# Design of integrated ring resonators with graphene oxide 2D films for four wave mixing

David J. Moss

Email: dmoss@swin.edu.au

Optical Sciences Center, Swinburne University of Technology, Hawthorn, VIC 3122, Australia.

**Abstract**—We theoretically investigate and optimize the performance of four-wave mixing (FWM) in microring resonators (MRRs) integrated with two-dimensional (2D) layered graphene oxide (GO) films. Owing to the interaction between the MRRs and the highly nonlinear GO films as well as to the resonant enhancement effect, the FWM efficiency in GO-coated MRRs can be significantly improved. Based on previous experiments, we perform detailed analysis for the influence of the GO film parameters and MRR coupling strength on the FWM conversion efficiency (CE) of the hybrid MRRs. By optimizing the device parameters to balance the trade-off between the Kerr nonlinearity and loss, we achieve a high CE enhancement of ~18.6 dB relative to the uncoated MRR, which is ~8.3 dB higher than previous experimental results. The influence of photo-thermal changes in the GO films as well as variations in the MRR parameters such as the ring radius and waveguide dispersion on the FWM performance is also discussed. These results highlight the significantly improved FWM performance that can be achieved in MRRs incorporating GO films and provide a guide for optimizing their FWM performance.

**Keywords** — Four-wave mixing, 2D materials, microring resonator, graphene oxide.

## I. INTRODUCTION

Graphene oxide (GO) has become a rising star in the family of two-dimensional (2D) materials owing to its potential for mass production as well as the flexibility in tuning its material properties [1-4]. Recently, the excellent nonlinear optical properties of GO have attracted significant interest [5-9]. It has been reported that GO has an ultrahigh Kerr nonlinearity ($n_2$) that is about 4 orders of magnitude higher than nonlinear bulk materials such as silicon and chalcogenide glasses [5, 6, 10]. In addition, GO has a large optical bandgap (typically > 2 eV [1, 11]), which yields a material absorption that is over 2 orders of magnitude lower than graphene as well as negligible two-photon absorption (TPA) in the telecom band [12, 13]. Another important advantage of GO is that it can be mass produced from natural graphite [3]. This, together with facile solution-based fabrication processes [14], is attractive for large-scale manufacturing of integrated devices that incorporate GO films [2, 15, 16].

Based on these advantages, many high performance nonlinear photonic devices that incorporate GO films [13, 17-

21] have been demonstrated – especially those based on complementary metal-oxide-semiconductor (CMOS) compatible integrated platforms [13, 17-19]. Enhanced four-wave mixing (FWM) in GO-coated doped silica and silicon nitride (SiN) waveguides has been reported [13, 17], where conversion efficiency (CE) enhancements of up to 6.9 dB and 9.1 dB relative to the uncoated waveguides were achieved. Significant spectral broadening of optical pulses in GO-coated silicon waveguides induced by self-phase modulation (SPM) has also been observed [19], achieving a high spectral broadening factor of 4.34 for a device with a patterned film including 10 layers of GO. A significant enhancement in the nonlinear figure of merit (FOM) for silicon nanowires by a factor of 20 was also achieved, resulting in a FOM > 5.

In our previous work [18], we experimentally demonstrated enhanced FWM in CMOS compatible doped silica microring resonators (MRRs) integrated with 2D layered GO films. Due to the resonant enhancement effect [22, 23], an increase of up to ~10.3 dB in the FWM CE was achieved. In this paper, we fully investigate and optimize the FWM performance of GO-coated MRRs based on previous experimental measurements of the GO film properties such as loss and Kerr nonlinearity, which are distinct from bulk materials and show a strong dependence on the film thickness and optical power. We perform a detailed analysis of the influence of the GO film parameters and MRR coupling strength on the FWM CE of the hybrid MRRs. By properly balancing the trade-off between the Kerr nonlinearity and loss, a high CE enhancement of ~18.6 dB relative to the uncoated MRR is achieved, which is ~8.3 dB higher than what has been achieved experimentally. We also discuss the influence of photo-thermal changes in the GO films as well as the variation of other MRR parameters such as ring radius and waveguide dispersion on the FWM performance. These results highlight the significant potential to improve on previous experimental results [18] and provide a guide for optimizing FWM performance of MRRs integrated with GO films.
## II. DEVICE STRUCTURE

Fig. 1(a) shows a schematic of an integrated MRR made from doped silica, with 1 layer of patterned GO film being coated on the planarized waveguide top surface. Inset shows a schematic illustration for the atomic structure of GO, including different oxygen-containing functional groups (OFGs) such as hydroxyl, epoxide, and carboxylic decorated on a graphene-like carbon lattice. In contrast to graphene, which has a metallic behavior with a zero bandgap [24], pristine GO is a dielectric material with a bandgap > 2 eV [1, 12]. This is larger than both the single photon (~0.8 eV) and two-photon (~1.6 eV) energies around 1550 nm, resulting in negligible linear light absorption or TPA in the telecom band. We consider MRRs that are fabricated on a high index doped silica glass (Hydex) platform [25] via CMOS compatible processes. More details about the Hydex device fabrication can be found in Refs. [22, 26, 27]. As compared with GO-coated waveguides, GO-coated MRRs can dramatically improve the FWM efficiency by virtue of the resonant enhancement of the optical intensity within the resonant cavities [22, 23], thus significantly reducing the required power. The upper cladding of the doped silica MRR is removed by chemical mechanical polishing (CMP) to obtain a planarized waveguide top surface for GO film coating. The GO film coating can be achieved using a solution-based method that yields layer-by-layer film deposition and precise control of the film thickness with an ultrahigh resolution of ~2 nm [12, 28]. Unlike graphene or other 2D materials that are typically prepared via non-solution-based deposition followed by cumbersome layer transfer processes [29-32], our coating method enables large-area, transfer-free, and high-quality GO film coating with high fabrication stability, mass producibility, and excellent film attachment onto integrated waveguides [2, 19]. Patterning of the films can be achieved via standard

<figure><img src="image_1.png" /><figcaption>Fig. 1. (a) Schematic illustration of an integrated doped silica MRR coated with 1 layer of patterned GO film. Inset shows a schematic of atomic structure of GO. (b) Schematic illustration of the cross section of the hybrid MRR in (a). (c) TE mode profile corresponding to (b).</figcaption></figure>

lithography and lift-off processes [18, 28]. This, together with the layer-by-layer deposition of GO films, forms the basis for the optimization of the FWM performance of the hybrid MRRs with different GO film thicknesses and pattern lengths.

Fig. 1(b) shows a schematic of the waveguide cross section of the hybrid MRR in Fig. 1(a). The corresponding transverse electric (TE) mode profile is shown in Fig. 1(c). We chose the TE polarization in our following analysis because it supports an in-plane interaction between the film and the evanescent field leaking from the MRR, which is much stronger than the

<table><caption>TABLE I
PARAMETERS OF DOPED SILICA MRR, GO FILM, AND CW LASER</caption><thead><tr><th></th><th></th><th>Refractive index <sup>a</sup></th><th>Extinction coefficient</th><th>Kerr coefficient (m<sup>2</sup>/W)</th></tr></thead><tbody><tr><td rowspan="3">Doped<br>Silica<br>MRR</td><td>Material<br>parameters</td><td><i>n</i><sub>hydex</sub> : 1.7 [25]</td><td><i>k</i><sub>hydex</sub> : 0 [18]</td><td><i>n</i><sub>2-hydex</sub> : 1.3 × 10<sup>-19</sup> [18]</td></tr><tr><td rowspan="2">Physical<br>parameters</td><td>Transmission / coupling coefficients</td><td>Radius <sup>c</sup></td><td>Propagation loss (dB/cm)</td></tr><tr><td><i>t</i>, κ<sup>b</sup></td><td><i>R</i></td><td>0.25 [18]</td></tr><tr><td rowspan="4">GO<br>film</td><td>Material<br>parameters</td><td>Refractive index</td><td>Extinction coefficient <sup>d</sup></td><td>Kerr coefficient (m<sup>2</sup>/W)</td></tr><tr><td rowspan="3">Physical<br>parameters</td><td><i>n</i><sub>GO</sub> : 1.97 [13]</td><td><i>k</i><sub>GO</sub>(N) : 0.0074 – 0.0189 [18]</td><td><i>n</i><sub>2-GO</sub>(N) : 1.7 × 10<sup>-14</sup> – 2.7 × 10<sup>-14</sup> [18]</td></tr><tr><td>Thickness for 1 layer <sup>e</sup></td><td>GO layer number</td><td>Coating length</td></tr><tr><td><i>d</i> : 2 nm [18]</td><td><i>N</i></td><td><i>L</i><sub>c</sub></td></tr><tr><td rowspan="2">CW<br>laser</td><td rowspan="2">Physical<br>parameters</td><td>CW power for loss measurement</td><td>Pump power for FWM</td><td>Signal power for FWM</td></tr><tr><td><i>P</i><sub>CW</sub></td><td><i>P</i><sub>p</sub></td><td><i>P</i><sub>s</sub></td></tr></tbody></table>

<footnote><sup>a</sup> Here we show the refractive indices at 1550 nm, the same applies for other material parameters in this Table.</footnote>

<footnote><sup>b</sup> $t^2 + \kappa^2 = 1$ for lossless coupling is assumed for the directional couplers.</footnote>

<footnote><sup>c</sup> The circumference of the MRR is $L = 2\pi R$.</footnote>

<footnote><sup>d</sup> Here we show the extinction coefficient and Kerr coefficient at $P_{CW} = 25$ dBm for $N = 1 – 50$ based on the measured results in Ref. [18].</footnote>

<footnote><sup>e</sup> Following our previous experimental measurements [18], the GO film thickness is assumed to be proportional to $N$, with a thickness of 2 nm per layer.</footnote>
out-of-plane interaction due to the significant optical anisotropy of 2D films [28, 31, 32]. Table I summarizes the parameters of the doped silica MRR, the GO film, and the continuous-wave (CW) laser used in our following analysis, with the former two being further classified into material and physical parameters. Four-port MRRs with two identical directional couplers are used in our following analysis, which is consistent with that used in Ref. [18]. The GO-coated MRRs are designed based on, but not limited to, the Hydex platform.

