coupling strength of the MRR.
Enhanced FWM in GO-Si 3 N 4 waveguides has also been demonstrated, [55] where FWM measurements were carried out for GO-coated planarized Si 3 N 4 waveguides having different GO film lengths and thicknesses, achieving a maximum CE of ≈-56.6 dB that corresponded to a CE improvement of ≈9.1 dB for a device with a 1.5 mm long patterned film including 5 GO layers (Figure 10c). The patterned device also showed a broadened conversion bandwidth compared to the uncoated and uniformly coated devices. A detailed analysis of the influence of the GO film parameters and the Si 3 N 4 waveguide geometry was provided in ref. [113] showing that the CE enhancement can be further increased to ≈20.7 dB and the conversion bandwidth can be improved by up to 4.4 times.
SPM is another fundamental third-order process that has wide applications in wideband optical sources, pulse compression, frequency metrology, and optical coherence tomography. [181,182] Enhanced SPM in GO-Si waveguides has been reported, [56] where SPM measurements were performed for Si wire waveguides conformally coated with GO films having different lengths and thicknesses. Significant spectral broadening of picosecond optical pulses after passing these waveguides was observed, showing a maximum broadening factor (BF) of ≈4.34 for a device with 10 GO layers (Figure 10d). By coating GO films, the effective nonlinear figure of merit (FOM) of the hybrid waveguide was improved by up to 20 times compared to the bare Si waveguide. According to theoretical calculations based on the experimental results 1, a maximum BF of ≈27.8 can be achieved by optimizing the GO film parameters and Si waveguide geometry. In addition to enhanced SPM, strong SA in the GO-coated Si waveguide was also observed, as evidenced by a decrease in the measured excess insertion loss relative to the bare Si waveguide for an increased pulse energy (Figure 10e). It was also observed that the hybrid waveguides with thicker GO films showed a more prominent SA, although at the expense of higher linear loss.

Comparison of Different Integrated Platforms Incorporating GO
As reviewed in Section 4, enhanced nonlinear optical responses have been achieved for integrated Si, Si 3 N 4 , and Hydex devices incorporating GO. In this section, we provide a detailed comparison of the nonlinear optical performance of these integrated platforms. We compare FWM using CW light and SPM-induced spectral broadening using optical pulses in GO-coated Si, Si 3 N 4 , and Hydex waveguides. We used the material parameters obtained from experimental measurements [55][56][57] to calculate the FWM and SPM performance parameters based on the theory in refs. [183][184][185][186] and accounted for the variation in loss arising from photo-thermal changes and SA in the GO films. The comparisons of the nonlinear figure-of-merits for different GO hybrid waveguides are also provided. Figure 11 shows the FWM CE as a function of waveguide length L and pump power P p for hybrid Si, Si 3 N 4 , and Hydex waveguides uniformly coated with GO films. Similar to Figure 6, we show the results for 5 different numbers of GO layers (i.e., N = 1, 2, 5, 10,20). For each of the hybrid waveguides, the CE increases with P p , while as a function of L, it first increases and then decreases, reaching a maximum value at an intermediate waveguide length. As the layer number N increases, the L corresponding to the maximum CE becomes smaller. These trends reflect the trade-off between third-order nonlinearity improvement and propagation loss increase for the hybrid waveguides, with the former dominating for relatively small N and L, and the latter becoming more obvious as N and L increase. For the waveguides with the same N, the CE of the GO-Si waveguide is much higher than the GO-Si 3 N 4 and GO-Hydex waveguides, although its waveguide length is shorter. This can be attributed to the larger third-order optical nonlinearity of Si as well as the stronger GO mode overlap in the GO-Si waveguide. Figure 12 compares the CE enhancement (∆CE) of the hybrid waveguides