Third-Order Optical Nonlinearities of 2D Materials at Telecommunications Wavelengths

All-optical signal processing based on nonlinear optical devices is promising for ultrafast information processing in optical communication systems. Recent advances in two-dimensional (2D) layered materials with unique structures and distinctive properties have opened up new avenues for nonlinear optics and the fabrication of related devices with high performance. This paper reviews the recent advances in research on third-order optical nonlinearities of 2D materials, focusing on all-optical processing applications in the optical telecommunications band near 1550 nm. First, we provide an overview of the material properties of different 2D materials. Next, we review different methods for characterizing the third-order optical nonlinearities of 2D materials, including the Z-scan technique, third-harmonic generation (THG) measurement, and hybrid device characterization, together with a summary of the measured n2 values in the telecommunications band. Finally, the current challenges and future perspectives are discussed.


Graphene and graphene oxide
Graphene, and its derivative, graphene oxide (GO), have been intensely studied due to their excellent mechanical, electrical, and optical properties [33,71,72].Graphene has a gapless band structure, in which the conduction and valence bands meet at the K point of Brillouin zone, resulting in its semimetal nature [31,44,73].In contrast, GO is an electronically hybrid material, featuring both conducting π-states from sp 2 carbon sites and a large energy gap between the σ-states of its sp 3 -bonded carbons [34,74].Their unique band structures result in novel electrical and optical properties, where for graphene, for example, the electrons and holes act as massless Dirac fermions resulting in extremely high carrier mobilities ( >10 5 cm 2 /Vs) even under ambient conditions [31].In contrast, GO exhibits a band gap that is tunable by adjusting the degree of reduction, which in turn affects the electric and optical properties.In addition, GO exhibits fluorescence in the near-infrared (NIR), visible and ultraviolet regions [34][35][36], which is very promising for light emitting devices.Moreover, the excellent nonlinear optical properties of both materials have been reported, including strong saturable absorption (SA) [75,76], a giant optical Kerr nonlinearity [58,59], leading to efficient self-phase modulation [77], FWM [78,79], as well as high harmonic generation [63].

Transition metal dichalcogenides
Transition metal dichalcogenides (TMDCs) with the formula of MX2 (where M is a transition metal and X is a chalcogen), is another widely studied family of 2D materials.
Different to the semimetal graphene, monolayer TMDCs, such as MoS2, MoSe2, WS2, and WSe2, are typically semiconductors that have bandgaps from 1 eV to 2.5 eV, covering the spectral range from the near infrared to the visible region [37,38].Moreover, TMDCs can exhibit a transition from direct-to indirect-bandgaps with increasing film thickness, resulting in strongly thickness-tunable optical and electrical properties.For instance, MoS2 exhibits layer-dependent photoluminescence, with monolayer films showing a much stronger photoluminescence [80].Monolayer hexagonal TMDCs also exhibit unique band structure valley-dependent properties, such as valley coherence and valley-selective circular dichroism [37,81], offering new prospects for novel applications in optical computing and information processing.For the nonlinear optical properties, TMDCs with odd numbers of layers have no inversion symmetry, and so exhibit a non-zero second-order (and higher even-order) nonlinearities that are absent in graphene and even-layer TMDCs [44,64].Recently, noble metal TMDCs, including PdSe2 and PtSe2, and PdTe2, have also attracted increasing interest in the fabrication of high performance electronic and optical devices, such as ultra-broadband photodetectors [39,40] as well as mode-locked lasers [82].

Black phosphorus
Black phosphorus (BP) is another attractive single element 2D layered material which has been widely studied.It has a puckered crystal structure, yielding a strong in-plane anisotropy in its physical properties in the "armchair" and "zigzag" directions, opening new avenues for anisotropic electronic and optoelectronic devices [44,45,83].Moreover, BP is a semiconductor that features a layer thickness dependent direct bandgap from 0.3 eV (bulk) to 2.0 eV (monolayer), bridging the gap between the zero-bandgap graphene and large-bandgap TMDCs [48,83].This broad bandgap tunability is very suitable for the photodetection and photonic applications from the visible to mid-infrared spectra regions [46,47,84].For the nonlinear optical properties, the layer thickness tunable and polarization dependent THG and optical Kerr nonlinearity have been demonstrated recently [65,83,85].Broadband SA has also been observed in BP, demonstrating its strong potential for ultrafast pulsed lasers [86][87][88].

