# Optical parametric amplifiers in silicon nitride nanowires integrated with 2D graphene oxide thin films

David Moss

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David Moss. Optical parametric amplifiers in silicon nitride nanowires integrated with 2D graphene oxide thin films. 2023. hal-04236527

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Preprint submitted on 11 Oct 2023

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# Optical parametric amplifiers in silicon nitride nanowires integrated with 2D graphene oxide thin films

David J. Moss

**Keywords: Integrated photonics, nonlinear optics, optical parametric process, 2D materials.**

## Abstract

Optical parametric amplification (OPA) represents a powerful solution to achieve broadband amplification in wavelength ranges beyond the scope of conventional gain media, for generating high-power optical pulses, optical microcombs, entangled photon pairs and a wide range of other applications. Here, we demonstrate optical parametric amplifiers based on silicon nitride (Si₃N₄) waveguides integrated with two-dimensional (2D) layered graphene oxide (GO) films. We achieve precise control over the thickness, length, and position of the GO films using a transfer-free, layer-by-layer coating method combined with accurate window opening in the chip cladding using photolithography. Detailed OPA measurements with a pulsed pump for the fabricated devices with different GO film thicknesses and lengths show a maximum parametric gain of ~24.0 dB, representing a ~12.2 dB improvement relative to the device without GO. We perform a theoretical analysis of the device performance, achieving good agreement with experiment and showing that there is substantial room for further improvement. This work demonstrates a new way of achieving high photonic integrated OPA performance by incorporating 2D materials.

<footnote n="1">¹Optical Sciences Centre, Swinburne University of Technology, Hawthorn, VIC 3122, Australia</footnote>
Introduction

Optical amplifiers are key to many applications¹⁻³ such as optical communications where they have been instrumental with rare-earth-doped fibers⁴⁻⁶ and III-V semiconductors⁷⁻⁹. However, these devices are restricted to specific wavelength ranges determined by the energy gaps between states¹,¹⁰. In contrast, optical parametric amplification (OPA) can achieve gain across virtually any wavelength range¹¹,¹², and so is capable of achieving broadband optical amplification outside of conventional wavelength windows¹¹,¹³. Since its discovery in 1965¹⁴, OPA has found applications in many fields such as ultrafast spectroscopy¹⁵,¹⁶, optical communications⁵,¹³, optical imaging¹⁷,¹⁸, laser processing¹⁹,²⁰, and quantum optics²¹,²². Notably, it has underpinned many new technological breakthroughs such as optical microcombs²³,²⁴ and entangled photon pairs²⁵,²⁶.

To achieve OPA, materials with a high optical nonlinearity are needed – either second- (χ²) or third-order (χ³) nonlinearities²⁷,²⁸, and has been demonstrated in birefringent crystals²⁹⁻³¹, optical fibers¹⁰,³²,³³, and photonic integrated chips¹,³,²⁴,³⁴,³⁵. Amongst these, photonic integrated chips offer the advantages of a compact footprint, low power consumption, high stability and scalability, as well as cost reduction through large-scale manufacturing³⁶⁻³⁸. Despite silicon's dominance as a platform for linear photonic integrated devices³⁹,⁴⁰, its significant two photon absorption (TPA) in the near infrared wavelength region and the resulting free carrier absorption lead to a high nonlinear loss³,²⁷, making it challenging to achieve any significant OPA gain in this wavelength range. Other nonlinear integrated material platforms, such as silicon nitride (Si₃N₄)¹,⁴¹, silicon rich nitride⁴²,⁴³, doped silica³⁶,⁴⁴, AlGaAs⁴⁵,⁴⁶, chalcogenide⁴⁷,⁴⁸, GaP⁴⁹, and tantalum⁵⁰, exhibit much lower TPA at near infrared wavelengths and have made significant progress over the past decade. However, their comparatively low third-order optical nonlinearity imposes a significant limitation on the OPA gain that they can achieve.
Recently, two-dimensional (2D) materials with ultrahigh optical nonlinearities and broadband response have been integrated on photonic chips to achieve exceptional nonlinear optical performance<sup>25,51-54</sup>, highlighted by the progress in realizing OPA by exploiting the high second-order optical nonlinearities of monolayer transition metal dichalcogenides (TMDCs)<sup>25</sup>. Previously<sup>55-59</sup>, we reported an ultra-high third-order optical nonlinearity in 2D graphene oxide (GO) films that is about 4 orders of magnitude larger than silicon, together with a large bandgap (> 2 eV) that yields a linear loss more than 2 orders of magnitude lower than graphene, and perhaps most importantly, low TPA at near infrared wavelengths – all of which are key to achieving high OPA. In addition, GO has demonstrated high compatibility with various integrated platforms<sup>12,38</sup>, along with the capability to achieve precise control over its film thickness and length<sup>56,60</sup>.

In this work, we demonstrate significantly increased optical parametric gain in Si₃N₄ waveguides by integrating them with 2D layered GO films. We employ a transfer-free, layer-by-layer coating method to achieve precise control over the GO film thickness, and by using photolithography to open windows in the waveguide cladding we are able to accurately control the GO film length and position. We perform a detailed experimental characterization of the OPA performance of the devices with different GO film thicknesses and lengths, achieving a maximum parametric gain of ~24.0 dB, representing a ~12.2 dB improvement over the uncoated device. By fitting experimental results with theory, we analyse the influence of the applied power, wavelength detuning, and GO film thickness and length on the OPA performance, and in the process demonstrate that there is still significant potential for improved performance. These results verify the effectiveness of the on-chip integration of 2D GO films to improve the OPA performance of photonic integrated devices.
Experimental results

**GO properties.** Figure 1(a) illustrates the atomic structure and bandgap of GO, which is a derivative of graphene. Unlike graphene, which consists solely of sp²-hybridized carbon atoms, GO contains various oxygen-containing functional groups (OCFGs) such as hydroxyl, carboxyl, and carbonyl groups¹². Some of the carbon atoms in GO are sp³-hybridized through σ-bonding with the OCFGs, resulting in a heterogeneous structure. In contrast to graphene, which has a zero bandgap, GO has an opened bandgap resulting from the isolated sp² domains within the sp³ C-O matrix. The bandgap of GO typically falls between 2.1 eV and 3.6 eV³⁸, resulting in both low linear light absorption and low nonlinear TPA at near-infrared wavelengths that are attractive for nonlinear optical applications⁵⁴. Moreover, the material properties of GO can be tuned by manipulating the OCFGs to engineer its bandgap, which has enabled a range of photonic, electronic, and optoelectronic applications¹².

