## 3.5.2 Discussion

### 3.5.2.1 Advancements and remaining challenges for fibers

Not surprisingly, the range of NLO parameter values measured from optical fibers as shown in Table 6 is nearly as expansive as the range of materials from which they are made. Ironically, it is this plenty that precludes an equally abundant coverage of all materials and values. Unless otherwise noted, Table 6 is meant to provide generalized values, ranges, and trends for each fiber material family and associated nonlinearity.

Over the past twenty years, since approximately 2000, the dominant trend one observes is in the range of (strong and weak) NLO materials contained within or integrated into the fibers. Some of this growth is due to the expansion in applications employing fibers, such as power-scaled high energy lasers and sensors, as well as in new fiber processing methods that permit the fiberization of materials previously not possible [Sazio2006, Ballato2018a]. Arguably, this renaissance in fiber materials has driven rapid progress in the range of NLO parameter values. This said, beyond telecommunications grade silica, losses are still relatively high in most glass and crystal core fibers, thus potentially reducing their efficiencies and range of applications. However, markedly higher NLO parameter values offset issues of loss in some cases, such as with the semiconductor core optical fibers since a very large material nonlinearity shortens, often by several orders-of-magnitude, the required fiber lengths.

### 3.5.2.2 Recommendations for future works on fibers

The aforementioned renaissance in optical fiber materials has opened two particularly intriguing doors to the world of NLO. First, the wide range of new materials has greatly expanded the achievable range of NLO parameter values. When coupled with fiber design (e.g., microstructured and photonic crystal fibers) and post-processing (e.g., tapering), unquestionable benefits to future applications arise [Sylvestre2021]. Second, the availability of new fiber materials has generated new insights and concepts relevant to nonlinear fiber optics. These include, for example, zero nonlinearity values based on carefully balanced fiber compositions. For instance, in the case of Brillouin scattering, positive and negative transverse photoelasticities [Ballato2018, Cavillon2018a] are balanced such that no spontaneous scattering occurs, thereby obviating its stimulated form. Such opportunities are not possible based only on fiber design. Needless to say, there are great possibilities ahead for fiber optics, both in terms of uniquely high and low nonlinearities. The Periodic Table can be construed to be a rich palette from which new materials with novel properties may be derived. Continued characterization sheds light on how to combine the base materials to achieve a desired outcome, be it using a hybrid or designer material approach. That being said, too few literature works go the extra mile to derive the relevant NLO material values from a system-level demonstration. For example, there are numerous examples of supercontinuum generation (SCG) from novel fibers / materials, but a large proportion of these papers lack sufficient detail from which the relevant nonlinearities may be quantified. Many other works, especially those in the area of hybrid fibers (see Section 3.7), refer back to bulk values for the nonlinearities. It is important to remember that many materials, including glasses, undergo very different thermal histories when found in either bulk or fiber form. If a material's structural properties depend on its fabrication history, this may have a significant impact on its NLO behavior. In the case of hybrid materials, secondary effects such as material inter-diffusion during fabrication may have a similar impact.

It is fortunate that many of the works cited herein set out from the beginning to quantify the nonlinearities in fibers made from novel materials, but the difficulty in doing so is evident from Table 6. The vast majority, with some exceptions, focus on one nonlinearity, while none have included three (i.e. $n_2$, Raman, and Brillouin together in the same work). That said, and even where there is a focus on a single nonlinearity, there are still gaps that can be seen in the Table, though not following any particular trend, where information is lacking but desirable. Included in the Table are those parameters that generally are most important to be included in publications reporting NLO measurements in
fibers. In other words, we consider the reporting of these parameters to be a “best practice,” in addition to the more general best practices described in Section 2. To further complicate things, additional fiber-specific measurement complexities can arise from such characteristics as the number of propagating modes (not just a V-Number alone), fiber splicing efficiency, fiber uniformity, attenuation at the operating wavelength(s), mode field diameter, mode index, dispersion, etc. that can have a strong impact on the strength of a nonlinearity and deserve discussion where relevant. For completeness, it is ideal to also include the compositional profile across the core since each chemical constituent influences a given nonlinearity in differing ways; see, for example, Table 1 in [Cavillon2018a], which qualifies changes in Raman, Brillouin, and $n_2$-mediated wave-mixing for a wide variety of glass components often used in silica-based optical fibers. This further epitomizes the need for all relevant data to be provided, through which a reader can at least formulate their own estimates of the NLO coefficients, or at least in the case of hybrid systems, an effective value for the nonlinearity (see Section 3.7). Such data is of critical importance, as it is key to the design of next-generation fibers.
### 3.5.3 Data table for fiber waveguiding materials

<table><caption>**Table 6.** NLO properties of fiber waveguiding materials from representative works since 2000. Legend for superscripts: see below the table.</caption><thead><tr><th rowspan="2">Material</th><th rowspan="2">Method</th><th colspan="2">Fiber Properties</th><th colspan="2">Measurement Details</th><th colspan="3">Nonlinear Properties</th><th rowspan="2">Reference</th></tr><tr><th>Length Loss</th><th>Core index contrast<br>Cladding material<br>Core Size<br>Effective area</th><th>Wavelength<br>Peak power</th><th>Rep. rate<br>Pulse width</th><th>n<sub>2,eff</sub>*</th><th>g<sub>Raman</sub><br>Frequency shift</th><th>g<sub>Brillouin</sub><br>Frequency shift<br>Linewidth</th></tr></thead><tbody><tr><td colspan="10" style="text-align:center; font-weight:bold;">Commercial telecommunications fiber</td></tr><tr><td>Pure SiO<sub>2</sub></td><td>IGA / SPM<br>/ SRS<br>Threshold</td><td>20 m<br>~ 0 dB/m</td><td>-<br>SiO<sub>2</sub><br>50 µm<sup>2</sup></td><td>1064 nm<br>5 – 25 W</td><td>100 MHz<br>50 – 70 ps</td><td>1.81 × 10<sup>-20</sup><br>m<sup>2</sup>/W</td><td>0.78 × 10<sup>-13</sup> m/W<br>-</td><td>-<br>-</td><td>Oguama 2005b</td></tr><tr><td>SMF-28</td><td>SpBS<br>Linewidth</td><td>500 m<br>0.022 dB/m</td><td>-<br>SiO<sub>2</sub><br>8.2 µm<br>101 µm<sup>2</sup></td><td>2000 nm<br>-</td><td>CW</td><td>2.44 × 10<sup>-20</sup><br>m<sup>2</sup>/W</td><td>-<br>-</td><td>2.525 × 10<sup>-11</sup> m/W<br>8.40 GHz<br>15 MHz</td><td>Deroh 2020</td></tr><tr><td>SMF-28</td><td>SpBS<br>Linewidth</td><td>500 m<br>0.0002 dB/m</td><td>-<br>SiO<sub>2</sub><br>8.2 µm<br>78 µm<sup>2</sup></td><td>1550 nm<br>-</td><td>CW</td><td>-</td><td>-<br>-</td><td>2.262 × 10<sup>-11</sup> m/W<br>10.85 GHz<br>28 MHz</td><td>Deroh 2020</td></tr><tr><td>DCF</td><td>IGA / SPM<br>/ SRS<br>Threshold</td><td>20 m<br>~ 0 dB/m</td><td>-<br>SiO<sub>2</sub><br>10.61 µm<sup>2</sup></td><td>1064 nm<br>5 – 25 W</td><td>100 MHz<br>50 – 70 ps</td><td>2.67 × 10<sup>-20</sup><br>m<sup>2</sup>/W</td><td>1.47 × 10<sup>-13</sup> m/W<br>-</td><td>-<br>-</td><td>Oguama 2005b</td></tr><tr><td>EDFAs</td><td>IGA / SPM</td><td>20 m<br>~ 0 dB/m</td><td>-<br>SiO<sub>2</sub><br>8.9 – 27.2 µm<sup>2</sup></td><td>1064 nm<br>5 – 25 W</td><td>100 MHz<br>50 – 70 ps</td><td>1.82 to 3.04 ×<br>10<sup>-20</sup> m<sup>2</sup>/W</td><td>-<br>-</td><td>-<br>-</td><td>Oguama 2005</td></tr><tr><td>GeO<sub>2</sub><br>doped SiO<sub>2</sub></td><td>SpBS<br>Reference<br>Fiber**</td><td>20 m<br>0.082 dB/m</td><td>≤ 5 × 10<sup>-3</sup><br>SiO<sub>2</sub><br>40 µm<br>-</td><td>1534 nm<br>-</td><td>CW</td><td>-</td><td>-<br>-</td><td>0.53 × 10<sup>-11</sup> m/W<br>10.71 GHz<br>80 MHz</td><td>Evert 2012</td></tr><tr><td colspan="10" style="text-align:center; font-weight:bold;">Silicate glass fibers</td></tr><tr><td>Y<sub>2</sub>O<sub>3</sub>-Al<sub>2</sub>O<sub>3</sub>-<br>SiO<sub>2</sub></td><td>FWM /<br>SpBS<br>Reference<br>Fiber</td><td>4 m<br>0.78, 0.47 dB/m</td><td>47.3, 32.9 × 10<sup>-3</sup><br>SiO<sub>2</sub><br>11.2, 20.7 µm<br>-</td><td>1542 nm<br>850 W</td><td>CW</td><td>1.8 to 2.0 ×<br>10<sup>-20</sup> m<sup>2</sup>/W</td><td>-<br>-</td><td>0.125 to 0.139 × 10<sup>-11</sup><br>m/W<br>~ 11.40 to 12.5 GHz<br>200 to 500 MHz</td><td>Tuggle 2017</td></tr></tbody></table>
<table><tr><td>La<sub>2</sub>O<sub>3</sub>-Al<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub></td><td>SpBS Reference Fiber</td><td>~ 2 m<br>1.0 dB/m</td><td>100 × 10<sup>-3</sup><br>SiO<sub>2</sub><br>~ 16 µm<br>5.8 µm MFD</td><td>1534 nm<br>-</td><td>CW</td><td>-</td><td>-</td><td>0.26 × 10<sup>-11</sup> m/W<br>11.476 GHz<br>82.0 MHz</td><td>Dragic 2014</td></tr><tr><td>Bi<sub>2</sub>O<sub>3</sub>-SiO<sub>2</sub></td><td>Nonlinear phase shift / SBS Pump-Probe</td><td>1 m<br>0.8 dB/m</td><td>-<br>SiO<sub>2</sub><br>-<br>3.08 µm<sup>2</sup></td><td>1550 nm</td><td>CW</td><td>8.17 × 10<sup>-19</sup><br>m<sup>2</sup>/W</td><td>-</td><td>6.43 × 10<sup>-11</sup> m/W<br>-<br>-</td><td>Lee 2005</td></tr></table>

Other oxide glass fibers

<table><tr><td>P<sub>2</sub>O<sub>5</sub>-based</td><td>SBS Threshold</td><td>1.245 m<br>5.47 dB/m</td><td>0.144 NA<br>Phosphate<br>27.7 µm<br>-</td><td>1064 nm<br>≤ 60 W</td><td>-<br>1 µs</td><td>-</td><td>-</td><td>2.1 × 10<sup>-11</sup> m/W<br>27.7 GHz<br>219 MHz</td><td>Lee 2007</td></tr><tr><td>Oxyfluoride</td><td>SpBS Reference Fiber, SpRS, FWM</td><td>800 m<br>0.65 dB/m</td><td>35 × 10<sup>-3</sup><br>SiO<sub>2</sub><br>18.6 µm<br>-</td><td>1540 nm<br>430 W</td><td>-<br>-</td><td>3 × 10<sup>-20</sup><br>m<sup>2</sup>/W</td><td>0.48 × 10<sup>-13</sup> m/W<br>-</td><td>0.56 × 10<sup>-11</sup> m/W<br>10.75 GHz<br>52 MHz</td><td>Cavillon 2018</td></tr></table>

Heavy metal oxides glass fibers

<table><tr><td>GeO<sub>2</sub>-SiO<sub>2</sub></td><td>SpBS Linewidth</td><td>3 m<br>0.1 dB/m</td><td>-<br>SiO<sub>2</sub><br>2 µm<br>5 µm<sup>2</sup></td><td>2000 nm<br>-</td><td>CW</td><td>4.97 × 10<sup>-20</sup><br>m<sup>2</sup>/W</td><td>-<br>-</td><td>7.45 × 10<sup>-12</sup> m/W<br>6.00 GHz<br>76 MHz</td><td>Deroh 2020</td></tr><tr><td>GeO<sub>2</sub>-SiO<sub>2</sub></td><td>SpBS Linewidth</td><td>3 m<br>0.2 dB/m</td><td>-<br>SiO<sub>2</sub><br>2 µm<br>3.5 µm<sup>2</sup></td><td>1550 nm<br>-</td><td>CW</td><td>-</td><td>-</td><td>1.05 × 10<sup>-11</sup> m/W<br>7.70 GHz<br>98 MHz</td><td>Deroh 2020</td></tr><tr><td>TZN (TeO<sub>2</sub> based)</td><td>SpBS Linewidth</td><td>2 m<br>0.5 dB/m</td><td>-<br>Tellurite<br>4 µm<br>10 µm<sup>2</sup></td><td>2000 nm<br>-</td><td>CW</td><td>38 × 10<sup>-20</sup><br>m<sup>2</sup>/W</td><td>-<br>-</td><td>13 × 10<sup>-11</sup> m/W<br>6.17 GHz<br>15 MHz</td><td>Deroh 2020</td></tr><tr><td>TZN (TeO<sub>2</sub> based)</td><td>SpBS Linewidth</td><td>2 m<br>0.5 dB/m</td><td>-<br>Tellurite<br>4 µm<br>8 µm<sup>2</sup></td><td>1550 nm<br>-</td><td>CW</td><td>-</td><td>-</td><td>16 × 10<sup>-11</sup> m/W<br>7.97 GHz<br>21 MHz</td><td>Deroh 2020</td></tr></table>

Chalcogenide glass fibers

<table><tr><td>As<sub>2</sub>S<sub>3</sub></td><td>SBS Threshold</td><td>0.1 m<br>0.57 dB/m</td><td>0.33 NA<br>-<br>4.2 µm<br>-</td><td>1548.4 nm<br>≤ 0.03 W</td><td>-<br>-</td><td>-</td><td>-</td><td>~ 3.9 × 10<sup>-9</sup> m/W<br>-<br>-</td><td>Florea 2006</td></tr></table>
<table><tbody><tr><td>As<sub>2</sub>S<sub>3</sub></td><td>SpBS<br>Linewidth</td><td>2 m<br>0.2 dB/m</td><td>0.26 NA<br>As-S glass<br>6.1 µm<br>26 µm<sup>2</sup></td><td>2000 nm<br>-</td><td>CW</td><td>-</td><td>-</td><td>1.17 × 10<sup>-9</sup> m/W<br>6.21 GHz<br>25 MHz</td><td>Deroh 2020</td></tr><tr><td>As<sub>2</sub>S<sub>3</sub></td><td>SpBS<br>Linewidth</td><td>2 m<br>0.2 dB/m</td><td>0.26 NA<br>As-S glass<br>6.1 µm<br>20 µm<sup>2</sup></td><td>1550 nm<br>-</td><td>CW</td><td>-</td><td>-</td><td>1.54 × 10<sup>-9</sup> m/W<br>7.96 GHz<br>33 MHz</td><td>Deroh 2020</td></tr><tr><td>As<sub>2</sub>Se<sub>3</sub></td><td>SBS<br>Threshold</td><td>0.1 m<br>0.9 dB/m</td><td>0.14 NA<br>-<br>6.5 µm<br>-</td><td>1548.4 nm<br>≤ 0.133 W</td><td>-</td><td>-</td><td>-</td><td>~ 6.75 × 10<sup>-9</sup> m/W<br>-<br>-</td><td>Florea 2006</td></tr><tr><td>As<sub>2</sub>Se<sub>3</sub></td><td>SPM, XPM</td><td>0.25 m<br>1 dB/m</td><td>Single mode,<br>As-Se glass<br>-<br>21 µm<sup>2</sup></td><td>1560, 1503,<br>1470 nm<br>73 W</td><td>100 MHz<br>15 ps</td><td>1.10 to 0.75 ×<br>10<sup>-17</sup> m<sup>2</sup>/W</td><td>2 to 3 × 10<sup>-11</sup> m/W<br>~ 7 THz</td><td>-<br>-<br>-</td><td>Tuniz 2008</td></tr><tr><td>Ge-Sb-S</td><td>SpBS, SRS<br>Pump-Probe</td><td>1.5 m<br>5.5 dB/m</td><td>-<br>PCF<br>50 µm<br>-</td><td>1553 nm<br>≤ 25 W</td><td>-<br>10 ns</td><td>-</td><td>1.8 × 10<sup>-11</sup> m/W<br>9.7 THz</td><td>8 × 10<sup>-10</sup> m/W<br>8.2 GHz<br>-</td><td>Fortier 2008</td></tr></tbody></table>

Fluoride glass fibers

<table><tbody><tr><td>Fluoride</td><td>SBS<br>Threshold</td><td>29 m<br>0.02 dB/m</td><td>0.23 NA<br>-<br>6.5 µm<br>-</td><td>1940 nm<br>≤ 7 W</td><td>CW</td><td>-</td><td>3.25 to 3.52 × 10<sup>-14</sup><br>m/W<br>17.35 THz</td><td>-<br>-<br>-</td><td>Fortin 2011</td></tr><tr><td>ZBLAN</td><td>SBS<br>Pump-Probe</td><td>10.4 m<br>0.25 dB/m</td><td>0.17 NA<br>Fluoride glass<br>-<br>-</td><td>1550 nm<br>≤ 5 W</td><td>CW</td><td>-</td><td>-<br>-</td><td>4±3 × 10<sup>-12</sup> m/W<br>7.76 GHz<br>&lt; 38 MHz</td><td>Lambin-lezzi 2013</td></tr><tr><td>ZBLAN</td><td>SpBS<br>Linewidth</td><td>5 m<br>0.25 dB/m</td><td>-<br>Fluoride glass<br>9 µm<br>66 µm<sup>2</sup></td><td>2000 nm<br>-</td><td>CW</td><td>2.93 × 10<sup>-20</sup><br>m<sup>2</sup>/W</td><td>-<br>-</td><td>5.28 × 10<sup>-12</sup> m/W<br>6.00 GHz<br>35 MHz</td><td>Deroh 2020</td></tr><tr><td>ZBLAN</td><td>SpBS<br>Linewidth</td><td>5 m<br>0.125 dB/m</td><td>-<br>Fluoride glass<br>9 µm<br>55 µm<sup>2</sup></td><td>1550 nm<br>-</td><td>CW</td><td>-</td><td>-<br>-</td><td>4.95 × 10<sup>-12</sup> m/W<br>7.75 GHz<br>59 MHz</td><td>Deroh 2020</td></tr></tbody></table>

Representative specialty core phase fibers

<table><tbody><tr><td>Perfluoro<br>polymer</td><td>SBS<br>Threshold</td><td>100 m<br>0.15 dB/m</td><td>0.185 NA<br>Polymer<br>120 µm<br>-</td><td>1550 nm<br>≤ 1 W</td><td>CW</td><td>-</td><td>-<br>-</td><td>3.09 × 10<sup>-11</sup> m/W<br>2.83 GHz<br>105 MHz</td><td>Mizuno 2010</td></tr></tbody></table>
<table><tr><td>Sapphire</td><td>SCG</td><td>0.001 m<br>***</td><td>-<br>Unclad<br>60 µm<br>-</td><td>784 nm<br>-</td><td>1 kHz<br>150 fs</td><td>3 × 10<sup>-20</sup><br>m²/W</td><td>-</td><td>-</td><td>-</td><td>Yin 2008</td></tr><tr><td>Sapphire</td><td>SCG</td><td>0.035 m<br>***</td><td>-<br>Unclad<br>115 µm<br>-</td><td>2000 nm<br>3 – 16 MW</td><td>-<br>150 fs</td><td>2.8 × 10<sup>-20</sup><br>m²/W</td><td>-</td><td>-</td><td>-</td><td>Kim 2008</td></tr><tr><td>Silicon</td><td>SPM</td><td>0.008 m<br>0.2 to 3 dB/m</td><td>3.9 NA<br>SiO<sub>2</sub><br>Depends on taper</td><td>1540 nm<br>0.04 – 1.2 kW</td><td>-<br>700 fs</td><td>3 × 10<sup>-18</sup><br>m²/W</td><td>-</td><td>-</td><td>-</td><td>Ren 2019</td></tr><tr><td>Silicon</td><td>SPM</td><td>0.01 m<br>2 dB/m</td><td>3.9 NA<br>SiO<sub>2</sub><br>Depends on taper</td><td>2400 nm<br>-</td><td>-<br>100 fs</td><td>1 × 10<sup>-17</sup><br>m²/W</td><td>-</td><td>-</td><td>-</td><td>Shen 2020</td></tr><tr><td>Poled<br>germanosilicate</td><td>SHG</td><td>0.32 m<br>~ 0 dB/m</td><td>0.11 NA<br>SiO<sub>2</sub><br>6 µm<br>-</td><td>1541 nm<br>200 W</td><td>3 MHz<br>-</td><td colspan="4">χ<sup>(2)</sup><sub>eff</sub> = 0.054 pm/V, 15.2% conversion efficiency</td><td>Canagasabey 2009</td></tr></table>

* Sometimes the value of n<sub>2,eff</sub> should be multiplied by 9/8 when comparing to bulk measurements to account for the effects of polarization randomization that occurs for fibers longer than several meters [Buckland1996] (see Section 1.1 on fused silica).