In the following sections, we first investigate the power-dependent propagation loss and nonlinear parameters of the hybrid MRRs induced by photo-thermal changes in the GO films. Next, by properly balancing the trade-off between loss and the Kerr nonlinearity, we optimize the FWM CE in the hybrid MRRs by regulating the GO film parameters ($N, L_c$) and the MRR coupling strength ($t$). Finally, we discuss the influence of photo-thermal changes in the GO films as well as the effect of varying other MRR parameters such as the ring radius and waveguide dispersion on the FWM performance of the hybrid MRRs.

### III. POWER-DEPENDENT PROPAGATION LOSS AND NONLINEAR PARAMETERS

As reported in previous work [18], the linear loss ($k$) and Kerr nonlinearity ($n_2$) of GO films coated on integrated waveguides change with input CW power, particularly at high powers. This can be attributed to photo-thermal changes in the GO films, which is a combined result of power sensitive photo-thermal reduction as well as self-heating and thermal dissipation in the multilayered film structure [17, 18, 33]. Such changes are not permanent and can revert back after the power is turned off. In addition, these changes have a slow time response on the order of millisecond, which is different to FWM and TPA that have ultrafast response times on the order of femtoseconds [17]. Photo-thermal changes in the GO films lead to power-dependent propagation loss and nonlinear parameters for GO-coated waveguides, and this is further amplified in GO-coated MRRs due to resonant enhancement. In this section, we investigate the power-dependent propagation loss and nonlinear parameters of the hybrid MRRs induced by the photo-thermal changes in GO films.

We first calculate the resonant build-up factor ($\Gamma$) of a MRR as a function of its coupling strength ($t$) and round-trip field transmission factor ($A$). The $\Gamma$ reflects the relationship between the input CW power ($P_{CW}$) and the intracavity power ($P_{intra}$) in a MRR, which will be used for calculating $P_{intra}$ directly related to the propagation loss and nonlinear linear parameters of the hybrid MRRs in our following analysis. Fig. 2(a) shows $\Gamma$ versus $t$ and $A$. The $\Gamma$ was calculated at resonant wavelengths based on [34, 35]:

$$ \Gamma = \frac{P_{intra}}{P_{CW}} = \frac{(1-t^2)t^2 A^2}{(1-2t^2 A+t^4 A^2)} \quad (1) $$

In Eq. (1), $A$ can be further expressed as:

$$ A = \exp(-\frac{1}{2}\alpha_u L_u) \exp(-\frac{1}{2}\alpha_c L_c) \quad (2) $$

<figure><img src="image_2.png" /><figcaption>Fig. 2. (a) $\Gamma$ versus $t$ and $A$. (b) ER versus $t$ and $A$. The insets in (a) and (b) show the corresponding zoom-in views.</figcaption></figure>

where $\alpha_{c,u}$ and $L_{c,u}$ are the loss factors and lengths of the GO coated and uncoated waveguide segments, respectively. In Fig. 2(a), the maximum $A$ is 0.989, which corresponds to the uncoated MRR (unless otherwise specified, the MRR radius used is 592 µm – the same as in Ref. [18]). The maximum $\Gamma$ is achieved at $t = 0.994$ and $A = 0.989$, which is determined by the balance between $t$ and $A$, as reflected by Eq. (1). Fig. 2(b) shows the MRR’s extinction ratio (ER) versus $t$ and $A$. The ER increases with $A$ but decreases with $t$, mainly due to the change in the difference between intracavity loss and external coupling loss of a four-port MRR with two identical directional couplers [36-42].

In previous work [18], we measured the propagation loss and nonlinear parameters versus input CW power ($P_{CW}$) for hybrid MRRs with 1–5 layers of uniformly coated and 10–50 layers of patterned (50-µm-long) GO, respectively. The coupling strength of the uncoated MRR was 0.912. In Figs. 3(a) and (b), we fit the measured power-dependent propagation loss and nonlinear parameters as functions of the intracavity power $P_{intra}$, which will be used for calculating FWM CE in next section. The input CW power $P_{CW}$ in Ref. [18] (from 15 dBm to 25 dBm) is converted to corresponding intracavity power $P_{intra}$ based on the calculated $\Gamma$ in Fig. 2(a). In Fig. 3(a), the propagation loss increases with GO layer number $N$. This is mainly due to an increase in mode overlap for the hybrid MRRs with thicker GO films. A small contribution is from an increase in the material absorption arising from inhomogeneous defects and imperfect contact between the multiple GO layers [13, 28]. As $P_{intra}$ increases, the hybrid MRRs show an increased propagation loss, in contrast to the uncoated MRR that manifests a constant propagation loss. This further confirms the power sensitive photo-thermal changes in GO films. Following the same trends with the propagation loss, the nonlinear parameter $\gamma$ in Fig. 3(b) increases with both $N$ and $P_{intra}$. This reflects the trade-off between the Kerr nonlinearity and linear loss, which
<figure><img src="image_3.png" /><figcaption>Fig. 3. (a)–(b) Fit propagation loss and nonlinear parameters $\gamma$ of GO-coated MRRs versus intracavity power $P_{\text{intra}}$ based on previous measured results for hybrid MRRs with (i) 1–5 layers of uniformly coated and (ii) 10–50 layers of patterned GO, respectively. The result for the uncoated MRR ($N = 0$) is also shown for comparison.</figcaption></figure>

is critical for optimizing the FWM performance. Note that in our calculation we neglect the influence of power-dependent loss on the round-trip field transmission factor $A$, since accounting for it would only lead to a maximum difference in $\Gamma < 0.7\%$.

For a fixed input power $P_{CW}$, varying the GO film parameters such as layer number $N$ and coating length $L_c$ changes the intracavity loss and hence intracavity power $P_{\text{intra}}$. Therefore, the power dependent propagation loss and nonlinear parameters of the hybrid MRRs are also affected by $N$ and $L_c$. Fig. 4(a) shows $P_{\text{intra}}$ versus $L_c$ for the hybrid MRRs with films including (i) 1–5 and (ii) 10–50 layers of GO. The other parameters are kept constant: $t = 0.912$ and $P_{CW} = 25$ dBm – taken from our previous experiments [18]. To clearly show the difference, we choose different ranges for $L_c$ in Figs. 4(a-i) and (a-ii) – with a smaller range for thicker films ($N \ge 10$). As can be seen, $P_{\text{intra}}$ decreases with $L_c$ and $N$, resulting from an increased intracavity loss in the hybrid MRRs. Figs. 4(b) and (c) show the corresponding propagation

<figure><img src="image_4.png" /><figcaption>Fig. 4. (a) Intracavity power $P_{\text{intra}}$, (b) propagation loss, and (c) nonlinear parameters $\gamma$ versus coating length $L_c$ for the hybrid MRRs with films including (i) $N = 1–5$ and (ii) $N = 10–50$ GO layers, respectively. In (a) – (c), $t = 0.912$, $R = 592$ µm, and $P_{CW} = 25$ dBm.</figcaption></figure>

loss and nonlinear parameters $\gamma$ versus $L_c$, respectively. Both the propagation loss and nonlinear parameters $\gamma$ decrease with $L_c$, showing a trend similar to that of $P_{\text{intra}}$ in Fig. 4(a) and reflecting that the power dependent propagation loss and nonlinear parameters of the hybrid MRRs is strongly dependent on $P_{\text{intra}}$.

## IV. OPTIMIZING FWM PERFORMANCE

In this section, we investigate the influence of the GO film parameters ($N$, $L_c$) and MRR coupling strength ($t$) on the FWM performance of the GO-coated MRRs, taking into account the power-dependent propagation loss and nonlinear parameter discussed in Section III.

The FWM CE of the GO-coated MRRs ($CE_{MRR}$) is calculated by [23,43]

$$CE_{MRR} = \frac{P_{\text{idler, out}}}{P_{\text{signal, in}}} = CE_{WG} \cdot FE_p^4 \cdot FE_s^2 \cdot FE_i^2 \quad (3)$$

<table><caption>TABLE II
PROCESS FLOW TO CALCULATE FWM CE IN GO-COATED MRRS</caption><thead><tr><th>Pre-step <sup>a</sup></th><th>Aim</th><th>Method & Theory</th><th>Used parameters</th></tr></thead><tbody><tr><td>0</td><td>Fit γ(P<sub>intra</sub>), α<sub>c</sub>(P<sub>intra</sub>) based on the experimental results in Ref. [18]</td><td>Matlab</td><td>Measured γ and α<sub>c</sub> in Ref. [18]</td></tr><tr><th>Step</th><th>Aim</th><th>Method & Theory</th><th>Used parameters</th></tr><tr><td>1</td><td>Calculate round-trip transmission A(N, L<sub>c</sub>, α<sub>c</sub>)</td><td>Eq. (2)</td><td>N, L<sub>c</sub>, α<sub>c</sub></td></tr><tr><td>2</td><td>Calculate build-up factor Γ(A, t)</td><td>Eq. (1)</td><td>t and results in Step 1</td></tr><tr><td>3</td><td>Calculate intracavity power P<sub>intra</sub>(Γ, P<sub>p</sub>, P<sub>s</sub>)</td><td>Eq. (1)</td><td>P<sub>p</sub>, P<sub>s</sub>, and results in Step 2</td></tr><tr><td>4</td><td>Calculate γ(P<sub>intra</sub>) and α<sub>c</sub>(P<sub>intra</sub>)</td><td>Matlab</td><td>Results in Pre-Step and Step 3</td></tr><tr><td>5</td><td>Calculate CE of GO-coated MRRs <sup>b</sup></td><td>Matlab<br>Eqs. (3) – (5)</td><td>t, κ, and results in Step 1, 4</td></tr></tbody></table>