**Figure 1(b)** illustrates the principle of signal amplification based on an optical parametric process⁶¹. In this process, when pump and idler photons travel collinearly through a nonlinear optical medium, a pump photon excites a virtual energy level. The decay of this energy level is stimulated by a signal photon, resulting in the emission of an identical second signal photon and an idler photon, while conserving both energy and momentum. In processes that involve optical absorption, such as photoluminescence and TPA, real photogenerated carriers are involved, which can alter the quiescent material nonlinear response¹²,²⁷. In contrast, the optical parametric process operates by virtual excitation of carriers without creating photogenerated carriers. This makes it quasi-instantaneous, with ultrafast response times on the order of femtoseconds¹,⁵⁴. We note that although the parametric gain itself is almost instantaneous, when influenced by nonlinear absorption with much slower recovery times such as that induced by free carriers in silicon²⁷, the net parametric gain can accordingly have a slow time response component.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** (a) Schematic of GO's atomic structure and bandgap. The colorful balls in the atomic structure represent the diverse oxygen-containing functional groups (OCFGs). (b) Schematic of signal amplification based on optical parametric process. (c) Schematic of a Si₃N₄ waveguide integrated with a single layer GO film. (d) Microscopic image of the fabricated Si₃N₄ integrated chip coated with a single layer GO film. (e) Measured Raman spectrum of the GO-coated Si₃N₄ chip in (d). (f) Dispersion (D) of the uncoated waveguide (GO-0) and hybrid waveguides with 1 and 2 layers of GO (GO-1, GO-2). Inset shows TE mode profile of the Si₃N₄ waveguide integrated with a single layer GO film.</figcaption></figure>
**Device design and fabrication.** Figure 1(c) illustrates the schematic of a Si₃N₄ waveguide integrated with a single layer GO film. Compared to silicon that has a small (indirect) bandgap of ~1.1 eV²⁷, Si₃N₄ has a large bandgap of ~5.0 eV³⁶ that yields low TPA in the near-infrared region. To enable the interaction between the GO film and the evanescent field of the waveguide mode, a portion of the silica upper cladding was removed to allow for the GO film to be coated on the top surface of the Si₃N₄ waveguide. Figure 1(d) shows a microscopic image of the fabricated Si₃N₄ chip integrated with a single layer GO film. The successful coating of the GO film is confirmed by the presence of the representative D (1345 cm⁻¹) and G (1590 cm⁻¹) peaks in the measured Raman spectrum, as shown in Figure 1(e). First, we fabricated low-loss Si₃N₄ waveguides via CMOS-compatible processes (see Methods). Next, we coated the waveguides with 2D GO films using a transfer-free, solution-based coating method (see Methods). This approach allows for large-area, layer-by-layer film coating with high repeatability and compatibility with various integrated material platforms¹²,³⁸,⁶². The thickness of the GO film, characterized via atomic force microscopy measurements, was ~2 nm. The high transmittance and excellent morphology of the fabricated device demonstrate that our GO coating method, based on self-assembly via electrostatic attachment, can achieve conformal film coating in the window opening area without any noticeable wrinkling or stretching. This offers advantages compared to film transfer techniques commonly used for coating other 2D materials like graphene and TMDCs¹⁹. The length and position of the GO films can be easily controlled by adjusting the length and position of the windows opened on the silica upper cladding, which provides high flexibility for optimizing the performance of the hybrid waveguides by altering the GO film parameters.

**Figure 1(f)** shows the dispersion *D* of the uncoated waveguide and the hybrid waveguides with 1 and 2 layers of GO, calculated with commercial mode solving software using the materials' refractive indices measured by spectral ellipsometry. The Si₃N₄ waveguides in all these devices
had a cross section of 1.60 µm × 0.72 µm, and the inset in **Figure 1(f)** depicts the transverse electric (TE) mode profile of the hybrid waveguide with 1 layer of GO. The interaction between the highly nonlinear GO film and the waveguide's evanescent field enhances the nonlinear optical response of the hybrid waveguide, which is the foundation for improving the OPA performance. We selected TE-polarization for our subsequent measurements since it supports in-plane interaction between the waveguide's evanescent field and the GO film, which is much stronger than the out-of-plane interaction due to the significant optical anisotropy in 2D materials<sup>63,64</sup>. In **Figure 1(f)**, it can be observed that all three waveguides exhibit anomalous dispersion, which is crucial for reducing phase mismatch and improving the parametric gain in the optical parametric process. Upon incorporating 1 layer of GO, the hybrid waveguide shows a slightly increased anomalous dispersion compared to waveguides without GO. For the hybrid waveguides with 2 layers of GO, the anomalous dispersion is further enhanced.

**Loss measurements.** The coating of GO films onto Si₃N₄ waveguides introduces extra linear and nonlinear loss. Before the OPA measurements, we used the experimental setup in **Figure S1** of the Supplementary Information to characterize the linear and nonlinear loss of the fabricated devices. Fiber-to-chip coupling was achieved via lensed fibers butt coupled to inverse-taper couplers at both ends of the Si₃N₄ waveguides. The coupling loss was ~4.2 dB / facet. We measured three devices, including the uncoated Si₃N₄ waveguide and hybrid waveguides with 1 and 2 layers of GO. The Si₃N₄ waveguides in these devices were all ~20 mm in length, while for the hybrid waveguides, windows with a length of ~1.4 mm were opened at a distance of ~0.7 mm from the input port. In our following discussion, the input light power quoted refers to the power coupled into the devices, with the fiber-to-chip coupling loss being excluded.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Experimental results for loss measurements. (a) Measured insertion loss versus wavelength of input continuous-wave (CW) light. The input CW power is ~1 mW. (b) Measured insertion loss versus input CW power. The input CW wavelength is ~1550 nm. (c) Measured insertion loss versus peak power $P_{peak}$ of 180-fs optical pulses. (d) Excess propagation loss induced by SA of GO ΔSA versus $P_{peak}$ extracted from (c). In (a) – (d), the curves for GO-0, GO-1, and GO-2 show the results for the uncoated $Si_3N_4$ waveguides, and the hybrid waveguides with 1 and 2 layers of GO, respectively.</figcaption></figure>

The linear loss was measured using continuous-wave (CW) light with a power of ~1 mW.