relative to the uncoated waveguides. In Figure 12a, we show the results for the waveguides uniformly coated with GO films. For all of these hybrid waveguides, the CE enhancement decreases with waveguide length L, reflecting the fact that a shorter length yields better CE enhancement. For the waveguides coated with thicker GO films, although the initial CE enhancement (at very small L) is higher, it decreases more rapidly with L, thus resulting in a decreased range of L with positive CE enhancement. Figure 12b presents the corresponding results for the waveguides with patterned GO films, where the length of the uncoated waveguide is fixed at L, and the GO film coating length L c varies from 0 to L. Similar to the relation between CE and L in Figure 11, the CE enhancement reaches a maximum for an  Reproduced with permission. [57] Copyright 2018, AIP Publishing. b) Reproduced with permission. [58] Copyright 2020, Wiley-VCH. c) Reproduced with permission. [55] Copyright 2020, Wiley-VCH. d,e) Reproduced with permission. [56] Copyright 2020, American Chemical Society. Rev. 2023, 17, 2200512 www.advancedsciencenews.com www.lpr-journal.org   intermediate L c , and the L c corresponding to the highest ∆CE decreases with GO layer number N. This also results from the trade-off between the third-order nonlinearity and loss. The CE enhancement of GO-Si waveguides is lower than the GO-Si 3 N 4 and GO-Hydex waveguides, in contrast to a higher CE achieved for the GO-Si waveguides in Figure 11. This reflects an interesting trade-off between achieving high relative CE enhancement versus high overall CE in these GO hybrid integrated waveguides. Figure 13 shows SPM-induced spectral evolution of optical pulses traveling along the hybrid Si, Si 3 N 4 , and Hydex waveguides uniformly coated with GO films. For comparison, we show the BFs at an intensity attenuation of -20 dB (i.e., BF -20 dB ) for different waveguides, together with the corresponding propagation lengths (L p ). For each of the hybrid waveguides, BF -20 dB first increases and then decreases with GO layer number N, achieving a maximum spectral broadening at an intermediate film thickness. As N increases, L p decreases and the optical pulses vanish at shorter propagation lengths, reflecting that the loss increase becomes dominant for the waveguides with longer lengths or thicker GO films. Similar to Figure 11, the larger n 2 of Si and stronger GO mode overlap result in the GO-Si waveguides showing a much more significant spectral broadening than comparable GO-Si 3 N 4 and GO-Hydex waveguides even for shorter lengths. Unlike the symmetric spectral evolution in the GO-Si 3 N 4 and GO-Hydex waveguides, the spectral evolution in the GO-Si waveguides exhibits a slight asymmetry due to free-carrier effects in Si. Figure 14a compares the relative BF (rBF) versus waveguide length (L) for hybrid Si, Si 3 N 4 , and Hydex waveguides uniformly coated with GO films, where the rBF is defined as the ratio of the BF of the hybrid waveguide to that of the uncoated waveguide. Note that the BF here corresponds to the value at the waveguide output, which is different from BF -20 dB in Figure 13. For the GO-Si and GO-Si 3 N 4 waveguides with thicker GO films (N ≥ 5), the maximum rBF is achieved for an intermediate L, whereas for these waveguides with thinner GO films and all the GO-Hydex waveguides, the rBF monotonically increases with L. This is consistent with the trade-off between the third-order nonlinearity and loss in Figure 13. Figure 14b compares the rBF versus GO coating length (L c ) for the waveguides with patterned GO films, where the length of the uncoated waveguide is fixed at L, with L c varying from 0 to L. Similar to the trend in Figure 14a, the maximum rBF is also achieved for an intermediate L c for the GO-Si and GO-Si 3 N 4 waveguides when N ≥ 5. In contrast to the higher BF achieved for the GO-Si waveguides in Figure 13, their rBF is lower than the GO-Si 3 N 4 waveguides, which is similar to the trade-off between achieving a high relative CE enhancement and a high overall CE in Figures 11 and 12.