** The Brillouin gain coefficient was determined by comparing the strength of Brillouin scattering to a reference fiber of known g<sub>Brillouin</sub>.

*** Not noted in stated reference but attenuation values of 0.3 dB/m at a wavelength of 2.94 µm have been reported [Harrington2014].
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## 3.6 On-chip waveguiding materials: data table and discussion

**Team:** Philippe Boucaud, Ksenia Dolgaleva, Daniel Espinosa, Rich Mildren, Minhao Pu (team leader), Nathalie Vermeulen, Kresten Yvind

### 3.6.1 Introduction

#### 3.6.1.1 On-chip waveguiding materials and their NLO applications

Integrated photonics deals with miniaturization of bulk-component optical setups including all their key components (light-emitting devices, light-steering optics and detectors) and functionalities on small chips, typically with dimensions < 1×1 cm². The on-chip miniaturization of photonic components allows building compact photonic integrated circuits (PICs) with high complexity, small footprint and potentially low cost when produced in large volumes. Thanks to the strong advancement in manufacturing technology over the past decades, a wide variety of materials can be combined nowadays through heterogeneous integration and bonding, thus covering a very wide spectral range and optimizing the performance of both active and passive devices by selecting the appropriate material platform for each on-chip functionality. Alternatively, monolithic photonic integration where active and passive integrated optical components are built on the same platform, with some variation of the material composition depending on the device functionality, is also possible using III-V semiconductor platforms.

Nonlinear integrated photonics exploits the NLO response of on-chip components. Some examples of on-chip nonlinear photonic devices include straight passive waveguides, micro-ring resonators or other compact structures, such as photonic-crystal waveguides. Fabrication of waveguides with dimensions smaller than the wavelength of operation [Karabchevsky2020] has enabled strong light confinement and, as such, high irradiances beneficial for efficient NLO interactions. Ultra-compact waveguides with large refractive index contrasts between the core and cladding can also exhibit strong waveguide dispersion, enabling dispersion engineering useful for establishing, e.g., phase-matched second-harmonic generation or four-wave mixing. Finally, besides basic waveguide cross-sections consisting of three material layers (guiding layer or core, substrate and cladding), more advanced quantum-well waveguide geometries featuring enhanced NLO interactions have also emerged over the years [Wagner2009a, Hutchings2010, Wagner2011].

In case the waveguide core material lacks inversion symmetry, NLO interactions of the second order can take place; otherwise, the waveguide will only exhibit a third-order NLO response. These two waveguide subcategories offer quite different NLO functionalities: whereas waveguides with a second-order nonlinearity allow, e.g., on-chip frequency doubling, DFG and EO modulation (the latter is not included in the tables), those with a third-order nonlinearity enable Kerr-based supercontinuum generation, Raman amplification, all-optical switching, etc. These functionalities are finding practical use in a wide variety of applications, ranging from on-chip biosensing, spectroscopy and LIDAR to optical datacom, signal processing, and quantum computing.

#### 3.6.1.2 Background prior to 2000

The NLO properties of the majority of materials used for on-chip integration were already studied in bulk form well before 2000, and many NLO experiments in waveguide configurations were reported before the turn of the century. These early studies were primarily concerned with determining effective NLO coefficients of the materials in waveguide arrangements. Furthermore, efforts in optimizing the light confinement and tailoring various phase-matching techniques in waveguides already began before the new millennium. Nevertheless, the field has still experienced tremendous growth after 2000 facilitated by the maturing fabrication technologies for PICs [Ottaviano2016, Roland2020].
### 3.6.1.2.1 Background for on-chip waveguide materials with second-order nonlinearity

Second-order NLO effects generally require non-centrosymmetric materials. Although it is possible to induce these effects in centrosymmetric materials by means of strain [Cazzanelli2011], by applying all-optical poling techniques [Nitiss2022] or by exploiting surface effects, the strongest second-order nonlinearities are generally found in materials that intrinsically lack inversion symmetry. Before 2000, the following non-centrosymmetric crystalline waveguide materials were used for establishing $\chi^{(2)}$ effects: III-V semiconductors, aluminum gallium arsenide (AlGaAs) and gallium arsenide (GaAs) [Anderson1971, VanDerZiel1974, VanDerZiel1976, Yoo1995, Ramos1996, Fiore1997a, Street1997a, Street1997b, Xu1997, Fiore1998, Fiore1997b, Yoo1996, Bravetti1998, Xu1998]; III-nitrides, aluminum nitride (AlN) and gallium nitride (GaN) [Blanc1995, Zhang1996]; and some II-VI semiconductors such as zinc selenide (ZnSe), zinc telluride (ZnTe), and zinc sulfide (ZnS), grown epitaxially on a GaAs substrate [Angell1994, Wagner1995, Wagner1997, Kuhnelt1998]; as well as some other materials [Sugita1999, Chui1995, Azouz1995]. Most of the III-V semiconductor optical waveguides used to demonstrate $\chi^{(2)}$ effects before the 1990s [Anderson1971, VanDerZiel1974, VanDerZiel1976] as well as all AlN, GaN [Blanc1995, Zhang1996] and II-VI waveguide demonstrations [Angell1994, Wagner1995, Wagner1997, Kuhnelt1998] were in slab waveguides with 1D confinement. As the means and tools for nanofabrication experienced further development, it became possible to routinely fabricate AlGaAs/GaAs channel or ridge waveguides with 2D confinement, exhibiting more efficient NLO interactions [Yoo1995, Ramos1996, Fiore1997a, Street1997a, Street1997b, Xu1997, Fiore1998, Fiore1997b, Yoo1996, Bravetti1998, Xu1998]. Among the specific second-order NLO effects in AlGaAs and GaAs, there were numerous experiments on SHG in the near-IR [VanDerZiel1974, VanDerZiel1976, Yoo1995, Fiore1997a, Street1997a, Street1997b, Xu1997, Fiore1998], mid-IR [Anderson1971], and visible (SHG of blue light) [Ramos1996]. There were also some DFG reports with generation of mid-IR [Fiore1997b, Bravetti1998], as well as near-IR radiation using 770-nm pump light [Yoo1996] and SFG of 780-nm red light with a near-IR pump [Xu1998]. AlN and GaN III-nitride and II-VI slab dielectric waveguides enabled the observation of SHG in the visible [Blanc1995, Zhang1996].

While crystalline birefringence is often used in bulk crystals to phase-match the widely spaced wavelengths in second-order NLO processes, other techniques are needed for materials that do not possess natural birefringence, such as GaAs and AlGaAs. Phase-matching techniques used to enhance the efficiency of second-order NLO effects include dispersion engineering of the slab waveguide structure [Anderson1971], and modal phase matching where the fundamental radiation occupied a lower-order mode and the second harmonic populated a higher-order mode for the effective refractive index matching [VanDerZiel1974, Blanc1995, Wagner1995]. Most of the demonstrations of phase-matched $\chi^{(2)}$ effects employed various QPM approaches [VanDerZiel1976, Yoo1995, Fiore1997a, Street1997a, Street1997b, Xu1997, Yoo1996, Xu1998, Angell1994, Wagner1997, Kuhnelt1998, Azouz1995, Sugita1999]. Specifically, many reports explored periodic domain inversion (PDI) where the sign of $\chi^{(2)}$ was periodically modulated by crystalline domain reorientation achieved through wafer bonding and subsequent epitaxial (MOCVD or MBE) regrowth of the structure with the domain orientation following that of the template [Yoo1995, Xu1997, Yoo1996, Xu1998, Angell1994]. This approach featured high propagation losses of 50-120 dB/cm, except for one study reporting much lower propagation losses of 5.5 dB/cm at the fundamental and 25 dB/cm at the 730-nm second-harmonic [Yoo1995]. QPM by PDI through proton exchange followed by thermal annealing in LiTaO₃ [Azouz1995] and by periodic electric-field poling of MgO:LiNbO₃ (with a very high efficiency of 31%) [Sugita1999] were also demonstrated. QPM by a periodic modulation of the refractive index was achieved via a corrugation formed by a grating etched in one of the waveguide heterostructure interfaces [VanDerZiel1976]. Furthermore, QPM by periodic modulation of the values of $\chi^{(2)}$ (their periodic suppression) was achieved via asymmetric coupled quantum-well reorientation [Fiore1997a], quantum-well intermixing [Street1997a, Street1997b] selective wet oxidation of AlAs in AlGaAs/GaAs structures [Fiore1998, Fiore1997b, Bravetti1998], and maskless focused-ion-beam implantation
in ZnTe and ZnSe waveguides [Wagner1997, Kuhnelt1998]. Thanks to the highest modulation contrast of $\chi^{(2)}$ achievable through PDI, this method has been shown to result in the highest conversion efficiencies despite the largest propagation losses. Some specific conversion efficiency figures are 1040 %/W/cm² for SHG [Xu1997] and 810 %/W/cm² for DFG [Xu1998] (PDI Al₀.₆Ga₀.₄As core with Al₀.₇Ga₀.₃As claddings, fundamental wavelengths around 1550 nm). Some other promising results include 190 %/W [Fiore1998] (AlGaAs/AlAs with form birefringence by selective wet oxidation), 450 %/W [Azouz1995] (LiTaO₃ formed by proton exchange), and 1500 %/W [Sugita1999] (SHG of 426 nm in MgO:LiNbO₃ waveguide with a periodically patterned domain structure).

### 3.6.1.2.2 Background for on-chip waveguide materials with third-order nonlinearity

Third-order NLO interactions demonstrated in waveguide platforms before 2000 include a wide variety of phenomena such as SPM, XPM, THG, Raman, Brillouin and FWM. The dominant number of experimental demonstrations were performed in the 1990s in III-V semiconductor optical devices based on AlGaAs [Espindola1995, Peschel1999, Millar1999, Le1990, Hamilton1996, Kang1996, Islam1992, Stegeman1994, Kang1995, Kang1998, Villeneuve1995a, Villeneuve1995b, Villeneuve1995c, Le1992] and InGaAsP [Nakatsuhara1998, Day1994, DOttavi1995, Donnelly1996, Darwish1996, Tsang1991]. Waveguides of planar configuration (featuring 1D confinement) [Kang1996, Day1994, Kang1998] and channel/rib waveguides (with 2D confinement) [Espindola1995, Stegeman1994, Nakatsuhara1998, Villeneuve1995c, DOttavi1995, Hamilton1996, Donnelly1996, Islam1992, Peschel1999, Le1990, Millar1999, Villeneuve1995b] were considered. The majority of studies were performed in waveguides with 2D confinement, while 1D structures were primarily used for spatial soliton demonstrations [Kang1996, Kang1998]. The NLO phenomena studied in III-V semiconductors included SPM and XPM [Kang1996, Day1994, Hamilton1996, Kang1998, Tsang1991, Villeneuve1995b], FWM [Espindola1995, DOttavi1995, Donnelly1996, Le1990, Darwish1996, Le1992], and other demonstrations of the third-order optical nonlinearity [Islam1992, Peschel1999, Millar1999].

InGaAsP-based works feature optical devices with both resonant [Day1994] and nonresonant [Nakatsuhara1998, DOttavi1995, Donnelly1996, Darwish1996, Tsang1991] nonlinearities in the vicinity of the bandgap. In contrast, AlGaAs-based works primarily concentrated on operation at wavelengths below half of the bandgap energy, typically the telecom C-band wavelengths, where it is possible to eliminate 2PA by manipulating the material compositions of the waveguide heterostructures [Kang1996, Villeneuve1995c, Stegeman1994, Peschel1999, Kang1998, Villeneuve1995b]. InGaAsP- and AlGaAs-based quantum-well devices have been shown to exhibit strong nonlinearities due to band-filling and excitonic effects [Day1994, Donnelly1996, Darwish1996, Tsang1991, Islam1992].

Most of the studies on the third-order nonlinearities in III-V semiconductor waveguides before 2000 were focusing on measuring the nonlinear coefficients such as $n_{2(\text{eff})}$ and $\alpha_2$. The values of $n_{2(\text{eff})}$ in AlGaAs of various material compositions at various wavelengths have been reported to fall within the range between $2.1 \times 10^{-14}$ and $3.3 \times 10^{-13} \text{cm}^2/\text{W}$, with the most cited values near half-the-bandgap of $(1.3 - 1.5) \times 10^{-13} \text{cm}^2/\text{W}$ in the telecom C-band [Espindola1995, Stegeman1994, Hamilton1996, Islam1992, Aitchison1997]. The 2PA coefficients $\alpha_2$ of AlGaAs below half-the-bandgap have been reported to span between 0.026 and 0.06 cm/GW [Espindola1995, Islam1992, Aitchison1997]. The values of $n_{2(\text{eff})}$ (in the range between $6 \times 10^{-13}$ and $9.5 \times 10^{-12} \text{cm}^2/\text{W}$) and $\alpha_2$ (3 - 60 cm/GW), typically measured in the vicinity of the bandgap, have been reported in InGaAsP waveguides [Donnelly1996, Darwish1996, Tsang1991]. The values of $\chi^{(3)}$ in AlGaAs [Le1990] and InGaAsP [Donnelly1996] waveguides have also been measured. A few studies report the conversion efficiencies for FWM processes in AlGaAs [Le1990, Le1992] and InGaAsP [Donnelly1996, Darwish1996] waveguides.

Organic polymers in waveguide configurations (not included in the data table) represent another large group of materials that has been extensively studied before 2000 [Prasad1987, Grabler1997, Rossi1991, Huang1999, Okawa1991, Chon1994, Muto1992, Hosoda1992, Driessen1998, Bartuch1997, Malouin1996, Malouin1998, Murata1998, Marques1991, Asobe1995, Lee1993, König1999]. Many
studies report the effective values of $\chi^{(3)}$ of a variety of polymer-based waveguides [Huang1999, Okawa1991, Chon1994, Rossi1991, Hosoda1992, Lee1993]. The typical value ranges for the nonlinear coefficients $n_2$ of these waveguide materials are between $2.7 \times 10^{-14}$ and $1.7 \times 10^{-12}$ cm$^2$/W, while $\alpha_2$ ranges between 0.08 and 5.8 cm/GW [Chon1994, Driessen1998, Bartuch1997, Malouin1998, Murata1998, Marques1991, Asobe1995, Malouin1996, Crabler1997]. Thanks to the wide transparency windows of the majority of the polymer waveguide platforms, most of these measurements have been performed in the visible wavelength range.

There were a few reports demonstrating third-order NLO interactions in waveguides made of other materials, namely: $Si_3N_4$ [Bertolotti1999], QPM KTP waveguides [Sundheimer1993], gelatin-gold nanoparticle composites [Bloemer1990], $SiO_2$-$TiO_2$ [Toruellas1991], and chalcogenide glasses (ChGs) [Cerqua-Richardson1998]. Notably, there was also a series of works on planar iron-doped and titanium-indiffused $LiTaO_3$ and $LiNbO_3$ waveguides where phase conjugation by anisotropic FWM and two-wave mixing has been demonstrated [Kip1994, Popov1992, Normandin1979, Kip1992, Fujimura1999, Kip1995].

The dominant driver behind studying the third-order phenomena in waveguide configurations before 2000 was the potential of developing all-optical signal processing devices for optical communication networks and optical information processing. As the fastest response time associated with most of the nonresonant third-order processes is at the sub-femtosecond time scale, high-speed switching at moderate optical powers is possible. Many proof-of-principle all-optical-switching devices such as nonlinear directional couplers and asymmetric Mach-Zender interferometers [Kang1995, Stegeman1994, Villeneuve1995a] have been demonstrated before 2000. Optical bistable devices in various waveguide platforms have also been realized [Nakatsuhara1998, Huang1999]. Yet, despite this interest in datacom and information processing applications, the NLO properties of Si waveguides remained largely unexplored before 2000.

### 3.6.1.3 Considerations for on-chip waveguides when performing NLO measurements

Determining the irradiance inside the on-chip waveguide is not straightforward and can represent the main source of error in NLO measurements. Apart from the determination of the optical beam characteristics such as the pulse width and the peak power, a careful evaluation of the coupling efficiency and the effective mode area is crucial for the irradiance determination. If the waveguide's cross-sectional dimensions change along the propagation direction, as in the case of devices with tapers, the subsequent change in the irradiance and phase matching conditions must also be accounted for. The propagation loss must be properly evaluated. It includes the linear absorption, which depends only on the constituent materials, the scattering off the waveguide's walls and the field leakage. The determining factors in the loss characteristics are the waveguide's fabrication process, its geometry, material composition, and the quality of the substrate. Although most of the selected waveguide materials do not exhibit 2PA at the wavelength of interest in their bulk states, the large surface area of the waveguides may give rise to linear absorption from impurities and defects generating free carriers and/or excited impurity or defect states that subsequently absorb. This 2-step process mimics 2PA making it difficult to experimentally separate its effects from direct 2PA. However, this is a fluence dependent (power dependent in waveguides) rather than an irradiance dependent process, and thus its effects are reduced in short-pulse measurements [Lin2007a, VanStryland1985, Christodoulides2010]. Using CW or long pulse high-repetition-rate sources helps to determine this contribution.

An effective NLO coefficient measured in heterostructure waveguides usually results from an irradiance-weighted average of the NLO coefficients of different layers. The contribution of the guiding layer is dominant in most cases. However, the precise effective NLO coefficient values depend on the confinement factor [Grant1996]. For this reason, the waveguide's NLO coefficients might deviate from the corresponding bulk values.
As for the measurements of the efficiency of the NLO process, the approach used to perform the calculation must be explicitly given. For example, one should state whether the power used in the calculation is the average or peak power, external or internal (coupled in), at the input or output of the device.

In multi-beam experiments, the group velocity mismatch (GVM) and phase mismatch, which depend on the material and waveguide dispersions, should also be properly quantified because for several NLO processes, such as FWM, these are some of the most crucial factors in determining the efficiency of the process. GVM is responsible for separating the probe pulse from the pump pulse in time as they propagate along the waveguide, while the phase mismatch between different wavelength components involved in the NLO process determines the coherence length of the process [Tishchenko2022]. The beauty of on-chip waveguides is that some of them enable dispersion engineering with the possibility of zero GVD at the wavelengths of interest to improve the efficiency of a NLO process [Pu2018, Dolgaleva2015, Meier2007]. Estimating the efficiency of the NLO process in a waveguide from the theoretical models that account for the dispersion, the irradiances, and NLO coefficients, and comparing it to the measured value is also a good practice [Espinosa2021a, Pu2018, Foster2007].

On-chip waveguides used in NLO are often quite short (< 1cm). For waveguide materials that are not highly nonlinear, one should test/account for possible nonlinearities in the rest of the characterization system by performing reference measurements. This is especially true for tapered fiber-coupled devices where a reference measurement without the device can be performed with the input power corrected for the insertion loss.

Besides the special considerations outlined here, also the general best practices of Section 2 should be taken into account when performing NLO measurements with on-chip waveguides.