**Figure 2a** shows the insertion loss of the fabricated devices versus wavelength. All devices exhibited nearly a flat spectral response, which suggests the absence of any material absorption or coupling loss that would generate a strong wavelength dependence. By using a cut-back method$^{65}$, we obtained a propagation loss of ~0.5 dB/cm for the $Si_3N_4$ waveguides buried in silica cladding. By comparing the $Si_3N_4$ waveguides with and without opened windows in the silica cladding, we deduced a higher propagation loss of ~3.0 dB/cm for the $Si_3N_4$ waveguides in the opened window
area, which can be attributed to the mitigating effect of the silica cladding on the Si₃N₄ surface roughness. Finally, using these values and the measured insertion loss of the hybrid waveguides, we extracted an excess propagation loss induced by the GO films of ~3.1 dB/cm and ~6.3 dB/cm for the 1- and 2-layer devices, respectively. Such a loss induced by the GO films is about 2 orders of magnitude lower than Si₃N₄ waveguides integrated with graphene films⁶⁶,⁶⁷, which can be attributed to the large bandgap of GO, resulting in low light absorption at near infrared wavelengths. This is a crucial advantage of GO in OPA applications where low loss is required to achieve a high net parametric gain.

**Figure 2b** shows the measured insertion loss versus input CW power at a wavelength of ~1550 nm. All devices showed no significant variation in insertion loss when the power was below 30 mW, indicating that the power-dependent loss induced by photo-thermal changes in the GO films was negligible within this range. This observation is consistent with our previous results where photo-thermal changes were only observed for average powers above 40 mW⁵⁶,⁶⁸.

The measurement of nonlinear loss was conducted using a fiber pulsed laser (FPL) capable of generating nearly Fourier-transform limited femtosecond optical pulses centered around 1557 nm. The pulse duration and repetition rate were ~180 fs and ~60 MHz, respectively. **Figure 2c** shows the measured insertion loss versus pulse peak power $P_{peak}$. The average power of the femtosecond optical pulses was adjusted using a variable optical attenuator, ranging from 0.32 mW to 1.94 mW, which corresponds to peak powers ranging from 30 W to 180 W. The insertion loss of the hybrid waveguides decreased as the pulse peak power increased, with the 2-layer device exhibiting a more significant decrease than the 1-layer device. In contrast, the insertion loss of the uncoated Si₃N₄ waveguide remained constant. These results reflect that the hybrid waveguides experienced saturable absorption (SA) in the GO films, consistent with observations in waveguides incorporating graphene⁶⁶,⁶⁹. Additionally, we note that the loss changes observed were not present
when using CW light with equivalent average powers. This suggests that the changes are
specifically induced by optical pulses with high peak powers. In GO, the SA can be induced by the
bleaching of the ground states that are associated with sp² orbitals (e.g., with an energy gap of ~0.5
eV⁵⁵) as well as the defect states. **Figure 2d** shows the SA-induced excess propagation loss (ΔSA)
versus pulse peak power *P*<sub>peak</sub>, which was extracted from the result in **Figure 2c**, with the linear
propagation loss being excluded. The negative values of ΔSA indicate that there is a decrease in
loss as the peak power increases in the SA process. Such decrease in loss is beneficial for increasing
the pump peak power in the OPA process, which helps improve the parametric gain.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Experimental setup for OPA experiments. CW laser: continuous-wave laser. FPL: fiber pulsed laser. PC: polarization controller. EDFA: Erbium doped fiber amplifier. VOA: variable optical attenuator. OPM: optical power meter. DUT: device under test. CCD: charged-coupled device. OSA: optical spectrum analyzer.</figcaption></figure>

**OPA experiments.** We conducted OPA experiments using the same devices that were fabricated and used for the loss measurements. A schematic of the experimental setup is shown in **Figure 3**.
To generate the pump light required for the OPA experiments, we employed the same FPL that was used for the loss measurements. On the other hand, the signal light was generated through amplification of the CW light from a tunable laser. The pulsed pump and the CW signal were combined by a broadband 50:50 coupler and sent to the device under test (DUT) for the optical parametric process. The polarization of both signals was adjusted to TE polarized using two polarization controllers (PCs). To adjust the power of the pulsed pump, a broadband variable optical attenuator (VOA) was utilized. The output after propagation through the DUT was directed towards an optical spectrum analyzer (OSA) for analysis.

**Figure 4a** shows the optical spectra after propagation through the uncoated Si₃N₄ waveguide and the hybrid waveguides with 1 and 2 layers of GO. For all three devices, the input pump peak power and signal power were kept the same at *P*<sub>peak</sub> = ~180 W and *P*<sub>signal</sub> = ~6 mW, respectively. As the pump light used for the OPA experiments was pulsed, the optical parametric process occurred at a rate equivalent to the repetition rate of the FPL. As a result, both the generated idler and amplified signal also exhibited a pulsed nature with the same repetition rate as that of the FPL. The optical spectra in **Figure 4a** were analyzed to extract the parametric gain *PG* experienced by the signal light for the three devices (see Methods). The *PG* for the uncoated Si₃N₄ waveguide and the hybrid waveguides with 1 and 2 layers of GO were ~11.8 dB, ~20.4 dB, and ~24.0 dB, respectively. The hybrid waveguides exhibited higher parametric gain compared to the uncoated waveguide, and the 2-layer device had higher parametric gain than the 1-layer device. These results confirm the improved OPA performance in the Si₃N₄ waveguide by integrating it with 2D GO films. We also note that the hybrid devices showed greater spectral broadening of the pulsed pump caused by self-phase modulation (SPM), which is consistent with our previous observations from SPM experiments⁵⁷.
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Optical parametric amplification (OPA) using a 180-fs pulsed pump and a continuous-wave (CW) signal. (a) Measured output optical spectra after propagation through uncoated (GO-0) and hybrid waveguides with 1 (GO-1) and 2 (GO-2) layers of GO. The peak power of the input pump light *P*<sub>peak</sub> was ~180 W. (b) Measured output optical spectra after propagation through the device with 2 layers of GO at different *P*<sub>peak</sub>. In (a) and (b), the power of the CW signal light was *P*<sub>signal</sub> = ~6 mW, and insets show zoom-in views around the signal and idler. (c) Measured (i) parametric gain *PG* and (ii) parametric gain improvement *ΔPG* versus *P*<sub>peak</sub>.</figcaption></figure>
The values of *PG* in **Figure 4** are the net parametric gain, over and above the waveguide loss induced by both the GO-coated and uncoated Si₃N₄ waveguide segments (see Methods). This is different to the “on/off” parametric gain often quoted ¹¹,⁴³, where the waveguide loss is excluded, resulting in higher values of parametric gain. Here, the on-off gains for the waveguides with 0, 1, and 2 layers of GO were ~13.2 dB, ~22.3 dB, and ~26.2 dB, respectively, which are only slightly higher than their corresponding net gains due to the low loss of the Si₃N₄ waveguides and the relatively short GO film length. Although the net gain can be increased closer to the on-off gain by reducing the waveguide loss via optimization of the fabrication processes, because the differences between the net and on-off gains are small in our case, there is not much incentive to do this. In the following, we focus our discussion on the net parametric gain *PG*. This can also ensure a fair comparison of the parametric gain improvement, as different waveguides have different waveguide loss.

