# Post-2000 nonlinear optical materials and measurements: Data tables and best practices

Nathalie Vermeulen, Daniel Espinosa, Adam Ball, John M Ballato, Phillippe Boucaud, Georges Boudebs, Cecília L a V Campos, Peter D Dragic, Anderson Gomes, Mikko J Huttunen, et al.

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Nathalie Vermeulen, Daniel Espinosa, Adam Ball, John M Ballato, Phillippe Boucaud, et al. Post-2000 nonlinear optical materials and measurements: Data tables and best practices. Journal of Physics: Photonics, In press, 10.1088/2515-7647/ac9e2f. hal-04087192

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Post-2000 nonlinear optical materials and measurements: Data tables
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**Post-2000 Nonlinear Optical Materials**
**and Measurements:**
**Data Tables and Best Practices**

Nathalie Vermeulen,¹,*,◇ Daniel Espinosa,² Adam Ball,³ John Ballato,⁴* Philippe Boucaud,⁵ Georges Boudebs,⁶ Cecília L. A. V. Campos,⁷ Peter Dragic,⁸ Anderson S. L. Gomes,⁷* Mikko J. Huttunen,⁹* Nathaniel Kinsey,³,* Rich Mildren,¹⁰ Dragomir Neshev,¹¹ Lázaro Padilha,¹² Minhao Pu,¹³,* Ray Secondo,³ Eiji Tokunaga,¹⁴ Dmitry Turchinovich,¹⁵,* Jingshi Yan,¹¹ Kresten Yvind,¹³ Ksenia Dolgaleva,² and Eric W. Van Stryland¹⁶,*

(1) Brussels Photonics (B-PHOT), Department of Applied Physics and Photonics (IR-TONA),
Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium

(2) School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON K1N 6N5, Canada

(3) Dept. Of Electrical & Computer Engineering, Virginia Commonwealth University, Richmond, VA, 23284, USA

(4) Dept of Materials Science and Engineering, Clemson University, Clemson, SC 29634, USA

(5) Université Côte d'Azur, CNRS, CRHEA, Rue Bernard Grégory, 06905 Sophia-Antipolis, France

(6) Univ Angers, LPHIA, SFR MATRIX, F-49000 Angers, France

(7) Departamento de Física, Universidade Federal de Pernambuco, 50670-901 Recife-PE, Brazil

(8) Dept. Of Electrical & Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA

(9) Tampere University, Photonics Laboratory, Physics Unit, Tampere FI-33014, Finland

(10) MQ Photonics Research Centre, Macquarie University 2109 NSW Australia

(11) ARC Centre of Excellence for Transformative Meta-Optical Systems (TMOS), Department of Electronic Materials Engineering, Research School of Physics, Australian National University, Canberra, ACT, 2601, Australia

(12) Instituto de Física "Gleb Wataghin", Universidade Estadual de Campinas, Campinas, Sao Paulo, Brazil 13083-970

(13) Department of Electrical and Photonics engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark

(14) Department of Physics, Faculty of Science, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

(15) Fakultät für Physik, Universität Bielefeld, Universitätsstr. 25, 33615 Bielefeld, Germany

(16) CREOL, The College of Optics and Photonics, University of Central Florida, Orlando, FL, USA

* Team leaders for the material categories considered in the article

◇ Corresponding author: Nathalie.Vermeulen@vub.be
**Abstract**

In its 60 years of existence, the field of nonlinear optics has gained momentum especially over the past two decades thanks to major breakthroughs in material science and technology. In this article, we present a new set of data tables listing nonlinear-optical properties for different material categories as reported in the literature since 2000. The papers included in the data tables are representative experimental works on bulk materials, solvents, 0D-1D-2D materials, metamaterials, fiber waveguiding materials, on-chip waveguiding materials, hybrid waveguiding systems, and materials suitable for nonlinear optics at THz frequencies. In addition to the data tables, we also provide best practices for performing and reporting nonlinear-optical experiments. These best practices underpin the selection process that was used for including papers in the tables. While the tables indeed show strong advancements in the field over the past two decades, we encourage the nonlinear-optics community to implement the identified best practices in future works. This will allow a more adequate comparison, interpretation and use of the published parameters, and as such further stimulate the overall progress in nonlinear-optical science and applications.
## List of symbols

$d_{(eff)}$: effective second-order nonlinear coefficient

$dk/dT$: change in wave-number with temperature

$dn/dT$: change in linear refractive index with temperature

$g_{Brillouin}$: Brillouin gain coefficient

$g_{Raman}$: Raman gain coefficient

$I_{sat}(eff)$: (effective) saturation irradiance

$n_0$: linear refractive index

$n_{2(eff)}$: (effective) nonlinear index

$\alpha_0$: linear loss coefficient

$\alpha_2$: two-photon absorption coefficient

$\alpha_3$: three-photon absorption coefficient

$\gamma_{(eff)}$: (effective) nonlinear coefficient

$\Gamma_B$: Brillouin gain factor

$\Gamma_R$: Raman gain factor

$\Delta\alpha$: change in absorption

$\Delta n$: change in refractive index

$\Delta n_g$: change in group index

$\Delta OD$: change in optical density

$\Delta T$: change in pulse duration

$\varepsilon$: dielectric permittivity

$\eta$: conversion efficiency

$\lambda$: wavelength

$\lambda_{pump}$: pump/excitation wavelength

$\lambda_{probe}$: signal/probe wavelength

$\sigma$: nonlinear conductivity

$\tau_{pump}$: pump/excitation pulse duration

$\tau_{probe}$: signal/probe pulse duration

$\chi^{(2)}$: second-order susceptibility

$\chi^{(3)}$: third-order susceptibility

$\omega$: frequency

## List of abbreviations

0D: zero-dimensional

1D: one-dimensional

2D: two-dimensional

2FBS: two-frequency beat signal

2PA: two-photon absorption

3PA: three-photon absorption

3WM: three-wave mixing

BD: beam deflection

BIC: bound states in the continuum

CAIBE: chemically assisted ion-beam etching

CDQW: coupled double quantum well

ChG: chalcogenide glass

CVD: chemical vapor deposition

CVT: chemical vapor transport

CW: continuous-wave

dB: decibels

DB: diffusion bonded

DFG: difference-frequency generation
EFISH: electric-field-induced second-harmonic generation