<footnote><sup>a</sup> The pre-step is done in Fig. 3 of Section III.</footnote>

<footnote><sup>b</sup> To optimize FWM CE, Step 1–5 were repeated to calculate the CEs for the hybrid MRRs with various $N$, $L_c$, and $t$.</footnote>
<figure><img src="image_5.png" /><figcaption>Fig. 5. FWM CE of GO-coated MRRs versus $L_c$ and $P_p$ when (a) $N = 1-5$ and (b) $N = 10-50$. In (a) and (b), $t = 0.912$, $R = 592$ µm. The corresponding result for the uncoated MRR (when $L_c = 0$ mm) is also shown.</figcaption></figure>

where $P_{idler, out}$ and $P_{signal, in}$ are the output power of the idler and input power of the signal, respectively. $CE_{WG}$ is the CE of an equivalent waveguide with the same length as the circumference of the MRR. The calculation of $CE_{WG}$ is based on the theory in Refs. [13, 17]. For the MRRs with patterned GO films, $CE_{WG}$ is calculated by dividing the equivalent waveguides into coated and uncoated segments that have different propagation loss and nonlinear parameters. $FE_{p,s,i}$ in Eq. (3) are resonant field enhancement factors for the pump, signal, and idler, respectively, which can be expressed as [18, 22, 44]:

$$FE_{p,s,i} = \kappa \cdot t / [1 - t^2 \cdot A \cdot \exp(j \cdot \phi_{p,s,i})] \quad (4)$$

where $t$ and $\kappa$ are the field transmission and coupling coefficients defined in Table I, respectively. $\phi_{p,s,i}$ are the round-trip phase shift of the pump, signal, and idler, respectively, which can be given by:

$$\phi_{p, s, i} = k_{pu, su, iu} L_u + k_{pc, sc, ic} L_c \quad (5)$$

$k_{pc, sc, ic}$ and $k_{pu, su, iu}$ are the wavenumbers of the pump, signal, and idler for the GO coated and uncoated segments, respectively. Table II summarizes the process flow to calculate the FWM CE of the hybrid MRRs. On the basis of the fit propagation loss and nonlinear parameter in Fig. 3, five steps were repeated to calculate the CE of hybrid MRRs with different GO film parameters ($N, L_c$) and coupling strength ($t$).

We first analyze the FWM CE of the hybrid MRRs with a fixed coupling strength ($t$) but different GO film parameters ($N, L_c$). The calculated FWM CE versus coating length $L_c$ and input pump power $P_p$ is shown in Fig. 5, with (a-i) – (a-v) and (b-i) – (b-v) showing the results for $N = 1-5$ and $N = 10-50$, respectively. Similar to Fig. 4, a smaller range of $L_c$ is chosen for thicker films ($N \ge 10$) to clearly show the difference. To simplify the discussion, we used the same power for the pump and signal in our calculation, therefore 12 – 22 dBm of $P_p$ in

<table><caption>TABLE III
COMPARISON OF HYBRID MRRS WITH OPTIMIZED GO COATING LENGTHS AND THOSE IN PREVIOUS EXPERIMENT</caption><thead><tr><th rowspan="2">N</th><th colspan="4">Experimental results <sup>a</sup></th><th colspan="4">Optimized L<sub>c</sub>' for fixed t = 0.912</th></tr><tr><th>L<sub>c</sub> (mm)</th><th>t</th><th>Max CE (dB)</th><th>Max CE enhancement (dB)</th><th>L<sub>c</sub>' (mm)</th><th>t</th><th>Max CE (dB)</th><th>Max CE enhancement (dB)</th></tr></thead><tbody><tr><td>0</td><td>0</td><td>0.912</td><td>-48.4</td><td>0</td><td>0</td><td>0.912</td><td>-48.4</td><td>0</td></tr><tr><td>1</td><td rowspan="5">3.67</td><td rowspan="5">0.912</td><td>-40.8</td><td>7.6</td><td>3.4</td><td rowspan="5">0.912</td><td>-40.7</td><td>7.7</td></tr><tr><td>2</td><td>-43.1</td><td>5.3</td><td>1.4</td><td>-41.0</td><td>7.4</td></tr><tr><td>3</td><td>-49.1</td><td>-0.7</td><td>0.6</td><td>-41.8</td><td>6.6</td></tr><tr><td>4</td><td>-54.9</td><td>-6.5</td><td>0.4</td><td>-41.7</td><td>6.7</td></tr><tr><td>5</td><td>-60.9</td><td>-12.5</td><td>0.3</td><td>-42.4</td><td>6.0</td></tr><tr><td>10</td><td rowspan="5">0.05</td><td rowspan="5">0.912</td><td>-45.9</td><td>2.5</td><td>0.081</td><td rowspan="5">0.912</td><td>-45.7</td><td>2.7</td></tr><tr><td>20</td><td>-43.8</td><td>4.6</td><td>0.041</td><td>-43.9</td><td>4.5</td></tr><tr><td>30</td><td>-42.5</td><td>5.9</td><td>0.029</td><td>-41.7</td><td>6.7</td></tr><tr><td>40</td><td>-40.7</td><td>7.7</td><td>0.021</td><td>-38.8</td><td>9.6</td></tr><tr><td>50</td><td>-38.1</td><td>10.3</td><td>0.017</td><td>-34.7</td><td>13.7</td></tr></tbody></table>

<footnote><sup>a</sup> The experimental results are based on the measured values at $P_p = P_s = 22$ dBm in Ref. [18].</footnote>
<figure><img src="image_6.png" /><figcaption>Fig. 6. (a) Optimized coating length $L_c'$ versus $t$. (b) CE of hybrid MRRs with the optimized coating length $L_c'$ in (a). (c) CE enhancement of the hybrid MRRs extracted from (b). (d) Insertion loss of the hybrid MRRs with the optimized coating lengths $L_c'$ in (a). In (a) – (d), $R = 592$ µm, $P_p = P_s = 22$ dBm, (i) and (ii) show the results for $N = 1–5$ and $N = 10–50$, respectively. In (b) and (d), the results for the uncoated MRRs ($N = 0$) are also shown for comparison.</figcaption></figure>

Fig. 5 corresponds to 15 – 25 dBm of $P_{cv}$ in Fig. 3. In our calculation, we used constant $t = 0.912$ and $R = 592$ µm. The corresponding result for the uncoated MRR (when $L_c = 0$ mm) is also shown for comparison, which achieves the maximum CE of -48.4 dB at $P_p = P_s = 22$ dBm.

In Fig. 5, the CE of the hybrid MRRs first increases with GO film length $L_c$ and then decreases, achieving maximum values at intermediate film lengths. The optimized film length $L_c'$ that corresponds to the maximum CE decreases with $N$. This reflects the fact that the Kerr nonlinearity enhancement dominates for the devices with relatively small $L_c$ and $N$, and the influence of loss increase becomes more significant as $L_c$ and $N$ increase.

In Table III, we compare the calculated CE of the hybrid MRRs with optimized GO film lengths and the measured CE in our previous experiment where we fabricated devices with fixed film coating lengths of ~3.67 mm (i.e., the circumference of the MRR) for $N = 1–5$ and $50$ µm for $N = 10–50$ [18]. For the devices with optimized GO film lengths, there is an improvement in the CE for all the considered GO layer numbers. Particularly, a maximum CE of -34.7 dB is achieved for $N = 50$ and $L_c = 17$ µm, which corresponds to a CE enhancement of 13.7 dB compared to the uncoated MRR and 3.4 dB further improvement relative to previous experimental result.

In addition to GO film parameters ($N$, $L_c$), the MRR coupling strength ($t$) also significantly affects the FWM performance of the hybrid MRRs. Based on the process flow in Table II, we further calculate the FWM CE of hybrid MRRs with different coupling strength ($t$). In our calculations, we chose 20 different values of $t$ ranging from 0.812 to 0.997. For each of them, the calculation processes for Fig. 5 with a fixed $t$ were repeated to obtain the optimized film length $L_c'$ and the corresponding maximum CE for different numbers of GO layers $N$.

Fig. 6(a) shows the calculated $L_c'$ versus $t$, (i) for $N = 1–5$ and (ii) for $N = 10–50$. The other device parameters are kept

the same, i.e., $R = 592$ µm and $P_p = P_s = 22$ dBm. As can be seen, $L_c'$ decreases with $t$. This reflects that the positive impact of the GO films in improving the FWM CE decreases with $t$. Fig. 6(b) shows the maximum CE of the hybrid MRRs corresponding to the calculated $L_c'$ in Fig. 6(a). The results for the uncoated MRRs ($N = 0$) are also shown for comparison. The CE enhancement compared to the uncoated MRR is further extracted from Fig. 6(b) and plot in Fig. 6(c). A maximum CE enhancement of 18.6 dB is achieved at $t = 0.812$, $L_c = 42$ µm, and $N = 50$, which is 4.9 dB higher than the maximum CE enhancement when $t = 0.912$. This reflects the fact that reducing $t$ further yields a better CE enhancement. The difference in CE between the hybrid and uncoated MRRs becomes smaller as $t$ increases, which is consistent with the trend for $L_c'$ in Fig. 6(a). When $t$ is close to 1, the CE enhancement approaches zero, indicating that incorporating GO films would not bring any benefits in improving the FWM performance in this case. In Fig. 6(d), we plot the insertion loss (at the drop port) of the hybrid MRRs with optimized film lengths $L_c'$ in Fig. 6(a). It can be seen that the insertion loss increases with $t$ and becomes > 8 dB when $t$ is close to 1, which is mainly induced by the four-port MRRs with two identical directional couplers. This indicates that despite the MRR with a weak coupling strength (i.e., high $t$) has a high CE, it suffers from a high insertion loss that limits their use in practical applications.