**Figure 4b** shows the measured output optical spectra after propagation through the device with 2 layers of GO for different *P*<sub>peak</sub>. **Figure 4c-i** shows the signal parametric gain *PG* for the uncoated and hybrid waveguides versus input pump peak power, and the parametric gain improvement *ΔPG* for the hybrid waveguides as compared to the uncoated waveguide is further extracted and shown in **Figure 4c-ii**. We varied the input pump peak power from ~30 W to ~180 W, which corresponds to the same power range used in **Figure 2d** for loss measurements. The *PG* is higher for the hybrid waveguide with 1 layer of GO compared to the uncoated waveguide, and lower than the device with 2 layers of GO. In addition, both *PG* and *ΔPG* increase with *P*<sub>peak</sub>, and a maximum *ΔPG* of ~12.2 dB was achieved for the 2-layer device at *P*<sub>peak</sub> = ~180 W. Likewise, we observed similar phenomena when using lower-peak-power picosecond optical pulses for the pump, as shown in **Figure S2** of the Supplementary Information.
To evaluate the OPA performance, we conducted experiments where we varied the wavelength detuning, CW signal power, and GO film length. Except for the varied parameters, all other parameters are the same as those in **Figure 4**. In **Figure 5a**, the measured signal parametric gain *PG* and parametric gain improvement *ΔPG* are plotted against the wavelength detuning *Δλ*, which is defined as the difference between the CW signal wavelength *λ*<sub>signal</sub> and the pump center wavelength *λ*<sub>pump</sub>. It is observed that both the *PG* and *ΔPG* increase as *Δλ* changes from -12 nm to -22 nm. In **Figure 5b**, the *PG* and *ΔPG* are plotted against the CW signal power *P*<sub>signal</sub>, showing a slight decrease as *P*<sub>signal</sub> increases, which is primarily due to the fact that an increase in *P*<sub>signal</sub> can result in a decrease in *PG* as per its definition (i.e., *PG* = *P*<sub>out,signal</sub> / *P*<sub>in,signal</sub>, see Methods). **Figure 5c** shows the *PG* and *ΔPG* versus GO film length. By measuring devices with various GO film lengths, ranging from ~0.2 mm to ~1.4 mm, we observed that those with longer GO films exhibited greater *PG* and *ΔPG* values. The *PG* achieved through the optical parametric process is influenced by several factors, such as the applied powers, optical nonlinearity, dispersion, and loss of the waveguides. These factors will be comprehensively analyzed in the following section.
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>

<figure><img src="image_11.png" /><figcaption>**Figure 5.** (a) Measured (i) parametric gain *PG* and (ii) parametric gain improvement *ΔPG* versus wavelength detuning *Δλ*. (b) Measured (i) *PG* and (ii) *ΔPG* versus input CW signal power *P*<sub>signal</sub>. (c) Measured (i) *PG* and (ii) *ΔPG* versus GO film length *L*<sub>GO</sub>. In (a) – (c), the peak power of the 180-fs pulsed pump centered around 1557 nm was *P*<sub>peak</sub> = ~180 W. Except for the varied parameters, all other parameters are kept the same as *Δλ* = ~22 nm, *P*<sub>signal</sub> = ~6 mW, and *L*<sub>GO</sub> = ~1.4 mm.</figcaption></figure>
Analysis and discussion

**Optical nonlinearity of hybrid waveguides and GO films.** We used the theory from Refs. $^{10,58,70}$
to model the OPA process in the fabricated devices (see Methods). By fitting the measured PG
with theory, we obtained the nonlinear parameter $\gamma$ of the uncoated and hybrid waveguides. The fit
$\gamma$ for the uncoated Si$_3$N$_4$ waveguide is ~1.11 W$^{-1}$m$^{-1}$, which is consistent with the previously
reported values in the literature$^{58,71-82}$. **Figure 6a** shows the fit $\gamma$ of the hybrid waveguides as a
function of pulse peak power $P_{peak}$. For both devices with different GO film thickness, the lack of
any significant variation in $\gamma$ with $P_{peak}$ indicates that the applied power has a negligible effect on
the properties of the GO films. This is in contrast to the effects of light with high average optical
powers, which can lead to changes in GO's properties via photo-thermal reduction$^{56,58}$. The fit
values of $\gamma$ for the devices with 1 and 2 layers of GO are ~14.5 and ~27.3 times greater than the
value for the uncoated Si$_3$N$_4$ waveguide. These agree with our earlier work$^{58,59}$ and indicate a
significant improvement in Kerr nonlinearity for the hybrid waveguides.