Laser Photonics
In Table 3 and Figure 15, we quantitatively compare the nonlinear optical performance of GO-Si, GO-Si 3 N 4 , and GO-Hydex waveguides, together with corresponding results for the bare integrated waveguides to highlight the benefit brought by incorporation of GO films into these integrated waveguides. We calculated two figure-of-merits, i.e., FOM 1 and Figure 14. a) SPM-induced relative BF (rBF) versus waveguide length (L) for hybrid Si, Si 3 N 4 , and Hydex waveguides uniformly coated with different numbers of GO layers. b) rBF versus GO coating length (L c ) for hybrid Si, Si 3 N 4 , and Hydex waveguides patterned with different numbers of GO layers. The lengths of the uncoated Si, Si 3 N 4 , and Hydex waveguides are L = 10 mm, L = 40 mm, and L = 16 cm, respectively. The patterned GO films are assumed to be coated from the start of the waveguides. In a,b), the parameters of the input optical pulses are the same as those in Figure 13.  The FOM 1 is defined in terms of nonlinear absorption, and it can be expressed as: [2,3] where n 2 and TPA are the effective Kerr coefficient and TPA coefficient of the waveguides, respectively, and is the light wavelength. The results of FOM 1 are provided in Table 3. It increases with GO layer number N, and the FOM 1 of GO-Si waveguide is lower than comparable GO-Si 3 N 4 and GO-Hydex waveguides. The former results from the increase in the third-order optical nonlinearity and the latter is due to the strong TPA of Si. The FOM 2 is defined based on the trade-off between thirdorder optical nonlinearity and linear loss. [187] It is a function of waveguide length L given by: where is the waveguide nonlinear parameter and L eff (L) = [1 -exp (-L × L)] / L is the effective interaction length, with L denoting the linear loss attenuation coefficient. Figures 15a,b show L eff and FOM 2 versus L for hybrid Si, Si 3 N 4 , and Hydex waveguides uniformly coated with 1 and 10 GO layers, respectively. Different ranges of L are chosen and the results for the bare waveguides (i.e., N = 0) are also shown. These results were calculated based on Equation (3) using the measured linear and nonlinear optical parameters of practical GO films in refs. [55,57,58]. For all of these hybrid waveguides, FOM 2 first rapidly increases with L and then increases more gradually as L becomes larger. For a small L, the FOM 2 's of the hybrid waveguides are higher than that of comparable uncoated waveguide, whereas when L becomes large enough, the FOM 2 of the uncoated waveguide gradually approaches and even surpasses those of the hybrid waveguides. This reflects that the negative influence induced by increased linear loss becomes more dominant as L increases, which are consistent with the results in Figures 11-14. In contrast to FOM 1 , the FOM 2 of GO-Si waveguide is higher than comparable GO-Si 3 N 4 and GO-Hydex waveguides, mainly due to the large n 2 of Si and its strong GO mode overlap.

Comparison of Nonlinear Integrated Devices Incorporating Different 2D Materials
In the past decade, many nonlinear integrated photonic devices incorporating different kinds of 2D materials have been demonstrated, showing improved performance than comparable devices without 2D materials. In Table 4, we provide a summary of these devices for applications based on a variety of nonlinear optical processes such as FWM, SPM, XPM, SHG, DFG, and SA. Compared to integrated waveguides incorporating other 2D materials, GO hybrid waveguides have lower linear propagation loss. Further, the highly precise control of the film size and thickness, along with the capability for conformal coating on complex structures, offers unique advantages in engineering and optimizing the performance of GO hybrid integrated devices. Given the high flexibility in changing the properties of GO, the potential for performance optimization is even larger, and the variety of GO based nonlinear integrated photonic devices is well beyond those based on a single 2D material.
In future research on GO nonlinear integrated photonic devices, some unexplored third-order optical nonlinear processes such as THG and XPM, various second-order nonlinear optical processes, and the comparison between the performance of nonlinear integrated photonic devices incorporating rGO and graphene will potentially be very hot topics, and similar work on integrated photonic devices incorporating graphene and TMDCs in Table 4 could provide a guidance for the design of experiments and for performance comparison.