Other emerging 2D materials
A wide range of other novel 2D low-dimensional materials have been investigated, including h-BN, MXenes, perovskites, as well as MOFs, which greatly enriches the family of 2D materials.h-BN is an electrical insulator with a large bandgap of around 5.9 eV [41,89] making h-BN a candidate for ultraviolet light applications.It also has an ultra-flat surface as well as excellent resistance to oxidation and corrosion, which are both highly useful as a dielectric or capping layer to protect the active materials or devices from degradation [41].
MXenes belong to another family of 2D materials, including 2D transition metal carbides, nitrides, and carbonitrides.Typically, the electronic structure of MXenes can be tuned by varying the surface functional groups.For instance, nonterminated Ti3C2 theoretically resembles a typical semimetal with a finite density of states at the Fermi level, whereas it can transition to a semiconductor when terminated with surface groups, such as OH and F groups [90].MXnens also exhibit superior optical properties, such as a high optical transmittance of visible light ( > 97% per nm) [38,91], and excellent nonlinear optical properties [57].
Organometal-halide perovskites have a general formula of ABX3, where typically A = CH3NH3 + , B = Pb 2+ , and X = I -, Br -, Cl -or mixtures [92].Due to their prominent photovoltaic features and luminescence properties, organometal-halide perovskite semiconductors have been widely used to design high performance solar cells as well as light-emitting diodes [51][52][53].Metal-organic frameworks (MOFs) are organic-inorganic hybrid porous crystalline materials with metal ions or metal-oxo clusters coordinated with organic linkers [93,94].Thanks to this unique structure, 2D MOFs exhibit enhanced photo-physical behaviour and are promising for various applications, from light emission and sensing to nonlinear optical applications [95,96].

Third-order optical nonlinearities of 2D materials in the telecommunications band
With their excellent third-order optical nonlinearities, 2D materials are promising functional materials for high-performance nonlinear optical devices.In this section, we review the different methods used to characterize their third-order nonlinear optical response.These include the Z-scan technique, THG measurement, and hybrid device characterization.We also summarize and compare the measured n2 values of different 2D materials in the telecommunications band.
A key component of χ (3) given by where n2 is the intensity-dependent refractive index change, known as the Kerr effect and the complex refractive index n can be expressed as [1,97]: where I is the light intensity, λ is the wavelength, n2 represents the Kerr coefficient or Kerr nonlinearity, α2 is the nonlinear absorption induced by the third-order susceptibility χ (3) , and n0 , α0 are the linear refractive index and absorption, respectively.
In this paper, we focus on χ (3) of 2D materials for key nonlinear processes that form the basis for ultra-high speed all-optical signal generation and processing, with response times on the order of femtoseconds [102,103].These include SPM and XPM, governed largely by n2 via the Re (χ (3) ), as well as FWM and THG that are mainly governed by the magnitude of |χ (3) |, although the latter are also sensitive to the complex value of χ (3) via phase-matching effects.The n2 component of χ (3) , accounts for two-photon absorption (TPA) via the Im (χ (3) ) and can also result in saturable absorption (SA).Both are intrinsic functions of the material's bandgap, but can also be influenced by free carrier effects.At photon energies well below the bandgap, all χ (3) components will become degenerate, but near, or above, the bandgap, they will in general be quite different.Finally, since nonlinear absorption is always present, it will affect the efficiency of all 3 rd order nonlinear optical processes, not just n2, even though it does not arise directly from other χ (3) components such as THG and FWM, for example.Further, these processes will generally scale differently with pump power to n2, and so the conventional nonlinear FOM may not be a useful benchmark.