Based on the fit $\gamma$ for the hybrid waveguides, we further extracted the Kerr coefficient $n_2$ of the
GO films (see Methods), as shown in **Figure 6b**. The extracted $n_2$ values for the films with 1 and
2 layers are similar, with the former being slightly higher than the latter. The lower $n_2$ for thicker
films is likely caused by an increase in inhomogeneous defects within the GO layers and imperfect
contact between multiple GO layers. The $n_2$ values for the films with 1 and 2 layers are about 5
orders of magnitude higher than that of Si$_3$N$_4$ (~2.62 × 10$^{-19}$ m$^2$/W, obtained by fitting the result for
the uncoated Si$_3$N$_4$ waveguide), highlighting the tremendous third-order optical nonlinearity of the
GO films.
<figure><img src="image_12.png" /><figcaption>Figure 6. (a) Nonlinear parameter $\gamma$ of hybrid waveguides with 1 (GO-1) and 2 (GO-2) layers of GO as a function of pump peak power $P_{peak}$. (b) Kerr coefficient $n_2$ of films with 1 (GO-1) and 2 (GO-2) layers of GO versus $P_{peak}$. (c) Effective interaction length $L_{eff}$ and (d) figure of merit FOM versus waveguide length L for the uncoated (GO-0) and hybrid waveguides with 1 (GO-1) and 2 (GO-2) layers of GO. (e) Parametric gain PG and (f) parametric gain improvement $\Delta PG$ versus waveguide length L for the uncoated Si$_3$N$_4$ waveguide (GO-0) and the hybrid waveguides uniformly coated with 1 (GO-1) and 2 (GO-2) layers of GO. In (e) and (f), the pump peak power, CW signal power, and the wavelength detuning are $P_{peak} = \sim 180$ W, $P_{signal} = \sim 6$ mW, and $\Delta \lambda = \sim 22$ nm, respectively.</figcaption></figure>

We also quantitatively compare the nonlinear optical performance of the Si$_3$N$_4$ waveguide and the hybrid waveguides by calculating their nonlinear figure of merit FOM. The FOM is determined by balancing a waveguide's nonlinear parameter against its linear propagation loss, and can be expressed as a function of waveguide length L given by:

$$FOM(L) = \gamma \times L_{eff}(L) \qquad (1)$$
where $\gamma$ is the waveguide nonlinear parameter and $L_{\text{eff}}(L) = [1 - \exp(-\alpha \times L)]/\alpha$ is the effective interaction length, with $\alpha$ denoting the linear loss attenuation coefficient. Note that the nonlinear figure of merit defined in Eq. (1) allows for comparison of the nonlinear optical performance of optical waveguides made from different materials. This is distinct from the nonlinear figure of merit commonly used for comparing the nonlinear optical performance of a single material, which is defined as $n_2/(\lambda \cdot \beta_{TPA})^{36}$, with $n_2$, $\lambda$, and $\beta_{TPA}$ denoting the Kerr coefficient, wavelength, TPA coefficient, respectively.

**Figure 6c** shows $L_{\text{eff}}$ versus $L$ for the Si$_3$N$_4$ waveguide and the hybrid waveguides with 1 and 2 layers of GO. The Si$_3$N$_4$ waveguide has a higher $L_{\text{eff}}$ due to its comparably lower linear propagation loss. **Figure 6d** shows the FOM versus $L$ for the three waveguides. Despite having a lower $L_{\text{eff}}$, the hybrid waveguides exhibit a higher FOM than the Si$_3$N$_4$ waveguide, owing to the significantly improved nonlinear parameter $\gamma$ for the hybrid waveguides. This indicates that the impact of enhancing the optical nonlinearity is much greater than the degradation caused by the increase in loss, resulting in a significant improvement in the device's overall nonlinear optical performance.

For the hybrid waveguides that we measured in the OPA experiments, only a specific section of the waveguides was coated with GO films. In **Figures 6e and 6f**, we compare PG and $\Delta$PG versus waveguide length $L$ for the hybrid waveguides uniformly coated with GO films, respectively, which were calculated based on the fit $\gamma$ values (at $P_{\text{peak}}$ = ~180 W) in **Figure 6a**. The pump peak power, CW signal power, and wavelength detuning were $P_{\text{peak}}$ = ~180 W, $P_{\text{signal}}$ = ~6 mW, and $\Delta\lambda$ = ~22 nm, respectively – the same as those in **Figure 4a**. The corresponding results for the uncoated Si$_3$N$_4$ waveguide are also shown for comparison. The 2-layer device has higher PG and $\Delta$PG values for $L$ < ~5.7 mm but lower values for $L$ > ~5.7 mm, reflecting the trade-off between the increase in optical nonlinearity and waveguide loss. At $L$ = 1.4 mm, the 1-layer and 2-layer
devices achieve *PG* of ~10.5 dB and ~15.6 dB, respectively. When compared to waveguides that have patterned GO films of the same length as those used in our OPA experiments, their total *PG* (including those provided by both the ~1.4-mm-long GO-coated section and the ~18.6-mm-long uncoated section) are ~20.4 dB and ~24.0 dB, respectively. This highlights the dominant role of the GO-coated section in providing the parametric gain, as well as the fact that a further improvement in *ΔPG* could be obtained by increasing the length of the GO-coated segments.

**Performance improvement by optimizing parameters.** Based on the OPA modeling (see Methods) and the fit parameters in **Figure 6**, we further investigate the margin for performance improvement by optimizing the parameters.

<figure><img src="image_13.png" /><figcaption>**Figure 7.** (a) Simulated parametric gain *PG* versus input pump peak power *P*<sub>peak</sub> and CW signal power *P*<sub>signal</sub>. (b) Simulated parametric gain improvement *ΔPG* versus *P*<sub>peak</sub> and *P*<sub>signal</sub>. In (a) and (b), (i) and (ii) show the results for the hybrid waveguides with 1 and 2 layers of GO (GO-1, GO-2), respectively. The black points mark the OPA experimental results, and the black crossing mark the results corresponding to the maximum values of *PG* and *ΔPG*. The wavelength detuning and the GO film length are Δλ = -22 nm and L<sub>GO</sub> = 1.4 mm, respectively.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Figure 8.** (a) Simulated (i) parametric gain *PG* and (ii) parametric gain improvement *ΔPG* versus wavelength detuning *Δλ*. (b) Simulated (i) *PG* and (ii) *ΔPG* versus GO coating length *L*<sub>GO</sub>. In (a) and (b), the measured and fit results are shown by the data points and the dashed curves, respectively. The pump peak power and the signal power are *P*<sub>peak</sub> = 180 W and *P*<sub>signal</sub> = 6 mW, respectively. In (a), *L*<sub>GO</sub> = 1.4 mm. In (b), *Δλ* = -22 nm.</figcaption></figure>