### 3.6.1.4 Description of general table outline

Tables 7A and 7B show a representative list of, respectively, second-order and third-order NLO properties of on-chip waveguiding materials taken from the literature since 2000. The selection of the papers included in the Tables has been based on the best practices in Section 2 and the considerations outlined above. Table 7B has the entries grouped into five subcategories to facilitate the search for a specific waveguide composition: III-V semiconductors; silicon and silicon carbide, nitride, and oxide; chalcogenide glasses; diamond; tantalum oxide and titanium oxide. Within each subcategory, the entries are ordered alphabetically. Tables 7A and 7B are subdivided into “Material properties,” “Measurement details” and “Nonlinear properties”. Within each column the information is given in the order of the header description, and powers of 10 (e.g., $10^{\pm\alpha}$) are written as $E\pm\alpha$ for compactness. “Material properties” include the waveguide dimensions (length and cross-section), fabrication methods, propagation loss, refractive index, and a reference to the sub-figure in Figs. 6-7 showing the fabricated device. Fig. 6 shows SEM pictures of devices with second-order NLO responses, while Fig. 7 shows SEM pictures of devices with third-order NLO responses. The peak power values in the Tables are nominally incoupled powers as specified in the papers. The table entries cover various material platforms and compositions, as well as various waveguide configurations and phase-matching techniques. In some instances, the waveguide structure was rather complex, and it was difficult to fit its detailed description in the Tables. In these cases, simplified descriptions were provided with references to the more detailed descriptions in the corresponding papers. The NLO technique used in each of the papers is provided in the “Method” column. Lastly, some papers specify the dependence of the NLO parameters or conversion efficiency $\eta$ on wavelength, waveguide dimension, temperature, etc. or have notes associated with their measurement/analysis. This information is listed within the “Comments” column. The works included in the Tables nominally report data obtained at room temperature, unless specified otherwise in the “Comments” column. If dispersive values for the NLO parameter were provided, the cited value represents the peak value for the material within the stated measurement range.
## 3.6.2 Discussion

The data in Tables 7A and 7B indicate a clear trend towards the development of high-confinement waveguides because of the benefit of enhanced NLO interactions for both the second- and third-order NLO processes. Novel and improved fabrication procedures have been developed to ensure high-quality materials and low surface roughness. Several new waveguide material platforms have been entering the scene, bringing about excellent NLO performance. These platforms will further stimulate the development of practical NLO integrated devices.

### 3.6.2.1 Advancement since 2000 and remaining challenges

Over the past twenty years, there have been significant advancements in the methods of micro- and nanofabrication. Apart from the major progress in photo-lithography and electron-beam lithography, novel nanofabrication approaches and techniques have appeared, and also photonic foundries offering multi-project wafer runs at a reduced cost per chip have facilitated the field's growth. In the early 2000s, the NLO community turned its attention to silicon-on-insulator (SOI) photonics as a promising nonlinear platform because of its potentially lower cost and high compatibility with CMOS technology. Various SOI components for parametric amplification, wavelength conversion, and Raman lasing have been demonstrated in the telecom wavelength range.

The success of silicon photonics, inspired by CMOS silicon electronics, relies on the tight light confinement enabled by the combination of a high-index material (Si) surrounded by a low-index oxide cladding. Not surprisingly, this semiconductor-on-oxide approach has also been applied to other material systems, such as AlGaAs, resulting in NLO devices with improved performances. Another enabling factor in the new platform development is significant progress in bonding and substrate removal technologies, opening the route to various types of heterogeneous integration. Nonlinear photonics with suspended semiconductor membranes has consequently emerged. Below we provide more detailed insight into the progress since 2000, the remaining challenges and the applications of on-chip waveguides with second- and third-order NLO effects.

#### 3.6.2.1.1 Advancement and challenges for on-chip waveguiding materials with second-order nonlinearity

There were many improvements in lowering the propagation losses and increasing conversion efficiencies of the second-order NLO interactions in the existing AlGaAs waveguide technologies. Specifically, selectively oxidized AlGaAs/Al<sub>x</sub>O<sub>y</sub> multilayer stacks with 2D-confined ridge waveguides with much lower propagation losses of 1.5 - 5 dB/cm featuring much higher conversion efficiencies ranging between 2.7 and 5 %/W were demonstrated [Savanier2011b (SHG), Savanier2011a (SFG), Ozanam2014]. Moreover, 2D-confined AlGaAs waveguides with symmetric Bragg reflectors in their top and bottom claddings have been realized [Han2009, Bijlani 2008, Han2010, Abolghasem2009], exhibiting SHG and SFG conversion efficiencies around 9 %/W [Han2009, Bijlani 2008] and DFG conversion efficiencies of 5.2 × 10<sup>-4</sup> %/W [Han2010]. Fabrication of QPM AlGaAs waveguides by PDI [Yu2005, Ota2009, Yu2007] and by a periodic suppression of (2) (periodic domain disorientation) achieved through quantum-well intermixing [Wagner2011, Hutchings2010, Wagner2009b] have seen significant improvements. PDI waveguides with propagation losses as low as 5 dB/cm and SHG conversion efficiencies over 40 %/W [Yu2007] have been demonstrated.

Another advancement in the established AlGaAs waveguide technologies resides in the capability to fabricate deeply etched waveguides with sub-micrometer dimensions. An example of such a waveguide has been demonstrated in [Duchesne2011] where 300-1000 nm-wide ultracompact AlGaAs waveguides with tight light confinement were used for SHG with modal phase matching. The normalized conversion efficiency was moderate, 1.4 × 10<sup>5</sup> %/(W m<sup>2</sup>), due to the high propagation losses of 18 dB/cm characteristic to such devices with exposed guiding-layer sidewalls.

In addition to the existing AlGaAs waveguide technologies, there appeared new waveguide platforms where an AlGaAs or GaAs guiding layer is surrounded by an insulator such as SiO<sub>2</sub> [Stanton2020,
Chang2019, Chang2018] or air [Morais 2017, Roland2020]. The propagation loss of 1.5 - 2 dB/cm in AlGaAs on SiO₂ is similar to that of the conventional AlGaAs strip-loaded waveguides, while conversion efficiencies as high as 40% / W [Stanton2020] and 250% / W [Chang2018] in the CW regime have been reported. Simple type-II phase matching between a fundamental transverse-electric (TE) mode and a high-order second-harmonic transverse-magnetic (TM) mode was implemented, combined with directional QPM in [Morais2017]. Further advancements in the reduction of the propagation losses will lead to even more efficient AlGaAs devices for second-order NLO interactions. However, there exists another factor limiting the conversion efficiencies of longer waveguide structures. The narrow phase-matching bandwidth combined with an extreme sensitivity of the phase-matched wavelength to the waveguide dimensions (a precision on the order of a few nm is required) makes phase matching over a long distance technologically difficult [Stanton2020].

There are several reports on other waveguide platforms used for phase-matched second-order NLO interactions, among which are AlN on SiO₂ [Bruch2018], GaP on SiO₂ [Wilson2020], GaN on SiO₂ [Xiong2011], AlGaN [Gromovyi2017], and periodically polled LiNbO₃ [Wang2018b]. A remarkably high SHG conversion efficiency of 17,000% / W for the fundamental wavelength around 1550 nm has been achieved in a 2D-confined AlN ring resonator [Bruch2018]. The 2D confinement represents the most significant advancement in AlN- and GaN-based waveguides since only structures with 1D confinement (slab dielectric waveguides) were accessible before 2000. It was not until recently that the fabrication of 2D-confined channel waveguides based on these platforms became possible. AlN and GaN represent wide-bandgap semiconductors exhibiting large hardness and posing challenges in both epitaxial growth and defect-free nanofabrication. Further mitigation of threading-dislocation density by optimizing the epitaxial growth and substrate choice [Awan2018] is expected to result in a significant improvement and more widespread use of such platforms in nonlinear photonics.

The observation of the second-order NLO interactions in waveguides is not limited to SHG or SFG. Spontaneous parametric down-conversion (SPDC) generating correlated photon pairs for applications in quantum technologies has been demonstrated in AlGaAs waveguides [Guo2017, Sarrafi2013]. OPO based on second-order processes has been demonstrated in GaAs/AlGaAs waveguides [Savanier2013], and, more recently, in AlN ring resonators [Bruch2019]. Supercontinuum generation (SCG) [Lu2019, Zheng2021, Okawachi2020] and frequency comb generation [Zhang2019] based on second-order processes have also been reported.

To illustrate the wide variety of components discussed here, Fig. 6 shows SEM images of some integrated waveguide devices used for second-order NLO interactions (see Table 7A).
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** SEM images of integrated photonic devices for second-order nonlinear interactions. The labels of the subfigures correspond to the labels given in Table 7A. Panels a, b, c, d, e, f, g, h, i and j are reprinted with permission from [Xiong2011, Wang2018b, Yu2005, Duchesne2011, Scaccabarozzi2006, Han2009, Morais2017, Savanier2011b, Ozanam2014, Stanton2020], ©2005, 2006, 2009, 2011, 2014, 2017, 2018, 2020 Optica Publishing Group.</figcaption></figure>

### 3.6.2.1.2 Advancement and challenges for on-chip waveguiding materials with third-order nonlinearity

There have been significant improvements in mitigating the propagation losses, optimizing the waveguide geometries, and achieving higher conversion efficiencies in the existing third-order nonlinear optical waveguide platforms, such as AlGaAs. Furthermore, there is a plethora of new works featuring novel waveguide materials that appeared after 2000 or waveguide materials that already existed but were not yet considered for NLO experiments until after 2000. These include various silicon-based platforms (SOI [Claps2002, Tsang2002, Liu2004, Rong2005, Zlatanovic2010, Turner-Foster2010, Liu2011, Kuyken2011, Liu2012, VanLaer2015, Zhang2020], Si₃N₄ [Levy2009, Tien2010, Kruckel2015b, Wang2018a], silicon-rich nitride [Wang2015, Kruckel2015a, Lacava2017, Ooi2017], SiC [Zheng2019b, Xing2019], amorphous silicon [Wang2012a, Wang2012b, Lacava2016, Girouard2020]), various chalcogenide glasses (ChGs) [Madden2007, Lamont2008, Gai2010], TiO₂ [Evans2013, Guan2018, Hammani2018], Hydex glass [Ferrera2008, Ferrera2009, Duchesne2009], diamond [Hausmann2014, Latawiec2015, Latawiec2018], and additional III-V semiconductor platforms not previously explored for nonlinear photonic devices (GaP [Wilson2020], InGaAs/AlAsSb [Tsuchida2007, Cong2008, Lim2010, Feng2013]). The overall trend indicates that higher effective nonlinearities can be obtained in high-index-contrast waveguides, often with a low-index dielectric like silica or sapphire below the waveguide core. High-index-contrast silicon-based waveguides typically feature sub-micron dimensions [Wang2015, Lacava2017, Ooi2017, Turner-Foster2010, Kuyken2011, Liu2012, VanLaer2015]. Furthermore, ultracompact AlGaAs waveguides with sub-micron dimensions, appearing after 2000, have also shown superior efficiencies of NLO interactions in comparison to their more conventional low-index-contrast counterparts [Apiratikul2014, Dolgaleva2015, Espinosa2021a]. Moreover, the SOI approach has been extended to other semiconductor platforms, enabling an increase in their refractive index contrasts and a decrease in the waveguide dimensions. Among those are AlGaAs-on-insulator (AlGaAs-OI) [Stassen2019, Pu2016, Pu2018, Kaminski2019, Hu2018, Ottaviano2016, Zheng2019a], GaP-OI [Wilson2020], and InGaP-OI [Colman2010, Dave2015a, Dave2015b]. Thanks to the strong light confinement, it became possible to push the effective nonlinear coefficient $\gamma_{eff}$ to the level of 100 m⁻¹W⁻¹ in NLO waveguides based on these material platforms. Further enhancement of the NLO interactions has been achieved through resonant effects in microring resonators [Absil2000, Li2021, Ramelow2019, Shi2021, Fu2020, Zheng2019a, Zheng2019b,
Ottaviano2016] and photonic-crystal structures [Jandieri2021, Monat2009 Liu2007, Zhu2006, Monat2010, Martin2017, Corcoran2009].

The effective nonlinearity is only one of the critical elements that determine the overall device performance. Another crucial parameter is propagation loss: the linear loss limits the effective nonlinear interaction length, while the nonlinear loss limits the maximum pump power that can be used for the specific NLO process. Significant efforts have been put into lowering both types of losses. As the linear loss is dominated by the scattering loss associated with the waveguide surface roughness and the refractive index contrast between the core and cladding, various approaches have been proposed to smoothen the waveguide surfaces (see, for example, [Awan2018, Liao2017]) and to passivate the waveguide surface for scattering reduction [Apiratikul2014, Wathen2014]. The nonlinear loss induced by multiphoton absorption is determined by the bandgap of the nonlinear material. The latter can be mitigated by using an appropriate material platform that lacks 2PA in the wavelength range of interest, which stimulated an effort in developing wide-bandgap NLO material platforms such as SiN, Hydex, Ta₂O₅ [Wu2015], SiC, AlN, and GaN. Some of the aforementioned platforms also exhibit modest index contrast compared to that associated with SOI and similar platforms. Although the effective nonlinearity that can be achieved in such low-index-contrast platforms is relatively low, their propagation losses are also extremely low. Ultra-low loss waveguides (with propagation losses < 0.5 dB/cm) can be easily realized, allowing for much longer propagation lengths and ultra-high-Q microring resonators, thereby magnifying the efficiency of the NLO interactions. In contrast, the propagation losses in most high-index-contrast waveguides are much higher (> 1 dB/cm) and do not permit long-length devices. Nevertheless, superior waveguide compactness and dispersion-management capability make them efficient NLO material platforms. Mitigating propagation losses, and improving waveguide designs, fabrication procedures, and NLO efficiencies continue to be the challenges on the path towards more practical integrated NLO devices.

Among the third-order NLO processes investigated after 2000, there are SPM, XPM, FWM, Raman effects, and Brillouin processes. If the works published before 2000 were focusing on determining the effective NLO coefficients of various waveguide structures, the trend after 2000 was partially shifted towards achieving higher NLO efficiencies with lower incident powers. The underlying idea is to push the proof-of-concept demonstrations towards practical implementations. In many emerging platforms, including AlGaAs-OI [Pu2016, Zheng2019a], SiN [Ramelow2019, Wu2021, Xue2016], Hydex [Reimer2014], SiC [Shi2021], and AlN [Jung2013, Jung2016], ultra-high-Q resonators have been realized to demonstrate FWM-based Kerr frequency comb generation, which has a wide variety of applications in spectroscopy, metrology, telecommunication, and quantum information processing. Furthermore, ultra-broadband (larger than half an octave) FWM bandwidths have been demonstrated [Pu2018, Moille2021], and supercontinuum generation (SCG) spanning more than an octave [Porcel2017, Lu2019, Zhao2015, Liu2016, Yu2019] has also been achieved in different waveguide platforms. All-optical signal processing operations and optical logic gates have been demonstrated [Pelusi2008, Willner2014, Koos2009, Yan2012, Jandier2018, Ma2016, Eggleton2012], targeting applications in optical communication networks and optical computing. An emerging application of on-chip nonlinear photonic devices that appeared after 2000 is nonlinear sources of correlated photon pairs for applications in quantum optics [Ma2018, Shi2019, Kultavewuti2016, Kultavewuti2019].

To illustrate the variety of structures discussed above, Fig. 7 displays SEM images of some integrated waveguide devices used for third-order NLO interactions (see Table 7B).
1
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<figure><img src="image_9.png" /><figcaption>**Fig. 7.** SEM images of integrated photonic devices for third-order NLO interactions. The labels of the sub-figures correspond to the labels given in Table 7B. Panels a, b, d, e, h, i, l, n, o, q, s, t, and v are reprinted with permission from [Liu2011, Wang2012b, Wathen2014, Apiratikul2014, Chiles2019, Dave2015a, Evans2013, Zheng2019b, Wu2015, Gajda2012, Kruckel2015a, Madden2007, Jung2013], ©2007, 2011, 2012, 2013, 2014, 2015, 2019 Optica Publishing Group. Panels c, j, k, p, r, and u are reprinted with permission from [Ferrera2008, Colman2010, Wilson2020, VanLaer2015, Kittlaus2016, Hausmann2014], Springer Nature. Panel f is reprinted with permission from [Espinosa2021a], Elsevier. Panels g and m are reprinted under CC BY license from [Stassen2019] and [Hammani2018].</figcaption></figure>

### 3.6.2.2 Recommendations for future works on on-chip waveguiding materials

Most papers noted in the Tables 7A and 7B present the measurements of one physical effect, e.g., SPM-induced spectral broadening, Raman scattering or harmonic generation. We encourage researchers to take into consideration the category-specific recommendations outlined above as well as the best practices in Section 2. Following these tips will help eliminate possible errors encountered in the process of determining the values of NLO coefficients and conversion efficiencies.

We recommend that the authors of papers reporting on the NLO performance of waveguides specify at least those parameters that are included in the Tables 7A and 7B. Furthermore, the completeness of such works could benefit from adding additional information. For example, it is instructive to separate the absorption and scattering losses, and to add the thermo-optic coefficients in resonator structures, whenever it is possible. Self-heating is an important consideration in resonator-based applications, while these parameters are rarely provided in waveguide characterization papers.

Another point of concern is nonlinear losses. The parameter $\alpha_2$ in the Tables is most often attributed to the “instantaneous” 2PA that would have been retrieved from low-duty-cycle pulsed-source
experiments. The highly nonlinear semiconductor waveguides with high refractive index contrast present a special challenge due to the high field amplitudes at the surfaces where surface states may be present [Espinosa2021b, Viswanath2001]. The same applies to amorphous/polycrystalline materials where surface effects may dominate the losses [Wronski1981, Grillanda2015, Girouard2020]. In all cases, a detailed description of the fabrication and surface passivation (if performed) should be provided. These surface effects can result in significant linear absorption creating free carriers and/or excited impurity or defect states which may have long lifetimes. These carriers/excited states can subsequently absorb resulting in an effective 2PA process not easily distinguished from direct 2PA [Espinosa2021b, Grillanda2015]. Such processes may be best characterized using long pulses with high repetition rates and/or CW sources, where the average power makes these nonlinear processes dominant [Grillanda2015]. In addition, if energetically allowed, direct 2PA can also lead to free-carrier generation which results in a higher-order nonlinearity [VanStryland1985, Christodoulides2010].

Although many of the NLO PICs aim in the end to use integrated lasers which have a limited output power, it would be good if the authors report damage thresholds of the waveguides. Special attention should also be paid to quantifying the actual incoupled powers inside the waveguides rather than the incident powers.