## V. DISCUSSION

In this section, we discuss the influence of photo-thermal changes in the GO films as well as the effect of varying some of the other MRR paramteres such as ring radius and waveguide dispersion on the FWM performance. This, together with the analysis in Section IV, provides a systematic approach for designing GO-coated MRRs in order to optimize the FWM performance.

As discussed in Section III, photo-thermal changes in the GO films lead to power-dependent propagation loss and
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. CE comparison of GO-coated MRRs with and without (W/O) considering photo-thermal changes (PTCs) in GO films when (a) $N = 1$, $L_c = 3.4$ mm and (b) $N = 50$, $L_c = 17$ µm. In (a) and (b), $t = 0.912$ and $R = 592$ µm.</figcaption></figure>

nonlinear parameter $\gamma$ for the hybrid MRRs. Both of these parameters affect the FWM CE and there is a trade-off between them. In Fig. 7, we compare the FWM CE of the hybrid MRRs with and without considering any photo-thermal changes. For the hybrid MRRs without any photo-thermal changes, we used a constant propagation loss and nonlinear parameter, equivalent to their values at low powers. In Figs. 7(a) and (b), we show the results for the hybrid MRRs with 1 and 50 layers of GO. For each of them, optimized film lengths were chosen. The other device parameters are kept the same, i.e., $t = 0.912$ and $R = 592$ µm. In Fig. 7(a), after including photo-thermal changes, the CE decreases, with a more notable difference occurring at higher powers. This reflects the fact that the influence of an increase in loss is more significant than the increase of $\gamma$ for the device with a thin GO film. In Fig. 7(b), the CE obtained when including photo-thermal effects is lower at low pump powers, while as the pump power increases, it gradually overtakes the CE obtained without including photo-thermal effects. This reflects a more complex influence of the photo-thermal changes on the FWM performance for the hybrid MRRs with thick GO films, which can be attributed to an increase of defects and imperfect

contact as well as more obvious thermal dissipation issue in the thick GO films.

Due to the resonant enhancement effect in the MRRs, the FWM CE can be significantly improved in GO-coated MRRs as compared with GO-coated waveguides. In Fig. 8, we compare the FWM CE of GO-coated MRRs and comparable GO-coated waveguides, (i) for the devices with 1 layer of GO and (ii) for the devices with 50 layers of GO. Similar to the case of Fig. 7, optimized film lengths were chosen for the hybrid MRRs and the other device parameters are kept the same as those in Fig. 7. The hybrid waveguides have the same length as the circumference of the MRRs, and both the MRR and the waveguides have the same GO film length. For the hybrid waveguides, we neglect the slight variation induced by photo-thermal changes in the GO films. As can be seen, the CEs of the hybrid MRRs are much higher than those of the hybrid waveguides for both $N = 1$ and $N = 50$, clearly reflecting the huge CE improvement enabled by the resonant structure.

For practical device fabrication, hybrid MRRs with uniformly coated GO films are easier to be fabricated since they do not need lithography or lift-off processes for film patterning. In Fig. 9, we further investigate the FWM performance of these hybrid MRRs. Fig. 9(a-i) shows the

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

<figure><img src="image_10.png" /><figcaption>Fig. 8. CE comparison of GO-coated MRRs and comparable GO-coated waveguides when (a) $N = 1$, $L_c = 3.4$ mm and (b) $N = 50$, $L_c = 17$ µm. In (a) and (b), $t = 0.912$ and $R = 592$ µm. WG: waveguide.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Fig. 9. Performance comparison of uniformly GO-coated MRRs when (a) $N = 1$ and (b) $N = 2$. In (a) – (b), $P_p = P_s = 22$ dBm, (i) – (iii) show the ER, CE, and CE enhancement versus $R$ and $t$, respectively. The black circles mark the experimental results in Ref. [18] and the black crosses mark the maximum values in each figure. ΔCE: CE enhancement compared to uncoated MRRs with the same $t$ and $R$.</figcaption></figure>

MRR’s ER versus its radius $R$ and coupling strength $t$ when $N = 1$ and $P_p = P_s = 22$ dBm. The ER decreases with both $R$ and $t$ – the former results from the increase of the intracavity loss with $R$, while the latter is consistent with the trend in Fig. 2(b). Fig. 9(a-ii) shows the CE versus $R$ and $t$. The CE enhancement relative to the uncoated MRR is further extracted from Fig. 9(a-ii) and shown in Fig. 9(a-iii). In our calculation, we neglect the slight difference in the MRR coupling strength $t$ between the GO coated and uncoated MRRs, since including it would result in a difference of only < 0.3%. In Fig. 9(a-ii), the CE (-40.8 dB) at $R = 592$ µm and $t = 0.912$ is marked, which corresponds to a CE enhancement of 7.6 dB in Fig. 9(a-iii), showing good agreement with the experimental result in Ref. [18]. The maximum CE (-24.9 dB) at $R = 135$ µm and $t = 0.992$ is also marked, which is 15.9 dB higher than the CE at $R = 592$ µm and $t = 0.912$ and corresponds to a CE enhancement of -1.8 dB. In Fig. 9(a-iii), a maximum CE enhancement of 14.6 dB is achieved at $R = 135$ µm and $t = 0.812$, which is different to the point corresponding to the maximum CE. This reflects the trade-off between achieving the maximum CE versus the maximum relative CE enhancement for the device design, which is consistent with the results in Figs. 6(b) and

<figure><img src="image_12.png" /><figcaption>Fig. 10. (a) Group-velocity dispersion $\beta_2$ for hybrid MRRs with (i) $N = 1$ and (ii) $N = 50$ layers of GO. (b) CE versus $\Delta\lambda/FSR$ for hybrid MRRs when (i) $N = 1$, $L_c = 3.4$ mm and (ii) $N = 1$, $L_c = 17$ µm. In (a) and (b), $t = 0.912$, $R = 592$ µm, and $P_p = P_s = 22$ dBm. The corresponding results for the uncoated MRR are also shown for comparison.</figcaption></figure>

(c). Fig. 9(b) shows the corresponding results for $N = 2$. The maximum CE enhancement is improved further by ~4.3 dB as compared with that for $N = 1$, while both the maximum ER and CE decrease due to the increase in loss with film thickness. This, on one hand, indicates that a high CE enhancement can be achieved for the hybrid MRRs with small radii even without the use of film patterning, while on the other hand, it reflects the fact that the CE significantly decreases with GO film thickness for the uniformly coated MRRs.

Finally, we investigate the influence of waveguide dispersion on the FWM performance of hybrid MRRs. Fig. 10(a) shows the group-velocity dispersion $\beta_2$ for the hybrid MRRs with (i) $N = 1$ and (ii) $N = 50$ layers of GO, together with the $\beta_2$ of the uncoated MRR. The material dispersion of GO and doped silica was taken from Refs. [12, 27]. The $\beta_2$ of the hybrid MRRs is slightly lower as compared with the uncoated MRR, with the difference becoming more significant for the device with thicker films. The reduced $\beta_2$ induced by the GO films yields an enhanced anomalous dispersion and consequently better phase matching for FWM [45]. Fig. 10(b) shows the CE versus $\Delta\lambda$ (defined as wavelength spacing between pump and signal) for the hybrid MRRs, (i) for $N = 1$, $L_c = 3.4$ mm and (ii) for $N = 50$, $L_c = 17$ µm. The corresponding result for the uncoated MRR is also shown for comparison. The other parameters are kept the same as $t = 0.912$ and $R = 592$ µm. The CE slightly decreases with $\Delta\lambda$, with a difference < 2 dB for $\Delta\lambda/FSR = 30$ when $N = 50$, $L_c = 17$ µm. This reflects the fact that both the doped silica and the GO film have a low material dispersion, which allows highly effective phase matching for broadband FWM.

These results could ultimately have significant implications for realizing microcomb devices with lower threshold powers for many applications including microwave photonics [46-78], microcombs generally [79-81] and other nonlinear applications [82-84]. MRRs are also very useful in terms of
dispersion management and compensation devices and other integrated devices [85 - 236].

## VI. CONCLUSION

In summary, the FWM performance of MRRs integrated with 2D layered GO films is theoretically studied and optimized based on material and device parameters from previous experiments. A detailed analysis for the influence of GO film parameters and MRR coupling strength on the FWM CE of the GO-coated MRRs is performed. By redesigning the device parameters to properly balance the trade-off between the Kerr nonlinearity and loss, up to ~18.6 dB enhancement in the FWM CE is achieved, corresponding to ~8.3 dB further improvement over what was achieved experimentally. The influence of photo-thermal changes in the GO films as well as the variation of some other MRR parameters such as ring radius and waveguide dispersion is also investigated. These results confirm the effectiveness of introducing GO films to improve the MRR's FWM performance and serve as a roadmap for optimizing the FWM performance of GO-coated MRRs.

Competing interests: The authors declare no competing interests.

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80. L. D. Lauro, J. Li, D. J. Moss, R. Morandotti, S. T. Chu, M. Peccianti, and A. Pasquazi, "Parametric control of thermal self-pulsation in micro-cavities," Opt. Lett. vol. 42, no. 17, pp. 3407-3410, Aug. 2017.

81. H. Bao, et al., "Type-II micro-comb generation in a filter-driven four wave mixing laser," Photonics Research, vol. 6, no. 5, pp. B67-B73, May 2018.

82. T. Monro, D. J. Moss, M. Bazylenko, C. Martijn de Sterke, and L. Poladian, "Observation of self-trapping of light in a self written channel in photosensitive glass", Physical Review Letters, vol. 80, 4072 (1998).

83. M. Rochette, L. Fu, V. Ta'eed, D. J. Moss, B.J. Eggleton, "2R optical regeneration: an all-optical solution for BER improvement", IEEE Journal of Selected Topics in Quantum Electronics, vol. 12, no. 4, 736-744 (2006).

84. C. Grillet et al., "Efficient coupling to chalcogenide glass photonic crystal waveguides via silica optical fiber nanowires", Optics Express, vol. 14, no. 3, 1070-1078 (2006).