Z-scan technique
Measuring the Kerr coefficient of a material is needed in order to design and fabricate nonlinear optical devices.The Z-scan method, introduced in the 1990s [104] is an elegant method to measure the third-order optical Kerr nonlinearity of a material.This technique involves open-aperture (OA) and closed-aperture (CA) measurements, which can be used to measure the third-order nonlinear absorption and nonlinear refraction, respectively.
CA Z-scan method is widely used to measure the nonlinear refractive index (Kerr coefficient) of an optical material.The valley-peak and peak-valley transmission curves are the typical results of the CA measurement, as shown in Figure 2(a).When the nonlinear material has a positive nonlinear refractive index (n2 > 0), self-focusing will occur which results in the valley-peak transmission curve.The peak-valley CA curve arises from de-focusing and occurs with a negative nonlinear refractive index (n2 < 0).The beam is focused onto the sample with a lens or an objective.During the measurements, samples are oriented perpendicular to the beam axis and translated along the Z axis with a linear motorized stage.For the measurements of small micrometer sized samples, a high-definition charge-coupled-device imaging system can be employed to align the light beam to the target area.Two PDs are employed to detect the transmitted light power for the signal and reference arms.
For the CA Z-scan method, the normalized transmittance can be written as [62,104]: where  = / 0 ,  0 =  0 2 /2 with  0 the beam waist radius and k the wave vector.
∆Φ 0 represents the on-axis phase shift at the focus, is defined as [62,104]: In equation (5),   = (1 −  − )/, with L denoting the sample length and  0 the linear absorption coefficient, k is the wave vector which is defined by  = 2/, and  0 is the laser irradiance intensity with in the sample [104].Based on the measured Z-scan curves, one can derive the Kerr coefficient n2 with the fitting equations.Graphene is the first 2D material to have been discovered, and its optical nonlinearities have been widely studied using Z-scan measurements and other methods.MXene films [57] measured at a wavelength of 1550 nm, where a positive and negative Kerr nonlinearity were observed, respectively.The different response of these two materials forms the basis of their applications in different functional devices.For example, a negative Kerr nonlinearity can be used to self-compress ultrashort pulses in the presence of positive group-velocity dispersion while the materials with positive nonlinearity are promising for achieving a net parametric modulational instability gain under abnormal dispersion conditions.

2D van der Waals (vdW) heterostructures offers many new features and possibilities
beyond what a single material can provide, and there has been significant activity in this field [108,109].Recently, the optical nonlinear response of 2D heterostructures has also been investigated via the Z-scan method.Figure 3(e) plots the CA curve of a MoS2/BP/MoS2 heterostructure at different laser intensities [107].A negative Kerr nonlinearity at the telecommunications wavelength of 1550 nm can be observed.The strong Kerr nonlinearity of graphene/Bi2Te3 at the same wavelength was also demonstrated recently [110].By fitting the experimental data, a large n2 of ⁓ 2 × 10 -12 m 2 /W was obtained, which is highly attractive for all-optical modulators and switches.One of the unique features of GO is its tunable optical and electrical properties through laser reduction, which is particularly attractive for nonlinear optical applications.
To investigate laser tunable optical nonlinearities, an in-situ third-order Kerr nonlinearity measurment for GO films has been conducted with the Z-scan method [60].Figures 4(a the laser intensity, GO reduction occurs and the positive nonlinearity finally transitions into a negative nonlinearity at an intensity of 4.63 GW/cm 2 , at which point GO completely reduces to graphene.In addition to the ability to laser tune optical nonlinearities in GO, the measured Kerr coefficient n2 of GO is as large as 4.5 × 10 -14 m 2 /W at 1550 nm, which is four orders of magnitude higher than single crystalline silicon.These properties render GO a promising candidate for nonlinear applications in the telecommunications band.

THG measurement
In addition to Z-scan method, another technique that can be used to directly characterize the third-order optical nonlinearity of a material is THG measurement.As introduced in section 3.1, THG is a fundamental third-order optical nonlinear process in which three photons at the same frequency (ω1) excite the nonlinear media to generate new signal (ω = 3ω1).Measuring the THG of a material provides a direct method to characterize its third-order optical nonlinearity.Figure 5 shows a typical setup for THG measurements [111] where a fundamental (ω, red) pulse is incident normally on the sample.The third harmonic (3ω, green) is detected in the reflected direction by a CCD camera, a spectrometer, or a photodiode connected to a lock-in amplifier.
To quantitatively analyze the THG effect, an equation for the THG intensity ( 3 ), can be introduced [112]: where  ̃ and  ̃3 are the complex refractive indexes at the fundamental and harmonic wavelengths, respectively, α is the absorption coefficient at the THG wavelength, Δk is the phase mismatch between the fundamental and harmonic waves, and  (3) is the third-order susceptibility of the sample.By fitting the THG data with Equation ( 6), an effective third order susceptibility χ (3) value can be obtained.Strong THG in graphene was demonstrated by Kumar et al. [111] Figure 6(a-i) shows the THG of monolayer graphene as a function of incident laser powers.The incident laser was 1720.4 nm.By fitting the experimental data, a large ꭓ (3) of ⁓ 0.4 × 10 -16 m 2 /V 2 was obtained.In addition, a thickness dependent THG signal can be observed (Figure 6(a-ii), while ꭓ (3) remains constant wth increasing graphene layer number.Recently, Jiang et al.
[113] investigated the gate-tuneable THG of graphene.THG in other 2D materials, such as TMDCs and BP, have also been investigated recently.Rosa et al. [114] characterized THG in mechanically exfoliated WSe2 flakes at an excitation wavelength of 1560 nm.By measuring the THG for different numbers of layers, a clear thickness-dependent behaviour was observed, as shown in Figures 7(a-i) and (aiii).The ꭓ (3) of WSe2 was measured to be in the order of 10 -19 m 2 /V 2 , which is comparable to other TMD [115] and BP [116].Youngblood et al. [116] reported THG in BP by using an ultrafast near-IR laser obtaining a ꭓ (3) of ⁓ 1.4 × 10 -19 m 2 /V 2 .In addition, an anisotropic THG were demonstrated, as shown in Figure 7(b-iii).Nonlinear optical properties of few-layer GaTe were also studied by characterizing the THG at a pump wavelength of 1560 nm [117].
The THG intensity was found to be sensitive to the number of GaTe layers (Figure 7(c-iii)).