ENZ: epsilon near zero

EO: electro-optic

ER: ellipse rotation

FCA: free-carrier absorption

FEL: free-electron laser

FEOS: free-space electrooptic sampling

FIB: focused ion beam

FWHM: full width at half maximum

FWM: four-wave mixing

GO: graphene oxide

GVD: group velocity dispersion

GVM: group velocity mismatch

HRS: hyper-Rayleigh scattering

HVPE: hydride vapor phase epitaxy

HW1/e²M: half width at 1/e² maximum

IGA: induced-grating autocorrelation

IR: infrared

IRS: inverse Raman scattering

ISBT: intersubband transitions

ITO: indium tin oxide

LED: light emitting diode

LIDAR: light detection and ranging

LN: lithium niobate

LO: longitudinal optical mode

LPCVD: low-pressure chemical vapor deposition

LSPR: localized surface plasmon resonance

MBE: molecular-beam epitaxy

MOCVD: metal-organic chemical vapor deposition

MOVPE: metal-organic vapor-phase epitaxy

MQWs: multiple quantum wells

NA: numerical aperture

NLA: nonlinear absorption

NLO: nonlinear optics / nonlinear-optical

NLR: nonlinear refraction

NSM: nanostructured material

NZI: near-zero index

OC: optically contacted

OP: orientation patterned

OPA: optical parametric amplification

OPG: optical parametric generation

OPO: optical parametric oscillation

PCF: photonic-crystal fiber

PDI: periodic domain inversion

PECVD: plasma-enhanced chemical vapor deposition

PhC: photonic crystal

PI: periodically inverted

PIC: photonic integrated circuit

QCSE: quantum-confined Stark effect

QD: quantum dot

QPM: quasi-phase-matching

QW: quantum well

rGO: reduced graphene oxide

RIE: reactive ion etching

SA: saturable absorption
SBS: stimulated Brillouin scattering

SCG: supercontinuum generation

SEED: self-electro-optic effect device

SEM: scanning electron microscope

SESAM: semiconductor saturable absorbing mirror

SFG: sum-frequency generation

SHG: second-harmonic generation

SLR: surface lattice resonance

SOI: silicon-on-insulator

SpBS: spontaneous Brillouin scattering

SPDC: spontaneous parametric down-conversion

SPM: self-phase modulation

SpRS: spontaneous Raman scattering

SRR: split-ring resonator

SRS: stimulated Raman scattering

SRTBC: spectrally resolved two-beam coupling

SWCNT: single-wall carbon nanotube

TDS: time-domain spectroscopy

TE: transverse-electric

THG: third-harmonic generation

TM: transverse-magnetic

TMD: transition metal dichalcogenide

TO: transverse optical mode

TPFP: tilted pulse front pumping

TRI: time-resolved interferometry

WZ: wurtzite

XPM: cross-phase modulation

ZB: zinc blende

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Table of contents

<table><tr><td>1</td><td>General introduction</td><td>10</td></tr><tr><td>1.1</td><td>Fused silica nonlinearity</td><td>12</td></tr><tr><td>2</td><td>NLO characterization techniques and their best practices</td><td>15</td></tr><tr><td>2.1</td><td>General best practices to obtain and report high-quality NLO measurement data</td><td>15</td></tr><tr><td>2.2</td><td>Technique-specific best practices</td><td>17</td></tr><tr><td>2.2.1</td><td>Best practices for second-order NLO techniques</td><td>17</td></tr><tr><td>2.2.1.1</td><td>Second-order wave mixing</td><td>17</td></tr><tr><td>2.2.1.2</td><td>Second-order nonlinear imaging</td><td>17</td></tr><tr><td>2.2.2</td><td>Best practices for third-order NLO techniques</td><td>18</td></tr><tr><td>2.2.2.1</td><td>Third-order parametric wave mixing</td><td>18</td></tr><tr><td>2.2.2.2</td><td>Raman/Brillouin gain measurement techniques</td><td>19</td></tr><tr><td>2.2.2.3</td><td>Third-order polarization rotation</td><td>21</td></tr><tr><td>2.2.2.4</td><td>Beam distortion/absorption</td><td>21</td></tr><tr><td>2.2.2.5</td><td>Nonlinear interferometry</td><td>24</td></tr><tr><td>2.2.2.6</td><td>Third-order nonlinear imaging</td><td>25</td></tr><tr><td>2.2.3</td><td>Remarks on choice of NLO technique</td><td>25</td></tr><tr><td>3</td><td>Data tables and discussion</td><td>27</td></tr><tr><td>3.1</td><td>Bulk materials: data table and discussion</td><td>29</td></tr><tr><td>3.1.1</td><td>Introduction</td><td>29</td></tr><tr><td>3.1.1.1</td><td>Bulk materials and their NLO applications</td><td>29</td></tr><tr><td>3.1.1.2</td><td>Background prior to 2000</td><td>29</td></tr><tr><td>3.1.1.2.1</td><td>Background for insulators/dielectrics</td><td>29</td></tr><tr><td>3.1.1.2.2</td><td>Background for semiconductors</td><td>30</td></tr><tr><td>3.1.1.2.3</td><td>Background for conductors</td><td>31</td></tr><tr><td>3.1.1.3</td><td>Considerations for bulk materials when performing NLO measurements</td><td>31</td></tr><tr><td>3.1.1.4</td><td>Description of general table outline</td><td>31</td></tr><tr><td>3.1.2</td><td>Discussion</td><td>32</td></tr><tr><td>3.1.2.1</td><td>Advancement since 2000 and remaining challenges</td><td>32</td></tr><tr><td>3.1.2.1.1</td><td>Advancement and challenges for insulators/dielectrics</td><td>32</td></tr><tr><td>3.1.2.1.2</td><td>Advancement and challenges for semiconductors</td><td>33</td></tr><tr><td>3.1.2.1.3</td><td>Advancement and challenges for conductors</td><td>33</td></tr><tr><td>3.1.2.2</td><td>Recommendations for future works on bulk materials</td><td>34</td></tr><tr><td>3.1.3</td><td>Data table for bulk materials</td><td>35</td></tr><tr><td>3.2</td><td>Solvents: data table and discussion</td><td>62</td></tr><tr><td>3.3</td><td>OD-1D-2D materials: data table and discussion</td><td>69</td></tr></table>
<table><tr><td>3.3.1</td><td>Introduction</td><td>69</td></tr><tr><td>3.3.1.1</td><td>0D-1D-2D materials and their NLO applications</td><td>69</td></tr><tr><td>3.3.1.2</td><td>Background prior to 2000</td><td>70</td></tr><tr><td>3.3.1.2.1</td><td>Background for 0D materials</td><td>70</td></tr><tr><td>3.3.1.2.2</td><td>Background for 1D materials</td><td>70</td></tr><tr><td>3.3.1.2.3</td><td>Background for 2D materials</td><td>71</td></tr><tr><td>3.3.1.3</td><td>Considerations for 0D-1D-2D materials when performing NLO measurements</td><td>71</td></tr><tr><td>3.3.1.4</td><td>Description of general table outline</td><td>72</td></tr><tr><td>3.3.2</td><td>Discussion</td><td>72</td></tr><tr><td>3.3.2.1</td><td>Advancement since 2000 and remaining challenges</td><td>72</td></tr><tr><td>3.3.2.1.1</td><td>Advancement and challenges for 0D materials</td><td>72</td></tr><tr><td>3.3.2.1.2</td><td>Advancement and challenges for 1D materials</td><td>73</td></tr><tr><td>3.3.2.1.3</td><td>Advancement and challenges for 2D materials</td><td>73</td></tr><tr><td>3.3.2.2</td><td>Recommendations for future works on 0D-1D-2D materials</td><td>74</td></tr><tr><td>3.3.3</td><td>Data table for 0D-1D-2D materials</td><td>75</td></tr><tr><td>3.4</td><td>Metamaterials: data table and discussion</td><td>100</td></tr><tr><td>3.4.1</td><td>Introduction</td><td>100</td></tr><tr><td>3.4.1.1</td><td>Metamaterials definitions</td><td>100</td></tr><tr><td>3.4.1.2</td><td>Mechanisms of nonlinearity enhancement</td><td>100</td></tr><tr><td>3.4.1.3</td><td>Historical development</td><td>102</td></tr><tr><td>3.4.1.4</td><td>Metamaterial-related best practices and considerations when performing NLO measurements</td><td>103</td></tr><tr><td>3.4.1.5</td><td>Description of general table outline</td><td>103</td></tr><tr><td>3.4.2</td><td>Discussion</td><td>105</td></tr><tr><td>3.4.2.1</td><td>Advancements and remaining challenges for metamaterials</td><td>105</td></tr><tr><td>3.4.2.2</td><td>Recommendations for future works on metamaterials</td><td>106</td></tr><tr><td>3.4.3</td><td>Data table for metamaterials</td><td>107</td></tr><tr><td>3.5</td><td>Fiber waveguiding materials: data table and discussion</td><td>119</td></tr><tr><td>3.5.1</td><td>Introduction</td><td>119</td></tr><tr><td>3.5.1.1</td><td>Background information</td><td>119</td></tr><tr><td>3.5.1.2</td><td>Considerations for fibers when performing NLO measurements</td><td>119</td></tr><tr><td>3.5.1.3</td><td>Description of general table outline</td><td>120</td></tr><tr><td>3.5.2</td><td>Discussion</td><td>121</td></tr><tr><td>3.5.2.1</td><td>Advancements and remaining challenges for fibers</td><td>121</td></tr><tr><td>3.5.2.2</td><td>Recommendations for future works on fibers</td><td>121</td></tr><tr><td>3.5.3</td><td>Data table for fiber waveguiding materials</td><td>123</td></tr></table>
<table><tr><td>3.6</td><td>On-chip waveguiding materials: data table and discussion</td><td>129</td></tr><tr><td>3.6.1</td><td>Introduction</td><td>129</td></tr><tr><td>3.6.1.1</td><td>On-chip waveguiding materials and their NLO applications</td><td>129</td></tr><tr><td>3.6.1.2</td><td>Background prior to 2000</td><td>129</td></tr><tr><td>3.6.1.2.1</td><td>Background for on-chip waveguide materials with second-order nonlinearity</td><td>130</td></tr><tr><td>3.6.1.2.2</td><td>Background for on-chip waveguide materials with third-order nonlinearity</td><td>131</td></tr><tr><td>3.6.1.3</td><td>Considerations for on-chip waveguides when performing NLO measurements</td><td>132</td></tr><tr><td>3.6.1.4</td><td>Description of general table outline</td><td>133</td></tr><tr><td>3.6.2</td><td>Discussion</td><td>134</td></tr><tr><td>3.6.2.1</td><td>Advancement since 2000 and remaining challenges</td><td>134</td></tr><tr><td>3.6.2.1.1</td><td>Advancement and challenges for on-chip waveguiding materials with second-order nonlinearity</td><td>134</td></tr><tr><td>3.6.2.1.2</td><td>Advancement and challenges for on-chip waveguiding materials with third-order nonlinearity</td><td>136</td></tr><tr><td>3.6.2.2</td><td>Recommendations for future works on on-chip waveguiding materials</td><td>138</td></tr><tr><td>3.6.3</td><td>Data table for on-chip waveguiding materials</td><td>140</td></tr><tr><td>3.7</td><td>Hybrid waveguiding systems: data table and discussion</td><td>177</td></tr><tr><td>3.7.1</td><td>Introduction</td><td>177</td></tr><tr><td>3.7.1.1</td><td>Hybrid waveguiding systems and their NLO applications</td><td>177</td></tr><tr><td>3.7.1.2</td><td>Background prior to 2000</td><td>177</td></tr><tr><td>3.7.1.2.1</td><td>Background for hybrid fibers</td><td>177</td></tr><tr><td>3.7.1.2.2</td><td>Background for hybrid on-chip waveguides</td><td>177</td></tr><tr><td>3.7.1.3</td><td>Considerations for hybrid waveguiding systems when performing NLO measurements</td><td>178</td></tr><tr><td>3.7.1.4</td><td>Description of general table outline</td><td>178</td></tr><tr><td>3.7.2</td><td>Discussion</td><td>179</td></tr><tr><td>3.7.2.1</td><td>Advancement since 2000 and remaining challenges</td><td>179</td></tr><tr><td>3.7.2.1.1</td><td>Advancement and challenges for hybrid fibers</td><td>179</td></tr><tr><td>3.7.2.1.2</td><td>Advancement and challenges for hybrid on-chip waveguides</td><td>180</td></tr><tr><td>3.7.2.2</td><td>Recommendations for future works on hybrid waveguiding systems</td><td>181</td></tr><tr><td>3.7.3</td><td>Data table for hybrid waveguiding systems</td><td>182</td></tr><tr><td>3.8</td><td>THz NLO: data table and discussion</td><td>191</td></tr><tr><td>3.8.1</td><td>Introduction</td><td>191</td></tr><tr><td>3.8.1.1</td><td>THz NLO mechanisms</td><td>191</td></tr><tr><td>3.8.1.2</td><td>Brief history of THz NLO research</td><td>192</td></tr><tr><td>3.8.1.3</td><td>Considerations for THz NLO research</td><td>193</td></tr></table>
<table><tr><td>3.8.1.4</td><td>Description of general table outline</td><td>193</td></tr><tr><td>3.8.2</td><td>Discussion</td><td>194</td></tr><tr><td>3.8.2.1</td><td>Advancement and remaining challenges in THz NLO research</td><td>194</td></tr><tr><td>3.8.2.2</td><td>Recommendations for future works on THz NLO research</td><td>195</td></tr><tr><td>3.8.3</td><td>Data table for THz NLO</td><td>196</td></tr><tr><td>4</td><td>Conclusion</td><td>206</td></tr><tr><td>5</td><td>Description of author contributions</td><td>207</td></tr></table>
# 1 General introduction