85. T. Ido et al., IEEE Photonics Technology Letters, Vol. 6, 1207 (1994). DOI: 10.1109/68.329640.

86. D. J. Moss, M. Lamont, S. Mclaughlin, G. Randall, P. Colbourne, S. Kiran and C. A. Hulse, "Tunable dispersion and dispersion slope compensators for 10Gb/s using all-pass multicavity etalons", IEEE Photonics Technology Letters, vol. 15, no. 5, 730-732 (2003). DOI: 10.1109/LPT.2003.809921.

87. L.M. Lunardi, D. Moss, S. Chandrasekhar, L.L. Buhl, A. Hulse, P. Colbourne, G. Randall, S. Mclaughlin, "Tunable dispersion compensators based on multi-cavity all-pass etalons for 40Gb/s systems", Journal of Lightwave Technology, vol. 20, no. 12, 2136 (2002). DOI: 10.1109/JLT.2002.806768.

88. D. J. Moss, et al., "Multichannel tunable dispersion compensation using all-pass multicavity etalons", paper TuT2 Optical Fiber Communications Conference, Anaheim (2002). Post-conference Technical Digest (IEEE Cat. No.02CH37339). Opt Soc. America. Part vol.1, 2002, pp. 132-3. Washington, DC, USA.

89. L.M. Lunardi, D. Moss, S. Chandrasekhar, L.L. Buhl, "An etalon based tunable dispersion compensator (TDC) device for 40Gb/s applications", European Conference on Optical Communications (ECOC), paper 5.4.6, Copenhagen, Sept. (2002). IEEE. Part vol. 2, 2002, pp. 2 vol. 2. Piscataway, NJ, USA. INSPEC Accession Number: 9153476, Print ISBN: 87-90974-63-8.

90. Wu, J. et al. 2D layered graphene oxide films integrated with micro-ring resonators for enhanced nonlinear optics. Small Vol. 16, 1906563 (2020).

91. Wu, J. et al. Graphene oxide waveguide and micro-ring resonator polarizers. Laser Photonics Rev. Vol. 13, 1900056 (2019).

92. Zhang, Y. et al. Enhanced Kerr nonlinearity and nonlinear figure of merit in silicon nanowires integrated with 2d graphene oxide films. ACS Appl. Mater. Interfaces Vol. 12, 33094-33103 (2020).

93. Qu, Y. et al. Enhanced four-wave mixing in silicon nitride waveguides integrated with 2d layered graphene oxide films. Advanced Optical Materials Vol. 8, 2001048 (2020).

94. Jia, L. et al. Highly nonlinear BiOBr nanoflakes for hybrid integrated photonics. APL Photonics Vol. 4, 090802 (2019).

95. Yuning Zhang, Jiayang Wu, Yunyi Yang, Yang Qu, Linnan Jia, Houssein El Dirani, Sébastien Kerdiles, Corrado Sciancalepore, Pierre Demongodin, Christian Grillet, Christelle Monat, Baohua Jia, and David J. Moss, "Enhanced supercontinuum generated in SiN waveguides coated with GO films", Advanced Materials Technologies 8 (1) 2201796 (2023). DOI:10.1002/admt.202201796.

96. Yuning Zhang, Jiayang Wu, Linnan Jia, Yang Qu, Baohua Jia, and David J. Moss, "Graphene oxide for nonlinear integrated photonics", Laser and Photonics Reviews 17 2200512 (2023). DOI:10.1002/lpor.202200512.

97. Jiayang Wu, H. Lin, David J. Moss, T. K. Loh, Baohua Jia, "Graphene oxide for electronics, photonics, and optoelectronics", Nature Reviews Chemistry 7 (3) 162-183 (2023). doi.org/10.1038/s41570-022-00458-7.

98. 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

99. Yuning Zhang, Jiayang Wu, Yunyi Yang, Yang Qu, Houssein El Dirani, Romain Crochemore, Corrado Sciancalepore, Pierre Demongodin, Christian Grillet, Christelle Monat, Baohua Jia, and David J. Moss, "Enhanced self-phase modulation in silicon nitride waveguides integrated with 2D graphene oxide films", IEEE Journal of Selected Topics in Quantum Electronics Vol. 29 (1) 5100413 (2023). DOI: 10.1109/JSTQE.2022.3177385

100. 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.

101. Jiayang Wu, Yuning Zhang, Junkai Hu, Yunyi Yang, Di Jin, Wenbo Liu, Duan Huang, Baohua Jia, David J. Moss, "Novel functionality with 2D graphene oxide films integrated on silicon photonic chips", Advanced Materials (2024).

102. Yuning Zhang, Jiayang Wu, Linnan Jia, Di Jin, Baohua Jia, Xiaoyong Hu, David Moss, Qihuang Gong, "Advanced optical polarizers based on 2D materials", njp Nanophotonics (2024).

103. Junkai Hu, Jiayang Wu, Wenbo Liu, Di Jin, Houssein El Dirani, Sébastien Kerdiles, Corrado Sciancalepore, Pierre Demongodin, Christian Grillet, Christelle Monat, Duan Huang, Baohua Jia, and David J. Moss, "2D graphene oxide: a versatile thermo-optic material", Advanced Functional Materials (2024).

104. Yang Qu, Jiayang Wu, Yuning Zhang, Yunyi Yang, Linnan Jia, Houssein El Dirani, Sébastien Kerdiles, Corrado Sciancalepore, Pierre Demongodin, Christian Grillet, Christelle Monat, Baohua Jia, and David J. Moss, "Optical parametric amplifiers based on silicon nitride waveguides integrated with 2D graphene oxide films", Light: Advanced Manufacturing 4 39 (2023). https://doi.org/10.37188/lam.2023.039.

105. Di Jin, Wenbo Liu, Linnan Jia, Junkai Hu, Duan Huang, Jiayang Wu, Baohua Jia, and David J. Moss, "Thickness and Wavelength Dependent Nonlinear Optical Absorption in 2D Layered MXene Films", Small Science 4 (2024). DOI:10.1002/smsc202400179.

106. 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 Vol. 6, 2101435 (2022). DOI:10.1002/smdt.202101435.

107. 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 Vol. 39 (20) 6553-6562 (2021). DOI:10.1109/JLT.2021.3101292.

108. 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.

109. 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.

110. Jiayang Wu, Linnan Jia, Yuning Zhang, Yang Qu, Baohua Jia, and David J. Moss, "Graphene oxide: versatile films for flat optics to nonlinear photonic chips", Advanced Materials Vol. 33 (3) 2006415, pp.1-29 (2021). DOI:10.1002/adma.202006415.

111. Y. Qu, J. Wu, Y. Zhang, L. Jia, Y. Yang, X. Xu, S. T. Chu, B. E. Little, R. Morandotti, B. Jia, and D. J. Moss, "Graphene oxide for enhanced optical nonlinear performance in CMOS compatible integrated devices", Paper No. 11688-30, PW21O-OE109-36, 2D Photonic Materials and Devices IV, SPIE Photonics West, San Francisco CA March 6-11 (2021). doi.org/10.1117/12.2583978

112. Yang Qu, Jiayang Wu, Yunyi Yang, Yuning Zhang, Yao Liang, Houssein El Dirani, Romain Crochemore, Pierre Demongodin, Corrado Sciancalepore, Christian Grillet, Christelle Monat, Baohua Jia, and David J. Moss, "Enhanced nonlinear four-wave mixing in silicon nitride waveguides integrated with 2D layered graphene oxide films", Small Science 4 (2024). DOI:10.1002/smsc202400179.
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113. Yuning Zhang, Yang Qu, Jiayang Wu, Linnan Jia, Yunyi Yang, Xingyuan Xu, Baohua Jia, and David J. Moss, "Enhanced Kerr nonlinearity and nonlinear figure of merit in silicon nanowires integrated with 2D graphene oxide films", ACS Applied Materials and Interfaces vol. 12 (29) 33094-33103 June 29 (2020). DOI:10.1021/acsami.0c07852

114. Jiayang Wu, Yunyi Yang, Yang Qu, Yuning Zhang, Linnan Jia, Xingyuan Xu, Sai T. Chu, Brent E. Little, Roberto Morandotti, Baohua Jia, and David J. Moss, "Enhanced nonlinear four-wave mixing in microring resonators integrated with layered graphene oxide films", Small vol. 16 (16) 1906563 (2020). DOI: 10.1002/smll.201906563

115. Jiayang Wu, Yunyi Yang, Yang Qu, Xingyuan Xu, Yao Liang, Sai T. Chu, Brent E. Little, Roberto Morandotti, Baohua Jia, and David J. Moss, "Graphene oxide waveguide polarizers and polarization selective micro-ring resonators", Paper 11282-29, SPIE Photonics West, San Francisco, CA, 4-7 February (2020). doi: 10.1117/12.2544584

116. Jiayang Wu, Yunyi Yang, Yang Qu, Xingyuan Xu, Yao Liang, Sai T. Chu, Brent E. Little, Roberto Morandotti, Baohua Jia, and David J. Moss, "Graphene oxide waveguide polarizers and polarization selective micro-ring resonators", Laser and Photonics Reviews vol. 13 (9) 1900056 (2019). DOI:10.1002/lpor.201900056.

117. Yunyi Yang, Jiayang Wu, Xingyuan Xu, Sai T. Chu, Brent E. Little, Roberto Morandotti, Baohua Jia, and David J. Moss, "Enhanced four-wave mixing in graphene oxide coated waveguides", Applied Physics Letters Photonics vol. 3 120803 (2018). doi: 10.1063/1.5045509.

118. Linnan Jia, Yang Qu, Jiayang Wu, Yuning Zhang, Yunyi Yang, Baohua Jia, and David J. Moss, "Third-order optical nonlinearities of 2D materials at telecommunications wavelengths", Micromachines (MDPI), 14, 307 (2023). https://doi.org/10.3390/mi14020307.