Most of the NLO measurements performed in waveguide structures yield an effective NLO coefficient, which represents an irradiance-weighted average over various waveguide constituents [Grant1996]. We recommend performing an “inverse” calculation to estimate nonlinear material parameters from the measured values. By comparing this result to the known bulk-material nonlinear coefficients, one can validate the model and determine a possible need for improvement.
### 3.6.3 Data table for on-chip waveguiding materials

<table><caption>**Table 7A.** Second-order NLO properties of on-chip waveguiding materials from representative works since 2000. Legend for superscripts: see below the table.</caption><thead><tr><th colspan="6">Second-Order Nonlinearities</th></tr><tr><th colspan="2">Core</th><th rowspan="2">Method</th><th colspan="3">Material Properties</th><th colspan="2">Measurement Details</th><th colspan="2">Nonlinear Properties</th></tr><tr><th>Cladding</th><th>Substrate</th><th>Length<sup>1</sup><br>Cross-section<sup>2</sup><br>Width<br>Height<sup>3</sup><br>SEM image<sup>4</sup></th><th>Growth/Deposition<br>Lithography<br>Other fabrication</th><th>Refractive Index<br>Propagation Loss<br>Wavelength</th><th>Pump<br>Wavelength<br>Peak Power<br>Pulse Width<br>Polarization<br>Rep. Rate</th><th>Probe/Signal<br>Wavelength<br>Peak Power<br>Pulse Width<br>Polarization</th><th>χ<sup>(2)</sup> [m/V]<br>d [m/V]<br>η<br>Normalized η<br>Bandwidth</th><th>Reference<br>Additional parameters and<br>comments</th></tr></thead><tbody><tr><td>Al<sub>0.19</sub>Ga<sub>0.81</sub>As</td><td>Air (suspended)<br>GaAs [001]</td><td>SHG</td><td>1.46 [mm]<br>Figs. 1 and 2<br>0.9 [μm]<br>0.123 [μm]<br>Fig. 6(g)</td><td>MBE<br>e-beam,<br>photolithography</td><td>-<br>4.5, 64 (SHG) [cm<sup>-1</sup>]<br>1593 [nm]</td><td>1596 [nm]<br>8.0E-4 [W]<br>CW<br>TE</td><td>-<br>-<br>-<br>-</td><td>-<br>-<br>1.2 [%/W]<br>-<br>-</td><td>[Morais2017]<br>Periodically bent (snake-like)<br>waveguide.<br>Conversion efficiency<br>dependence on pump<br>wavelength shown in Fig. 4(b)<br>of the reference paper.</td></tr><tr><td>Al<sub>0.19</sub>Ga<sub>0.81</sub>As</td><td>Air (suspended)<br>GaAs [001]</td><td>SHG</td><td>1 [mm]<br>Figs. 1, and 2<br>0.9 [μm]<br>0.123 [μm]<br>-</td><td>MBE<br>e-beam,<br>photolithography</td><td>-<br>3.7, 38 (SHG) [cm<sup>-1</sup>]<br>1593 [nm]</td><td>1593 [nm]<br>8.0E-4 [W]<br>CW<br>TE</td><td>-<br>-<br>-<br>-</td><td>-<br>-<br>2.7 [%/W]<br>-<br>-</td><td>[Morais2017]<br>Straight waveguide.<br>Conversion efficiency<br>dependence on pump<br>wavelength shown in Fig. 4(b)<br>of the reference paper.</td></tr><tr><td>Al<sub>0.2</sub>Ga<sub>0.8</sub>As</td><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As<br>GaAs [001]</td><td>SHG<br>Modal phase<br>matching</td><td>1.26 [mm]<br>Fig. 1<br>0.65 [μm]<br>0.5 [μm]<br>Fig. 6(d)</td><td>-<br>e-beam</td><td>-<br>18.3 [dB/cm]<br>1582 [nm]</td><td>1582.6 [nm]<br>1.6E-4 [W]<br>CW<br>TE and TM</td><td>-<br>-<br>-<br>-</td><td>-<br>-<br>1.4E+5 [%/(W.m<sup>2</sup>)]<br>-</td><td>[Duchesne2011]</td></tr></tbody></table>
<table><tbody><tr><td>Al<sub>0.4</sub>Ga<sub>0.6</sub>As</td><td>SHG</td><td>2.12 [mm]<br>Fig. 1</td><td>MOCVD</td><td>-</td><td>1600 [nm]</td><td>-</td><td>-</td><td>[Bijlani2008]</td></tr><tr><td>Al<sub>0.6</sub>Ga<sub>0.4</sub>As and<br>Al<sub>0.2</sub>Ga<sub>0.8</sub>As</td><td>Bragg<br>reflection<br>waveguide</td><td>3 [µm]<br>4 [µm]</td><td>photolithography</td><td>5.9 [cm<sup>-1</sup>]</td><td>2.0E-12 [s](FWHM)</td><td>-</td><td>8.6 [%/W]<sup>a</sup><br>2.1E+6 [%/(W.m<sup>2</sup>)]</td><td>The upper and lower reflectors are made of 8 and 10 periods, respectively. Each period: 278 nm of Al<sub>0.6</sub>Ga<sub>0.4</sub>As and 118 nm of Al<sub>0.2</sub>Ga<sub>0.8</sub>As.</td></tr><tr><td>GaAs</td><td></td><td>-</td><td>-</td><td>1555 [nm]</td><td>TE<br>7.6E+7 [Hz]</td><td>-</td><td>5.3E+11 [Hz]<br>(FWHM)</td><td></td></tr><tr><td>Al<sub>0.5</sub>Ga<sub>0.5</sub>As/Al<sub>x</sub>O<sub>y</sub><br>multilayer</td><td>SHG</td><td>0.6 [mm]<br>Fig. 1</td><td>MBE</td><td>-</td><td>1570 [nm]</td><td>-</td><td>-</td><td>[Scaccabarozzi2006]</td></tr><tr><td>Al<sub>x</sub>O<sub>y</sub></td><td>Birefringent<br>phase<br>matching</td><td>0.8-1 [µm]</td><td>e-beam</td><td>23 [dB/cm]</td><td>2.3E-5 [W]<br>CW<br>TE</td><td>-</td><td>5 [%/W]<sup>a</sup></td><td>Conversion efficiency dependence on pump wavelength shown in Fig. 2(b) of the reference paper.</td></tr><tr><td>-</td><td></td><td>-<br>Fig. 6(e)</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td><td>The reported pump power is taken at the waveguide's output.</td></tr><tr><td>-</td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>The Al<sub>x</sub>O<sub>y</sub> layers are obtained by thermal oxidation of the Al<sub>0.93</sub>Ga<sub>0.07</sub>As layers.</td></tr><tr><td>Al<sub>0.61</sub>Ga<sub>0.39</sub>As</td><td>DFG</td><td>1.5 [mm]</td><td>MOCVD</td><td>-</td><td>775 [nm]</td><td>1545.9 [nm]</td><td>-</td><td>[Han2010]</td></tr><tr><td>Al<sub>0.70</sub>Ga<sub>0.30</sub>As and<br>Al<sub>0.25</sub>Ga<sub>0.75</sub>As</td><td>Bragg<br>reflection<br>waveguide</td><td>4.4 [µm]<br>3.6 [µm]</td><td>photolithography</td><td>2 (TE), 2.2 (TM) [cm<sup>-1</sup>]</td><td>2.0E-12 [s]<br>TM<br>7.6E+7 [Hz]</td><td>2.9E-3 [W]<br>CW<br>TE</td><td>1.2E-4 [%/W]<sup>b</sup><br>5.4E+1 [%/(W.m<sup>2</sup>)]<br>>5E+12 [Hz]</td><td>The symmetric top and bottom Bragg reflectors are made of 6 periods of Al<sub>0.70</sub>Ga<sub>0.30</sub>As/ Al<sub>0.25</sub>Ga<sub>0.75</sub>As.</td></tr><tr><td>GaAs [100]</td><td></td><td>-</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Al<sub>0.61</sub>Ga<sub>0.39</sub>As</td><td>DFG</td><td>1.5 [mm]</td><td>MOCVD</td><td>-</td><td>775 [nm]</td><td>1545.9 [nm]</td><td>-</td><td>[Han2010]</td></tr><tr><td>Al<sub>0.70</sub>Ga<sub>0.30</sub>As and<br>Al<sub>0.25</sub>Ga<sub>0.75</sub>As</td><td>Bragg<br>reflection<br>waveguide</td><td>4.4 [µm]<br>3.6 [µm]</td><td>photolithography</td><td>2 [cm<sup>-1</sup>]</td><td>2.0E-12 [s]<br>TE<br>7.6E+7 [Hz]</td><td>2.9E-3 [W]<br>CW<br>TE</td><td>5.2E-4 [%/W]<sup>b</sup><br>2.3E+2 [%/(W.m<sup>2</sup>)]<br>>5E+12 [Hz]</td><td>The symmetric top and bottom Bragg reflectors are made of 6 periods of Al<sub>0.70</sub>Ga<sub>0.30</sub>As/ Al<sub>0.25</sub>Ga<sub>0.75</sub>As.</td></tr><tr><td>GaAs [100]</td><td></td><td>-</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Al<sub>0.61</sub>Ga<sub>0.39</sub>As</td><td>DFG</td><td>1.5 [mm]</td><td>MOCVD</td><td>-</td><td>775 [nm]</td><td>1545.9 [nm]</td><td>-</td><td>[Han2010]</td></tr><tr><td>Al<sub>0.70</sub>Ga<sub>0.30</sub>As and<br>Al<sub>0.25</sub>Ga<sub>0.75</sub>As</td><td>Bragg<br>reflection<br>waveguide</td><td>4.4 [µm]<br>3.6 [µm]</td><td>photolithography</td><td>2 (TE), 2.2 (TM) [cm<sup>-1</sup>]</td><td>6.3E-2 [W]<br>CW<br>TM<br>-</td><td>2.9E-3 [W]<br>CW<br>TE</td><td>1.7E-4 [%/W]<sup>b</sup><br>7.6E+1 [%/(W.m<sup>2</sup>)]<br>>5E+12 [Hz]</td><td>The symmetric top and bottom Bragg reflectors are made of 6 periods of Al<sub>0.70</sub>Ga<sub>0.30</sub>As/ Al<sub>0.25</sub>Ga<sub>0.75</sub>As.</td></tr><tr><td>GaAs [100]</td><td></td><td>-</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>Al<sub>0.61</sub>Ga<sub>0.39</sub>As</td><td>DFG</td><td>1.5 [mm]</td><td>MOCVD</td><td>-</td><td>775 [nm]</td><td>1545.9 [nm]</td><td>-</td><td>[Han2010]</td></tr><tr><td>Al<sub>0.70</sub>Ga<sub>0.30</sub>As and<br>Al<sub>0.25</sub>Ga<sub>0.75</sub>As</td><td>Bragg<br>reflection</td><td>4.4 [µm]</td><td>photolithography</td><td>2 [cm<sup>-1</sup>]</td><td>6.3E-2 [W]</td><td>2.9E-3 [W]</td><td>1.3E-3 [%/W]<sup>b</sup></td><td>The symmetric top and bottom</td></tr><tr><td>GaAs [100]</td><td>waveguide</td><td>3.6 [µm]</td><td>-</td><td>1550 [nm]</td><td>CW</td><td>CW</td><td>5.8E+2 [%/(W.m<sup>2</sup>)]</td><td>Bragg reflectors are made of 6<br>periods of Al<sub>0.70</sub>Ga<sub>0.30</sub>As/<br>Al<sub>0.25</sub>Ga<sub>0.75</sub>As.</td></tr><tr><td>Al<sub>0.61</sub>Ga<sub>0.39</sub>As</td><td>SFG</td><td>2.2 [mm]</td><td>-</td><td>-</td><td>1555 [nm]</td><td>1552-1556 [nm]</td><td>-</td><td>[Han2009]</td></tr><tr><td>Al<sub>0.70</sub>Ga<sub>0.30</sub>As and</td><td>Bragg</td><td>Fig. 1(b)</td><td>-</td><td>2 (TE), 2.2 (TM) [cm<sup>-1</sup>]</td><td>4.2E-3 [W]</td><td>3.5E-4 [W]</td><td>4.0E-11</td><td>The effective mode areas:</td></tr><tr><td>Al<sub>0.25</sub>Ga<sub>0.75</sub>As</td><td>reflection</td><td>4.4 [µm]</td><td>-</td><td>-</td><td>CW</td><td>CW</td><td>2.9E-2 [%]</td><td>Pump: 6.7E-12 m<sup>2</sup></td></tr><tr><td>GaAs [100]</td><td>waveguide</td><td>3.6 [µm]</td><td>-</td><td>1550 [nm]</td><td>TM</td><td>TE</td><td>3.0E+6 [%/(W.m<sup>2</sup>)]<sup>c</sup></td><td>Probe: 6.6E-12 m<sup>2</sup></td></tr><tr><td></td><td></td><td>Fig. 6(f)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>>7.5E+12 [Hz]</td><td>The symmetric top and bottom</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>(FWHM)</td><td>Bragg reflectors are made of 6<br>periods of Al<sub>0.70</sub>Ga<sub>0.30</sub>As/<br>Al<sub>0.25</sub>Ga<sub>0.75</sub>As.</td></tr><tr><td>Al<sub>0.67</sub>Ga<sub>0.33</sub>As</td><td>SHG</td><td>8 [mm]</td><td>MBE</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td>[Yu2007]</td></tr><tr><td>Al<sub>0.70</sub>Ga<sub>0.30</sub>As</td><td>Orientation</td><td>Fig. 1</td><td>e-beam</td><td>5.5, 25-45 (SHG) [dB/cm]</td><td>3.9E-3 [W]</td><td>-</td><td>-</td><td>Conversion efficiency</td></tr><tr><td>Ge-on-GaAs</td><td>patterned</td><td>7 [µm]<br>1.1 [µm]</td><td>-</td><td>1550 [nm]</td><td>CW</td><td>-</td><td>4.3E+1 [%/W]</td><td>dependence on sample length<br>shown in Fig. 4(b) of the<br>reference paper.</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>Quasi-phase matching periods<br>from 4.7E-6 to 4.9E-6 m.</td></tr><tr><td>Al<sub>0.67</sub>Ga<sub>0.33</sub>As</td><td>SHG</td><td>5 [mm]</td><td>MBE</td><td>-</td><td>1559.1 [nm]</td><td>-</td><td>-</td><td>[Yu2005]</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>Periodic<br>domain</td><td>Fig. 1</td><td>photolithography</td><td>6-7 [dB/cm]</td><td>1.9E-3 [W]</td><td>-</td><td>-</td><td></td></tr><tr><td>GaAs [001]</td><td>disordering</td><td>6 [µm]</td><td>-</td><td>1550 [nm]</td><td>CW</td><td>-</td><td>2.3E+1 [%/W]</td><td></td></tr><tr><td></td><td></td><td>1.1 [µm]</td><td>-</td><td>-</td><td>TE</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td>Fig. 6(c)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>AlGaAs/AlO<sub>x</sub> multilayer</td><td>SHG</td><td>1.5 [mm]<br>Fig. 1(a)</td><td>MBE</td><td>Fig. 1</td><td>4420 [nm]</td><td>-</td><td>-</td><td>[Ozanam2014]</td></tr><tr><td></td><td>GaAs</td><td>Birefringent<br>phase</td><td>15.3 [µm]</td><td>e-beam</td><td>1 [cm<sup>-1</sup>]</td><td>1.6E-2 [W]</td><td>-</td><td>-</td><td>The multilayer is formed by Al<sub>0.19</sub>Ga<sub>0.81</sub>As, GaAs and AlO<sub>x</sub>.</td></tr><tr><td></td><td>GaAs</td><td>matching</td><td>-</td><td>-</td><td>4500 [nm]</td><td>3.0E-7 [s]<br>TE</td><td>-</td><td>4.4E+3 [%/(W.m<sup>2</sup>)]<sup>d</sup></td><td>The AlO<sub>x</sub> layers are obtained by oxidation of the Al<sub>0.98</sub>Ga<sub>0.02</sub>As layers.</td></tr><tr><td>AlGaAs/AlO<sub>x</sub> multilayer</td><td>DFG</td><td>0.5 [mm]</td><td>MBE</td><td>-</td><td>773.2 [nm]</td><td>1559 [nm]</td><td>-</td><td>-</td><td>[Savanier2011a]</td></tr><tr><td></td><td>GaAs</td><td>Birefringent<br>phase</td><td>4 [µm]</td><td>-</td><td>1.6 [cm<sup>-1</sup>]</td><td>CW</td><td>CW</td><td>-</td><td>The multilayer is formed by Al<sub>0.2</sub>Ga<sub>0.8</sub>As/AlO<sub>x</sub> and Al<sub>0.25</sub>Ga<sub>0.75</sub>As/AlO<sub>x</sub>.</td></tr><tr><td></td><td>GaAs</td><td>matching</td><td>-</td><td>-</td><td>1580 [nm]</td><td>TE</td><td>TE</td><td>9.7E+4 [%/(W.m<sup>2</sup>)]<sup>e</sup></td><td>The AlO<sub>x</sub> layers are obtained by selective oxidation of the Al<sub>0.98</sub>Ga<sub>0.02</sub>As layers.</td></tr><tr><td>AlGaAs/AlO<sub>x</sub> multilayer</td><td>SFG</td><td>0.5 [mm]</td><td>MBE</td><td>-</td><td>1543 [nm]</td><td>1550.4 [nm]</td><td>-</td><td>-</td><td>[Savanier2011a]</td></tr><tr><td></td><td>GaAs</td><td>Birefringent<br>phase</td><td>4 [µm]</td><td>-</td><td>1.6 [cm<sup>-1</sup>]</td><td>CW</td><td>CW</td><td>2.7 [%/W]</td><td>The multilayer is formed by Al<sub>0.2</sub>Ga<sub>0.8</sub>As/AlO<sub>x</sub> and Al<sub>0.25</sub>Ga<sub>0.75</sub>As/AlO<sub>x</sub>.</td></tr><tr><td></td><td>GaAs</td><td>matching</td><td>-</td><td>-</td><td>1580 [nm]</td><td>TE</td><td>TE</td><td>1.1E+7 [%/(W.m<sup>2</sup>)]<br>7.2 [nm] (at -3 dB)</td><td>The AlO<sub>x</sub> layers are obtained by selective oxidation of the Al<sub>0.98</sub>Ga<sub>0.02</sub>As layers.</td></tr><tr><td>AlGaAs/AlO<sub>x</sub> multilayer</td><td>SHG</td><td>0.5 [mm]<br>Fig. 4</td><td>MBE</td><td>Fig. 1</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td><td>[Savanier2011b]</td></tr><tr><td></td><td>GaAs</td><td>Birefringent<br>phase</td><td>4 [µm]</td><td>-</td><td>1.13 [cm<sup>-1</sup>]</td><td>CW</td><td>-</td><td>2.8 [%/W]</td><td>The multilayer is formed by Al<sub>0.2</sub>Ga<sub>0.8</sub>As/AlO<sub>x</sub> and Al<sub>0.25</sub>Ga<sub>0.75</sub>As/AlO<sub>x</sub>.</td></tr><tr><td></td><td>GaAs</td><td>matching</td><td>-</td><td>-</td><td>1550 [nm]</td><td>TE</td><td>-</td><td>1.1E+7 [%/(W.m<sup>2</sup>)]<br>2.9 [nm] (at -3 dB)</td><td>The AlO<sub>x</sub> layers are obtained by post-etching lateral oxidation of the Al<sub>0.98</sub>Ga<sub>0.02</sub>As layers.</td></tr></tbody></table>
<table><tbody><tr><td>AlN</td><td>SHG</td><td>0.188 [mm]</td><td>MOCVD</td><td>-</td><td>1590 [nm]</td><td>-</td><td>-</td><td>[Bruch2018]</td></tr><tr><td>Sapphire and SiO<sub>2</sub></td><td>Temperature tuning</td><td>1.2-1.3 [µm]</td><td>e-beam</td><td>-</td><td>2.6E-4 [W]</td><td>-</td><td>-</td><td>Conversion efficiency dependence on temperature shown in Fig. 3(b) of the reference paper.</td></tr><tr><td>Sapphire c-plane</td><td></td><td>1.1 [µm]</td><td></td><td>-</td><td>CW</td><td>-</td><td>1.7E+4 [%/W]<sup>a</sup></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>TM</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td>-</td><td>-</td><td></td></tr><tr><td>AlN</td><td>SHG</td><td>0.188 [mm]</td><td>MOCVD</td><td>-</td><td>1556 [nm]</td><td>-</td><td>6.2E-12</td><td>[Bruch2018]</td></tr><tr><td>Sapphire and SiO<sub>2</sub></td><td>Temperature tuning</td><td>1.2-1.3 [µm]</td><td>e-beam</td><td>-</td><td>2.6E-4 [W]</td><td>-</td><td>-</td><td>Conversion efficiency dependence on temperature shown in Fig. 3(b) of the reference paper.</td></tr><tr><td>Sapphire c-plane</td><td></td><td>1.1 [µm]</td><td></td><td>-</td><td>CW</td><td>-</td><td>1.5E+4 [%/W]<sup>a</sup></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>TM</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td>-</td><td>-</td><td></td></tr><tr><td>GaAs</td><td>SHG</td><td>2.9 [mm]<br>Fig. 4(a)</td><td>MBE</td><td>-</td><td>1968 [nm]</td><td>-</td><td>-</td><td>[Stanton2020]</td></tr><tr><td>Air and SiO<sub>2</sub></td><td>Birefringent phase matching</td><td>-</td><td>e-beam</td><td>1.5 [dB/cm]</td><td>-</td><td>-</td><td>1.8E-10</td><td>Conversion efficiency dependence on pump wavelength and temperature shown in Fig. 7 of the reference paper.</td></tr><tr><td>Silicon</td><td></td><td>0.158 [µm]<br>Fig. 6(j)</td><td>wafer bonding</td><td>1968 [nm]</td><td>CW</td><td>-</td><td>3.95E+3 [%/W]<sup>a</sup></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>TE</td><td>-</td><td>-</td><td>1.48E+11 [Hz]</td><td>The linear loss at the SH wavelength is one order of magnitude larger than that at the FF wavelength.</td></tr><tr><td>GaAs</td><td>SHG</td><td>1.4 [mm]<br>Fig. 1(a)</td><td>MOCVD</td><td>-</td><td>2009.8 [nm]</td><td>-</td><td>-</td><td>[Chang2018]</td></tr><tr><td>SiO<sub>2</sub></td><td>Modal phase matching</td><td>1.53 [µm]<br>0.15 [µm]</td><td>DUV</td><td>2 [dB/cm]</td><td>2.5E-3 [W]</td><td>-</td><td>2.5E2 [%/W]</td><td>Conversion efficiency dependence on pump wavelength shown in Fig. 4(c) of the reference paper.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>wafer bonding</td><td>2000 [nm]</td><td>CW</td><td>-</td><td>1.3E+8 [%/(W.m<sup>2</sup>)]<sup>d</sup></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>TE</td><td>-</td><td>0.93 [nm] (at -3 dB)</td><td></td></tr><tr><td>GaAs</td><td>SHG</td><td>-</td><td>MOCVD</td><td>-</td><td>2000 [nm]</td><td>-</td><td>-</td><td>[Chang2019]</td></tr><tr><td>SiO<sub>2</sub></td><td>Ring resonator phase matching</td><td>1.3 [µm]<br>0.15 [µm]</td><td>DUV</td><td>2 [dB/cm]</td><td>6.1E-5 [W]</td><td>-</td><td>4 [%], 6.5E4 [%/W]</td><td>The efficiency reported is for a ring resonator device.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>wafer bonding</td><td>2000 [nm]</td><td>CW</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>GaAs/Al<sub>0.85</sub>Ga<sub>0.15</sub>As superlattice</td><td>DFG</td><td>1 [mm]<br>Fig. 1</td><td>MBE</td><td>-</td><td>792.9 [nm]<br>3.1E-2 [W]</td><td>1535-1555 [nm]<br>5.2E-2 [W]</td><td>-</td><td>[Wagner2011]</td></tr><tr><td>Al<sub>0.56</sub>Ga<sub>0.44</sub>As,<br>Al<sub>0.60</sub>Ga<sub>0.40</sub>As and<br>Al<sub>0.85</sub>Ga<sub>0.15</sub>As</td><td>Periodic<br>domain<br>disordering</td><td>3 [µm]<br>0.6 [µm]</td><td>-</td><td>1.8 (TE), 3.7 (TM) [cm<sup>-1</sup>]</td><td>CW<br>TE</td><td>CW<br>TE and TM</td><td>-</td><td>1.2E+2 [%/(W.m<sup>2</sup>)]<sup>e</sup></td><td>14:14 GaAs:Al<sub>0.85</sub>Ga<sub>0.15</sub>As monolayers superlattice.</td></tr><tr><td>GaAs</td><td></td><td>-</td><td>-</td><td>1550 [nm]</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GaAs/Al<sub>0.85</sub>Ga<sub>0.15</sub>As superlattice</td><td>DFG</td><td>1 [mm]<br>Fig. 1</td><td>MBE</td><td>-</td><td>791.7 [nm]<br>2.4E-2 [W]</td><td>1535-1555 [nm]<br>4.9E-2 [W]</td><td>-</td><td></td><td>[Wagner2011]</td></tr><tr><td>Al<sub>0.56</sub>Ga<sub>0.44</sub>As,<br>Al<sub>0.60</sub>Ga<sub>0.40</sub>As and<br>Al<sub>0.85</sub>Ga<sub>0.15</sub>As</td><td>Periodic<br>domain<br>disordering</td><td>3 [µm]<br>0.6 [µm]</td><td>-</td><td>1.8 (TE), 3.7 (TM) [cm<sup>-1</sup>]</td><td>CW<br>TM</td><td>CW<br>TE</td><td>-</td><td>7.2E+2 [%/(W.m<sup>2</sup>)]<sup>e</sup></td><td>14:14 GaAs:Al<sub>0.85</sub>Ga<sub>0.15</sub>As monolayers superlattice.</td></tr><tr><td>GaAs</td><td></td><td>-</td><td>-</td><td>1550 [nm]</td><td></td><td></td><td></td><td></td><td>The conversion bandwidth is the maximum separation between the signal and idler.</td></tr><tr><td>GaN</td><td>SHG</td><td>4 [mm]<br>Fig. 3</td><td>MBE, MOVPE</td><td>-</td><td>1263 [nm]<br>9.0E+1 [W]</td><td>-</td><td>-</td><td>-</td><td>[Gromovyi2017]</td></tr><tr><td>Al<sub>0.65</sub>Ga<sub>0.35</sub>N</td><td>Modal phase matching</td><td>-</td><td>-</td><td>1 [dB/cm]</td><td>4.0E-9 [s]<br>TM</td><td>-</td><td>-</td><td>2 [%]<br>1.5E+3 [%/(W.m<sup>2</sup>)]</td><td></td></tr><tr><td>Sapphire</td><td></td><td>1.2 [µm]</td><td>-</td><td>1260 [nm]</td><td>1.0E+3 [Hz]</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>GaN</td><td>SHG</td><td>-</td><td>MOCVD, PECVD</td><td>2.3</td><td>1550 [nm]<br>1.2E-1 [W]</td><td>-</td><td>-</td><td>1.6E-11</td><td>[Xiong2011]</td></tr><tr><td>SiO<sub>2</sub></td><td></td><td>Figs. 2(b), 4(b)-(c)<br>0.86 [µm]</td><td>e-beam</td><td>-</td><td>CW</td><td>-</td><td>-</td><td>3.2E-3 [%]</td><td></td></tr><tr><td>Silicon</td><td></td><td>0.4 [µm]<br>Fig. 6(a)</td><td>wafer bonding</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Lithium niobate</td><td>SHG</td><td>4 [mm]<br>Fig. 1(a)-(b)</td><td>-</td><td>-</td><td>1550 [nm]<br>2E-3-2.2E-1 [W]</td><td>-</td><td>-</td><td>-</td><td>[Wang2018b]</td></tr><tr><td>Air and SiO<sub>2</sub></td><td>Periodically poled</td><td>1.4 [µm]<br>0.6 [µm]</td><td>photolithography,<br>e-beam</td><td>2.5 [dB/cm]</td><td>CW<br>TE</td><td>-</td><td>-</td><td>2.6E+7 [%/(W.m<sup>2</sup>)]<sup>d</sup></td><td>Conversion efficiency dependence on pump wavelength shown in Fig. 3 of the reference paper.</td></tr><tr><td>LN-on-insulator</td><td></td><td>Fig. 6(b)</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td><td>7 [nm] (at -3 dB)</td><td></td></tr></tbody></table>
1: The length of ring resonators was calculated from the ring radius.