**Figure 7a** shows the calculated *PG* for the hybrid waveguides versus pulse peak power *P*<sub>peak</sub> and CW signal power *P*<sub>signal</sub>. The corresponding results for *ΔPG* are shown in **Figure 7b**. In each figure, (i) and (ii) show the results for the devices with 1 and 2 layers of GO, respectively. The black points mark the experimental results in **Figure 4**, and the black crossings mark the results corresponding to the maximum values of *PG* or *ΔPG*. As can be seen, both *PG* and *ΔPG* increase with *P*<sub>peak</sub> but decrease with *P*<sub>signal</sub>, showing agreement with the trends observed in the experimental results. For the device with 1 layer of GO, the maximum *PG* of ~32.7 dB and *ΔPG* of ~10.7 dB are achieved at *P*<sub>peak</sub> = 400 W and *P*<sub>signal</sub> = 1 mW. Whereas for the device with 2 layers of GO, the maximum *PG* and *ΔPG* are ~36.9 dB and ~15.0 dB at the same *P*<sub>peak</sub> and *P*<sub>signal</sub>, respectively. This
reflects that there is a large room for improvement by further optimizing the pulse peak power and the CW signal power. In our experiments, the maximum output power of our FPL limited the applied pulse peak power. In addition, we opted to avoid using excessively low CW signal power due to two reasons. First, the CW signal power does not exert a significant influence on PG. Second, as the power of the output pulsed signal diminishes with the decrease of the input CW signal power, it becomes increasingly challenging to extract PG accurately.

**Figure 8a** shows the calculated *PG* and *ΔPG* versus wavelength detuning *Δλ*. The dashed curves were calculated based on the fit result at *Δλ* = -22 nm, and the data points mark the measured results in **Figure 5a**. The curves with an 'M' shape are consistent with the results in Refs. ³,¹⁰,¹¹, reflecting the anomalous dispersion of these waveguides. The experimental data points match closely with the simulation curves, thereby confirming the consistency between our experimental results and theory. For the device with 1 layer of GO, the maximum *PG* of ~34.7 dB and *ΔPG* of ~14.7 dB are achieved at *Δλ* = ~67 nm and ~80 nm, respectively. Whereas for the 2-layer device, the maximum *PG* of ~37.6 dB and *ΔPG* of ~17.3 dB are achieved at *Δλ* = ~61.8 nm and ~57.8 nm, respectively. These results highlight the significant potential for improvement through further optimization of the wavelength detuning. In our experiments, the range of wavelength detuning was limited by the operation bandwidth of the erbium-doped fiber amplifier used to amplify the CW signal power.

We also investigate the performance improvement by optimizing the GO film length $L_{GO}$.

**Figure 8b** shows the calculated *PG* and *ΔPG* versus $L_{GO}$. The dashed curves were calculated based on the fit result at $L_{GO}$ = 1.4 mm, and the data points mark the measured results in **Figure 5a**. For the device with 1 layer of GO, the maximum *PG* of ~26.3 dB and *ΔPG* of ~19.9 dB are achieved at $L_{GO}$ = ~7 mm and ~9.7 mm, respectively. Whereas for the device with 2 layers of GO, the maximum *PG* of ~27.0 dB and *ΔPG* of ~17.2 dB are achieved at $L_{GO}$ = ~3.3 mm and ~3.9 mm,
respectively. These results suggest that the OPA performance can be improved by further
optimizing the length of the GO film. In our experiments, the lengths of the GO films were
restricted by the size of the opened windows on the silica cladding (as shown in **Figure 1d**). Aside
from optimizing the GO film length, we would anticipate even higher values of *PG* and *ΔPG* for
devices with an increased number of GO layers at *L*<sub>GO</sub> = 1.4 mm, similar to what we observed in
our previous nonlinear optics experiments<sup>56,57</sup>. This is due to the considerably increased optical
nonlinearity of devices with thicker GO films. However, such an increase in optical nonlinearity is
accompanied by a rise in loss, making it imperative to balance the trade-off between them.

We investigate the performance by optimizing both Δλ and LGO simultaneously (see **Figure S4** of the Supplementary Information), finding that the 1-layer device has a maximum PG of ~37.4 dB and maximum ΔPG of ~31.5 dB, while the 2-layer device reaches PG up to ~37.8 dB and ΔPG up to ~27.3 dB. In addition, by further increasing the pump peak power from 180 W to 400 W, even higher performance is achieved, with the 1-layer device reaching a maximum PG of ~43.7 dB and maximum ΔPG of ~40.1 dB, and the 2-layer device a maximum PG of ~43.8 dB and maximum ΔPG of ~37.3 dB (see **Figure S5** of the Supplementary Information). According to these simulation results, it is found that if both Δλ and LGO are optimized simultaneously, there is not much difference between the maximum PG for the 1- and 2-layer devices. However, the 1-layer device still yields a slightly higher ΔPG because of its lower loss compared with the 2-layer device.

For this reason, devices coated with more GO layers will have lower maximum ΔPG.

Finally, we also investigate the improvement in *PG* and *ΔPG* by optimizing the coating
position of the GO films (see **Figure S6** of the Supplementary Information), as well as the influence
of the SA of GO on the OPA performance (see **Figure S7** of the Supplementary Information). We
find that although optimizing the coating position can lead to further improvements in *PG* and *ΔPG*,
the extent of these improvements is not as substantial as those achieved through optimization of *Δλ*
and $L_{GO}$. In addition, we find that the SA of GO has a positive impact on enhancing *PG* and *ΔPG*, especially for devices with thicker GO films. These results have significant implications for devices and applications involving microcombs$^{83-136}$ that require high on-chip parametric gain, as well as other linear and nonlinear$^{137-159}$ devices and potentially quantum$^{160-174}$ optical chips where on-chip parametric gain will be needed.

## Conclusion

In summary, we experimentally demonstrate significantly improved OPA performance in Si₃N₄ waveguides integrated with 2D GO films compared to uncoated waveguides. We fabricate GO-Si₃N₄ hybrid waveguides with precise control of the thickness, length, and position of the GO films. Detailed OPA measurements are performed for the fabricated devices using a pulsed pump and CW signal. The results show that up to ~24.0 dB parametric gain is achieved for the hybrid devices, representing a ~12.2 dB improvement relative to the device without GO. Based on the experimental results, the influence of the pump / signal power, wavelength detuning, and GO film thickness / length on the OPA performance is theoretically analyzed, showing that further improvement can be achieved by optimizing these parameters. We calculate that a parametric gain of ~37.8 dB and a parametric gain improvement of ~31.5 dB should be possible by optimizing the wavelength detuning and GO film length, and even higher to 43.8 dB by increasing the pump peak power to 400 W. Our study provides valuable insights into the promising potential of on-chip integration of 2D GO films for enhancing the OPA performance of photonic integrated devices, of benefit to many nonlinear optical applications.