Challenges and Perspectives
As discussed above, GO has distinct nonlinear optical properties with excellent compatibility with different integrated platforms, yielding many high-performance hybrid nonlinear integrated photonic devices. Despite the current successes, this is just the beginning of a huge field, there is still much room for future improvement in material properties, device fabrication, and in creating new applications. In this section, we discuss the challenges and perspectives for fully exploiting the significant potential of GO for nonlinear integrated photonics.
Most of the state-of-the-art GO nonlinear integrated photonic devices incorporate GO films with little modification or optimization of their properties. The reality, however, as discussed in Section 2, is that GO's properties can be significantly changed by manipulating the OCFGs. This offers a high degree of flexibility   in engineering its capabilities for different nonlinear optical processes. For example, a large optical bandgap of GO could benefit the FWM, SPM, and XPM processes by reducing the linear loss and nonlinear loss such as TPA. Whereas for SA, a small optical bandgap is often needed to enhance the light absorption and improve the modulation depth. As shown in Figure 16, the methods for tuning GO's material properties can be classified into two categories-reduction and doping. The reduction methods mainly involve thermal, [200] laser, [108,201] chemical, [202,203] or microwave based reduction. [178] Among them, thermal and laser reduction are simple and rapid, but usually suffer from limitations in terms of residual OCFGs and generated defects. Whereas chemical and microwave reduction show better capability in completely removing the OCFGs and well preserving the carbon network without introducing many defects. [200,201] By using wet chemistry and microwave reduction methods, [178,204] synthesizing high-quality rGO with properties extremely close to those of graphene has been realized. The synthesis of graphene-like materials via GO reduction can exploit the advantages offered by GO fabrication processes including a high production yield and a high CMOS compatibility, providing a viable solution for the mass production of graphene based devices.
In contrast to the removal of OCFGs that occurs during the reduction of GO, doping methods introduce foreign atoms such as nitrogen, boron, and sulfur into the chemical structure of GO, thus enabling new material properties. The doping methods mainly consist of laser, [105] chemical, [205] plasma, [206] and annealing based doping. [207] For laser doping, the doped area can be well controlled and patterned with a focused laser beam, but is often challenging for patterning large areas in a short time. In contrast, plasma, chemical, and annealing doping methods have shown strong ability to achieve highly efficient GO doping over large areas at the expense of a low patterning accuracy. [205][206][207] Although the linear propagation loss of the state-of-the-art integrated waveguides incorporating GO films is already over 100 times lower than comparable devices incorporating graphene, there is still significant room to reduce the loss even further. In principle, GO with a bandgap >2 eV has negligible linear absorption below its bandgap, e.g., at near-infrared wavelengths (with a photon energy of ≈0.8 eV at 1550 nm). The light absorption of practical GO films is mainly caused by defects as well as scattering loss stemming from imperfect layer contact and film unevenness. [57,64] The loss from these sources can be reduced further by modifying the GO synthesis and film coating processes, e.g., by using GO solutions with improved purity and optimized flake sizes. Reducing the linear loss of the GO films will not only enhance the performance of state-of-the-art GO FWM and SPM devices, but also facilitate many new nonlinear optical applications such as supercontinuum generation (SCG) [181,208] and optical micro-comb generation. [31,209] The current research on GO nonlinear integrated photonic devices mainly focuses on their large third-order optical nonlinearity. However, in addition to this, an excellent second-order optical nonlinearity of GO has been reported, [118,119] which will underpin future research on GO devices for many second-order optical nonlinear processes such as second-harmonic generation (SHG), sum/difference frequency generation (SFG/DFG), the Pockels effect, and optical rectification. Unlike the third-order optical nonlinearity that exists for all materials, the second-order optical nonlinearity can only occur in noncentrosymmetric materials or at the surface of centrosymmetric materials where the inversion symmetry is