2: Figure of the reference paper showing the cross-section geometry.

3: For heterostructure waveguides, the reported height is the guiding layer thickness.

4: Selected SEM images presented in this work for each geometry and material platform.

a: Conversion efficiency formula: $\eta = P_{SH}/P_{FF}^2$ [SH – Second Harmonic, FF – Fundamental Frequency]

b: Conversion efficiency formula: $\eta = P_{DF}/(P_{P}P_{S})$ [DF – Difference frequency, P – Pump, S – Signal]

c: Conversion efficiency formula: $\eta = P_{SF}\lambda_{SF}/(P_{S}\lambda_{S})$ [SF – Sum frequency, P – Pump, S – Signal]

d: Normalized conversion efficiency formula: $\eta_N = P_{SH}/(P_{FF}L)^2$ [Second Harmonic, FF – Fundamental Frequency, L – Length]

e: Normalized conversion efficiency formula: $\eta_N = P_{DF}/(P_{P}P_{S}L^2)$ [DF – Difference frequency, P – Pump, S – Signal]
<table><caption>**Table 7B.** Third-order NLO properties of on-chip waveguiding materials from representative works since 2000. Legend for superscripts: see below the table.</caption><thead><tr><th colspan="10">Third-Order Nonlinearities</th></tr><tr><th colspan="2">Core<br>Cladding<br>Substrate</th><th rowspan="2">Method</th><th colspan="3">Material Properties</th><th colspan="2">Measurement Details</th><th colspan="2">Nonlinear Properties</th></tr><tr><th>Length<sup>1</sup><br>Cross section<sup>2</sup><br>Width<br>Height<sup>3</sup><br>SEM Image<sup>4</sup></th><th>Crystallinity<br>Growth/Deposition<br>Lithography<br>Other fab</th><th>Refractive Index<br>Propagation Loss<br>Wavelength<br>Bandgap<br>GVD<br>Dispersion curve<sup>5</sup></th><th>Pump<br>Wavelength<br>Peak Power<br>Pulse Width<br>Polarization<br>Rep. Rate<br>Effective Area</th><th>Probe/Signal<br>Wavelength<br>Peak Power<br>Pulse Width<br>Polarization<br>Rep. Rate<br>Effective Area</th><th>n<sub>2</sub><br>α<sub>2</sub><br>γ<sub>eff</sub><br>η<br>Bandwidth</th><th>Reference</th><th>Additional parameters and comments</th></tr></thead><tbody><tr><td colspan="10" style="text-align: center; font-weight: bold;">III-V semiconductors</td></tr><tr><td>AlN</td><td></td><td></td><td>0.376 [mm]<br>Fig. 1(c)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>2.3E-19 [m<sup>2</sup>/W]</td><td rowspan="4">[Jung2013]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td></td><td>3.5 [μm]<br>0.65 [μm]<br>Fig. 7(v)</td><td>Sputtering</td><td>1555 [nm]</td><td>5.0E-1 [W]<br>CW<br>TE</td><td>-</td><td>-</td></tr><tr><td>Silicon</td><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td></td><td>-</td><td>Fig. 1(a)</td><td>1.3E-12 [m<sup>2</sup>]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Al<sub>0.12</sub>Ga<sub>0.88</sub>As</td><td></td><td></td><td>0.81 [mm]<br>-</td><td>-</td><td>-</td><td>1566 [nm]<br>3.8E-4 [W]<br>CW</td><td>1564 [nm]<br>-<br>CW</td><td>-</td><td rowspan="4">[Zheng2019a]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td></td><td>0.44 [μm]<br>0.3 [μm]</td><td>MOVPE</td><td>1.2 [dB/cm]<br>1550 [nm]</td><td>TE</td><td>-</td><td>-</td></tr><tr><td>Sapphire</td><td></td><td></td><td>-</td><td>E-beam</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td></td><td>-</td><td>Wafer bonding,<br>substrate removal</td><td>-</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>
<table><tbody><tr><td>Al<sub>0.18</sub>Ga<sub>0.82</sub>As</td><td></td><td></td><td></td><td>1470-1540 [nm]</td><td>1540-1560 [nm]</td><td>-</td><td>[Espinosa2021a]</td></tr><tr><td>Al<sub>0.65</sub>Ga<sub>0.35</sub>As and Al<sub>0.35</sub>Ga<sub>0.65</sub>As</td><td>FWM</td><td>1 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>2.8E-2 [W]</td><td>-</td><td>The length of the 900-nm-wide part is 1 mm, but the total length is 5.26 mm, which includes the 2-µm-wide couplers.</td></tr><tr><td>GaAs [100]</td><td></td><td>0.9 [µm]<br>0.8 [µm]</td><td>-</td><td>3.0E-12 [s](FWHM)<br>TE</td><td>CW<br>TE</td><td>5.1E+1 [m<sup>-1</sup>W<sup>-1</sup>]<br>15.8 [%]<sup>c</sup></td><td></td></tr><tr><td></td><td></td><td></td><td>E-beam</td><td>-</td><td>7.7E+7 [Hz]<br>1.4E-12 [m<sup>2</sup>]</td><td>-</td><td>3.2E+12 [Hz]<br>(at -20dB)</td><td>Conversion efficiency dependence on pump-probe detuning shown in Fig. 9 of the reference paper.</td></tr><tr><td>Al<sub>0.18</sub>Ga<sub>0.82</sub>As</td><td></td><td>2 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>1470-1540 [nm]</td><td>1540-1560 [nm]</td><td>-</td><td>[Espinosa2021a]</td></tr><tr><td>Al<sub>0.65</sub>Ga<sub>0.35</sub>As</td><td>FWM</td><td>0.6 [µm]<br>1.4 [µm]</td><td>-</td><td>40 [dB/cm]<br>1520 [nm]</td><td>2.8E-2 [W]</td><td>-</td><td>1.8E+2 [m<sup>-1</sup>W<sup>-1</sup>]</td><td>The length of the 600-nm-wide part is 2 mm, but the total length is 5.33 mm, which includes the 2-µm-wide couplers.</td></tr><tr><td>GaAs [100]</td><td></td><td>-</td><td>E-beam</td><td>-</td><td>3.0E-12 [s](FWHM)<br>TE</td><td>CW<br>TE</td><td>31.6 [%]<sup>c</sup></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>-7.5E-25 [s<sup>2</sup>/m]<br>Fig. 5</td><td>7.7E+7 [Hz]<br>3.2E-13 [m<sup>2</sup>]</td><td>-</td><td>3.8E+12 [Hz]<br>(at -20dB)</td><td>Conversion efficiency dependence on pump-probe detuning shown in Fig. 9 of the reference paper.</td></tr><tr><td>Al<sub>0.18</sub>Ga<sub>0.82</sub>As</td><td></td><td>1 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>1470-1540 [nm]</td><td>1540-1560 [nm]</td><td>-</td><td>[Espinosa2021a]</td></tr><tr><td>Al<sub>0.65</sub>Ga<sub>0.35</sub>As</td><td>FWM</td><td>0.8 [µm]<br>0.7 [µm]</td><td>-</td><td>7 [dB/cm]<br>1520 [nm]</td><td>2.8E-2 [W]</td><td>-</td><td>9.0E+1 [m<sup>-1</sup>W<sup>-1</sup>]</td><td>The length of the 800-nm-wide part is 1 mm, but the total length is 5.87 mm, which includes the 2-µm-wide couplers.</td></tr><tr><td>GaAs [100]</td><td></td><td>Fig. 7(f)</td><td>E-beam</td><td>-</td><td>3.0E-12 [s](FWHM)<br>TE</td><td>CW<br>TE</td><td>12.6 [%]<sup>c</sup></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>1.5E-24 [s<sup>2</sup>/m]<br>Fig. 5</td><td>7.7E+7 [Hz]<br>7.3E-13 [m<sup>2</sup>]</td><td>-</td><td>-</td><td>Conversion efficiency dependence on pump-probe detuning is shown in Fig. 9 of the reference paper.</td></tr><tr><td>Al<sub>0.18</sub>Ga<sub>0.82</sub>As</td><td></td><td>25 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>1550.5 [nm]</td><td>1551.9 [nm]</td><td>1.1E-17 [m<sup>2</sup>/W]</td><td>[Apiratikul2014]</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>FWM</td><td>1.2 [µm]<br>1.7 [µm]</td><td>MBE</td><td>1.9 [dB/cm]<br>1550 [nm]</td><td>8.0E-1 [W]</td><td>-</td><td>5.0E-13 [m/W]</td><td></td></tr><tr><td>GaAs</td><td></td><td>-</td><td>Photolithography</td><td>1.64 [eV]<br>9.0E-25 [s<sup>2</sup>/m]</td><td>CW<br>TE</td><td>CW<br>TE</td><td>-</td><td>Conversion efficiency dependence on pump power is shown in Fig. 4 of the reference paper.</td></tr><tr><td></td><td></td><td></td><td></td><td>-</td><td>-</td><td>-</td><td>10 [%]<sup>a</sup></td><td></td></tr></tbody></table>
<table><tbody><tr><td>Al<sub>0.18</sub>Ga<sub>0.82</sub>As</td><td rowspan="3">FWM</td><td>25 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>1550.5 [nm]</td><td>1551.9 [nm]</td><td>7.0E-18 [m<sup>2</sup>/W]</td><td rowspan="3">[Apiratikul2014]</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>1.35 [µm]</td><td>MBE</td><td>0.56 [dB/cm]<br>1550 [nm]</td><td>8.0E-1 [W]</td><td>-</td><td>3.0E-13 [m/W]</td></tr><tr><td>GaAs</td><td>1.7 [µm]</td><td>Photolithography</td><td>1.64 [eV]<br>9.0E-25 [s<sup>2</sup>/m]</td><td>CW</td><td>CW</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>Reflown resist</td><td>Fig. 6</td><td>8.2E-13 [m<sup>2</sup>]</td><td>-</td><td>22.9 [%]<sup>a</sup></td><td>Photoresist reflow was used to achieve smoother sidewalls.</td></tr><tr><td>Al<sub>0.18</sub>Ga<sub>0.82</sub>As</td><td rowspan="3">FWM</td><td>5 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>1550.5 [nm]</td><td>1551.9 [nm]</td><td>-</td><td rowspan="3">[Apiratikul2014]</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>0.69 [µm]</td><td>MBE</td><td>-</td><td>8.0E-1 [W]</td><td>-</td><td>-</td></tr><tr><td>GaAs</td><td>1.7 [µm]</td><td>Photolithography</td><td>1.64 [eV]<br>2.2E-25 [s<sup>2</sup>/m]</td><td>CW</td><td>CW</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>Fig. 6</td><td>4.4E-13 [m<sup>2</sup>]</td><td>-</td><td>0.16 [%]<sup>a</sup><br>8.0E+12 [Hz]<br>(at -3dB)</td><td>Uncoated.</td></tr><tr><td>Al<sub>0.18</sub>Ga<sub>0.82</sub>As</td><td rowspan="3">FWM</td><td>5 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>1550.5 [nm]</td><td>1551.9 [nm]</td><td>-</td><td rowspan="3">[Apiratikul2014]</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>0.69 [µm]</td><td>MBE</td><td>-</td><td>8.0E-1 [W]</td><td>-</td><td>-</td></tr><tr><td>GaAs</td><td>1.7 [µm]</td><td>Photolithography</td><td>1.64 [eV]<br>4.4E-25 [s<sup>2</sup>/m]</td><td>CW</td><td>CW</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>Fig. 6</td><td>4.7E-13 [m<sup>2</sup>]</td><td>-</td><td>0.25 [%]<sup>a</sup><br>5.5E+12 [Hz]<br>(at -3dB)</td><td>Coated with SiN<sub>x</sub>.</td></tr><tr><td>Al<sub>0.20</sub>Ga<sub>0.80</sub>As</td><td rowspan="4">Nonlinear<br>transm./refl.</td><td>10 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td rowspan="4">[Dolgaleva2011]</td></tr><tr><td>Al<sub>0.50</sub>Ga<sub>0.50</sub>As and<br>Al<sub>0.24</sub>Ga<sub>0.76</sub>As</td><td>2 [µm]<br>1.2 [µm]</td><td>MOCVD</td><td>3.2 [dB/cm]<br>1550 [nm]</td><td>1.5E+2 [W]</td><td>-</td><td>-</td></tr><tr><td>GaAs</td><td>-</td><td>E-beam,<br>photolithography</td><td>-<br>1.2E-24 [s<sup>2</sup>/m]</td><td>2.0E-12 [s](FWHM)</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>4.4E-12 [m<sup>2</sup>]</td><td>3.6E+7 [Hz]<br>4.4E-12 [m<sup>2</sup>]</td><td>-</td><td>-</td></tr><tr><td>Al<sub>0.21</sub>Ga<sub>0.79</sub>As</td><td rowspan="3">FWM</td><td>9 [mm]<br>Fig. 1</td><td>-</td><td>-</td><td>1549.5 [nm]</td><td>-</td><td>-</td><td rowspan="3">[Ros2017]</td></tr><tr><td>SiO<sub>2</sub> and HSQ</td><td>0.63 [µm]</td><td>Epitaxy, PECVD</td><td>1.5 [dB/cm]<br>1549.5 [nm]</td><td>1.1E-1 [W]</td><td>-</td><td>-</td></tr><tr><td>SOI</td><td>0.29 [µm]</td><td>E-beam</td><td>1.69 [eV]<br>250 [ps/(nm.km)]</td><td>CW</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>Wafer bonding</td><td>Fig. 3</td><td>-</td><td>-</td><td>-12 [dB]<sup>d</sup><br>55 [nm]<br>(at -3 dB)</td><td>Conversion efficiency dependence on length, pump power and signal-pump spacing shown in Fig. 5 of the reference paper.</td></tr></tbody></table>
<table><tbody><tr><td>Al<sub>0.23</sub>Ga<sub>0.77</sub>As</td><td></td><td>Monocrystalline</td><td>1538-1563 [nm]</td><td>1565 [nm]</td><td>-</td><td>[Mahmood2014]</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As and SiN<sub>x</sub></td><td>FWM</td><td>10.8 [mm]<br>Fig. 1</td><td>-</td><td>1.2E-1 [W]</td><td>3.2E-2 [W]</td><td>-</td></tr><tr><td>GaAs</td><td></td><td>0.2-1 [µm]<br>2.1 [µm]</td><td>5.1 [dB/cm]<br>1550 [nm]</td><td>CW</td><td>CW</td><td>-</td></tr><tr><td></td><td></td><td>Projection<br>lithography</td><td>-</td><td>TM</td><td>TM</td><td>0.2 [%]<sup>e</sup></td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.0E+12 [Hz]</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>6.2E-13 [m<sup>2</sup>]</td><td>-</td><td>(at -3dB)</td></tr><tr><td>Al<sub>0.26</sub>Ga<sub>0.74</sub>As PhC</td><td></td><td>Monocrystalline</td><td>1550 [nm]</td><td>1605.8 [nm]</td><td>-</td><td>[Oda2008]</td></tr><tr><td></td><td></td><td>1 [mm]</td><td>-</td><td>4.4E+0 [W]</td><td>2.8E-4 [W]</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>9.1 [cm<sup>-1</sup>]</td><td>5.0E-12 [s]</td><td>CW</td><td>-</td></tr><tr><td>Air</td><td>SRS Pump</td><td>-</td><td>1606 [nm]</td><td>TE</td><td>TE</td><td>-</td></tr><tr><td></td><td>Probe</td><td>-</td><td>-</td><td>2.0E+7 [Hz]</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Al<sub>0.32</sub>Ga<sub>0.68</sub>As</td><td></td><td>Monocrystalline</td><td>1560 [nm]</td><td>-</td><td>-</td><td>[Chiles2019]</td></tr><tr><td></td><td></td><td>4 [mm]<br>Fig. 1(a)-(b)</td><td>-</td><td>0.45 [dB/cm]</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>0.48 [µm]</td><td>2400 [nm]</td><td>6.1E-14 [s]</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>0.54 [µm]</td><td>1.82 [eV]</td><td>TE</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>Fig. 7(h)</td><td>20 [ps/(nm.km)]<br>Figs. 4(c) and 5(c)</td><td>1.6E+8 [Hz]</td><td>-</td><td>1200 [nm]</td></tr><tr><td></td><td></td><td></td><td></td><td>2.2E-13 [m<sup>2</sup>]</td><td>-</td><td>(at -20dB)</td></tr><tr><td>Al<sub>0.32</sub>Ga<sub>0.68</sub>As</td><td></td><td>Monocrystalline</td><td>3060 [nm]</td><td>-</td><td>-</td><td>[Chiles2019]</td></tr><tr><td></td><td></td><td>2.3 [mm]<br>Fig. 1(a)-(b)</td><td>-</td><td>0.45 [dB/cm]</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>2.15 [µm]</td><td>2400 [nm]</td><td>8.5E-14 [s]</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>0.54 [µm]</td><td>1.82 [eV]</td><td>TE</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>Fig. 7(h)</td><td>20 [ps/(nm.km)]<br>Figs. 4(c) and 5(c)</td><td>1.0E+8 [Hz]</td><td>-</td><td>4200 [nm]</td></tr><tr><td></td><td></td><td></td><td></td><td>1.2E-12 [m<sup>2</sup>]</td><td>-</td><td>(at -20dB)</td></tr></tbody></table>
<table><tbody><tr><td>AlGaAs</td><td></td><td>10 [mm]</td><td>Monocrystalline</td><td>1552.45 [nm]</td><td>1551.9 [nm]</td><td>2.3E-17 [m²/W]</td><td rowspan="4">[Wathen2014]<br>The 2PA coefficient was measured at 1550 nm by the nonlinear transmittance technique with:<br>Pulse width: 1.26E-12 s<br>Rep. rate: 1E+7 Hz<br>Peak irradiance: &lt;3.5E+13 W/m²</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>FWM</td><td>Figs. 1 and 2</td><td>-</td><td>1.5 [dB/cm]<br>1550 [nm]</td><td>CW</td><td>3.3E-11 [m/W]</td></tr><tr><td>GaAs</td><td></td><td>-</td><td>1.6 [eV]</td><td>TE</td><td>TE</td><td>1.6 [%]a</td></tr><tr><td></td><td></td><td>Fig. 7(d)</td><td>1.1E-24 [s²/m]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>AlGaAs</td><td></td><td>10 [mm]</td><td>Monocrystalline</td><td>1552.45 [nm]</td><td>1551.9 [nm]</td><td>1.5E-17 [m²/W]</td><td rowspan="4">[Wathen2014]<br>3PA coefficient = 8.3E-26 m³/W² at 1550 nm, measured by nonlinear transmittance with:<br>Pulse width: 1.26E-12 s<br>Rep. rate: 1E+7 Hz<br>Peak irradiance &lt;8E+13 W/m²</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>FWM</td><td>Figs. 1 and 2</td><td>-</td><td>0.74 [dB/cm]<br>1550 [nm]</td><td>CW</td><td>-</td></tr><tr><td>GaAs</td><td></td><td>-</td><td>1.66 [eV]</td><td>TE</td><td>TE</td><td>0.6 [%]a</td></tr><tr><td></td><td></td><td>Fig. 7(d)</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>AlGaAs</td><td></td><td>25 [mm]</td><td>Monocrystalline</td><td>1552.45 [nm]</td><td>1551.9 [nm]</td><td>9.0E-18 [m²/W]</td><td rowspan="4">[Wathen2014]<br>3PA coefficient = 8.3E-26 m³/W² at 1550 nm, measured by nonlinear transmittance with:<br>Pulse width: 1.26E-12 s<br>Rep. rate: 1E+7 Hz<br>Peak irradiance &lt;8E+13 W/m²</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>FWM</td><td>Figs. 1 and 2</td><td>-</td><td>0.56 [dB/cm]<br>1550 [nm]</td><td>CW</td><td>-</td></tr><tr><td>GaAs</td><td></td><td>-</td><td>1.77 [eV]</td><td>TE</td><td>TE</td><td>22.9 [%]a<br>1.6E+12 [Hz]<br>(at -3dB)</td></tr><tr><td></td><td></td><td>Fig. 7(d)</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>AlGaAs</td><td></td><td>5 [mm]</td><td>Monocrystalline</td><td>1552.45 [nm]</td><td>1551.9 [nm]</td><td>8.5E-18 [m²/W]</td><td rowspan="4">[Wathen2014]<br>3PA coefficient = 8.3E-26 m³/W² at 1550 nm, measured by nonlinear transmittance with:<br>Pulse width: 1.26E-12 s<br>Rep. rate: 1E+7 Hz<br>Peak irradiance &lt;8E+13 W/m²</td></tr><tr><td>Al<sub>0.7</sub>Ga<sub>0.3</sub>As</td><td>FWM</td><td>Figs. 1 and 2</td><td>-</td><td>3 [dB/cm]<br>1550 [nm]</td><td>CW</td><td>-</td></tr><tr><td>GaAs</td><td></td><td>-</td><td>1.79 [eV]</td><td>TE</td><td>TE</td><td>0.4 [%]a<br>5.5E+12 [Hz]<br>(at -3dB)</td></tr><tr><td></td><td></td><td>Fig. 7(d)</td><td>4.5E-25 [s²/m]</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>
<table><tbody><tr><td>AlGaAs</td><td></td><td>3 [mm]<br>Fig. 1(c)</td><td>-</td><td>1543.6 [nm]</td><td>1538.2 [nm]</td><td>-</td><td>[Stassen2019]</td></tr><tr><td rowspan="2">SiO<sub>2</sub> and HSQ</td><td rowspan="2">FWM</td><td rowspan="2">0.465 [µm]<br>0.29 [µm]<br>Fig. 7(g)</td><td>MOVPE, PECVD</td><td>2 [dB/cm]<br>1545 [nm]</td><td>-</td><td>-</td><td rowspan="2">7.2E+2 [m<sup>-1</sup>W<sup>-1</sup>]<br>-16 [dB]<br>130 [nm] (at -3dB)</td></tr><tr><td>E-beam</td><td>-</td><td>CW</td><td>CW</td></tr><tr><td>SOI</td><td></td><td></td><td>Wafer bonding,<br>substrate removal</td><td>-</td><td>-</td><td>-</td><td>The nonlinear coefficient was measured on a straight waveguide device, while the FWM efficiency was measured on a microring. The conversion bandwidth is the same for the waveguide and microring.</td></tr><tr><td>AlGaAs</td><td></td><td>3 [mm]<br>Fig. 1(b)</td><td>-</td><td>3.3<br>1.3 [dB/cm]</td><td>1550 [nm]<br>4.0E-1 [W]</td><td>1549 [nm]<br>1.0E-4 [W]</td><td>-</td><td rowspan="2">[Pu2018]</td></tr><tr><td rowspan="2">SiO<sub>2</sub> and HSQ</td><td rowspan="2">FWM</td><td rowspan="2">0.64 [µm]<br>0.28 [µm]</td><td>MOVPE, PECVD</td><td>-</td><td>CW</td><td>CW</td></tr><tr><td>E-beam</td><td>-</td><td>TE</td><td>TE</td></tr><tr><td>SOI</td><td></td><td>-</td><td>Wafer bonding,<br>substrate removal</td><td>46 [ps/(nm.km)]</td><td>-</td><td>-</td><td>6.3E+2 [m<sup>-1</sup>W<sup>-1</sup>]<br>-4.2 [dB]<br>750 [nm] (at -3dB)</td></tr><tr><td>AlGaAs</td><td></td><td>9 [mm]</td><td>-</td><td>MOVPE, PECVD</td><td>8 [dB/cm]</td><td>1550 [nm]<br>1.6E-1 [W]</td><td>1545 [nm]<br>-</td><td>[Kaminski2019]</td></tr><tr><td rowspan="2">SiO<sub>2</sub> and HSQ</td><td rowspan="2">FWM</td><td rowspan="2"></td><td>E-beam</td><td>-</td><td>CW</td><td>CW</td></tr><tr><td></td><td>TE</td><td>TE</td></tr><tr><td>SOI</td><td></td><td>-</td><td>Wafer bonding,<br>substrate removal</td><td>164 [ps/(nm.km)]</td><td>-</td><td>-</td><td>3.5E+2 [m<sup>-1</sup>W<sup>-1</sup>]<br>-15 [dB]</td></tr><tr><td>AlGaAs</td><td></td><td>5 [mm]<br>Fig. 1(b)</td><td>-</td><td>Epitaxy, PECVD</td><td>1.5 [dB/cm]<br>1542 [nm]</td><td>1542 [nm]<br>5.6E+0 [W]</td><td>-</td><td>[Hu2018]</td></tr><tr><td rowspan="2">SiO<sub>2</sub> and HSQ</td><td rowspan="2">SPM/XPM<br>spectral<br>broadening</td><td>0.6 [µm]<br>0.28 [µm]</td><td>E-beam</td><td>-</td><td>1.5E-12 [s](FWHM)<br>TE</td><td>-</td><td>-</td><td>0.66 [%]<sup>f</sup></td></tr><tr><td></td><td></td><td>1.0E+10 [Hz]</td><td>-</td><td>-</td><td>44 [nm]<br>(at -20 dB)</td></tr><tr><td>SOI</td><td></td><td>-</td><td>Wafer bonding,<br>substrate removal</td><td>Fig. S1</td><td>-</td><td>-</td><td>The generated comb wavelength ranges from 1520 nm to 1539.8 nm, and from 1546.1 nm to 1570 nm, as informed in the supplementary material.</td></tr></tbody></table>
<table><tbody><tr><td></td><td>InGaAs/AlAs/AlAsSb<br>CDQW</td><td>SPM/XPM</td><td>0.24 [mm]</td><td>-</td><td>1550.1 [nm]</td><td>1559.9 [nm]</td><td>-</td><td>[Tsuchida2007]</td></tr><tr><td></td><td>InAlAs</td><td>spectral<br>broadening</td><td>2 [µm]</td><td>-</td><td>2.3E-12 [s]<br>TM</td><td>CW<br>TE</td><td>-</td><td>XPM efficiency = 4.9E11 [rad/J].</td></tr><tr><td></td><td></td><td></td><td></td><td>-</td><td>1.0E+10 [Hz]</td><td>-</td><td>-</td><td>See the reference paper for quantum<br>well layers thicknesses.</td></tr><tr><td></td><td>InGaAs/AlAsSb<br>CDQW</td><td>SPM/XPM</td><td>0.25 [mm]<br>Fig. 1(b)</td><td>-</td><td>400 [cm<sup>-1</sup>]</td><td>1560 [nm]</td><td>-</td><td>[Cong2009]</td></tr><tr><td></td><td>AlGaAsSb and InP</td><td>spectral<br>broadening</td><td>2 [µm]</td><td>-</td><td>1560 [nm]</td><td>2.0E-12 [s]<br>TM</td><td>-</td><td>See the reference paper for quantum<br>well layers thicknesses.</td></tr><tr><td></td><td>InP</td><td></td><td>-</td><td>-</td><td>1.0E+10 [Hz]</td><td>-</td><td>-</td><td>XPM efficiency dependence on doping<br>density shown in Fig. 2(c) of the<br>reference paper.</td></tr><tr><td></td><td>InGaAs/AlAsSb<br>CDQW</td><td>SPM/XPM</td><td>1 [mm]</td><td>-</td><td>MBE</td><td>1560 [nm]</td><td>1545 [nm]</td><td>[Feng2013]</td></tr><tr><td></td><td>InP</td><td>spectral<br>broadening</td><td>1.3 [µm]</td><td>-</td><td>E-beam</td><td>2.4E-12 [s]<br>TM</td><td>CW<br>TE</td><td>XPM efficiency = 9.3E11 [rad/J].</td></tr><tr><td></td><td>InP</td><td></td><td>-</td><td>-</td><td>-</td><td>1.0E+10 [Hz]</td><td>-</td><td>The experimental setup and the<br>waveguide fabrication details given in<br>Feng J. et al, Optics Express 20, B279-<br>B287 (2012).</td></tr><tr><td></td><td>GaP</td><td></td><td>0.314 [mm]<br>Fig. 2(d)</td><td>Monocrystalline</td><td>3.1</td><td>1560 [nm]</td><td>-</td><td>1.1E-17 [m<sup>2</sup>/W]</td></tr><tr><td></td><td>SiO<sub>2</sub></td><td>FWM</td><td>0.5 [µm]<br>0.3 [µm]</td><td>MOCVD</td><td>1.2 [dB/cm]<br>1560 [nm]</td><td>CW</td><td>-</td><td>2.4E+2 [m<sup>-1</sup>W<sup>-1</sup>]</td></tr><tr><td></td><td>Silicon</td><td></td><td>Fig. 7(k)</td><td>Wafer bonding</td><td>2.1 [eV]<br>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>Fig. 2(e)</td><td>1.5E-13 [m<sup>2</sup>]</td><td>-</td><td>-</td></tr></tbody></table>
In$_{0.63}$Ga$_{0.37}$As$_{0.8}$P$_{0.2}$