The idea of composing a new set of data tables for nonlinear-optical (NLO) materials emerged in 2020 on the occasion of 60 years of NLO research [Franken1961, Kaiser1961]. In those 60 years, the field has witnessed tremendous growth, and several NLO data tables were published before the turn of the century [Robinson1967, Chase1994, Van Stryland1994, Sutherland1996, Dmitriev1999]. After the year 2000, additional data tables were introduced for specific material types [Nikogosyan2005, Smith2018], but a data table that focuses on the post-2000 NLO research developments for a wide range of materials has not yet been presented. Nevertheless, there have been major advances in materials science and technology since 2000, and these have also accelerated the overall progress in NLO research. Whereas the idea of creating a new set of NLO data tables was originally introduced by John Dudley, we further elaborated on it along the following approach: the data tables presented here have been composed based on a representative set of experimental works published since 2000. In other words, the list of publications included in the table is not comprehensive. We mostly focused on experimental papers that not only provided NLO coefficients, but also reported experimental parameters that give the context and limits of validity for using the quoted coefficient values. In this regard, we also listed best practices for performing and reporting NLO experiments. Some of these best practices are appropriate for any NLO measurement, while others are specific for the chosen NLO characterization technique, e.g., second-harmonic generation (SHG), Z-scan, four-wave mixing (FWM), etc. In turn, many of these NLO techniques are appropriate only for specific categories of NLO materials: bulk materials, 0D-1D-2D materials, metamaterials, fiber waveguiding materials, on-chip waveguiding materials, and/or hybrid waveguiding systems. Both the NLO techniques and the material categories are defined in more detail in the specific devoted sections. With this work, besides providing a set of NLO data tables focused on the progress since 2000, we also aim at stimulating the use of the listed best practices in future NLO publications to allow a better comparison, interpretation and use of the published parameters. The long-term goal of this article is to help advance the development of innovative NLO materials, devices and systems for real-life applications in optical data communication, signal processing, metrology, medical imaging, sensing, lasers and laser wavelength conversion, quantum light generation, and many other areas.

Most of the NLO materials listed in the data tables are solids, but we also included some solvents as they are often used as reference materials in NLO measurements or for preparing solutions or dispersions. However, we did not consider organic/polymeric NLO materials since these are so numerous that tabulating them is outside the scope of this work. Gases are not included either, except for a few examples in the hybrid waveguiding systems category. More specifics of what is and is not included are given in the respective material category sections. We point out that these will be ‘living’ data tables that can be updated, so the materials that are currently absent might be added in the future. To build the data tables presented here, we started by identifying the different material categories while also listing the different NLO techniques and their associated best practices. We then performed a literature search for experimental NLO papers published since 2000 and made a selection based on the listed best practices. Note that we did not limit our search to optical-wavelength-based experiments only but also included works on THz NLO. Finally, we filled out the data in dedicated table templates per material category. To minimize errors, the data filled out by each co-author were also cross-checked by another co-author. Hence, the parameter values listed in the tables should match with those provided in the selected papers.

The main NLO coefficients that we considered for composing the data tables are: the second-order nonlinear susceptibility $\chi^{(2)}$, the effective second-order nonlinear coefficient $d_{\text{eff}}$, the third-order nonlinear susceptibility $\chi^{(3)}$, the effective nonlinear index $n_{2,\text{eff}}$, the effective third-order nonlinear coefficient $\gamma_{\text{eff}}$, the two- and three-photon absorption coefficients $\alpha_2, \alpha_3$, the saturation irradiance $I_{\text{sat}}$ specified for saturation of the linear absorption, and the Raman and Brillouin gain coefficients $g_{\text{Raman}}, g_{\text{Brillouin}}$. Further information about the underlying physics for each of these coefficients can be found,
for example, in [Sutherland1996, Bloembergen1996, Shen2002, Stegeman2012, Boyd2020]. We have not tabulated hyperpolarizabilities, photorefractive effects, electro-optic effects, stimulated polariton scattering, nor cascaded NLO processes. Note that the meaning of ‘effective’ is different for $d_{eff}$ than for $n_{2,eff}$ and Re($\gamma_{eff}$). For $d_{eff}$ the subscript ‘effective’ implies that the coefficient comprises all contributions from the different tensor components being studied during the experiment. In contrast, $n_{2,eff}$ and Re($\gamma_{eff}$) are effective coefficients in the sense that they might not be solely due to bound-electronic nonlinear transitions as one would expect for a ‘pure’ $n_2$ and Re($\gamma$), but instead could also contain contributions from, e.g., nuclear and/or thermal effects (see also Section 2.1). Finally, we point out that some works in the data tables do not only report a NLO coefficient but also provide NLO conversion efficiencies $\eta$ and bandwidths in case techniques such as SHG, THG, Raman, Brillouin and FWM are used. These parameters are then also tabulated for those works since they are important to assess the practical use of the material in wavelength conversion applications.

The outline of the manuscript is as follows: in Section 2 we list various NLO measurement techniques and describe some best practices for performing and reporting NLO experiments. Here we make a distinction between best practices that can be applied in general and those that are technique-specific. In Section 3 we present the actual data tables per material category, together with background information of the status prior to 2000, a brief discussion of the advancements since 2000 and of the remaining challenges, and some recommendations for future works. Finally, we summarize and conclude in Section 4.

As an intermezzo before the main body of the manuscript, we want to visit what is arguably the single most studied material in NLO, namely fused silica. We think this digression is instructive on the difficulties inherent in making NLO measurements as well as in obtaining a complete theoretical understanding. It is also of significant importance because fused silica has been used as a reference in many studies of other materials, i.e., if the reference value is in error, so is the reported value of the measured material. This history of measurements of the nonlinear refraction in fused silica is also illustrative of how NLO materials properties are not as well understood as one often assumes.