broken. [48,210,211] In contrast to graphene that has a centrosymmetric atomic structure, GO has a highly heterogenous atomic structure that yields a large second-order optical nonlinearity that can be tuned by changing the atomic structure of GO via reduction or doping methods. This, along with its high compatibility with integrated platforms, will enable functional second-order nonlinear integrated photonic devices with many applications, such as ultrafast signal processing and generation based on the SHG, [48] tunable terahertz plasmon generation based on the DFG, [194] high-speed electro-optic modulators based on the Pockels effect, [212] and broadband photodetectors based on the optical rectification. [213] The use of GO films as saturable absorbers in mode-locked fiber lasers has already been demonstrated, [47,48] and the SA in integrated waveguides incorporating GO has also been observed. [56] Although GO has a large optical bandgap with relatively low SA as compared with graphene, its SA capability can be improved by engineering the defect states in GO or by reducing it to obtain a graphene-like material. In the near future, integrated photonic devices incorporating GO or rGO with strong SA capability are expected to open new horizons for implementing on-chip mode-locked lasers, [214] broadband all-optical modulators, [128] pulse compression systems, [215] and photonic neural networks. [216] The overall nonlinear optical performance of GO hybrid integrated photonic devices depends on many factors related to GO's material properties, including not only nonlinear properties such as second-order or third-order optical nonlinearity and nonlinear light absorption, but also linear properties such as linear loss and dispersion. It is complicated by effects such as changes in GO's material properties with light power and film thickness. In the meantime, these extraordinary properties of layered GO films also yield a lot of new capabilities that cannot be achieved with conventional integrated devices made from only bulk materials, which allow more degrees of freedom to engineer the device performance and functionality.
As discussed in Section 2, there are photothermal changes in the GO films that result in the PDLL in practical GO films. In contrast to the reversible photothermal changes at low light powers, the loss increase induced by the photo-thermal changes can become permanent at high powers that exceed certain thresholds. The permanent loss increase of GO limits its use for high-power nonlinear optical applications. Recently, it was found that by us-ing an electrochemical method to modify the degree of oxidation of GO, [217] it can retain a high third-order optical nonlinearity with significantly improved (> 100 times) material stability under high-power laser illumination. In future work, the on-chip integration of this modified GO is promising to yield GO hybrid integrated photonic devices with superior power handling capability.
For practical GO films under light irradiation, different nonlinear optical processes coexist [218,219] and the interplay between these can result in complex behaviors. For example, the loss induced by TPA can deteriorate the FWM and SPM performance, whereas the reduced loss arising from SA could have a positive effect. In addition, different nonlinear optical processes may have different excitation conditions. For example, TPA occurs when the photon energy of incident light is larger than half of the material's bandgap, whereas SA can be efficiently excited when the single photon energy of incident light is just above the bandgap energy. In practical applications, the different nonlinear optical processes in GO need to be appropriately managed and balanced depending on the specific nonlinear optical application and the wavelength region of interest. For instance, the bandgap of GO can be engineered via reduction or doping to meet the requirements of specific nonlinear optical applications in specific wavelength regions.
Assembling different 2D materials to construct van der Waals heterostructures has ushered in many significant breakthroughs in recent years. [220,221] Due to the ease of fabrication and high flexibility for changing its properties, GO offers vast possibilities for implementing heterostructures based on different materials. Currently, some heterostructures including GO or rGO have been investigated, e.g., polymer / GO heterostructure, [222] titanium carbide/rGO heterostructure, [223] and vanadium pentoxide/rGO heterostructure. [224] However, the optical nonlinearity of GO or rGO heterostructures, particularly in the form of integrated devices, are yet to be investigated, hinting at more significant breakthroughs to come.