119. 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 vol. (2019). DOI: 10.1063/1.5116621

120. 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.

121. Moss, D. J., Morandotti, R., Gaeta, A. L. & Lipson, M. New CMOS compatible platforms based on silicon nitride and Hydex for nonlinear optics. Nat. Photonics Vol. 7, 597-607 (2013).

122. L. Razzari, et al., "CMOS-compatible integrated optical hyperparametric oscillator," Nature Photonics, vol. 4, no. 1, pp. 41-45, 2010.

123. A. Pasquazi, et al., "Sub-picosecond phase-sensitive optical pulse characterization on a chip", Nature Photonics, vol. 5, no. 10, pp. 618-623 (2011).

124. M. Ferrera et al., "On-Chip ultra-fast 1st and 2nd order CMOS compatible all-optical integration", Optics Express vol. 19 (23), 23153-23161 (2011).

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127. M. Kues, et al., "Passively modelocked laser with an ultra-narrow spectral width", Nature Photonics, vol. 11, no. 3, pp. 159, 2017.

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132. M. Ferrera, et al., "On-chip CMOS-compatible all-optical integrator", Nature Communications, vol. 1, Article 29, 2010.

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137. M. Ferrera et al., "Low Power CW Parametric Mixing in a Low Dispersion High Index Doped Silica Glass Micro-Ring Resonator with Q-factor > 1 Million", Optics Express, vol.17, no. 16, pp. 14098-14103 (2009).

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139. A.Pasquazi, et al., "Self-locked optical parametric oscillation in a CMOS compatible microring resonator: a route to robust optical frequency comb generation on a chip," Optics Express, vol. 21, no. 11, pp. 13333-13341, 2013.

140. A.Pasquazi, et al., "Stable, dual mode, high repetition rate mode-locked laser based on a microring resonator," Optics Express, vol. 20, no. 24, pp. 27355-27362, 2012.

141. Pasquazi, A. et al. Micro-combs: a novel generation of optical sources. Physics Reports 729, 1-81 (2018).

142. Yang Sun, Jiayang Wu, Mengxi Tan, Xingyuan Xu, Yang Li, Roberto Morandotti, Arnan Mitchell, and David J. Moss, "Applications of optical micro-combs", Advances in Optics and Photonics **15** (1) 86-175 (2023). https://doi.org/10.1364/AOP.470264.

143. H. Bao, et al., Laser cavity-soliton microcombs, Nature Photonics, vol. 13, no. 6, pp. 384-389, Jun. 2019.

144. Antonio Cutrona, Maxwell Rowley, Debayan Das, Luana Olivieri, Luke Peters, Sai T. Chu, Brent L. Little, Roberto Morandotti, David J. Moss, Juan Sebastian Totero Gongora, Marco Peccianti, Alessia Pasquazi, "High Conversion Efficiency in Laser Cavity-Soliton Microcombs", Optics Express Vol. 30, Issue 22, pp. 39816-39825 (2022). https://doi.org/10.1364/OE.470376.

145. M.Rowley, P.Hanzard, A.Cutrona, H.Bao, S.Chu, B.Little, R.Morandotti, D. J. Moss, G. Oppo, J. Gongora, M. Peccianti and A. Pasquazi, "Self-emergence of robust solitons in a micro-cavity", Nature vol. 608 (7922) 303-309 (2022).

146. A. Cutrona, M. Rowley, A. Bendahmane, V. Cecconi, L. Peters, L. Olivieri, B. E. Little, S. T. Chu, S. Stivala, R. Morandotti, D. J. Moss, J. S. Totero-Gongora, M. Peccianti, A. Pasquazi, "Nonlocal bonding of a soliton and a blue-detuned state in a microcomb laser", *Nature Communications Physics* **6** Article 259 (2023). https://doi.org/10.1038/s42005-023-01372-0.

147. Aadhi A. Rahim, Imtiaz Alamgir, Luigi Di Lauro, Bennet Fischer, Nicolas Perron, Pavel Dmitriuk, Celine Mazoukh, Piotr Roztocki, Cristina Rimoldi, Mario Chemnitz, Armaghan Eshaghi, Evgeny A. Viktorov, Anton V. Kovalev, Brent E. Little, Sai T. Chu, David J. Moss, and Roberto Morandotti, "Mode-locked laser with multiple timescales in a microresonator-based nested cavity", *APL Photonics* **2** 031302 (2024). DOI:10.1063/5.0174697.

148. A. Cutrona, M. Rowley, A. Bendahmane, V. Cecconi, L. Peters, L. Olivieri, B. E. Little, S. T. Chu, S. Stivala, R. Morandotti, D. J. Moss, J. S. Totero-Gongora, M. Peccianti, A. Pasquazi, "Stability Properties of Laser Cavity-Solitons for Metrological Applications", Applied Physics Letters vol. 122 (12) 121104 (2023); doi: 10.1063/5.0134147.

149. X. Xu, J. Wu, M. Shoeiby, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and D. J. Moss, "Reconfigurable broadband microwave photonic intensity differentiator based on an integrated optical frequency comb source," APL Photonics, vol. 2, no. 9, 096104, Sep. 2017.
150. Xu, X., et al., Photonic microwave true time delays for phased array antennas using a 49 GHz FSR integrated micro-comb source, Photonics Research, vol. 6, B30-B36 (2018).

151. X. Xu, M. Tan, J. Wu, R. Morandotti, A. Mitchell, and D. J. Moss, "Microcomb-based photonic RF signal processing", IEEE Photonics Technology Letters, vol. 31 no. 23 1854-1857, 2019.

152. Xu, et al., "Advanced adaptive photonic RF filters with 80 taps based on an integrated optical micro-comb source," Journal of Lightwave Technology, vol. 37, no. 4, pp. 1288-1295 (2019).

153. X. Xu, et al., "Photonic RF and microwave integrator with soliton crystal microcombs", IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 12, pp. 3582-3586, 2020. DOI:10.1109/TCSII.2020.2995682.

154. X. Xu, et al., "High performance RF filters via bandwidth scaling with Kerr micro-combs," APL Photonics, vol. 4 (2) 026102. 2019.

155. M. Tan, et al., "Microwave and RF photonic fractional Hilbert transformer based on a 50 GHz Kerr micro-comb", Journal of Lightwave Technology, vol. 37, no. 24, pp. 6097–6104, 2019.

156. M. Tan, et al., "RF and microwave fractional differentiator based on photonics", IEEE Transactions on Circuits and Systems: Express Briefs, vol. 67, no.11, pp. 2767-2771, 2020. DOI:10.1109/TCSII.2020.2965158.

157. M. Tan, et al., "Photonic RF arbitrary waveform generator based on a soliton crystal micro-comb source", Journal of Lightwave Technology, vol. 38, no. 22, pp. 6221-6226 (2020). DOI: 10.1109/JLT.2020.3009655.

158. M. Tan, X. Xu, J. Wu, R. Morandotti, A. Mitchell, and D. J. Moss, "RF and microwave high bandwidth signal processing based on Kerr Micro-combs", Advances in Physics X, VOL. 6, NO. 1, 1838946 (2021). DOI:10.1080/23746149.2020.1838946.

159. 123. X. Xu, et al., "Advanced RF and microwave functions based on an integrated optical frequency comb source," Opt. Express, vol. 26 (3) 2569 (2018).

160. M. Tan, X. Xu, J. Wu, B. Corcoran, A. Boes, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Lowery, A. Mitchell, and D. J. Moss, ""Highly Versatile Broadband RF Photonic Fractional Hilbert Transformer Based on a Kerr Soliton Crystal Microcomb", Journal of Lightwave Technology vol. 39 (24) 7581-7587 (2021).

161. Wu, J. et al. RF Photonics: An Optical Microcombs’ Perspective. IEEE Journal of Selected Topics in Quantum Electronics Vol. 24, 6101020, 1-20 (2018).

162. T. G. Nguyen et al., "Integrated frequency comb source-based Hilbert transformer for wideband microwave photonic phase analysis," Opt. Express, vol. 23, no. 17, pp. 22087-22097, Aug. 2015.

163. X. Xu, et al., "Broadband RF channelizer based on an integrated optical frequency Kerr comb source," Journal of Lightwave Technology, vol. 36, no. 19, pp. 4519-4526, 2018.

164. X. Xu, et al., "Continuously tunable orthogonally polarized RF optical single sideband generator based on micro-ring resonators," Journal of Optics, vol. 20, no. 11, 115701. 2018.

165. X. Xu, et al., "Orthogonally polarized RF optical single sideband generation and dual-channel equalization based on an integrated microring resonator," Journal of Lightwave Technology, vol. 36, no. 20, pp. 4808-4818. 2018.

166. X. Xu, et al., "Photonic RF phase-encoded signal generation with a microcomb source", J. Lightwave Technology, vol. 38, no. 7, 1722-1727, 2020.

167. X. Xu, et al., Broadband microwave frequency conversion based on an integrated optical micro-comb source", Journal of Lightwave Technology, vol. 38 no. 2, pp. 332-338, 2020.

168. M. Tan, et al., "Photonic RF and microwave filters based on 49GHz and 200GHz Kerr microcombs", Optics Comm. vol. 465,125563, Feb. 22. 2020.

169. X. Xu, et al., "Broadband photonic RF channelizer with 90 channels based on a soliton crystal microcomb", Journal of Lightwave Technology, Vol. 38, no. 18, pp. 5116 – 5121 (2020). doi: 10.1109/JLT.2020.2997699.

170. M. Tan et al., "Orthogonally polarized Photonic Radio Frequency single sideband generation with integrated micro-ring resonators", IOP Journal of Semiconductors, Vol. 42 (4), 041305 (2021). DOI: 10.1088/1674-4926/42/4/041305.