InP

Nonlinear
transm./refl.

8 [mm]

Fig. 1

1.7 [µm]

0.9 [µm]

Monocrystalline

3.4

3 [dB/cm]

1568 [nm]

MOCVD

E-beam

2.2E-23 [s$^2$/m]

1568 [nm]

4.8E+1 [W]

3.0E-12 [s]

TM

7.6E+7 [Hz]

1.1E-12 [m$^2$]

-

-

-

-

-

-

1.9E-10

[Saeidi2018]

InGaAsP QW

InP

FWM

InP

Monocrystalline

-

-

-

0.83 [eV]

1548 [nm]

2.5E-2 [W]

CW

-

-

-

10-nm shift [nm]

-

CW

-

-

-

[Thoen2000]

10-nm-thick InGaAsP quantum wells with 15-nm InP barriers centered in InGaAsP guiding layer.

## Silicon and silicon carbide, nitride, and oxide

a-Si

FWM

Silicon

18.3 [mm]

-

0.48 [µm]

0.225 [µm]

-

PECVD

E-beam

3.39

6 [dB/cm]

1550 [nm]

1602 [nm]

2.3E-1 [W]

CW

TE

-

-

1-nm shift [nm]

-

CW

-

-

-

1.5E-17 [m$^2$/W]

-

-

3.39 [%]$^a$

[Girouard2020]

a-Si

FWM

Silicon

1 [mm]

Fig. 1

0.48 [µm]

0.22 [µm]

-

PECVD

E-beam

-

4.7 [dB/cm]

1550 [nm]

-

-4.8E-25 [s$^2$/m]

1550 [nm]

7.0E-2 [W]

CW

TE

-

-

1550.5 [nm]

-

CW

TE

-

-

8.0E+2 [m$^{-1}$W$^{-1}$]

0.25 [%]$^a$

6.0E+12 [Hz]

(at -3dB)