## References of Section 1

[Bloembergen1996] Bloembergen N, 1996, *Nonlinear Optics, 4th Edition* (World Scientific Printing)

[Boyd2020] Boyd R, 2020, *Nonlinear Optics, 4th Edition* (Academic Press)

[Chase1994] Chase L and Van Stryland E, *Nonlinear Refractive Index: inorganic materials*, in: M. Weber (Ed.), 1994, *Handbook of Laser Science and Technology*, supplement 2, Section 8, 269-288 (CRC Press)

[Dmitriev1999] Dmitriev V G, Gurzadyan G G, and Nikogosyan D N, 1999, *Handbook of Nonlinear Optical Crystals, 3rd Revised Edition* (Springer-Verlag, Berlin-Heidelberg-New York)

[Franken1961] Franken P A, Hill A E, Peters C W, and Weinreich G, *Generation of Optical Harmonics*, 1961, Phys. Rev. Lett. 7, 118

[Kaiser1961] Kaiser W and Garrett C G B, *Two-Photon Excitation in CaF$_2$:Eu$^{2+}$*, 1961, Phys. Rev. Lett. 7, 229-231

[Nikogosyan2005] Nikogosyan D N, 2005, *Nonlinear Optical Crystals* (Springer-Verlag, Berlin-Heidelberg-New York)

[Robinson1967] Robinson F N H, *Nonlinear optical coefficients*, 1967, The Bell System Technical Journal 46, 913-956

[Shen2002] Shen Y R, 1992, *The Principles of Nonlinear Optics* (John Wiley & Sons, Hoboken, NJ)

[Smith2018] Smith A V, 2018, *Crystal Nonlinear Optics, 2nd Edition*, (AS-Photonics, Albuquerque), link to software program SNLO: https://as-photonics.com/products/snlo/

[Stegeman2012] Stegeman G I and Stegeman R A, 2012, *Nonlinear Optics: Phenomena, Materials and Devices* (John Wiley & Sons, Hoboken, NJ)

[Sutherland1996] Sutherland R L, 1996, *Handbook of Nonlinear Optics* (Marcel Dekker, New York)

[Van Stryland1994] Van Stryland E and Chase L, *Two Photon Absorption: inorganic materials*, in: M. Weber (Ed.), 1994, *Handbook of Laser Science and Technology*, supplement 2, Section 8, 299-328 (CRC Press)
## 1.1 Fused silica nonlinearity

To illustrate the difficulties in reporting accurate values of nonlinear parameters, let us look at $n_2$ of fused silica (see Table 1 below). Fused silica is often used as a reference for determining the $n_2$, or $n_{2,eff}$ of other materials. We use $n_{2,eff}$ since while the bound-electronic nonlinearity is essentially instantaneous, other nonlinearities, including those involving nuclei, depend on the pulsewidth used. The values found in the literature for fused silica do not always agree, and, of course, there is dispersion. [Milam1998] attempted to determine the best experimental values at various wavelengths by taking a weighted average, determined by experimental error bars, of the published values up to 1998. This approach gave a value of ~2.7 x 10⁻²⁰ m²/W in the near-infrared (IR) with little dispersion from 1–1.6µm, with values increasing toward the UV. As summarized in [Agrawal2013] the nuclear (Raman) contribution to the nonlinear refractive index of fused silica may be of the order of ~20% as first discussed by the seminal work of [Hellwarth1975, Hellwarth1977]. Under this assumption, the bound-electronic nonlinearity is $n_2 \approx 2.2 \times 10^{-20}$ m²/W. However, the nuclear contribution estimated in other publications varies from 13% [Smolorz1999] to 26% [Heiman1979]. Following [Agrawal2013], for pulses much longer than ~1 ps, the nuclear contribution should be fully established. However, [Santran2004] calculates a response function, from which they determine a pulsewidth dependence curve indicating that the nuclear contribution would not be fully developed until >10 ps. It appears that [Stolen1992] was the first to predict the pulsewidth dependence of $n_{2,eff}$ for FS, showing the effective Raman contribution decreasing for pulsewidths ≤100 fs, going to zero for a pulsewidth of ~30 fs, and then predicting that it actually turns negative for even shorter pulses. These two publications are the only ones we find that present the projected pulsewidth dependence for $n_{2,eff}$. Note that when using femtosecond experiments, the finite duration/finite bandwidth of the pulses results in spectral-filtering effects on the intrinsic material response that can result in difficulties in interpreting the experimental data [McMorrow1990]. For much longer pulses (>1ns) electrostriction can become important and can further significantly increase the measured $n_{2,eff}$. This is particularly important in fibers [Buckland1996]. Additionally, more recent measurements tend to use shorter pulses and yield smaller values of $n_{2,eff}$ (see Table 1). [Buckland1996] also calculates that $n_{2,eff}$ is reduced by a factor of ⁸/₉ due to the polarization randomization in fibers as indicated in Table 1. We also note that measurements of $n_{2,eff}$ reported for fibers have rarely been corrected for any modal overlap with the cladding. In principle, there could be a small systematic difference between fiber measurements and bulk measurements, but given the spread of data it is challenging to discern.

Among the several publications where attempts were made to measure the temporal response function, e.g., [Kang1996, Aber2000, Santran2004, Patwardhan2021], the only one to see a temporal dependence is [Smolorz1999], which used "spectrally-resolved two-beam coupling" with 18 fs, 800 nm pulses. They observed a small oscillatory signal in fused silica lasting for 100s of femtoseconds after excitation indicating a ~13% nuclear contribution to $n_{2,eff}$.

In all the papers of which we are aware where fused silica is used as a reference, its $n_{2,eff}$ is assumed constant. For all the materials reported in the tables in this publication that have been referenced to FS, this adds to the uncertainty of the reported $n_{2,eff}$ values. For very short pulses, ~10 fs, the nonlinear response could be reduced by as much as the above quoted fractions of the Raman contribution, the highest estimate being 26%.

We are not aware of any direct measurement of the variation of $n_{2,eff}$ with pulsewidth in the picosecond to femtosecond regime to determine its time dependence. Future measurements of the temporal dependence of the nonlinear response of fused silica and other materials would be quite useful, as has been done for solvents (see Section 3.2).
<table><caption>**Table 1:** Nonlinear refractive index of fused silica giving some historical references to early works as well as a representative group of more recent publications (not inclusive) – listed in order of year published. Note: fused silica is high purity synthetic glass (amorphous SiO₂) and different from naturally occurring or synthetic quartz (crystalline α-SiO₂). All measurements listed use linearly polarized inputs except where noted. Legend for superscripts: see below the table. The following abbreviations have been used: de-pol=de-polarized; pol-maint=polarization maintaining; ER=ellipse rotation; SF-Pcr self-focusing using the critical power for self-focusing, Pcr; Freq Mix=frequency mixing; TRI=time-resolved interferometry; SPM self-phase modulation; 3WM=three-wave mixing; XPM=cross-phase modulation; 2FBS=two frequency beat signal; Multiple=multiple techniques were used in this compilation of publication data; SRTBC=spectrally resolved two-beam coupling; IGA=induced-grating autocorrelation-based upon time-delayed four-beam coupling in a photorefractive crystal</caption><thead><tr><th>Method</th><th>n<sub>2,eff</sub><br>(x10<sup>-20</sup> m<sup>2</sup>/W)</th><th>λ (nm)</th><th>Fiber/Bulk</th><th>Pulse width</th><th>Notes</th><th>Ref.</th></tr></thead><tbody><tr><td>ER</td><td>3.2</td><td>694</td><td>bulk</td><td>13 ns</td><td>fused quartz</td><td>[Owyoung1972, 1973]</td></tr><tr><td>SF Pcr</td><td>3.94</td><td>1064</td><td>bulk</td><td>30 ps</td><td></td><td>[Smith1975]</td></tr><tr><td>Freq Mix</td><td>5.2</td><td>~525</td><td>bulk</td><td>3 ns</td><td></td><td>[Levenson1974]</td></tr><tr><td>TRI</td><td>2.73</td><td>1064</td><td>bulk</td><td>125 ps</td><td></td><td>[Milam1976]</td></tr><tr><td>TRI</td><td>2.73</td><td>1064</td><td>bulk</td><td>100-150 ps</td><td></td><td>[Weber1978]</td></tr><tr><td>SPM</td><td>2.7; 3.3</td><td>515</td><td>100 m fiber</td><td>90 ps</td><td>2nd entry x9/8</td><td>[Stolen1978]</td></tr><tr><td>3WM</td><td>2.4</td><td>1064</td><td>bulk</td><td>3 ns</td><td>CS<sub>2</sub> used as ref</td><td>[Adair1992]</td></tr><tr><td>SPM</td><td>2.36; 2.66</td><td>1319</td><td>250 m fiber</td><td>110 ps</td><td>2nd entry x9/8</td><td>[Kim1994]</td></tr><tr><td>XPM</td><td>2.48; 2.79</td><td>1550</td><td>fiber</td><td>CW</td><td>1% F doping</td><td>[Kato1995]</td></tr><tr><td>2FBS</td><td>2.2; 2.5<sup>#</sup></td><td>1550</td><td>fiber</td><td>CW</td><td>2nd entry x9/8</td><td>[Boskovic1996]</td></tr><tr><td>XPM</td><td>2.47</td><td>1550</td><td>fiber</td><td>CW</td><td>de-pol input<br>no x9/8</td><td>[Wada1996]</td></tr><tr><td>Z-scan</td><td>2.14</td><td>1064</td><td>bulk</td><td>30 ps</td><td></td><td>[DeSalvo1996]</td></tr><tr><td>Z-scan</td><td>2.24</td><td>532</td><td>bulk</td><td>22 ps</td><td></td><td>[DeSalvo1996]</td></tr><tr><td>Z-scan</td><td>2.41</td><td>355</td><td>bulk</td><td>17 ps</td><td></td><td>[DeSalvo1996]</td></tr><tr><td>Z-scan</td><td>7.8</td><td>266</td><td>bulk</td><td>15 ps</td><td></td><td>[DeSalvo1996]</td></tr><tr><td>Multiple</td><td>2.56</td><td>800-<br>1550</td><td>bulk</td><td>ps to ns</td><td>compilation of<br>ref. data</td><td>[Milam1998]</td></tr><tr><td>SRTBC</td><td>2.3</td><td>~800</td><td>bulk</td><td>18 fs</td><td></td><td>[Smolorz1999, 2000]</td></tr><tr><td>IGA</td><td>2.44</td><td>1064</td><td>24 m fiber<br>pol-maint</td><td>53 ps</td><td>no x9/8</td><td>[Garcia2003]</td></tr><tr><td>IGA</td><td>2.2; 2.5</td><td>1064</td><td>23 m fiber</td><td>50-70 ps</td><td>2nd entry x9/8</td><td>[Oguama2005a]</td></tr><tr><td>IGA</td><td>1.81; 2.04</td><td>1064</td><td>~100 m fiber</td><td>56 ps</td><td>2nd entry x9/8</td><td>[Oguama2005b]</td></tr><tr><td>IGA</td><td>2.22</td><td>1064</td><td>short fiber<br>pol-maint</td><td>50-70 ps</td><td>no x9/8</td><td>[Oguama2005c]</td></tr><tr><td>ER</td><td>2.5</td><td>775</td><td>bulk</td><td>150 fs</td><td></td><td>[Miguez2015]</td></tr><tr><td>SPM</td><td>2.1; 2.4</td><td>1550</td><td>fiber</td><td>telecom</td><td>Vascade fiber</td><td>[Makovejs2016]</td></tr><tr><td>SRTBC</td><td>1.94</td><td>2300</td><td>bulk</td><td>&gt;65 fs</td><td></td><td>[Patwardhan2021]</td></tr><tr><td>SRTBC</td><td>2.0</td><td>3500</td><td>bulk</td><td>&gt;65 fs</td><td></td><td>[Patwardhan2021]</td></tr></tbody></table>