## Materials and methods

**Fabrication of Si₃N₄ waveguides.** The Si₃N₄ waveguides were fabricated via CMOS compatible processes$^{72}$. First, a Si₃N₄ film was deposited on a silicon wafer with a 3-µm-thick wet oxidation
layer on its top surface, using a low-pressure chemical vapor deposition (LPCVD) method. The deposition was carried out in two steps involving a twist-and-grow process, resulting in a crack-free film. Next, waveguides were created using 248-nm deep ultraviolet lithography followed by fluorocarbon-based dry etching with $CF_4/CHF_3/Ar$, which resulted in a low sidewall surface roughness for the waveguides. After waveguide patterning, we employed a multi-step, chemical-physical, in-situ annealing sequence using $H_2$, $O_2$, and $N_2$ to further reduce the loss of the $Si_3N_4$ waveguides. Subsequently, a silica upper cladding was deposited to encapsule the $Si_3N_4$ waveguides via multi-step low-temperature oxide deposition at 400 °C. This was achieved through a low-rate deposition of a liner, followed by the filling of the silica layer using high-density plasma enhanced chemical vapor deposition (HD-PECVD). Finally, we employed lithography and dry etching to create windows on the silica cladding extending to the top surface of the $Si_3N_4$ waveguides.

**Synthesis and coating of GO films.** Before GO film coating, a GO solution with small GO flack size ($< 100$ nm) was prepared by using a modified Hummers method followed by vigorous sonication via a Branson Digital Sonifier$^{62}$. The coating of 2D layered GO films was then achieved by using a transfer-free method that allows for layer-by-layer GO film deposition with precise control of the film thickness, as we did previously$^{169,170}$. During the coating process, four steps for in-situ assembly of monolayer GO films were repeated to construct multi-layered films on the fabricated $Si_3N_4$ chips with opened windows, including (i) immerse substrate into a 2.0% (w/v) aqueous PDDA (Sigma-Aldrich) solution; (ii) rinse with a stream of deionized distilled water and dry with $N_2$; (iii) immerse the PDDA-coated substrate into GO solution; and (iv) rinse with a stream of deionized water and dry with $N_2$. After the film coating, the chip was dried in a drying oven.

**Extracting parametric gain from the measured optical spectra.** We used the same methods as those in Refs.$^{11,43}$ to extract the signal parametric gain from the measured optical spectra we
obtained through OPA experiments. The peak power of the pulsed signal after propagation through the fabricated devices was derived from the measured output optical spectra according to:

$$P_{\text{signal, peak}} = \frac{\iint P_{\text{signal, out}}(\lambda) d\lambda}{f_{\text{rep}} \times T} \qquad (2)$$

where $P_{\text{signal, out}}(\lambda)$ is the average output power spectrum of the signal as a function of wavelength $\lambda$, $f_{\text{rep}}$ is the repetition rate of the FPL, and $T$ is the pulse width. In our calculation of $P_{\text{signal, peak}}$, the power residing in the CW signal line was subtracted from the spectrum of $P_{\text{signal, out}}(\lambda)$.

After deriving $P_{\text{signal, peak}}$, the signal parametric gain PG was calculated as:

$$PG (\text{dB}) = 10 \times \log_{10} (P_{\text{signal, peak}} / P_{\text{signal}}) \qquad (3)$$

where $P_{\text{signal}}$ is the CW signal power at the input of the waveguide. According to Eq. (3), the PG in our discussion is the net gain over and above the waveguide loss (including that induced by both the Si₃N₄ waveguide and the GO film). In contrast, the on/off parametric gain is defined as¹¹,⁴³

$$PG_{\text{on-off}} (\text{dB}) = 10 \times \log_{10} (P_{\text{signal, peak}} / P_{\text{signal, out}}) \qquad (4)$$

where $P_{\text{signal,out}}$ is the CW signal power at the output of the waveguide when the pump is turned off. The parametric gain calculated using Eq. (4) is higher than that calculated using Eq. (3) since $P_{\text{signal,out}}$ is lower than $P_{\text{signal}}$.

**OPA Modeling.** The third-order optical parametric process in the GO-coated Si₃N₄ waveguides was modeled based on the theory from Refs.¹⁰,⁵⁸,⁷⁰. Assuming negligible depletion of the pump and signal powers due to the generation of the idler, and considering only the short wavelength idler, the coupled differential equations for the dominant degenerate FWM process can be given by¹⁰,⁶⁵

$$\begin{aligned} \frac{dA_p(z)}{dz} = & -\frac{\alpha_p}{2} A_p(z) + j\gamma_p \left[ |A_p(z)|^2 + 2|A_s(z)|^2 + 2|A_i(z)|^2 \right] A_p(z) \\ & + j2\gamma_p A_p^*(z) A_s(z) A_i(z) \exp(j\Delta\beta z) \end{aligned} \qquad (5)$$

$$\frac{dA_s(z)}{dz} = -\frac{\alpha_s}{2} A_s(z) + j\gamma_s \left[ |A_s(z)|^2 + 2|A_p(z)|^2 + 2|A_i(z)|^2 \right] A_s(z)$$
$$ + j\gamma_s A_i^*(z) A_p^2(z) \exp(-j\Delta\beta z) \qquad (6) $$

$$ \frac{dA_i(z)}{dz} = -\frac{\alpha_i}{2} A_i(z) + j\gamma_i \left[ |A_i(z)|^2 + 2|A_p(z)|^2 + 2|A_s(z)|^2 \right] A_i(z) \\ + j\gamma_i A_s^*(z) A_p^2(z) \exp(-j\Delta\beta z) \qquad (7) $$

where $A_{p,s,i}$ are the amplitudes of the pump, signal and idler waves along the z axis, which is defined as the light propagation direction, $\alpha_{p,s,i}$ are the loss factor including both the linear loss and the SA-induced nonlinear loss, $\Delta\beta = \beta_s + \beta_i - 2\beta_p$ is the linear phase mismatch, with $\beta_{p,s,i}$ denoting the propagation constants of the pump, signal and idler waves, and $\gamma_{p,s,i}$ are the waveguide nonlinear parameters. In our case, where the wavelength detuning range was small ($\le 10$ nm), the linear loss and the nonlinear parameter are assumed to be constant, i.e., $\alpha_p = \alpha_s = \alpha_i = \alpha$, $\gamma_p = \gamma_s = \gamma_i = \gamma$.