Hybrid device characterization
Z-scan and THG measurements are usually employed to characterize the material property directly.While on the one hand, the properties of a material form the basis for applications to electronic and optical devices, the reverse is true -device performance can also provide key information about the material properties.A typical example is field effect transistors (FETs) which have been one of the main techniques to evaluate the electrical properties of 2D materials.Optical structures and waveguides can also be exploited to characterize the material optical properties.By integrating 2D materials with photonic cavities and optical waveguides, the third-order optical nonlinearity of atomically thin 2D material has been characterized by measuring the nonlinear optical responses of the hybrid devices, such as FWM [78], SPM [99], and supercontinuum generation [118].This method also enables the investigation of the layer-dependence of the nonlinear properties, which is challenging for conventional Z-scan methods due to the weak response of ultrathin 2D films.For the hybird device characterization, the data analysis is performed in the following steps.First, by fitting the measured FWM or SPM spectra of corresponding hybrid devices, one can obtain the nonlinear parameters (γ) for the bare and hybrid waveguides.Then based on the fit γ of the hybrid waveguides, the Kerr coefficient (n2) of the coated 2D films can be extracted using [120][121][122]: where λ is the central wavelength, D is the integral of the optical fields over the material regions, Sz is the time-averaged Poynting vector calculated using mode solving software, n0 (x, y) and n2 (x, y) are the refractive index profiles calculated over the waveguide cross section and the Kerr coefficient of the different material regions, respectively.
FWM is a fundamental third-order nonlinear optical process that has been widely used for all optical signal generation and processing, including wavelength conversion [98,123], optical frequency comb generation [124,125], optical sampling [126,127], quantum entanglement [29,30], and many other processes.The conversion efficiency (CE) of FWM is mainly determined by the third-order Kerr nonlinearity of the material that makes of the device.Therefore, it is useful to obtain the Kerr coefficient of a material by measuring its FWM CE.Gu al. [118] fabricated a silicon nanocavity covered with graphene (Figure 8(a-i)) and measured the FWM CE with different pump and signal detuning wavelengths around 1550 nm, as shown in Figures 8(a-ii) and (a-iii).From the CE data, a n2 of ⁓ 4.8 × 10 -17 m 2 /W was obtained for a graphene integrated with a silicon cavity.The layer-dependence of the Kerr nonlinearity of GO films has been investigated by measuring the FWM performance of GO hybrid devices based on doped-silica and SiN optical waveguides and microring resonators (MRRs) [78,[128][129][130]. Figure 8(b-i) shows a fabricated doped-silica MRR covered with patterned GO films.[78] By fitting the CE to theory for a device with different GO thicknesses, the layer thickness dependence of n2 of GO at 1550 nm was characterized, as shown in Figure 8(b-iii).Recently, electrically tuneable optical nonlinearities of graphene at 1550 nm was also demonstrated by measuring FWM in graphene-SiN waveguides at different gate voltages, as shown in Figure 8(c) [119].
SPM is another third-order nonlinear optical process that can be used to characterize the optical nonlinearity of 2D materials.Feng et al. [131] studied the Kerr nonlinearities of graphene/Si hybrid waveguides with enhanced SPM (Figure 9(a)).The n2 of the Graphene on Si hybrid waveguides was measured to be ⁓ 2 × 10 -17 m 2 /W, which is three times larger than that of the Si waveguide.Even though the intrinsic n2 of graphene is orders of magnitude larger than bulk silicon, the monolayer thickness of the graphene film results in a very low optical mode overlap, which yields only a factor of three improvement in the effective nonlinearity of the waveguide.For GO, on the other hand, comparatively larger film thicknesses are achievable which result in an overall much higher waveguide nonlinearity.Optical nonlinearities of GO films have also been investigated by SPM experiments.
Zhang et al. [99] demonstrated the enhanced optical nonlinearity of silicon nanowires integrated with 2D GO Films (Figure 9(b-i)).Figure 9(b-ii) shows the experimental SPM spectra of the devices with different numbers of GO layers, where increased spectral broadening can be observed in GO coated silicon nanowires.The layer dependent Kerr n2 coefficient of GO was also characterized by fitting the spectra to theory, as shown in Figure 9(b-iii).In addition to graphene and GO, the optical Kerr nonlinearity of MoS2 monolayer films was also characterized by analysing the SPM of MoS2-silicon waveguides [132].The experiments demonstrated a large Kerr coefficient n2 of ⁓ 1.1 × 10 -16 m 2 /W for a monolayer of MoS2 in the telecommunications band.