# Values should be reduced by 16% [Smolorz1999] due to electrostrictive contribution estimated by [Buckland1996].

References of Section 1.1

[Aber2000] Janice E. Aber, Maurice C. Newstein, and Bruce A. Garetz, 2000, Femtosecond optical Kerr effect measurements in silicate glasses, J. Opt. Soc. Am. B 17, 120-127.

[Adair1992] R. Adair, L. L. Chase, and S. A. Payne, 1992, Dispersion of the nonlinear refractive index of optical crystals, Opt. Materials, 1, 185-194.

[Agrawal2013] G. P. Agrawal, 2013, Nonlinear fiber optics, Fifth ed. (Academic Press).

[Boskovic1996] A. Boskovic, S. V. Chernikov, and J. R. Taylor, L. Gruner-Nielsen and O. A. Levring, 1996, Direct continuous-wave measurement of n2 in various types of telecommunication fiber at 1.55 µm, Opt. Lett. 21, 1966-8.

[Buckland1996] Eric L. Buckland and Robert W. Boyd, 1996, Electrostrictive contribution to the intensity-dependent refractive index of optical fibers, Opt. Lett. 21, 1117-9.
[DeSalvo1996] R. DeSalvo, A. Said, D. Hagan, and E. Van Stryland, 1996, Infrared to Ultraviolet Measurements of 2-Photon Absorption and n₂ in Wide Bandgap Solids, JQE QE-32, 1324-1333.

[Garcia2003] H. Garcia, A. M. Johnson, F. A. Oguama, and S. Trivedi, 2003, A new approach to the measurement of the nonlinear refractive index of short (~25 m) lengths of silica and erbium doped fibers, Opt. Lett. 28, 1796-1798.

[Heinman1979] D. Heiman, R.W. Hellwarth, D.S. Hamilton, 1979, Raman Scattering and Nonlinear Refractive Index Measurements of Optical Glasses, J. Non-Crystalline Solids 34, 63-79.

[Hellwarth1975] Robert Hellwarth, Joel Cherlow, and Tien-Tsai Yang, 1975, Origin and frequency dependence of nonlinear optical susceptibilities of glasses, Phys. Rev. B 11, 964-7.

[Hellwarth1977] R. Hellwarth, 1977, Third-order optical susceptibilities of liquids and solids, Progress in Quantum Electronics 5, 1-68.

[Kang1996] I. Kang, S. Smolorz, T. Krauss, F. Wise, B. G. Aitken and N. F. Borrelli, 1996, Time-domain observation of nuclear contributions to the optical nonlinearities of glasses, Phys. Rev. B, 54, 641-644.

[Kato1995] T. Kato, Y. Suetsugu, M. Takagi, E. Sasaoka, and M. Nishimura, 1995, Opt. Lett. 20, 988.

[Kim1994] K. S. Kim, R. H. Stolen, W. A. Reed, and K. W. Quoi, 1994, Measurement of the nonlinear index of silica-core and dispersion-shifted fibers, Opt. Lett. 19, 257.

[Levenson1974] Marc D. Levenson, 1974, Feasibility of Measuring the Nonlinear Index of Refraction by Third-Order Frequency Mixing, J. Quant. Elect. 10, 110-115.

[Makovejs 2016] Sergejs Makovejs, John D. Downie, Jason E. Hurley, Jeffrey S. Clark, Ioannis Roudas, Clifton C. Roberts, Hazel B. Matthews, Florence Palacios, David A. Lewis, Dana T. Smith, Paul G. Diehl, Jeffery J. Johnson, Christopher R. Towery, and Sergey Y. Ten, J., 2016, Towards Superior Transmission Performance in Submarine Systems: Leveraging UltraLow Attenuation and Large Effective Area, Lightwave Tech, 34, 114-120.

[Miguez2015] M. L. Miguez, E. C. Barbano, J. A. Coura, S. C. Zílio, and L. Misoguti, 2015, Nonlinear ellipse rotation measurements in optical thick samples, Appl. Phys. B, 120, 653-658.

[Milam1976] D. Milam and M. J. Weber, 1976, Measurement of nonlinear refractive index coefficients using time resolved interferometry: application to optical materials for high power neodymium lasers, J. Appl. Phys., 47, 2497-2501.

[Milam1998] D. Milam, 1998, Review and assessment of measured values of the nonlinear refractive-index coefficient of fused silica, Appl. Opt. 37, 546.

[Oguama2005a] F.A. Oguama, A. Tchouassi, A. M. Johnson, and H. Garcia, 2005, Numerical modeling of the induced grating autocorrelation for studying optical fiber nonlinearities in the picosecond regime, Appl. Phys. Lett. 86, 091101-1-3.

[Oguama2005b] F. A. Oguama, H. Garcia, and A. M. Johnson, 2005, Simultaneous measurement of the Raman gain coefficient and the nonlinear refractive index of optical fibers: theory and experiment, J. Opt. Soc. Am. B 22, 426-436

[Oguama2005c] F. A. Oguama, A. M. Johnson, and W. Reed, 2005, Measurement of the nonlinear coefficient of Er-Al-Ge doped fibers as a function of the doping profile, using the photorefractive beam coupling technique, J. Opt. Soc. Am. B, 22, 1600-1604.

[Owyoung1972] Adelbert Owyoung, R. W. Hellwarth and Nicholas George, 1972, Intensity-Induced Changes in Optical Polarizations in Glasses, Phys. Rev. B 5, 628-633.

[Owyoung1973] Adelbert Owyoung, 1973, Ellipse Rotation Studies in Laser Host Materials, IEEE J. Quant. Elect. 9, 1164-9.

[Patwardhan2021] Gauri N. Patwardhan, Jared S. Ginsberg, Cécilia Y. Chen, M. Mehdi Jadidi, and Alexander L. Gaeta, 2021, Nonlinear refractive index of solids in mid-infrared, Opt. Lett. 46, 1824-7.

[Reichert2014] M. Reichert, H. Hu, M.R. Ferdinandus, M. Seidel, P. Zhao, T.R. Ensley, D. Peceli, J.M. Reed, D.A. Fishman, S. Webster, D.J. Hagan, & E.W. Van Stryland, 2014, Temporal, spectral, and polarization dependence of the nonlinear optical response of carbon disulfide, Optica 1, 436-445. See erratum, 2016, Optica 3, 657-658.

[Santran 2004] Stephane Santran, Lionel Canioni, and Laurent Sarger, Thierry Cardinal and Evelyne Fargin, 2004, Precise and absolute measurements of the complex third-order optical susceptibility, J. Opt. Soc. Am. B 21, 2180-90.

[Smith1975] W. L. Smith, J. H. Bechtel, and N. Bloembergen, 1975, Dielectric-breakdown threshold and nonlinear-refractive-index measurements with picosecond laser pulses, Phys. Rev. B 12, 706-714.