171. Mengxi Tan, X. Xu, J. Wu, T. G. Nguyen, S. T. Chu, B. E. Little, R. Morandotti, A. Mitchell, and David J. Moss, "Photonic Radio Frequency Channelizers based on Kerr Optical Micro-combs", IOP Journal of Semiconductors Vol. 42 (4), 041302 (2021). DOI:10.1088/1674-4926/42/4/041302.

172. B. Corcoran, et al., "Ultra-dense optical data transmission over standard fiber with a single chip source", Nature Communications, vol. 11, Article:2568, 2020.

173. X. Xu et al, "Photonic perceptron based on a Kerr microcomb for scalable high speed optical neural networks", Laser and Photonics Reviews, vol. 14, no. 8, 2000070 (2020). DOI: 10.1002/lpor.202000070.

174. X. Xu, et al., "11 TOPs photonic convolutional accelerator for optical neural networks", Nature vol. 589, 44-51 (2021).

175. Xingyuan Xu, Weiwei Han, Mengxi Tan, Yang Sun, Yang Li, Jiayang Wu, Roberto Morandotti, Arnan Mitchell, Kun Xu, and David J. Moss, "Neuromorphic computing based on wavelength-division multiplexing", *IEEE Journal of Selected Topics in Quantum Electronics* **29** (2) 7400112 (2023). DOI:10.1109/JSTQE.2022.3203159.

176. Yunping Bai, Xingyuan Xu,1, Mengxi Tan, Yang Sun, Yang Li, Jiayang Wu, Roberto Morandotti, Arnan Mitchell, Kun Xu, and David J. Moss, "Photonic multiplexing techniques for neuromorphic computing", Nanophotonics vol. 12 (5): 795-817 (2023). DOI:10.1515/nanoph-2022-0485.

177. Chawaphon Prayoonyong, Andreas Boes, Xingyuan Xu, Mengxi Tan, Sai T. Chu, Brent E. Little, Roberto Morandotti, Arnan Mitchell, David J. Moss, and Bill Corcoran, "Frequency comb distillation for optical superchannel transmission", Journal of Lightwave Technology vol. 39 (23) 7383-7392 (2021). DOI: 10.1109/JLT.2021.3116614.

178. Mengxi Tan, Xingyuan Xu, Jiayang Wu, Bill Corcoran, Andreas Boes, Thach G. Nguyen, Sai T. Chu, Brent E. Little, Roberto Morandotti, Arnan Mitchell, and David J. Moss, "Integral order photonic RF signal processors based on a soliton crystal micro-comb source", IOP Journal of Optics vol. 23 (11) 125701 (2021). https://doi.org/10.1088/2040-8986/ac2eab

179. Yang Sun, Jiayang Wu, Yang Li, Xingyuan Xu, Guanghui Ren, Mengxi Tan, Sai Tak Chu, Brent E. Little, Roberto Morandotti, Arnan Mitchell, and David J. Moss, "Optimizing the performance of microcomb based microwave photonic transversal signal processors", Journal of Lightwave Technology vol. 41 (23) pp 7223-7237 (2023). DOI: 10.1109/JLT.2023.3314526.

180. Mengxi Tan, Xingyuan Xu, Andreas Boes, Bill Corcoran, Thach G. Nguyen, Sai T. Chu, Brent E. Little, Roberto Morandotti, Jiayang Wu, Arnan Mitchell, and David J. Moss, "Photonic signal processor for real-time video image processing based on a Kerr microcomb", Communications Engineering vol. 2 94 (2023). DOI:10.1038/s44172-023-00135-7

181. Mengxi Tan, Xingyuan Xu, Jiayang Wu, Roberto Morandotti, Arnan Mitchell, and David J. Moss, "Photonic RF and microwave filters based on 49GHz and 200GHz Kerr microcombs", Optics Communications, vol. 465, Article: 125563 (2020). doi:10.1016/j.optcom.2020.125563. doi.org/10.1063/1.5136270.

182. Yang Sun, Jiayang Wu, Yang Li, Mengxi Tan, Xingyuan Xu, Sai Chu, Brent Little, Roberto Morandotti, Arnan Mitchell, and David J. Moss, "Quantifying the Accuracy of Microcomb-based Photonic RF Transversal Signal Processors", IEEE Journal of Selected Topics in Quantum Electronics vol. 29 no. 6, pp. 1-17, Art no. 7500317 (2023). 10.1109/JSTQE.2023.3266276.

183. Yang Li, Yang Sun, Jiayang Wu, Guanghui Ren, Bill Corcoran, Xingyuan Xu, Sai T. Chu, Brent. E. Little, Roberto Morandotti, Arnan Mitchell, and David J. Moss, "Processing accuracy of microcomb-based microwave photonic signal processors for different input signal waveforms", MDPI Photonics 10, 10111283 (2023). DOI:10.3390/photonics10111283

184. Caitlin E. Murray, Mengxi Tan, Chawaphon Prayoonyong, Sai T. Chu, Brent E. Little, Roberto Morandotti, Arnan Mitchell, David J. Moss and Bill Corcoran, "Investigating the thermal robustness of soliton crystal microcombs", *Optics Express* **31**(23), 37749-37762 (2023).

185. Yang Sun, Jiayang Wu, Yang Li, and David J. Moss, "Comparison of
microcomb-based RF photonic transversal signal processors implemented with discrete components versus integrated chips", *MDPI Micromachines* **14**, 1794 (2023). https://doi.org/10.3390/mi14091794

186. Kues, M. et al. "Quantum optical microcombs", Nature Photonics vol. 13, (3) 170-179 (2019). doi:10.1038/s41566-019-0363-0

187. C.Reimer, L. Caspani, M. Clerici, et al., "Integrated frequency comb source of heralded single photons," Optics Express, vol. 22, no. 6, pp. 6535-6546, 2014.

188. C. Reimer, et al., "Cross-polarized photon-pair generation and bichromatically pumped optical parametric oscillation on a chip", Nature Communications, vol. 6, Article 8236, 2015. DOI: 10.1038/ncomms9236.

189. L. Caspani, C. Reimer, M. Kues, et al., "Multifrequency sources of quantum correlated photon pairs on-chip: a path toward integrated Quantum Frequency Combs," Nanophotonics, vol. 5, no. 2, pp. 351-362, 2016.

190. C. Reimer et al., "Generation of multiphoton entangled quantum states by means of integrated frequency combs," Science, vol. 351, no. 6278, pp. 1176-1180, 2016.

191. M. Kues, et al., "On-chip generation of high-dimensional entangled quantum states and their coherent control", Nature, vol. 546, no. 7660, pp. 622-626, 2017.

192. P. Roztocki et al., "Practical system for the generation of pulsed quantum frequency combs," Optics Express, vol. 25, no. 16, pp. 18940-18949, 2017.

193. Y. Zhang, et al., "Induced photon correlations through superposition of two four-wave mixing processes in integrated cavities", Laser and Photonics Reviews, vol. 14, no. 7, pp. 2000128, 2020. DOI: 10.1002/lpor.202000128

194. C. Reimer, et al., "High-dimensional one-way quantum processing implemented on d-level cluster states", Nature Physics, vol. 15, no.2, pp. 148-153, 2019.

195. P.Roztocki et al., "Complex quantum state generation and coherent control based on integrated frequency combs", Journal of Lightwave Technology vol. 37 (2) 338-347 (2019).

196. S. Sciara et al., "Generation and Processing of Complex Photon States with Quantum Frequency Combs", IEEE Photonics Technology Letters vol. 31 (23) 1862-1865 (2019). DOI: 10.1109/LPT.2019.2944564.

197. Stefania Sciara, Piotr Roztocki, Bennet Fisher, Christian Reimer, Luis Romero Cortez, William J. Munro, David J. Moss, Alfonso C. Cino, Lucia Caspani, Michael Kues, J. Azana, and Roberto Morandotti, "Scalable and effective multilevel entangled photon states: A promising tool to boost quantum technologies", Nanophotonics vol. 10 (18), 4447-4465 (2021). DOI:10.1515/nanoph-2021-0510.

198. L. Caspani, C. Reimer, M. Kues, et al., "Multifrequency sources of quantum correlated photon pairs on-chip: a path toward integrated Quantum Frequency Combs," Nanophotonics, vol. 5, no. 2, pp. 351-362, 2016.

199. Hamed Arianfard, Saulius Juodkazis, David J. Moss, and Jiayang Wu, "Sagnac interference in integrated photonics", *Applied Physics Reviews* **10** (1) 011309 (2023). doi: 10.1063/5.0123236.

200. Hamed Arianfard, Jiayang Wu, Saulius Juodkazis, and David J. Moss, "Optical analogs of Rabi splitting in integrated waveguide-coupled resonators", *Advanced Physics Research* **2** 2200123 (2023). DOI:10.1002/apxr.202200123.

201. Hamed Arianfard, Jiayang Wu, Saulius Juodkazis, and David J. Moss, "Spectral shaping based on optical waveguides with advanced Sagnac loop reflectors", Paper No. PW220-OE201-20, SPIE-Opto, Integrated Optics: Devices, Materials, and Technologies XXVI, SPIE Photonics West, San Francisco CA January 22 - 27 (2022). doi: 10.1117/12.2607902

202. Hamed Arianfard, Jiayang Wu, Saulius Juodkazis, David J. Moss, "Spectral Shaping Based on Integrated Coupled Sagnac Loop Reflectors Formed by a Self-Coupled Wire Waveguide", IEEE Photonics Technology Letters vol. 33 (13) 680-683 (2021). DOI:10.1109/LPT.2021.3088089.

203. Hamed Arianfard, Jiayang Wu, Saulius Juodkazis and David J. Moss, "Three Waveguide Coupled Sagnac Loop Reflectors for Advanced

Spectral Engineering", Journal of Lightwave Technology vol. 39 (11) 3478-3487 (2021). DOI: 10.1109/JLT.2021.3066256.