[Lacava2016]
<table><tr><td>a-Si</td><td></td><td>8 [mm]<br>Fig. 1</td><td>-</td><td>7.2 [dB/cm]<br>1550 [nm]</td><td>1540 [nm]<br>3.0E-4 [W]<br>CW</td><td>-</td><td>7.4E-17 [m²/W]<br>-</td><td>[Wang2012a]</td></tr><tr><td>SiO₂</td><td>FWM</td><td>0.5 [µm]<br>0.205 [µm]</td><td>PECVD</td><td>-</td><td>TE</td><td>CW<br>TE</td><td>-</td><td>0.1 [%]ᵃ<br>2.0E+13 [Hz]<br>(at -3dB)</td><td>Conversion efficiency dependence on<br>converted wavelength shown in Fig. 2 of<br>the reference paper.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>E-beam</td><td>-1.6E-25 [s²/m]</td><td>-</td><td>-</td><td>-</td><td></td><td></td></tr><tr><td>a-Si</td><td></td><td>-</td><td>-</td><td>7.2 [dB/cm]<br>1550 [nm]</td><td>1560 [nm]<br>1.3E-2 [W]<br>2.8E-12 [s]</td><td>1540 [nm]<br>-<br>2.8E-12 [s]</td><td>7.4E-17 [m²/W]<br>-</td><td>[Wang2012a]</td></tr><tr><td>SiO₂</td><td>FWM</td><td>0.5 [µm]<br>0.205 [µm]</td><td>PECVD</td><td>-</td><td>TE</td><td>TE<br>1.0E+10 [Hz]</td><td>-</td><td>5 [%]ᵃ<br>2.0E+13 [Hz]<br>(at -3dB)</td><td></td></tr><tr><td>Silicon</td><td></td><td>-</td><td>E-beam</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td><td></td></tr><tr><td>a-Si</td><td></td><td>6 [mm]<br>Fig. 1</td><td>-</td><td>3.5 [dB/cm]<br>1550 [nm]</td><td>1550 [nm]<br>6.3E-2 [W]<br>1.9E-12 [s]</td><td>1560 [nm]<br>8.0E-4 [W]<br>2.1E-12 [s]</td><td>-</td><td></td><td></td></tr><tr><td>SiO₂</td><td>FWM</td><td>0.5 [µm]<br>0.198 [µm]</td><td>PECVD</td><td>-</td><td>TE</td><td>TE<br>1.0E+10 [Hz]</td><td>3.0E+3 [m⁻¹W⁻¹]<br>5 [%]ᵃ</td><td>[Wang2012b]</td></tr><tr><td>Silicon</td><td></td><td>Fig. 7(b)</td><td>E-beam</td><td>-1.3E-26 [s²/m]<br>Fig. 1</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Si and PIN</td><td></td><td>40 [mm]</td><td>-</td><td>-</td><td>1552.5 [nm]</td><td>-</td><td>-</td><td></td><td></td></tr><tr><td>SiO₂ and Si₃N₄</td><td>FWM</td><td>0.5 [µm]<br>0.22 [µm]</td><td>Photolithography</td><td>-</td><td>4.0E-1 [W]<br>CW<br>TE</td><td>CW<br>TE</td><td>9.0E-12 [m/W]<br>2.0E+2 [m⁻¹W⁻¹]<br>79.4 [%]ᵃ</td><td>[Gajda2012]</td></tr><tr><td>Silicon</td><td></td><td>Fig. 7(q)</td><td>-</td><td>-1.3E-24 [s²/m]</td><td>-</td><td>-</td><td>-</td><td></td></tr></table>
<table><tbody><tr><td>Si</td><td>24 [mm]</td><td>Monocrystalline</td><td>1560 [nm]</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td>-</td><td>-</td><td>0.46 [cm<sup>-1</sup>]</td><td>4.0E+2 [W]</td><td>-</td><td></td></tr><tr><td></td><td>-</td><td>-</td><td>1560 [nm]</td><td>9.0E-13 [s]</td><td>-</td><td>4.4E-12 [mW]</td></tr><tr><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td>-</td><td>-</td><td>-</td><td>2.5E+7 [Hz]</td><td>-</td><td>-</td></tr><tr><td></td><td>-</td><td>-</td><td>-</td><td>8.1E-12 [m<sup>2</sup>]</td><td>-</td><td>-</td></tr><tr><td>Si</td><td>2.9 [mm]</td><td>Monocrystalline</td><td>1550 [nm]</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td>Fig. 1(a)-(g)</td><td>-</td><td>0.18 [dB/cm]</td><td>6.2E-2 [W]</td><td>-</td><td>-</td></tr><tr><td></td><td>1 [µm]</td><td>-</td><td>1550 [nm]</td><td>CW</td><td>-</td><td>-</td></tr><tr><td>Air (suspended)</td><td>0.08 [µm]</td><td>E-beam</td><td>-</td><td>TE</td><td>-</td><td>-</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td>Fig. 7(r)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Si</td><td>2.7 [mm]</td><td>Monocrystalline</td><td>1550 [nm]</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td>Fig. 1(c)</td><td>-</td><td>2.6 [dB/cm]</td><td>2.5E-2 [W]</td><td>-</td><td>-</td></tr><tr><td></td><td>0.45 [µm]</td><td>-</td><td>1550 [nm]</td><td>CW</td><td>-</td><td>-</td></tr><tr><td>Air and SiO<sub>2</sub></td><td>0.23 [µm]</td><td>Photolithography</td><td>-</td><td>TE</td><td>-</td><td>-</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td>Fig. 7(p)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Si</td><td>20 [mm]</td><td>Monocrystalline</td><td>1550 [nm]</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td>Fig. 1(c)</td><td>-</td><td>2.6 [dB/cm]</td><td>1.2E-2 [W]</td><td>-</td><td>-</td></tr><tr><td></td><td>0.45 [µm]</td><td>-</td><td>1550 [nm]</td><td>CW</td><td>-</td><td>-</td></tr><tr><td>Air and SiO<sub>2</sub></td><td>0.23 [µm]</td><td>Photolithography</td><td>-</td><td>TE</td><td>-</td><td>-</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td>Fig. 7(p)</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>Si</td><td></td><td>Monocrystalline</td><td>1545 [nm]</td><td>1680 [nm]</td><td></td><td>[Liu2004]</td></tr><tr><td>SiO<sub>2</sub> and air</td><td>SRS Pump Probe</td><td>Fig. 1</td><td>4.7E-1 [W]</td><td>2.0E-3 [W]</td><td></td><td>g<sub>Raman</sub> = 1.05E-10 m/W</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td></td><td>1.52 [µm]</td><td>1.7E-8 [s](FWHM)</td><td>CW</td><td></td><td>Raman shift = 5.2E+4 m<sup>-1</sup></td></tr><tr><td></td><td></td><td>1.45 [µm]</td><td>TE</td><td>TM</td><td></td><td>Pump peak irradiance = 3E11 W/m<sup>2</sup></td></tr><tr><td></td><td></td><td>-</td><td>1.0E+4 [Hz]</td><td>-</td><td></td><td>Free-carrier lifetime = 2.5E-8 s</td></tr><tr><td></td><td></td><td>-</td><td>1.6E-12 [m<sup>2</sup>]</td><td>1.4E-12 [m<sup>2</sup>]</td><td></td><td></td></tr><tr><td>Si</td><td></td><td>Monocrystalline</td><td>1536 [nm]</td><td>-</td><td></td><td>[Rong2005]</td></tr><tr><td>SiO<sub>2</sub> and air</td><td>SRS Pump Probe</td><td>Fig. 1(a)</td><td>2.0E+0 [W]</td><td>-</td><td></td><td>g<sub>Raman</sub> = 7.5E-11 m/W</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td></td><td>1.5 [µm]</td><td>1.3E-7 [s]</td><td>-</td><td></td><td>Raman shift = 5.2E+4 m<sup>-1</sup></td></tr><tr><td></td><td></td><td>1.55 [µm]</td><td>-</td><td>-</td><td>10 [%]</td><td>Free-carrier lifetime = 1E-8 s.</td></tr><tr><td></td><td></td><td>-</td><td>1.0E+4 [Hz]</td><td>-</td><td></td><td>The conversion efficiency is the slope efficiency of average Raman lasing output vs average input power.</td></tr><tr><td>Si</td><td></td><td>Monocrystalline</td><td>1427 [nm]</td><td>-</td><td></td><td>[Claps2002]</td></tr><tr><td>SiO<sub>2</sub> and air</td><td>SpRS cross-section</td><td>Fig. 2</td><td>1.0E+0 [W]</td><td>-</td><td></td><td>g<sub>Raman</sub> = 7.6E-10 m/W</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td></td><td>5 [µm]</td><td>CW</td><td>-</td><td></td><td>Raman shift = 5.2E+4 m<sup>-1</sup></td></tr><tr><td></td><td></td><td>2.5 [µm]</td><td>TE</td><td>-</td><td></td><td></td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td></td><td></td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td></td><td></td></tr><tr><td>Si</td><td></td><td>Monocrystalline</td><td>1240 [nm]</td><td>-</td><td></td><td>[Zhang2020]</td></tr><tr><td>SiO<sub>2</sub> and air</td><td>Raman Laser</td><td>Fig. 1(f)</td><td>1.0E-3 [W]</td><td>-</td><td></td><td>g<sub>Raman</sub> = 3.66E-10 m/W</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td>Threshold</td><td>2 [µm]</td><td>CW</td><td>-</td><td></td><td>Raman shift = 5.2E+4 m<sup>-1</sup></td></tr><tr><td></td><td></td><td>0.22 [µm]</td><td>TE</td><td>-</td><td></td><td>Gain dependence on pump wavelength shown in Fig. 6(b) of the reference paper.</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td></td><td></td></tr><tr><td></td><td></td><td>-</td><td>3.7E-13 [m<sup>2</sup>]</td><td>-</td><td></td><td></td></tr></tbody></table>
<table><tbody><tr><td>Si</td><td></td><td>Monocrystalline</td><td>2200 [nm]</td><td>-</td><td>-</td><td>[Liu2011]</td></tr><tr><td>SiO<sub>2</sub> and Si<sub>3</sub>N<sub>4</sub></td><td>Nonlinear transm./refl.</td><td>4 [mm]<br/>Fig. 1(a)-(c)<br/>0.6 [µm]<br/>0.22 [µm]</td><td>4.5 - 7.0 [dB/cm]<br/>1800-2300 [nm]</td><td>6.0E+0 [W]<br/>2.0E-12 [s](FWHM)</td><td>3.0E-13 [m/W]</td><td>Nonlinearity dependence on wavelength shown in Table 1 of the reference paper.</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td></td><td>Photolithography</td><td>TE<br/>7.6E+7 [Hz]</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Si</td><td></td><td>-</td><td>1946 [nm]</td><td>2440 [nm]</td><td>-</td><td>[Liu2012]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>20 [mm]<br/>Fig. 1(b)<br/>0.9 [µm]<br/>0.22 [µm]</td><td>2.6 [dB/cm]<br/>1810-2410 [nm]</td><td>3.7E+1 [W]<br/>2.0E-12 [s]<br/>TE</td><td>3.5E-5 [W]<br/>CW<br/>TE</td><td>The conversion efficiency refers to the parametric gain.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-5.0E-25 [s<sup>2</sup>/m]<br/>Fig. S4(b)</td><td>7.6E+7 [Hz]</td><td>2.8E+2 [m<sup>-1</sup>W<sup>-1</sup>]<br/>8912.5 [%]<sup>e</sup><br/>6.2E+13 [Hz]</td><td>Parametric gain dependence on wavelength shown in Fig. 2 of the reference paper.</td></tr><tr><td></td><td></td><td></td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Si</td><td></td><td>-</td><td>2173 [nm]</td><td>2209-2498 [nm]</td><td>-</td><td>[Kuyken2011]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>20 [mm]<br/>Fig. 1(b)<br/>0.9 [µm]<br/>0.22 [µm]</td><td>2.8 [dB/cm]<br/>2173 [nm]</td><td>1.4E+1 [W]<br/>2.0E-12 [s]<br/>TE</td><td>6.0E-5 [W]<br/>CW<br/>TE</td><td>The conversion efficiency refers to the parametric gain.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-6.0E-25 [s<sup>2</sup>/m]</td><td>7.6E+7 [Hz]</td><td>1.5E+2 [m<sup>-1</sup>W<sup>-1</sup>]<br/>1000000 [%]<br/>580 [nm]</td><td>Parametric gain dependence on wavelength shown in Fig. 3 of the reference paper.</td></tr><tr><td></td><td></td><td></td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Si</td><td></td><td>-</td><td>2025 [nm]</td><td>1912-1994 [nm]</td><td>1.1E-17 [m<sup>2</sup>/W]</td><td>[Zlatanovic2010]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>3.8 [mm]<br/>Fig. S1<br/>1.06 [µm]<br/>0.25 [µm]</td><td>2.8 [dB/cm]<br/>2025 [nm]</td><td>1.8E-1 [W]<br/>1.0E-9 [s]<br/>TE</td><td>-<br/>CW<br/>TE</td><td>Conversion efficiency dependence on pump-signal detuning shown in Fig. 2(b) of the reference paper.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-</td><td>1.0E+6 [Hz]<br/>3.5E-13 [m<sup>2</sup>]</td><td>9.7E+1 [m<sup>-1</sup>W<sup>-1</sup>]<br/>0.5 [%]<sup>a</sup><br/>292 [nm] (at -3dB)</td><td></td></tr></tbody></table>
<table><tbody><tr><td>Si</td><td></td><td>15 [mm]<br>Fig. 1</td><td>-</td><td>1554 [nm]</td><td>1555-2078 [nm]</td><td>-</td><td>[Turner-Foster2010]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>0.55 [µm]<br>0.3 [µm]</td><td>E-beam</td><td>1554 [nm]</td><td>1.1E-1 [W]<br>CW<br>TE</td><td>2.5E-4 [W]<br>CW<br>TE</td><td>Conversion efficiency dependence on<br>converted wavelength shown in Fig. 2 of<br>the reference paper.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.58 [%]<sup>a</sup><br>9.7E+13 [Hz]<br>(at -3dB)</td><td></td></tr><tr><td>Si</td><td></td><td>17 [mm]<br>Fig. 1</td><td>Monocrystalline</td><td>0.1 [dB/cm]<br>1540 [nm]</td><td>1540 [nm]<br>2.0E+1 [W]<br>5.4E-11 [s](FWHM)</td><td>-<br>-<br>-</td><td>-</td></tr><tr><td>SiO<sub>2</sub></td><td>Nonlinear<br>transm./refl.</td><td>-</td><td>-</td><td>1.2E-24 [s<sup>2</sup>/m]<br>Fig. 5</td><td>-<br>6.2E-12 [m<sup>2</sup>]</td><td>-<br>-</td><td>4.5E-12 [m/W]<br>-<br>-</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>4H-SiC</td><td></td><td>3 [mm]</td><td>-</td><td>2.4</td><td>1565 [nm]<br>1.3E-1 [W]</td><td>-<br>1.0E-3 [W]</td><td>6.0E-19 [m<sup>2</sup>/W]<br>-<br>7.4E+0 [m<sup>1</sup>W<sup>-1</sup>]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>0.51 [µm]<br>0.5 [µm]</td><td>E-beam</td><td>1565 [nm]<br>>2.4 [eV]<br>325 [ps/(nm.km)]</td><td>CW<br>TE</td><td>-<br>TE</td><td>0.00032 [%]<sup>a</sup><br>1.6E+13 [Hz]<br>(at -3dB)</td></tr><tr><td>Silicon</td><td></td><td>Fig. 7(n)</td><td>Wafer bonding</td><td>Fig. 5(a)</td><td>-</td><td>-</td><td>Nonlinearity dependence on waveguide<br>width shown in Fig. 4 of the reference<br>paper.</td></tr><tr><td>a-SiC</td><td>SPM/XPM</td><td>12 [mm]<br>Fig. 2(a)</td><td>PECVD</td><td>2.45<br>3 [dB/cm]</td><td>1550 [nm]<br>1.3E+1 [W]</td><td>-<br>-</td><td>4.8E-18 [m<sup>2</sup>/W]<br>-<br>4.0E+1 [m<sup>1</sup>W<sup>-1</sup>]</td></tr><tr><td>SiO<sub>2</sub></td><td>spectral<br>broadening</td><td>1.2 [µm]<br>0.35 [µm]</td><td>E-beam</td><td>1550 [nm]<br>2.3 [eV]<br>-400 [ps/(nm.km)]</td><td>-<br>-</td><td>-<br>-</td><td>-</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-</td><td>-</td><td>4.2E-13 [m<sup>2</sup>]</td><td>-</td><td>-</td></tr></tbody></table>
<table><tbody><tr><td>Si<sub>3</sub>N<sub>4</sub></td><td></td><td>1000 [mm]<br>Fig.1(a)</td><td>-</td><td>-</td><td>1563 [nm]<br>2.1E+0 [W]</td><td>1562 [nm]<br>7.7E-2 [W]</td><td>-</td><td></td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>2.8 [µm]<br>0.1 [µm]</td><td>-</td><td>0.06 [dB/cm]<br>1550 [nm]</td><td>CW<br>TE</td><td>CW<br>TE</td><td>2.9E-1 [m<sup>-1</sup>W<sup>-1</sup>]<br>0.245 [%]<sup>a</sup></td><td>[Kruckel2015b]</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-</td><td>-5.0E-25 [s<sup>2</sup>/m]</td><td>-</td><td>-</td><td>6.2E+11 [Hz]<br>(at -3dB)</td><td></td></tr><tr><td>Si<sub>3</sub>N<sub>4</sub></td><td></td><td>22 [mm]<br>Fig. 2(a)</td><td>-</td><td>-</td><td>1550 [nm]<br>1.6E-1 [W]</td><td>1550.8 [nm]<br>1.1E-1 [W]</td><td>6.9E-19 [m<sup>2</sup>/W]</td><td></td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>2 [µm]<br>0.72 [µm]</td><td>PECVD</td><td>0.58 [dB/cm]<br>1550 [nm]</td><td>CW<br>TE</td><td>CW<br>TE</td><td>2.6E+0 [m<sup>-1</sup>W<sup>-1</sup>]<br>0.00012 [%]<sup>e</sup></td><td>[Wang2018a]</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>Photolithography</td><td>3.27 [eV]</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Si<sub>3</sub>N<sub>4</sub></td><td></td><td>61 [mm]<br>Fig. 2(a)</td><td>-</td><td>-</td><td>1550 [nm]<br>2.4E+1 [W]</td><td>1470-1630 [nm]</td><td>2.5E-19 [m<sup>2</sup>/W]</td><td>[Levy2009]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>1.45 [µm]<br>0.725 [µm]</td><td>LPCVD, PECVD</td><td>0.5 [dB/cm]<br>1550 [nm]</td><td>1.0E-11 [s]<br>TE</td><td>CW<br>TE</td><td>-</td><td>The reported conversion efficiency is the parametric OPO gain achieved in microresonators.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>E-beam</td><td>6.4E-27 [s<sup>2</sup>/m]<br>Fig. 2(a)</td><td>1.0E+9 [Hz]</td><td>-</td><td>229 [%]<sup>a</sup><br>150 [nm]<br>(at -3.6dB)</td><td>Signal gain dependence on wavelength shown in Fig. 2(b) of the reference paper.</td></tr><tr><td>Si<sub>3</sub>N<sub>4</sub></td><td>SPM/XPM</td><td>6000 [mm]<br>Fig. 1(a)</td><td>-</td><td>-</td><td>1549.9 [nm]<br>4.0E-1 [W]</td><td>1550.3 [nm]<br>4.0E-1 [W]</td><td>9.0E-20 [m<sup>2</sup>/W]</td><td>[Tien2010]</td></tr><tr><td>SiO<sub>2</sub></td><td>spectral<br>broadening</td><td>2.8 [µm]<br>0.08 [µm]</td><td>LPCVD</td><td>1550 [nm]</td><td>CW<br>TE</td><td>CW<br>TE</td><td>6.0E-2 [m<sup>-1</sup>W<sup>-1</sup>]</td><td>Nonlinearity dependence on core thickness shown in Fig. 2 of the reference paper.</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>Si<sub>7</sub>N<sub>3</sub></td><td></td><td>7 [mm]</td><td>-</td><td>3.1</td><td>1555 [nm]</td><td>-</td><td>-</td><td>[Ooi2017]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>0.55 [µm]</td><td>PECVD</td><td>4.5 [dB/cm]<br/>1550 [nm]</td><td>2.3E-2 [W]</td><td>2.3E-4 [W]</td><td>5.0E+2 [m<sup>-1</sup>W<sup>-1</sup>]</td><td>Conversion efficiency dependence on pump wavelength shown in Fig. 3(b) of the reference paper.</td></tr><tr><td>Silicon</td><td></td><td>0.3 [µm]</td><td>E-beam</td><td>2 [eV]<br/>-2.5E-25 [s<sup>2</sup>/m]<br/>Fig. 2(b)</td><td>CW</td><td>CW</td><td>0.323 [%]</td><td></td></tr><tr><td>Si<sub>7</sub>N<sub>3</sub></td><td></td><td>7 [mm]</td><td>-</td><td>3.1</td><td>1550 [nm]</td><td>-</td><td>2.8E-17 [m<sup>2</sup>/W]</td><td></td></tr><tr><td>SiO<sub>2</sub></td><td>SPM/XPM</td><td>0.6 [µm]</td><td>PECVD</td><td>10 [dB/cm]<br/>1550 [nm]</td><td>1.4E+2 [W]</td><td>-</td><td>5.5E+2 [m<sup>-1</sup>W<sup>-1</sup>]</td><td></td></tr><tr><td>Silicon</td><td>spectral<br/>broadening</td><td>0.3 [µm]</td><td>E-beam</td><td>2.05 [eV]<br/>-2.4E-25 [s<sup>2</sup>/m]<br/>Fig. 2(c)</td><td>1.8E-12 [s]</td><td>-</td><td>7.7E+13 [Hz]</td><td></td></tr><tr><td>Si<sub>x</sub>N<sub>y</sub></td><td></td><td>-</td><td>-</td><td>2.49</td><td>1550.1 [nm]</td><td>1550 [nm]</td><td>1.6E-18 [m<sup>2</sup>/W]</td><td>[Wang2015]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>0.7 [µm]</td><td>PECVD</td><td>1.5 [dB/cm]<br/>1550 [nm]</td><td>3.2E-1 [W]</td><td>3.2E-2 [W]</td><td>8.0E-12 [m/W]</td><td></td></tr><tr><td>Silicon</td><td></td><td>0.22 [µm]</td><td>E-beam</td><td>-</td><td>CW</td><td>CW</td><td>1.6E+1 [m<sup>-1</sup>W<sup>-1</sup>]</td><td></td></tr><tr><td>Si<sub>x</sub>N<sub>y</sub></td><td></td><td>0.7 [µm]</td><td>-</td><td>-</td><td>TE</td><td>TE</td><td>0.0032 [%]<sup>a</sup></td><td></td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>1.65 [µm]</td><td>PECVD</td><td>1.2 [dB/cm]<br/>1570 [nm]</td><td>-</td><td>-</td><td>6.1E+0 [m<sup>-1</sup>W<sup>-1</sup>]</td><td></td></tr><tr><td>Silicon</td><td></td><td>0.7 [µm]</td><td>E-beam</td><td>2.3 [eV]<br/>-2.0E-26 [s<sup>2</sup>/m]<br/>Fig. 3(b)</td><td>-</td><td>-</td><td>0.016 [%]<sup>a</sup></td><td></td></tr><tr><td>Si<sub>x</sub>N<sub>y</sub></td><td></td><td>9.4 [mm]</td><td>-</td><td>2.1</td><td>1563 [nm]</td><td>1562 [nm]</td><td>1.4E-18 [m<sup>2</sup>/W]</td><td>[Kruckel2015a]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>Fig. 1(b)</td><td>PECVD</td><td>1.2 [dB/cm]<br/>1570 [nm]</td><td>1.0E+0 [W]</td><td>7.9E-2 [W]</td><td>6.1E+0 [m<sup>-1</sup>W<sup>-1</sup>]</td><td></td></tr><tr><td>Silicon</td><td></td><td>Fig. 7(s)</td><td>E-beam</td><td>2.3 [eV]<br/>-2.0E-26 [s<sup>2</sup>/m]<br/>Fig. 3(b)</td><td>CW</td><td>CW</td><td>0.016 [%]<sup>a</sup></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>TE</td><td>TE</td><td>2.0E+12 [Hz]</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>-</td><td>-</td><td>(at -3dB)</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td>9.0E-13 [m<sup>2</sup>]</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>Hydex</td><td></td><td>0.3 [mm]<br>Fig. 1</td><td>Amorphous<br>1.7<br>0.06 [dB/cm]</td><td>1553.38 [nm]<br>5.0E-3 [W]</td><td>1558.02 [nm]<br>5.5E-4 [W]</td><td>1.2E-19 [m²/W]<br>-</td><td>[Ferrera2008]</td></tr><tr><td>SiO₂ and air</td><td>FWM</td><td>1.5 [µm]<br>1.45 [µm]</td><td>CVD<br>1550 [nm]</td><td>CW<br>TM</td><td>CW<br>TM</td><td>2.3E-1 [m⁻¹W⁻¹]<br>0.0013 [%]</td><td>Ring radius around 48 µm, Q-factor of<br>65,000, FSR 575 GHz.</td></tr><tr><td>SiO₂</td><td></td><td>Fig. 7(c)</td><td>Photolithography<br>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>2.0E-12 [m²]</td><td>-</td><td>-</td><td></td></tr><tr><td>Hydex</td><td></td><td>0.85 [mm]</td><td>Amorphous<br>1.7</td><td>1551 [nm]</td><td>1553 [nm]</td><td>-</td><td>[Ferrera2009]</td></tr><tr><td>SiO₂ and air</td><td>FWM</td><td>-</td><td>CVD<br>1550 [nm]</td><td>8.8E-3 [W]</td><td>1.3E-3 [W]</td><td>-</td><td>The radius of the ring resonator is 135<br>µm. The FSR is 200 GHz.</td></tr><tr><td>SiO₂</td><td></td><td>-</td><td>Photolithography<br>-1.0E-26 [s²/m]</td><td>CW<br>TE</td><td>CW<br>TE</td><td>0.25 [%]</td><td></td></tr><tr><td></td><td></td><td>-</td><td>Fig. 3</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>Hydex</td><td></td><td>450 [mm]</td><td>Amorphous<br>1.7</td><td>1560 [nm]</td><td>-</td><td>1.1E-19 [m²/W]</td><td>[Duchesne2009]</td></tr><tr><td>SiO₂</td><td>SPM/XPM<br>spectral<br>broadening</td><td>Fig. 1<br>1.5 [µm]<br>1.45 [µm]</td><td>CVD<br>1550 [nm]</td><td>3.9E+1 [W]</td><td>-</td><td>-</td><td>2.2E-1 [m⁻¹W⁻¹]</td></tr><tr><td>SiO₂</td><td></td><td>-</td><td>Photolithography<br>20E-26 [s²/m]</td><td>1.7E-12 [s](FWHM)</td><td>-</td><td>-</td><td>Peak irradiance &lt;25E+13 W/m².</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>1.7E+7 [Hz]</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>2.0E-12 [m²]</td><td>-</td><td>-</td><td></td></tr></tbody><tfoot><tr><td colspan="9">Chalcogenide glasses</td></tr></tfoot></table>
<table><tbody><tr><td>As<sub>2</sub>S<sub>3</sub></td><td>SPM/XPM</td><td>60 [mm]<br>Fig. 1</td><td>Amorphous<br>Thermal evaporation</td><td>2.38<br>0.6 [dB/cm]<br>1550 [nm]</td><td>1550 [nm]<br>6.8E+1 [W]<br>6.1E-13 [s](FWHM)</td><td>-<br>-<br>-</td><td>6.2E-15 [m/W]<br>1.0E+1 [m<sup>-1</sup>W<sup>-1</sup>]</td><td rowspan="3">[Lamont2008]</td></tr><tr><td>SiO<sub>2</sub></td><td>spectral<br>broadening</td><td>2 [µm]<br>0.87 [µm]</td><td>-</td><td>-</td><td>TM<br>1.0E+7 [Hz]<br>1.2E-12 [m<sup>2</sup>]</td><td>-<br>-<br>-</td><td>750 [nm]<br>(at -30 dB)</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-</td><td>3.7E-26 [s<sup>2</sup>/m]<br>Fig. 2</td><td></td><td></td><td></td></tr><tr><td>As<sub>2</sub>S<sub>3</sub></td><td></td><td>70 [mm]<br>Fig. 1(a)</td><td>Thermal evaporation</td><td>4 [dB/cm]<br>1550 [nm]</td><td>1547 [nm]<br>1.35E-1 [W]<br>CW</td><td>1554-1564 [nm]<br>-<br>CW</td><td>-<br>-<br>10 [m<sup>-1</sup>W<sup>-1</sup>]</td><td rowspan="3">[Pelusi2010]</td></tr><tr><td>SiO<sub>2</sub></td><td>FWM</td><td>2 [µm]<br>0.85 [µm]</td><td>-</td><td>Photolithography</td><td>-<br>28 [ps/nm km]</td><td>-<br>-</td><td>-37.8 [dB]</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>-</td><td>-</td><td>1E-12 [m<sup>2</sup>]</td><td>-</td><td>-</td></tr><tr><td>Ge<sub>11.5</sub>As<sub>24</sub>Se<sub>64.5</sub></td><td></td><td>18 [mm]<br>Fig. 3(a)</td><td>Amorphous<br>Thermal evaporation</td><td>2.66<br>2.6 [dB/cm]<br>1550 [nm]</td><td>1550.8 [nm]<br>135E-3 [W]<br>CW</td><td>1552.6 [nm]<br>2.8E-3 [W]<br>CW</td><td>-<br>9.3E-14 [m/W]<br>1.36E+2 [m<sup>-1</sup>W<sup>-1</sup>]</td><td rowspan="3">[Gai2010]</td></tr><tr><td>SiO<sub>2</sub> and polymer</td><td>FWM</td><td>0.63 [µm]<br>0.5 [µm]</td><td>-</td><td>-</td><td>TM<br>0.27E-12 [m<sup>2</sup>]</td><td>-<br>-</td><td>-<br>-</td></tr><tr><td>Silicon</td><td></td><td>-</td><td>E-beam</td><td>-</td><td></td><td></td><td>Supercontinuum generation in the range between 1200 and 2400 nm was demonstrated.</td></tr><tr><td colspan="9" style="background-color: #D9D9D9; text-align: left; font-weight: bold;">Diamond</td></tr><tr><td>Diamond</td><td></td><td>0.188 [mm]<br>Fig. 2(a)</td><td>Monocrystalline</td><td>-<br>-</td><td>750 [nm]<br>2.0E-2 [W]</td><td>-<br>-</td><td>-<br>-</td><td rowspan="3">[Latawiec2018]</td></tr><tr><td>SiO<sub>2</sub> and air</td><td>Raman<br>Laser</td><td>0.3 [µm]<br>0.3 [µm]</td><td>-</td><td>-<br>5.5 [eV]</td><td>CW<br>TE</td><td>-<br>-</td><td>-<br>1.7 [%]</td></tr><tr><td>SiO<sub>2</sub>/Si</td><td>Threshold</td><td>-</td><td>E-beam</td><td>-<br>-</td><td>-<br>-</td><td>-<br>-</td><td>-<br>-</td></tr></tbody></table>
<table><tbody><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>efficiency.</td></tr><tr><td>Diamond</td><td></td><td>Monocrystalline</td><td>-</td><td>1600 [nm]</td><td>-</td><td>8.2E-20 [m²/W]</td><td></td></tr><tr><td>SiO₂</td><td>FWM</td><td>HPHT</td><td>0.34 [dB/cm]</td><td>7.8E-2 [W]</td><td>-</td><td>-</td><td>[Hausmann2014]</td></tr><tr><td>SiO₂/Si</td><td></td><td>E-beam</td><td>1545.1 [nm]</td><td>CW</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td>5.5 [eV]</td><td>TE</td><td>-</td><td>5 [%]g</td><td>Technique: OPO based on FWM.</td></tr><tr><td></td><td></td><td></td><td>Figs. 1(b) and 5</td><td>5.0E-13 [m²]</td><td>-</td><td>-</td><td></td></tr><tr><td>Diamond</td><td>Raman</td><td>Monocrystalline</td><td>-</td><td>1575 [nm]</td><td>-</td><td>-</td><td>[Latawiec2015]</td></tr><tr><td>SiO₂</td><td>Laser</td><td>CVD</td><td>-</td><td>8.5E-2 [W]</td><td>-</td><td>-</td><td>Raman lasing.</td></tr><tr><td>SiO₂/Si</td><td>Threshold</td><td>E-beam</td><td>5.5 [eV]</td><td>CW</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td>-</td><td>TE</td><td>-</td><td>0.43 [%]</td><td></td></tr><tr><td></td><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>The conversion efficiency is the external Raman lasing slope efficiency.</td></tr><tr><td colspan="8" style="background-color: #D9D9D9; text-align: center; font-weight: bold;">Tantalum oxide, titanium oxide</td></tr><tr><td>Ta₂O₅</td><td></td><td>-</td><td>2.1</td><td>1555.465 [nm]</td><td>1556.08 [nm]</td><td>1.0E-18 [m²/W]</td><td></td></tr><tr><td>SiO₂</td><td>FWM</td><td>Sputtering, PECVD</td><td>1.5 [dB/cm]</td><td>3.5E-2 [W]</td><td>4.0E-3 [W]</td><td>-</td><td>[Wu2015]</td></tr><tr><td>Silicon</td><td></td><td>E-beam</td><td>1550 [nm]</td><td>CW</td><td>CW</td><td>5.2E+0 [m⁻¹W⁻¹]</td><td></td></tr><tr><td></td><td></td><td></td><td>-1400 [ps/(nm.km)]</td><td>TE</td><td>TE</td><td>0.001 [%]e</td><td></td></tr><tr><td></td><td></td><td></td><td>Fig. 5(a)</td><td>7.7E-13 [m²]</td><td>-</td><td>-</td><td></td></tr><tr><td>TiO₂</td><td></td><td>-</td><td>2.31</td><td>1550.1 [nm]</td><td>1551.3 [nm]</td><td>3.6E-18 [m²/W]</td><td></td></tr><tr><td>SiO₂</td><td>FWM</td><td>Sputtering</td><td>5.4 [dB/cm]</td><td>6.0E-1 [W]</td><td>1.9E-2 [W]</td><td>-</td><td>[Guan2018]</td></tr><tr><td>Silicon</td><td></td><td>E-beam</td><td>1550 [nm]</td><td>CW</td><td>CW</td><td>3.4E+1 [m⁻¹W⁻¹]</td><td></td></tr><tr><td></td><td></td><td></td><td>3.4 [eV]</td><td>TE</td><td>TE</td><td>0.024 [%]a</td><td></td></tr><tr><td></td><td></td><td></td><td>-50 [ps/(nm.km)]</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td></td><td></td><td></td><td>Fig. 7</td><td>4.3E-13 [m²]</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>TiO<sub>2</sub></td><td>SPM/XPM</td><td>22 [mm]<br>Fig. 1</td><td>-</td><td>2.35<br>5.5 [dB/cm]</td><td>1640 [nm]<br>1.3E+3 [W]</td><td>-</td><td>-</td><td rowspan="3">[Hammani2018]</td></tr><tr><td>SiO<sub>2</sub></td><td>spectral<br>broadening</td><td>1.345 [µm]<br>0.45 [µm]</td><td>Sputtering</td><td>1640 [nm]<br>3.4 [eV]</td><td>9.0E-14 [s]<br>TE</td><td>-</td><td>-</td></tr><tr><td>Silicon</td><td></td><td>Fig. 7(m)</td><td>Photolithography</td><td>20 [ps/(nm.km)]<br>Fig. 4(a)</td><td>8.0E+7 [Hz]<br>5.4E-13 [m<sup>2</sup>]</td><td>-</td><td>860 [nm]<br>(at -20dB)</td></tr><tr><td>TiO<sub>2</sub></td><td>SPM/XPM</td><td>9 [mm]<br>Fig. 1</td><td>-</td><td>2.4<br>8 [dB/cm]</td><td>1565 [nm]<br>2.9E+4 [W]</td><td>-</td><td>1.6E-19 [m<sup>2</sup>/W]</td><td rowspan="3">[Evans2013]</td></tr><tr><td>SiO<sub>2</sub></td><td>spectral<br>broadening</td><td>0.9 [µm]<br>0.25 [µm]</td><td>Sputtering</td><td>1560 [nm]<br>3.1-3.3 [eV]</td><td>1.7E-13 [s]<br>TE</td><td>-</td><td>1.5E+0 [m<sup>-1</sup>W<sup>-1</sup>]</td></tr><tr><td>Silicon</td><td></td><td>Fig. 7(l)</td><td>E-beam</td><td>1.5E-24 [s<sup>2</sup>/m]<br>-</td><td>8.0E+7 [Hz]<br>4.3E-13 [m<sup>2</sup>]</td><td>-</td><td>-</td></tr><tr><td>TiO<sub>2</sub></td><td>SPM/XPM</td><td>6 [mm]<br>Fig. 1</td><td>-</td><td>2.4<br>8 [dB/cm]</td><td>794 [nm]<br>2.9E+4 [W]</td><td>-</td><td>1.6E-18 [m<sup>2</sup>/W]<br>7.0E-12 [m/W]</td><td rowspan="3">[Evans2013]</td></tr><tr><td>SiO<sub>2</sub></td><td>spectral<br>broadening</td><td>0.9 [µm]<br>0.25 [µm]</td><td>Sputtering</td><td>794 [nm]<br>3.1-3.3 [eV]</td><td>8.5E-14 [s]<br>TM</td><td>-</td><td>7.9E+1 [m<sup>-1</sup>W<sup>-1</sup>]</td></tr><tr><td>Silicon</td><td></td><td>Fig. 7(l)</td><td>E-beam</td><td>1.5E-24 [s<sup>2</sup>/m]<br>-</td><td>1.1E+7 [Hz]<br>1.6E-13 [m<sup>2</sup>]</td><td>-</td><td>-</td></tr></tbody></table>