[Smolorz1999] Sylvia Smolorz, Frank Wise, N. F. Borrelli, 1999, Measurement of the nonlinear optical response of optical fiber materials by use of spectrally resolved two-beam coupling, Opt. Lett. 24, 1103-5.

[Smolorz2000] Sylvia Smolorz and Frank Wise, 2000, Femtosecond two-beam coupling energy transfer from Raman and electronic nonlinearities, J. Opt. Soc. Am. B 17, 1636-44.

[Stolen1978] R. H. Stolen and C. Lin, 1978, Self-phase-modulation in silica optical fibers, Phys. Rev. A 17, 1448.

[Stolen1989] R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, 1989, The Raman response function of silica-core fibers, J. Opt. Soc. Am. B 6, 1159-1166.

[Stolen1992] R. H. Stolen, W. J. Tomlinson, 1992, Effect of the Raman part of the nonlinear refractive index on propagation of ultrashort optical pulses in fibers, J. Opt. Soc. Am. B 9, 565-573.

[Tofighi2021] Salimeh Tofighi, Natalia Munera, Matthew, Reichert, David J. Hagan, And Eric W. Van Stryland, 2021, Transient Mid-IR Nonlinear Refraction in Air, Op. Ex. 29, 10863-10878.

[Wada1996] Akira Wada, Satoshi Okude, Tetsuya Sakai, and Ryozo Yamauchi, 1996, GeO₂ Concentration Dependence of Nonlinear Refractive Index Coefficients of Silica-Based Optical Fibers, Electronics and Communications in Japan, Part 1, 79, 811-817. Translated from Denshi Joho Tsushin Gakkai Ronbunshi, 1995, 78-B-1, 811-817.

[Weber1978] M. W. Weber, D. Milam, and W. L. Smith, 1978, Nonlinear Refractive Index of Glasses and Crystals, Opt. Eng. 17, 463-469.
# 2 NLO characterization techniques and their best practices

## 2.1 General best practices to obtain and report high-quality NLO measurement data

Before addressing the existing NLO characterization techniques, we provide some general ‘best practices’ that apply to most of them, i.e., some general rules for obtaining and reporting high-quality, useful NLO measurement data regardless of the technique employed:

- First, the material’s composition, dimensions, method of fabrication and linear optical properties as well as temperature need to be known. Particularly, the linear loss/absorption at the wavelengths used in the NLO measurements is an essential parameter, but also other linear optical characteristics such as dispersion coefficients and the properties of optically excited free carriers can be relevant.

- Second, a careful quantification of the NLO pump/excitation parameters *inside* the material and, if relevant for the technique used, also of the signal/probe parameters is required. These parameters, relevant for both pulsed and continuous-wave (CW) operation, include (but are not limited to):

* Wavelength

* Peak power, irradiance (or in some cases electric field amplitude), and/or pulse energy

* Beam size (specified as, e.g., FWHM, $HW1/e^2$M) and beam shape

* Pulse width (specified as, e.g., FWHM, $HW1/e^2$M) and pulse shape

* Pulse repetition rate (for pulsed operation)

* Beam polarization and orientation with respect to crystal axes if appropriate and relative polarization for 2-beam experiments

- Last, the generated NLO response needs to be carefully measured, and the measurement results should be appropriately analyzed to extract the NLO coefficient(s). This can be done by means of a model for the technique used, by means of a benchmark measurement on a sample with well-known characteristics, etc. Models should also account for other effects that may interfere with the NLO measurements, and additional supporting information for the conclusions drawn (e.g., investigation of the dependence on pump power/irradiance/energy, the wavelength dependence, or the temporal dependence of the NLO response) is often required (see previous Section 1.1). In addition, special attention should be paid to the influence of the sample substrate (if any) and to the possible occurrence of sample damage when performing high-irradiance NLO experiments. When specifying conversion efficiencies and bandwidths, it should be clear which formulas were used for determining them. Finally, the inclusion of error bars on the data sets is very valuable to understand the limitations of the measurements and the extracted parameters.

We consider these general best practices to be an appropriate set of rules for carrying out, analyzing and reporting NLO measurements, independently from the type of technique used. It is also important to keep in mind the following general insights valid for any kind of NLO measurement: whenever long pulse durations and/or high pulse repetition rates are employed in NLO experiments, thermal effects can occur. They can build up collectively over many pulses or arise within the pulse duration, depending upon the material absorption and pulse width. These irradiance-dependent thermal effects can mask the NLO effect one aims to study. More generally speaking, it is unusual for a single nonlinearity to fully
determine the overall NLO response. Hence, one should try to unravel the various contributions, e.g., by studying the power/irradiance/energy dependence, the wavelength dependence, the temporal dependence, etc., or at least consider the measured nonlinearity as an ‘effective’ coefficient for the input parameters quoted. We note that long and short pulses can trigger very different NLO processes (see, e.g., Section 3.2 on the NLO response of solvents) and could also exhibit different damage thresholds for the material under study. Also, measuring the wavelength dependence of the NLO response provides crucial information, since knowing the spectrum of the nonlinear absorption (NLA) and the dispersion curve of the nonlinear refraction (NLR) of a material is extremely helpful for understanding the fundamental physical interactions leading to the observed NLO effects. In some cases, the nonlinear absorption spectra/dispersion curves are necessary information for a proper interpretation of the experimental results. A more detailed discussion of the underlying physics can be found in [Christodoulides2010, Van Stryland2009a, Van Stryland2009b, Boyd2020, Stegeman2012, Sutherland2003, Shen2002, Bloembergen1996].

### References of Section 2.1

[Bloembergen1996] Bloembergen N., 1996, *Nonlinear Optics*, 4th Edition (World Scientific Printing)

[Boyd2020] Boyd R., 2020, *Nonlinear Optics*, 4th Edition (Academic Press).

[Christodoulides2010] Christodoulides D.N., Choon Khoo I., Salamo G.J., Stegeman G.I., and Van Stryland E., 2010, *Nonlinear Refraction and Absorption: Mechanisms and Magnitudes, Advances in Optics and Photonics 2*, 60-200.

[Shen2002] Shen Y. R., 1992, *The Principles of Nonlinear Optics* (John Wiley & Sons, Hoboken, NJ)

[Stegeman2012] Stegeman G.I. and Stegeman R.A., 2012, *Nonlinear Optics: Phenomena, Materials and Devices* (John Wiley & Sons, Hoboken, NJ).

[Sutherland2003] Sutherland R. L., 2003, *Handbook of nonlinear optics, 2nd edition* (Boca Raton, FL, CRC Press).

[Van Stryland2009a] Van Stryland E. and Hagan D., 2009, *Measuring Nonlinear Refraction and Its Dispersion via Propagation, in: Boyd R., Lukishova S., Shen R. (Ed.), 2009, Self-focusing: Past and Present*, Springer Topics of Applied Physics Series, **114**, 573-591 (Springer Verlag).

[Van Stryland2009b] Van Stryland E., Hagan D., Webster S., and Padilha L., *Nonlinear spectroscopy: absorption and refraction*, 2009, Proc. SPIE **7504**, 750415.
## 2.2 Technique-specific best practices

Besides the general best practices identified above, one should also consider additional best practices that are specific for the NLO technique used. In what follows, we list the most common technique families<fnref n="1" />, the NLO coefficients they yield and the technique-specific best practices we have identified for each of them.

### 2.2.1 Best practices for second-order NLO techniques

#### 2.2.1.1 Second-order wave mixing

Second-order wave mixing processes, mainly second-harmonic generation (SHG), sum-frequency generation (SFG) and difference-frequency generation (DFG) [Shen1989, Shen2002, Sutherland2003, Wang2009, Liang2017, Prylepa2018], are often utilized in characterization of bulk materials, 0D-1D-2D materials, metamaterials, fiber waveguiding materials, on-chip waveguiding materials, and hybrid waveguiding systems. The developed techniques allow one to extract the material's $\chi^{(2)}$ and $d_{eff}$ coefficients, and the conversion efficiency of the associated process. In some cases, the techniques also allow characterization of the relevant components of the $\chi^{(2)}$ tensor, or the conversion bandwidth of the process. Second-order wave mixing is also at the heart of optical parametric oscillation (OPO), generation (OPG), and amplification (OPA) [Shen2002, Sutherland2003]. We note that electric-field-induced second-harmonic generation (EFISH) is in fact a third-order wave mixing process that in the presence of an external static electric field gives rise to second-harmonic generation.

Besides the general best practices in Section 2.1, it is important to verify successful phase matching of the NLO interaction in the material and to determine the parameters on which the considered phase matching approach relies (e.g., dispersion, poling parameters in some cases of quasi-phase-matching (QPM), etc.). Furthermore, when reporting the conversion efficiency and conversion bandwidth of the material, the used parameter definitions should be clearly stated. Finally, when performing SHG experiments, it is important to verify that the SHG response is not masked by two-photon-excited fluorescence effects.