Comparison of measured results
By using different characterization techniques discussed above, Kerr coefficient n2 or THG  (3) value of graphene, GO, TMDCs, BP, and different heterostructures at telecommunication wavelengths have been obtained.In Table 1, we compare these parameters characterizing the third-order optical nonlinearity.It can be seen that monolayer graphene exhibits the largest n2 value (up to 10 -11 m 2 /W).The n2 value of GO films is on the magnitude of 10 14 m 2 /W, which is relatively smaller than graphene, but still more than 3 orders of magnitudes larger than that of bulk silicon.For MoS2, MXene film, and 2D heterostructures, the measured n2 varies from 10 -16 to 10 -22 m 2 /W.In terms of  (3) susceptivity obtained by using THG measurements, the value ranges from 10 -19 to 10 -15 m 2 /V 2 for graphene, TMDCs, and BP.

Outlook and prospects
Despite these remarkable achievements, challenges still exist for engineering the nonlinear optical properties of 2D materials.First, accurate and efficient characterization of the linear and nonlinear optical properties remains challenging.Although the Z-scan method has been highly successful, the very weak Z-scan signals of ultra-thin films limit its applications in mono-or few layer 2D materials, especially for the layer-dependent measurements.In contrast, integrating 2D films with optical waveguides provides a powerful method to obtain accurate nonlinear parameters of atomic-thin 2D materials by analyzing the nonlinear optical performance of the hybrid device.However, the complicated device fabrication process and resulting relatively low efficiency make this method unsuitable for rapid material characterization which is required for future industrial applications.Second, 2D materials are a large family which include thousands of different materials.For applications of the third-order optical nonlinearity in the telecommunications band, only a very small fraction of them have been investigated.
Many newer materials, such as perovskites, MOFs, and graphdiyne, still need more research, which hinders the full exploitation of 2D materials in the fabrication of nextgeneration nonlinear optical devices.Finally, tuning or engineering the properties of materials is important for both optimizing the device performance and enabling new functionalities, as well as the fundamental study of 2D materials.Nevertheless, current advances in the study of third-order optical nonlinearities of 2D materials focus mainly on their fundamental properties.The relative lack of effective methods of tuning the material properties poses another obstacle for 2D materials to move forward to practical device fabrication.While challenges remain and more work is needed, there is no doubt that 2D materials will underpin key breakthroughs and greatly accelerate the developments of next-generation nonlinear optical devices for many applications, particularly high bandwidth optical communications systems.

Conclusions
In conclusion, we review recent progress in the study of the third-order optical nonlinearities of 2D materials in the telecommunications wavelength band.We introduce the representative 2D materials, together with their basic material properties followed by a discussion of the main methods for characterizing the third-order optical nonlinearity, reviewing recent achievements in the field.These advances highlight the significant potential of 2D materials in enabling high-performance nonlinear optical devices for all-optical processing functions in optical communications systems.
Funding: Please add: This research received no external funding.
Data Availability Statement: Not applicable.

Conflicts of Interest:
The authors declare no conflict of interest.

Figure 2 (
Figure 2(b) shows a typical Z-scan setup [62].To measure the ultrafast nonlinear response, a femtosecond pulsed laser is used to excite the samples.A half-wave plate combined with a linear polarizer can be employed to control the power of the incident light.