In Eqs. (5) – (7), the dispersions $\beta_{p,s,i}$ were calculated via commercial mode solving software using the refractive index $n$ of layered GO films measured by spectral ellipsometry. Given that the photo-thermal changes are sensitive to the average power in the hybrid waveguides, which was below 2 mW for the femtosecond optical pulses studied here, they were considered negligible. By numerically solving Eqs. (5) – (7), the PG was calculated via

$$ PG (\text{dB}) = 10 \times \log_{10} \left[ \frac{|A_s(L)|^2}{|A_s(0)|^2} \right] \qquad (8) $$

where $L$ is the length of the Si$_3$N$_4$ waveguide (i.e., 20 mm). For our devices with patterned GO films, the waveguides were divided into uncoated Si$_3$N$_4$ (without GO films) and hybrid (with GO films) segments with different $\alpha$, $\gamma$ and $\beta_{p,s,i}$. The differential equations were solved for each segment, with the output from the previous segment as the input for the subsequent segment.

**Extracting $n_2$ of GO films.** The Kerr coefficient $n_2$ of the layered GO films is extracted from the nonlinear parameter $\gamma$ of the hybrid waveguides according to:⁵⁶,⁷⁰
$$ \gamma = \frac{2\pi \int_D n_0^2(x, y)n_2(x, y)S_z^2 dx dy}{\left[ \int_D n_0(x, y)S_z dx dy \right]^2} \quad (9) $$

where $\lambda_c$ is the pulse central wavelength, $D$ is the integral of the optical fields over the material regions, $S_z$ is the time-averaged Poynting vector calculated using Lumerical FDTD commercial mode solving software, $n_0(x, y)$ and $n_2(x, y)$ are the linear refractive index and $n_2$ profiles over the waveguide cross section, respectively. The values of $n_2$ for silica and $Si_3N_4$ used in our calculation were $2.60 \times 10^{-20} \text{ m}^2/\text{W}^{36}$ and $2.62 \times 10^{-19} \text{ m}^2/\text{W}$, respectively, the latter obtained by fitting the experimental results for the uncoated $Si_3N_4$ waveguide.

## Conflict of interest

The authors declare no competing financial interest.

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73. Yang Qu, Jiayang Wu, Yuning Zhang, Yunyi Yang, Linnan Jia, Baohua Jia, and David J. Moss, "Photo thermal tuning in GO-coated integrated waveguides", Micromachines Vol. 13 1194 (2022). doi.org/10.3390/mi13081194

74. Yuning Zhang, Jiayang Wu, Yunyi Yang, Yang Qu, Linnan Jia, Baohua Jia, and David J. Moss, "Enhanced spectral broadening of femtosecond optical pulses in silicon nanowires integrated with 2D graphene oxide films", Micromachines Vol. 13 756 (2022). DOI:10.3390/mi13050756.

75. Linnan Jia, Jiayang Wu, Yuning Zhang, Yang Qu, Baohua Jia, Zhigang Chen, and David J. Moss, "Fabrication Technologies for the On-Chip Integration of 2D Materials", Small: Methods 6, 2101435 (2022). DOI:10.1002/smtd.202101435.

76. Yuning Zhang, Jiayang Wu, Yang Qu, Linnan Jia, Baohua Jia, and David J. Moss, "Design and optimization of four-wave mixing in microring resonators integrated with 2D graphene oxide films", Journal of Lightwave Technology 39 (20) 6553-6562 (2021). DOI:10.1109/JLT.2021.3101292. Print ISSN: 0733-8724, Online ISSN: 1558-2213 (2021).

77. Yuning Zhang, Jiayang Wu, Yang Qu, Linnan Jia, Baohua Jia, and David J. Moss, "Optimizing the Kerr nonlinear optical performance of silicon waveguides integrated with 2D graphene oxide films", Journal of Lightwave Technology Vol. 39 (14) 4671-4683 (2021). DOI: 10.1109/JLT.2021.3069733.

78. Yang Qu, Jiayang Wu, Yuning Zhang, Yao Liang, Baohua Jia, and David J. Moss, "Analysis of four-wave mixing in silicon nitride waveguides integrated with 2D layered graphene oxide films", Journal of Lightwave Technology Vol. 39 (9) 2902-2910 (2021). DOI: 10.1109/JLT.2021.3059721.

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108. Yang Sun, Jiayang Wu, Mengxi Tan, Xingyuan Xu, Yang Li, Roberto Morandotti, Arnan Mitchell, and David Moss, "Applications of optical micro-combs", Advances in Optics and Photonics Vol. 15 (1) 86-175 (2023). DOI:10.1364/AOP.470264.
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144. Hamed Arianfard, Jiayang Wu, Saulius Juodkazis and David J. Moss, "Advanced multi-functional integrated photonic filters based on coupled Sagnac loop reflectors", Paper 11691-4, PW21O-OE203-44, Silicon Photonics XVI, SPIE Photonics West, San Francisco CA March 6-11 (2021). doi.org/10.1117/12.2584020

145. Jiayang Wu, Tania Moein, Xingyuan Xu, and David J. Moss, "Advanced photonic filters via cascaded Sagnac loop reflector resonators in silicon-on-insulator integrated nanowires", Applied Physics Letters Photonics vol. 3 046102 (2018). DOI:/10.1063/1.5025833

146. Jiayang Wu, Tania Moein, Xingyuan Xu, Guanghui Ren, Arnan Mitchell, and David J. Moss, "Micro-ring resonator quality factor enhancement via an integrated Fabry-Perot cavity", Applied Physics Letters Photonics vol. 2 056103 (2017). doi: 10.1063/1.4981392.

147. Linnan Jia, Dandan Cui, Jiayang Wu, Haifeng Feng, Tieshan Yang, Yunyi Yang, Yi Du, Weichang Hao, Baohua Jia, David J. Moss, "BiOBr nanoflakes with strong nonlinear optical properties towards hybrid integrated photonic devices", Applied Physics Letters Photonics vol. 4 090802 (2019). DOI: 10.1063/1.5116621

148. Linnan Jia, Jiayang Wu, Yunyi Yang, Yi Du, Baohua Jia, David J. Moss, "Large Third-Order Optical Kerr Nonlinearity in Nanometer-Thick PdSe2 2D Dichalcogenide Films: Implications for Nonlinear Photonic Devices", ACS Applied Nano Materials vol. 3 (7) 6876-6883 (2020). DOI:10.1021/acsanm.0c01239.

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