#### References of Section 2.2.1.1

[Liang2017] Liang J., Zhang J., Li Z., Hong H., Wang J., Zhang Z., Zhou X., Qiao R., Xu J., Gao P., Liu Z., Liu Z., Sun Z., Meng S., Liu K., and Yu D., 2017, Monitoring local strain vector in atomic-layered MoSe2 by second-harmonic generation, Nano letters 17, 7539-7543.

[Prylepa2018] Prylepa A., Reitböck C., Cobet M., Jesacher A., Jin X., Adelung R., Schatzl-Linder M., Luckeneder G., Stellnberger K.-H., Steck T., Faderl J., Stehrer T. and Stifter D., 2018, Material characterisation with methods of nonlinear optics, Journal of Physics D: Applied Physics 51, 043001.

[Shen1989] Shen Y. R., 1989, Surface properties probed by second-harmonic and sum-frequency generation, Nature 337, 519-525.

[Shen2002] Shen Y. R., 1992, *The Principles of Nonlinear Optics* (John Wiley & Sons, Hoboken, NJ)

[Sutherland2003] Sutherland R. L., 2003, *Handbook of nonlinear optics, 2nd edition* (Boca Raton, FL, CRC Press)

[Wang2009] Wang F. X., Rodriguez F. J., Albers W. M., Ahorinta R., Sipe J. E., and Kauranen M, 2009, Surface and bulk contributions to the second-order nonlinear optical response of a gold film, Phys. Rev. B 80, 233402.

#### 2.2.1.2 Second-order nonlinear imaging

Second-order nonlinear imaging techniques, most notably SHG imaging [Gannaway1978, Kumar2013, Yin2014, Woodward2016], can be meaningfully applied to material categories exhibiting spatially varying second-order nonlinear parameters (0D-1D-2D materials, metamaterials, on-chip waveguiding

<footnote n="1">¹ There exist very specialized techniques that are not addressed in this section as they are only employed in very specific or rather uncommon experiments. Some of these specialized techniques are used in a few papers included in the tables of this work. The reader is directed to those papers for further information on these techniques.</footnote>
materials, and hybrid waveguiding systems). Second-order nonlinear imaging allows one to characterize the magnitude of $\chi^{(2)}$ along with the conversion efficiency associated with the material and the performed experiments.

While the general best practices listed in Section 2.1 also apply for second-order nonlinear imaging, we further stress the importance of carefully characterizing the NLO excitation parameters (the peak power/irradiance/energy, beam size, pulse width and polarization) inside the material. This is particularly important, because optical components such as microscope objective lenses may considerably modify the properties of incident pulses. Furthermore, when using SHG imaging, the occurrence of two-photon-excited fluorescence effects should be avoided.

### References of Section 2.2.1.2

[Gannaway1978] Gannawa, J. N. and Sheppard C. J. R., 1978, Second-harmonic imaging in the scanning optical microscope, Optical and Quantum Electronics 10, 435-439.

[Kumar2013] Kumar N., Najmaei S., Cui Q., Ceballos F., Ajayan P. M., Lou J., and Zhao H., 2013, Second harmonic microscopy of monolayer MoS₂, Phys. Rev. B 87, 161403.

[Woodward2016] Woodward R. I., Murray R. T., Phelan C. F., de Oliveira R. E. P., Runcorn T. H., Kelleher E. J. R., Li S., de Oliveira E. C., Fechine G. J. M., Eda G. and de Matos C. J. S., 2016, Characterization of the second- and third-order nonlinear optical susceptibilities of monolayer MoS₂ using multiphoton microscopy, 2D Materials 4, 011006.

[Yin2014] Yin X., Ye Z., Chenet D. A., Ye Y., O'Brien K., Hone J. C., Zhang X., 2014, Edge nonlinear optics on a MoS₂ atomic monolayer, Science 344, 488-490.

## 2.2.2 Best practices for third-order NLO techniques

### 2.2.2.1 Third-order parametric wave mixing

Third-order parametric wave mixing refers to techniques such as four-wave mixing (FWM) [Jain1979, Friberg1987, Agrawal2001], third-harmonic generation (THG) [Ward1969, Soon2005], and self-/cross-phase modulation (SPM/XPM) [Alfano1986, Agrawal2001], and can be applied to all material categories considered in this work. Third-order parametric wave mixing allows measuring the magnitude of Re($\chi^{(3)}$), $n_{2,eff}$ (which is usually assumed to be real), and Re($\gamma_{eff}$). Specifically in the case of SPM/XPM one can also extract the sign of these nonlinearities [Vermeulen2016a]. When using THG one most often quantifies a Re($\chi^{(3)}$) value that is specifically associated with bound-electronic nonlinear transitions. Note also that FWM may be more complex than THG and SPM/XPM as often the imaginary part of the third-order nonlinearity cannot be neglected. To separate the real and imaginary parts of the nonlinearity in a FWM signal, special experimental modifications and careful analysis involving also two-photon absorption (2PA) and Raman contributions, which will be described in the following sections, are generally required [Burris1985].

In FWM and THG experiments one most often measures the power/energy of the new signal generated by these wave mixing interactions, whereas SPM/XPM experiments are focused on measuring the phase modulation effects (e.g., spectral broadening, supercontinuum generation (SCG) [Dudley2010], ...) that these processes induce. Besides the general best practices listed in Section 2.1, FWM and THG also require that their phase matching conditions are addressed. When the conversion efficiency of FWM or THG is measured, attention needs to be paid as to how the conversion efficiency and bandwidth are defined. For SPM experiments the spectral shape and phase information, i.e., chirp, of the input pulses also need to be known to allow for a correct measurement of the NLO coefficients [Vermeulen2016a]. However, in the case of wideband SCG, the input chirp typically has a negligible impact on the output spectrum and hence does not necessarily have to be known to allow for a correct extraction of the NLO coefficients. Finally, it is important to keep in mind that, besides the material's Kerr nonlinearity, other effects can also contribute to its third-order parametric wave mixing response (e.g., free-carrier effects contributing to SPM- and XPM-induced spectral broadening [Vermeulen2018, Zhang2016]).
### References of Section 2.2.2.1

[Agrawal2001] Agrawal G P, 2001, Nonlinear fiber optics, 3rd Edition (Academic Press)

[Alfano1986] Alfano R R, Li Q X, Jimbo T, Manassah J T, and Ho P P, 1986, Induced spectral broadening of a weak picosecond pulse in glass produced by an intense picosecond pulse, Opt. Lett. 11, 626-628

[Burris1985] Burris J and McIlrath T J, 1985, Theoretical study relating the two-photon absorption cross section to the susceptibility controlling four-wave mixing, J. Opt. Soc. Am. B 2, 1313-1317

[Dudley2010] Dudley J and Taylor R, 2010, Supercontinuum generation in optical fibers (Cambridge University Press)

[Friberg1987] Friberg S and Smith P, 1987, Nonlinear optical glasses for ultrafast optical switches, IEEE J. Quantum Electron. 23, 2089-2094

[Jain1979] Jain R K and Klein M B, 1979, Degenerate four-wave mixing near the band gap of semiconductors, Appl. Phys. Lett. 35, 454

[Soon2005] Soon B.Y. and Haus J.W., Third-Harmonic Generation, in: Guenther R.D. (Ed.), 2005, *Encyclopedia of Modern Optics* (Elsevier)

[Vermeulen2016a] Vermeulen N, Castelló-Lurbe D, Cheng J L, Pasternak I, Krajewska A, Ciuk T, Strupinski W, Thienpont H, and Van Erps J, 2016, Negative Kerr Nonlinearity of Graphene as seen via Chirped-Pulse-Pumped Self-Phase Modulation, Phys. Rev. Applied 6, 044006

[Vermeulen2018] Vermeulen N, Castelló-Lurbe D, Khoder M, Pasternak I, Krajewska A, Ciuk T, Strupinski W, Cheng JL, Thienpont H, Van Erps J, 2018, Graphene's nonlinear-optical physics revealed through exponentially growing self-phase modulation, Nat. Commun. 9, 2675

[Ward1969] Ward J F and New G H C, 1969, Optical Third Harmonic Generation in Gases by a Focused Laser Beam, Phys. Rev. 185, 57

[Zhang2016] Zhang Y., Husko C., Lefrancois S., Rey I. H., Krauss T. F., Schroder J., and Eggleton B. J., 2016, Cross-phase modulation-induced spectral broadening in silicon waveguides, Opt. Express 24, 443-451