1: The length of ring resonators was calculated from the ring radius.

2: Figure of the reference paper with the cross-section image or drawing.

3: For heterostructure waveguides, the reported height is the guiding layer thickness.

4: Selected SEM images presented in this work for each geometry and material platform.

5: Figure of the reference paper showing a dispersion curve.

a: Conversion efficiency formula: $\eta = P_{l, output}/P_{S, output}$ [I – Idler, and S – Signal for this and the following formulas]

b: Conversion efficiency formula: $\eta = 10\log(P_{l, output}/P_{S, input})$

c: Conversion efficiency formula: $\eta = P_{l, output, peak}/P_{S, input}$

d: Conversion efficiency formula: $\eta = 10\log(P_{l, output}/P_{S, output})$
e: Conversion efficiency formula: $\eta = P_{l output}/P_{s input}$

f: Conversion efficiency formula: $\eta = \sum P_{\text{all comb lines}}/P_{\text{pump}}$

g: Conversion efficiency formula: $\eta = \sum P_{\text{side bands}}/P_{\text{pump}}$
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# 3.7 Hybrid waveguiding systems: data table and discussion

**Team:** John Ballato, Peter Dragic, Minhao Pu, Nathalie Vermeulen (team leader), Kresten Yvind

## 3.7.1 Introduction

### 3.7.1.1 Hybrid waveguiding systems and their NLO applications

Optical fibers and on-chip waveguides are often employed for NLO applications as the strong light confinement enabled by these waveguiding structures benefits the efficiency of NLO phenomena. At the same time, NLO researchers have been exploring whether fibers and on-chip waveguides, typically made of glasses or semiconductor materials, can be combined with very different materials, such as low-dimensional materials, metals, organic solids, liquids, gasses, etc. The goal of adding other materials to the waveguiding structures is to modify, and in most cases to enhance, the efficiency of a given NLO process. The resulting hybrid waveguiding systems find applications in the same domains as their ‘bare’ counterparts (see Sections 3.5 – 3.6) but can also acquire other NLO functionalities, depending on the properties of the added material. For example, whereas ‘bare’ fibers have always been the preferred medium when targeting low-loss NLO applications, hybrid fibers enhanced with low-dimensional materials such as carbon nanotubes or graphene can also fulfill absorptive functionalities such as fiber-based saturable absorption in laser cavities with pulsed operation [Liu2020, Teng2020]. As such, the development of hybrid fibers and hybrid on-chip waveguides has allowed combining the best of both worlds, i.e. the intrinsic strengths of the bare waveguiding structures plus the special NLO properties of the added materials. Further details on the importance of NLO hybrid fibers and NLO hybrid on-chip waveguides can be found in several recent review papers (see, for example, [Li2018, Debord2019, Guo2019, Liu2020, Teng2020, Tuniz2021, Steglich2021, Vermeulen2022]).

### 3.7.1.2 Background prior to 2000

#### 3.7.1.2.1 Background for hybrid fibers

Research on NLO hybrid fibers started already in the 1970s, with a focus on hollow fiber capillaries filled with NLO solids [Stevenson1974, Babai1977]. Around the same period, light guidance in fiber capillaries with liquid cores was demonstrated by several groups [Stone1972, Payne1972, Ogilvie1972]. In contrast, laser transmission in fiber capillaries containing gasses became a subject of study from the 1990s onward [Olshanii1993]. Not only can hollow fiber structures be employed for realizing NLO hybrid fibers, but solid-core fibers with their cross-sectional geometry modified by, e.g., side polishing or tapering can also be used for this purpose. This way, the added NLO material can be brought in close proximity to the light-guiding fiber core, such that it can interact with the evanescent tails of the fiber mode. The first demonstrations of this concept date back to the 1980s [Bergh1980, Lamouroux1983, Lacroix1986]. Both the hybrid fibers based on hollow capillaries and those relying on side-polished or tapered solid-core fibers were successfully employed in various NLO experiments before the turn of the century (see, e.g., [Stevenson1974, Kanbara1992, Nesterova1996, Lee1998]). Nevertheless, the research area of NLO hybrid fibers has experienced the strongest growth after 2000, thanks to the emergence of new special fiber structures as well as new exotic materials that can enhance the fibers’ NLO response (see further on).

#### 3.7.1.2.2 Background for hybrid on-chip waveguides

Similarly, as for hybrid fibers, the first hybrid on-chip waveguides developed for NLO applications comprised NLO organics, and this approach allowed demonstrating the EO effect on a silicon chip already in the 1990s [Faderl 1995]. Also here, the evanescent tails of the waveguide mode allowed ‘sensing’ the presence of the NLO organics deposited on top, even when working with a standard strip waveguide geometry [Faderl 1995]. Due to their planar structure, photonic chips in fact provided a very
suitable platform for the deposition of NLO solids on top, whereas NLO liquids and gasses were more
easily combined with hollow fiber structures (see previous Section). Nevertheless, the most important
breakthroughs in the development of hybrid on-chip waveguides would be triggered by major
advancements in both waveguide technology and material science shortly after 2000 (see further on).

### 3.7.1.3 Considerations for hybrid waveguiding systems when performing NLO measurements

When characterizing hybrid fibers and hybrid on-chip waveguides, both the considerations for the bare fibers/waveguides (see Sections 3.5.1.2 and 3.6.1.3) and those for the added materials need to be taken into account. For NLO measurements requiring phase matching, it is important to account for the phase matching conditions of the entire hybrid system. Also interfacial aspects such as (lack of) adhesion of the added materials, uniformity and/or diffusion are important to verify prior to the NLO experiments. From the measured NLO response, the effective nonlinearity for the hybrid system as a whole can be extracted. If, however, one wants to go one step further and assess the contributions from each constituent to the overall NLO response, careful analysis is required: the cross-sectional distribution of the modal power in the hybrid waveguiding structure needs to be evaluated, and this information subsequently fed into a weighted contributions model to extract the individual nonlinear properties of the fiber/waveguide structure and the added material (see, e.g., [Vermeulen2016a] and Appendix of [Vermeulen2016b]). Here, it is also important to keep in mind that the different NLO contributions do not always add up. For example, when studying nonlinear refraction in a silicon waveguide covered with undoped graphene while using excitation wavelengths in the near-IR telecom domain, the silicon will have a positive nonlinearity whereas the graphene top layer will exhibit a negative nonlinearity [Vermeulen2016a, CastelloLurbe2020]. Therefore, in the weighted contributions analysis, it is crucial to implement the correct nonlinearity signs for each of the constituting media. In case the signs are not known upfront, this information can be obtained, for example, using a phase-sensitive NLO technique such as SPM-based spectral broadening and by comparing the NLO response of the hybrid waveguiding structure to that of the bare waveguide/fiber [Vermeulen2016a]. This allows evaluating whether there are nonlinearities of opposite sign present in the hybrid system.

### 3.7.1.4 Description of general table outline

Tables 8A and 8B show a representative list of NLO properties of, respectively, hybrid fibers and hybrid on-chip waveguides taken from the literature since 2000, with the entries arranged in alphabetical order. The selection of works included in the Tables has been based on the general best practices in Section 2 and the considerations outlined above. Taking into account that an extremely large number of material combinations are possible in hybrid systems, this selection has been limited to just a few representative works for different combinations of bare fibers/waveguides with other media systems, and therefore does not provide an extensive overview. The selection also contains a few papers with organic solids, liquids and gasses, although in this article the focus is rather on inorganic solids, as mentioned in the general introduction. The included works nominally report data obtained at room temperature. Tables 8A and 8B are subdivided into “Material properties,” “Measurement details” and “Nonlinear properties.” Within each column the information is given in the order of the header description, and powers of 10 (e.g., $10^{\pm\alpha}$) are written as $E^{\pm\alpha}$ for compactness. “Material properties” include the characteristics of both constituents of the hybrid system, as well as references to the sub-figures in Fig. 8 showing SEM images of the fabricated devices. The peak power values in the Tables are nominally incoupled powers as specified in the papers. The NLO technique used in each of the papers is provided in the “Method” column. As most works report on third-order NLO effects, the focus in the Tables is on third-order NLO parameters such as $|\text{Re}(\gamma_{\text{eff}})|$ and the effective saturation irradiance $I_{\text{sat,eff}}$ together with the saturable loss, extracted from the hybrid system as a whole. That said, also a limited number of papers reporting on second-order NLO parameters are included in the Tables, with their parameter