Figure 3 .
Figure 3. (a) CA Z-scan result of graphene under an excitation laser wavelength at 1550 nm.(b) Measured n2 of graphene as a function of laser intensity [105].(c) CA Z-scan result of CH3NH3PbI3 under an excitation laser wavelength at 1560 nm [106].(d) CA Z-scan result of MXene films under an excitation laser wavelength at 1550 nm [57].(e) CA Z-scan result of MoS2/BP/MoS2 heterostructure at different laser intensities.The excitation laser wavelength is 1550 nm [107].

Figure 3
(a)    shows the CA Z-scan signal of a graphene film with an excitation laser wavelength at 1550 nm.[105]A peak-valley configuration can be observed, indicating a negative Kerr nonlinearity.The measured Kerr coefficient n2 of graphene is as large as 10 -11 m 2 /W which is about 6 orders of magnitude larger than bulk Si, demonstrating the strong potential of 2D materials for nonlinear optical devices.A laser peak intensity dependent n2 has also been observed (Figure3(b)), providing a potential method for modulating its nonlinear properties.Figures3(c) and (d) show the CA curves of CH3NH3PbI3 perovskite[106] and Ti3C2Tx
)-(d) show the CA signal of GO films at different laser intensities.At low intensity, GO exhibits a positive Kerr nonlinearity with a valley-peak CA configuration.With increasing

Figure 6 (
b-ii) shows the THG signal as a function of chemical potential generated at different wavelengths.When tuning the doping level of graphene, an enhanced THG and ꭓ(3) were observed.

Figure 6 .
Figure 6.(a) THG in graphene:[111] (i) The average power of the THG signals as a function of the average power of the incident laser.Inset is the THG spectrum.(ii) The average power of the THG signals as a function of the number of atomic layers for an average fundamental power of 1 mW.(b)Gate-tunable THG in graphene:[113] (i) Schematic of an ion-gel-gated graphene monolayer on a fused silica substrate covered by ion-gel and voltage biased by the top gate.(ii) THG signal as a function of 2μ generated by different input wavelengths: 1,300 nm, 1,400 nm, 1,566 nm and 1,650 nm.

Figure 8 .
Figure 8.(a) FWM in graphene-clad silicon nanocavities:[118] (i) Scanning electron micrograph (SEM) of the photonic crystal cavity partially covered by graphene monolayer.(ii) Measured transmission spectrum of the cavity device with pump laser fixed on cavity resonance, and signal laser detuning scanned from 20.04 to 20.27 nm.(iii) Measured and simulated conversion efficiencies of the cavity.Solid and dashed black lines are modelled conversion efficiencies for the graphenesilicon and monolithic silicon cavities, respectively.(b) Layer dependent optical nonlinearities in GO-coated integrated MRR:[78] (i) Microscopic image of an integrated MRR patterned with 50 layers of GO.Inset shows zoom-in view of the patterned GO film.(ii) Optical spectra of FWM at a pump power of 22 dBm for the MRRs with 1−5 layers coated GO. (iii) n2 of GO versus layer number at fixed pump powers of 12 and 22 dBm.(c) Electrically tunable optical nonlinearities in graphenecovered SiN Waveguides:[119] (i) Sketch of the gating scheme (up) and optical microscope image (down) of the device.Calculated values of third-order conductivity as a function of Fermi energy for different wavelength detunings (ii) and as a function of detuning for a range of Fermi energies (iii).

Figure 9 .
Figure 9. (a) SPM experiments in graphene-silicon hybrid waveguides:[131] (i) Schematic diagram and Raman spectra of the device.(ii) Measured transmission spectra of comparison between the Si (green solid curve) and G/Si hybrid (blue solid curve) waveguides under the same input energy with 1.5 ps input pulse (spectrum denoted by the red dashed curve).(iii) Output SPM spectra of the hybrid waveguide under various coupled energies.(b) SPM in GO-silicon waveguide:[99] (i) Microscopic image of a GO-coated silicon nanowire.(ii) Optical spectra of SPM at a coupled pulse energy of∼51.5 pJ with 1−3 layers coated GO. (iii) n2 of GO vs layer number at fixed coupled pulse energies of 8.2 and 51.5 pJ.(c) SPM experiments in MoS2-coated silicon waveguides:[132] (i) scanning electron microscope image of the device, with MoS2 covering both the grating couplers and waveguide regions.(ii) Measured transmission spectra of the devices with and without MoS2.(iii) Simulation result for the redshift of the grating to estimate the refractive index of MoS2.(iv) SPM spectra of MoS2-silicon waveguide and bare silicon waveguide.