204. Hamed Arianfard, Jiayang Wu, Saulius Juodkazis and David J. Moss, "Advanced Multi-Functional Integrated Photonic Filters based on Coupled Sagnac Loop Reflectors", Journal of Lightwave Technology vol. 39 Issue: 5, pp.1400-1408 (2021). DOI:10.1109/JLT.2020.3037559.

205. 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, PW210-OE203-44, Silicon Photonics XVI, SPIE Photonics West, San Francisco CA March 6-11 (2021). doi.org/10.1117/12.2584020

206. 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

207. 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.

208. MD Pelusi, F Luan, E Magi, MRE Lamont, DJ Moss, BJ Eggleton, ... et al., "High bit rate all-optical signal processing in a fiber photonic wire", Optics Express vol. 16 (15), 11506-11512 (2008).

209. M Shokooh-Saremi, VG Ta'Eed, NJ Baker, ICM Littler, DJ Moss, ... et al., "High-performance Bragg gratings in chalcogenide rib waveguides written with a modified Sagnac interferometer", JOSA B vol. 23 (7), 1323-1331 (2006).

210. C Grillet, C Smith, D Freeman, S Madden, B Luther-Davies, EC Magi, ... "Efficient coupling to chalcogenide glass photonic crystal waveguides via silica optical fiber nanowires", Optics Express vol. 14 (3), 1070-1078 (2006).

211. S Tomljenovic-Hanic, MJ Steel, CM de Sterke, DJ Moss, "High-Q cavities in photosensitive photonic crystals" Optics Letters vol. 32 (5), 542-544 (2007).

212. E Ghahramani, DJ Moss, JE Sipe, "Second-harmonic generation in odd-period, strained, (Si(Ge/Si superlattices and at Si/Ge interfaces", Physical Review Letters vol. 64 (23), 2815 (1990).

213. E.D Ghahramani, DJ Moss, JE Sipe, "Full-band-structure calculation of first-, second-, and third-harmonic optical response coefficients of ZnSe, ZnTe, and CdTe", Physical Review B 43 (12), 9700 (1991)

214. VG Ta'eed et al., "Error free all optical wavelength conversion in highly nonlinear As-Se chalcogenide glass fiber", Optics Express vol. 14 (22), 10371-10376 (2006).

215. M Rochette, L Fu, V Ta'eed, DJ Moss, BJ Eggleton, "2R optical regeneration: an all-optical solution for BER improvement", IEEE Journal of Selected Topics in Quantum Electronics vol. 12 (4), 736-744 (2006).

216. TD Vo, et al., "Silicon-chip-based real-time dispersion monitoring for 640 Gbit/s DPSK signals", Journal of Lightwave Technology vol. 29 (12), 1790-1796 (2011).

217. C Monat, C Grillet, B Corcoran, DJ Moss, BJ Eggleton, TP White, ..., et al., "Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics", Optics Express vol. 18 (7), 6831-6840 (2010). L Carletti, P Ma, Y Yu, B Luther-Davies, D Hudson, C Monat, ..., et al., "Nonlinear optical response of low loss silicon germanium waveguides in the mid-infrared", Optics Express vol. 23 (7), 8261-8271 (2015).

219. MRE Lamont, VG Ta'eed, MAF Roelens, DJ Moss, BJ Eggleton, DY Choi, ... et al., "Error-free wavelength conversion via cross-phase modulation in 5cm of As2S3 chalcogenide glass rib waveguide", Electronics Letters vol. 43 (17), 945-947 (2007).

220. C Grillet, C Monat, CLC Smith, BJ Eggleton, DJ Moss, S Frédérick, ... et al., "Nanowire coupling to photonic crystal nanocavities for single photon sources", Optics Express vol. 15 (3), 1267-1276 (2007).

221. VG Ta'Eed, MRE Lamont, DJ Moss, BJ Eggleton, DY Choi, S Madden, ... et al., "All optical wavelength conversion via cross phase modulation in chalcogenide glass rib waveguides", Optics Express vol. 14 (23), 11242-11247 (2006).
222. TM Monro, D Moss, M Bazylenko, CM De Sterke, L Poladian, "Observation of self-trapping of light in a self-written channel in a photosensitive glass", Physical Review Letters vol. 80 (18), 4072 (1998).

223. C. Mazoukh, L. Di Lauro, I. Alamgir B. Fischer, A. Aadhi, A. Eshaghi, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, "Genetic algorithm-enhanced microcomb state generation", *Nature Communications Physics* Vol. 7, Article: 81 (2024). DOI: 10.1038/s42005-024-01558-0.

224. Mengxi Tan, David J. Moss, "The laser trick that could put an ultraprecise optical clock on a chip", *Nature* **624**, (7991) 256-257 (2023). doi.org/10.1038/d41586-023-03782-0

225. Junkai Hu, Jiayang Wu, Di Jin, Sai Tak Chu, Brent E. Little, Duan Huang, Roberto Morandotti, and David J. Moss, "Thermo-optic response and optical bistability of integrated high index doped silica ring resonators", *MDPI Sensors* **23** 9767 (2023). https://doi.org/10.3390/s23249767.

226. M. Zerbib, V.T. Hoang, J. C. Beugnot, K. P. Huy, B. Little, S. T. Chu, D. J. Moss, R. Morandotti, B. Wetzel, and T. Sylvestre, "Observation of Brillouin scattering in a high-index doped silica chip waveguide", *Results in Physics* **52** 106830 (2023). https://doi.org/10.1016/j.rinp.2023.106830.

227. Stefania Sciara, Hao Yu, Farzam Nosrati, Piotr Roztocki, Bennet Fischer, Mario Chemnitz, Christian Reimer, Luis Romero Cortés, William J. Munro, David J. Moss, Rosario Lo Franco, Alfonso C. Cino, Lucia Caspani, Michael Kues, Zhiming Wang, José Azaña, and Roberto Morandotti, "Generation of integrated quantum frequency combs on microring resonators for the realization of complex entangled two-photon states", Early Access *IEEE Journal of Selected Topics in Quantum Electronics* **28** (2022).

228. Linnan Jia, Yang Qu, Jiayang Wu, Yuning Zhang, Yunyi Yang, Baohua Jia, and David J. Moss, "Third-order optical nonlinearities of 2D materials at telecommunications wavelengths", *Micromachines*, **14** 307 (2023). https://doi.org/10.3390/mi14020307.

229. Alberto Della Torre, Remi Armand, Milan Sinobad, Kokou Firmin Fiaboe, Barry Luther-Davies, Stephen Madden, Arnan Mitchell, Thach Nguyen, David J. Moss, Jean-Michel Hartmann, Vincent Reboud, Jean-Marc Fedeli, Christelle Monat, and Christian Grillet, "Mid-Infrared Supercontinuum Generation in a Varying Dispersion Waveguide for Multi-Species Gas Spectroscopy", *IEEE Journal of Selected Topics in Quantum Electronics* **29** (1) 5100509 (2023). DOI: 10.1109/JSTQE.2022.3185169.

230. Andrew Cooper, Luana Olivieri, Antonio Cutrona, Debayan Das, Luke Peters, Sai Tak Chu, Brent Little, Roberto Morandotti, David J Moss, Marco Peccianti, and Alessia Pasquazi, "Parametric interaction of laser cavity-solitons with an external CW pump", *Optics Express* **32** (12), 21783-21794 (2024).

231. Weiwei Han, Zhihui Liu, Yifu Xu, Mengxi Tan, Chaoran Huang, Jiayang Wu, Kun Xu, David J. Moss, and Xingyuan Xu, "Photonic RF Channelization Based on Microcombs", *IEEE Journal of Selected Topics in Quantum Electronics* **30** (5) 7600417 (2024). DOI:10.1109/JSTQE.2024.3398419.

232. Yonghang Sun, James Salamy, Caitlin E. Murry, Brent E. Little, Sai T. Chu, Roberto Morandotti, Arnan Mitchell, David J. Moss, Bill Corcoran, "Enhancing laser temperature stability by passive self-injection locking to a micro-ring resonator", *Optics Express* (2024)

233. Yang Li, Yang Sun, Jiayang Wu, Guanghui Ren, Xingyuan Xu, Mengxi Tan, Sai Chu, Brent Little, Roberto Morandotti, Arnan Mitchell, and David Moss, "Feedback control in micro-comb-based microwave photonic transversal filter systems", *IEEE Journal of Selected Topics in Quantum Electronics* Vol. 30 (5) 2900117 (2024). DOI: 10.1109/JSTQE.2024.3377249.

234. Weiwei Han, Zhihui Liu, Yifu Xu, Mengxi Tan, Yuhua Li, Xiaotian Zhu, Yanni Ou, Feifei Yin, Roberto Morandotti, Brent E. Little, Sai Tak Chu, Xingyuan Xu, David J. Moss, and Kun Xu, "Dual-polarization RF Channelizer Based on Microcombs", *Optics Express* **32**, No. 7, 11281-11295 (2024). DOI: 10.1364/OE.519235.

235. Aadhi A. Rahim, Imtiaz Alamgir, Luigi Di Lauro, Bennet Fischer, Nicolas Perron, Pavel Dmitriev, Celine Mazoukh, Piotr Roztocki, Cristina Rimoldi, Mario Chemnitz, Armaghan Eshaghi, Evgeny A. Viktorov, Anton V. Kovalev, Brent E. Little, Sai T. Chu, David J. Moss, and Roberto Morandotti, "Mode-locked laser with multiple timescales in a microresonator-based nested cavity", *APL Photonics* **9** 031302 (2024).

DOI:10.1063/5.0174697.

236. C. Mazoukh, L. Di Lauro, I. Alamgir B. Fischer, A. Aadhi, A. Eshaghi, B. E. Little, S. T. Chu, D. J. Moss, and R. Morandotti, "Genetic algorithm-enhanced microcomb state generation", Special Issue Microresonator Frequency Combs - New Horizons, *Nature Communications Physics* Vol. 7, Article: 81 (2024). DOI: 10.1038/s42005-024-01558-0.