Phase matching is a prerequisite for achieving efficient nonlinear processes such as FWM, SPM, XPM, and THG. For GOcoated integrated waveguides, their waveguide dispersion can be engineered by reducing or patterning GO films to alleviate the phase mismatch. This would improve the FWM bandwidth and the SPM spectral broadening, and pave the way for broadband frequency comb generation [225,226] and SCG. [208,227] In materials with a positive Kerr coefficient n 2 (e.g., Si, Si 3 N 4 and Hydex glass), phase matching occurs for anomalous dispersion. This requires growing thick films to achieve anomalous dispersion in the telecom band, which has been a major challenge for Si 3 N 4 films due to stress-induced cracking. [29] Recently, laser-reduced GO films with negative values of n 2 have been reported. [62,63] In future work, it is anticipated that the use of rGO with a negative n 2 can reduce the phase mismatch in Si 3 N 4 waveguides with normal dispersion, which would lower the requirements for achieving phase matching in normal-dispersion devices, thus rendering them capable of playing more important roles in nonlinear optical applications.
Slot waveguides, with enhanced light-matter interaction enabled by the strong light confinement in the subwavelength slot regions, provide a better structure to exploit the material properties of GO. [33,228] Although GO has shown advantages in confor-Laser Photonics Rev. 2023, 17,2200512 mal coating integrated wire waveguides, [79] this is still challenging for narrow slot regions with widths < 100 nm and heights > 200 nm. This is mainly limited by the size of GO flakes used for self-assembly, which is typically ≈50 nm. By modifying the GO synthesis methods and using more vigorous ultrasonication, GO flakes with smaller sizes can be obtained, which are expected to address this issue and enable the implementation of GO hybrid slot waveguides with the significantly improved nonlinear optical performance. In addition to MRRs, [58] other resonant device structures can be employed to enhance the light-GO interaction based on the resonant enhancement effect, such as subwavelength gratings, [229] photonic crystal cavities, [36] and whisper-gallery-mode cavities. [230,231] Although there has been a lot of works investigating the nonlinear optical performance of GO and rGO, many of these have been semi-empirical. More physical insights, such as the anisotropy of the optical nonlinearity, the dependence of the nonlinear optical properties on the reduction/doping degree, and the interplay between Re ( (3) ) and Im ( (3) ) processes, remain to be explored. Previously, the optical nonlinearity of thick GO films (>1 μm) was characterized via the widely used Z-scan method, [62,63] However, for extremely thin 2D films (<20 nm), it is very difficult to accurately distinguish the weak response induced by the 2D films from the backgroud noise in the Z-scan measurements. Moreover, the ultrathin 2D films are easily damaged by the perpendicularly focused laser beam. The fabrication techniques for integrating GO films allow for precise control of their thicknesses and sizes, which yields new possibilities for investigating fundamental physical insights of 2D GO films. This, in turn, will also facilitate the full exploitation of the great potential of GO in nonlinear integrated photonic devices. This synergy will have a long-lasting positive impact, which will be a strong driving force for the continuous improvement of device performance and broadening of applications.
Accompanying the continuous improvement in the knowledge and control of GO's material properties as well as the development of its fabrication techniques, it is expected that many new breakthroughs in GO nonlinear integrated photonics will happen. The delivery of mass-producible hybrid nonlinear integrated photonic devices with significantly improved performance serves the common interest of many photonic industries, which will accelerate the applications of 2D materials out of laboratory and assure that the research in this area will benefit the broader community.

Conclusion
The on-chip integration of GO with a large optical nonlinearity and a high degree of flexibility in changing its properties represents a promising frontier for implementing high-performance nonlinear integrated photonic devices for a wide range of applications. In this paper, we review the progress in GO nonlinear integrated photonics. We summarize the optical properties of GO and the fabrication technologies for its on-chip integration. We review a range of GO hybrid integrated devices for different nonlinear optical applications, and compare the nonlinear optical performance of different integrated platforms. We also discuss the challenges and perspectives of this nascent field. Accompanying the advances in this interdisciplinary field, we be-lieve that GO-based nonlinear integrated photonics will become a new paradigm for both scientific research and industrial applications in exploiting the enormous opportunities arising from the merging of integrated devices and 2D materials.