### 2.2.2.2 Raman/Brillouin gain measurement techniques

The material intrinsic NLO parameter that most often characterizes stimulated scattering for the Raman/Brillouin processes is the gain coefficient $g_{\text{Raman/Brillouin}}$ (m/W). In the context of waveguides, the parameter can be expressed as a gain factor $\Gamma_{\text{Raman/Brillouin}}$ (m$^{-1}$W$^{-1}$). Two classes of measurement methods are distinguishable: (1) direct methods – that rely on the amplification of a Stokes field, and (2) indirect methods that rely on the determination of the spontaneous scattering cross-section and the dephasing time. Both methods can in principle be applied to all material categories considered in this work. Although most of the literature has focused on the Raman gain coefficient, the considerations often apply analogously to Brillouin scattering. Besides the general best practices listed in Section 2.1, we have identified the following best practices specifically for Raman and Brillouin gain measurements:

- Direct methods are based on measuring the threshold for stimulated Raman/Brillouin scattering (SRS/SBS) [Ippen1972, Zverev1999], the threshold of laser action [McQuillan 1970] and probing gain in an amplifier [Stappaerts1980, Niklès1997]. In the tables presented further on, these are indicated as “SRS/SBS threshold,” “Raman/Brillouin laser threshold,” and “SRS/SBS pump-probe,” respectively. Major contributors to the measurement uncertainty include the precision of beam sizes and shapes, and the specification of the relative polarization of pump and Stokes (in relation to crystal axes in the case of crystals) and the pulse shape. In cases where the Rayleigh range of the beams are comparable to or shorter than the material length, the variation in beam waist upon propagation through the medium should be factored-in [Boyd1969]. The gain is a function of the pump and Stokes linewidths, decreasing markedly as the widths approach that of the phonon resonance [Georges1991, Agrawal2001, Bonner2014] or, equivalently, as pulse durations approach the $T_2$ phonon relaxation time [Basiev1999b]. For methods involving co-propagating multi-longitudinal mode beams, correlations between the pump and Stokes irradiances also need to be considered [Sabella2015] [Stappaerts1980]. Benchmarking against better known values of other materials [Basiev1999b], or the Kerr nonlinearity [Sabella2015], are valuable ways to increase confidence in the obtained values. For measurements at frequencies approaching the bandgap, a model is needed that includes a description of other nonlinearities occurring in the material (2PA, multiphoton absorption, free-
carrier absorption (FCA), ...). It should be noted that measurements of the stimulated scattering threshold often use a chosen exponential gain value *G* in the vicinity of *G* = 20, i.e., it is assumed that for typical spontaneous seeding, an irradiance growth of *e*<sup>*G*</sup> with *G* ~ 20 leads to a readily observable stimulated scattering signal [Grasyuk1998, Ippen1972]. However, there is no universally accepted value for *G* which may lead to some variability between reported values. In waveguides, two-color pump-probe techniques have been used to better separate the gain signal from background noise and other complications [Yang2020, Renninger2016].

- The gain coefficient may be determined indirectly by measuring the total cross-section for spontaneous scattering and the peak linewidth (*T*₂ dephasing time) [Basiev1999a], which are indicated in the tables, by the terms “SpRS/SpBS cross-section” and “SpRS, SpBS linewidth”. Absolute measurements of the cross section are rare due to the increased practical difficulties associated with precise photometric measurements; a problem often mitigated by benchmarking against better known materials. It has also been shown that inverse Raman scattering (IRS) of a probe beam at the anti-Stokes frequency also gives access to absolute values without benchmarking [Schneebeli2013]. For Brillouin scattering, the cross-section may be determined from the photoelastic tensor [Ippen1972]. Determination of the linewidth may be readily achieved using a spectrometer provided that the instrument width is sufficiently small or is adequately deconvolved. The linewidth may also be determined from direct measurements of *T*₂ by using fast pump – probe optical pulses [Waldermann2008].

### References of Section 2.2.2.2

[Agrawal2001] Agrawal, G.P., 2001. Nonlinear fiber optics, 3rd Edition (Academic Press) https://doi.org/10.1016/C2018-0-01168-8

[Basiev1999a] Basiev, T.T., Sobol, A.A., Zverev, P.G., Ivleva, L.I., Osiko, V. V., Powell, R.C., 1999. Raman spectroscopy of crystals for stimulated Raman scattering. Opt. Mater. (Amst). 11, 307-314. https://doi.org/10.1016/S0925-3467(98)00030-5

[Basiev1999b] Basiev, T.T., Sobol, A.A., Zverev, P.G., Osiko, V. V., Powell, R.C., 1999. Comparative spontaneous Raman spectroscopy of crystals for Raman lasers. Appl. Opt. 38, 594-598. https://doi.org/10.1016/S0925-3467(98)00030-5

[Bonner2014] Bonner, G.M., Lin, J., Kemp, A.J., Wang, J., Zhang, H., Spence, D.J., Pask, H.M., 2014. Spectral broadening in continuous-wave intracavity Raman lasers. Opt. Express 22, 7492. https://doi.org/10.1364/oe.22.007492

[Boyd1969] Boyd, G.D., Johnston, W.D., Kaminow, I.P., 1969. Optimization of the Stimulated Raman Scattering Threshold. IEEE J. Quantum Electron. 5, 203-206. https://doi.org/10.1109/JQE.1969.1075751

[Georges1991] Georges, A.T., Dixit, S.N., 1991. Dependence of broadband Raman amplification in dispersive media on the pump-Stokes input correlation. J. Opt. Soc. Am. B 8, 780. https://doi.org/10.1364/josab.8.000780

[Grasyuk1998] Grasyuk, A., Kurbasov, S. V., Losev, L.L., Lutsenko, A.P., Kaminski, A.A., Semenov, V.B., 1998. Determination of the Raman gain coefficient in leucosapphire. Quantum Electron. 28, 162-166.

[Ippen1972] Ippen, E.P., Stolen, R.H., 1972. Stimulated Brillouin scattering in optical fibers. Appl. Phys. Lett. 21, 539-541.

[McQuillan1970] McQuillan, A. K., Clements, W.R.L., Stoicheff, B.P., 1970. Stimulated Raman Emission in Diamond: Spectrum, Gain, and Angular Distribution of Intensity. Phys. Rev. A 1, 628-635.

[Niklès1997] Niklès, M., Thévenaz, L., Robert, P.A., 1997. Brillouin gain spectrum characterization in single-mode optical fibers. J. Light. Technol. 15, 1842-1851. https://doi.org/10.1109/50.633570

[Renninger2016] Renninger, W.H., Behunin, R.O. and Rakich, P.T., 2016. Guided-wave Brillouin scattering in air. Optica 3, 1316-1319.

[Sabella2015] Sabella, A., Spence, D., Mildren, R., 2015. Pump-Probe Measurements of the Raman Gain Coefficient in Crystals Using Multi-Longitudinal-Mode Beams. IEEE J. Quantum Electron. 51, 1-1. https://doi.org/10.1109/JQE.2015.2503404

[Schneebeli 2013] Schneebeli, L., Kieù, K., Merzlyak, E., Hales, J.M., DeSimone, A., Perry, J.W., Norwood, R.A. and Peyghambarian, N., 2013. Measurement of the Raman gain coefficient via inverse Raman scattering. JOSA B 30, 2930-2939.

[Stappaerts1980] Stappaerts, E.A., Long, W.H., Komine, H., 1980. Gain enhancement in Raman amplifiers with broadband pumping. Opt. Lett. 5, 4-6.

[Waldermann2008] Waldermann, F., Sussman, B., Nunn, J., Lorenz, V., Lee, K., Surmacz, K., Jaksch, D., Walmsley, I., Spizziri, P., Olivero, P., Prawer, S., 2008. Measuring phonon dephasing with ultrafast pulses using Raman spectral interference. Phys. Rev. B 78, 1-6. https://doi.org/10.1103/PhysRevB.78.155201

[Yang2020] Yang, F., Gyger, F. and Thévenaz, L., 2020. Intense Brillouin amplification in gas using hollow-core waveguides. Nature photonics 14, 700-708.

[Zverev1999] Zverev, P.G., Basiev, T.T., Prokhorov, A.M., 1999. Stimulated Raman scattering of laser radiation in Raman crystals. Opt. Mater. (Amst). 11.
### 2.2.2.3 Third-order polarization rotation

Third-order polarization rotation refers to techniques where the change of polarization of an intense pump beam, or of a probe beam, is monitored to determine the real (or imaginary) part of the nonlinear susceptibility $\chi^{(3)}$, which may also yield the nonlinear refractive index $n_{2,eff}$ or a nonlinear absorption coefficient, e.g., $\alpha_2$. Examples are ellipse rotation (ER) measurements [Maker1964, Owyoung1972, Miguez2014], specifically for linearly isotropic materials such as liquids (see Section 3.2 on solvents), or Optical Kerr Gating [Duguay1969, McMorrow1988]. If the polarization is changed solely by refractive index changes, this refers to the quadratic Kerr effect. These techniques are most often used for bulk materials, such as isotropic liquids or linearly isotropic or cubic symmetry solids, but can also be applied to other material categories such as fiber materials and on-chip waveguiding materials.

Besides the general best practices listed in Section 2.1, third-order polarization rotation measurements also require special attention to precisely knowing the polarization of the source, or sources in the case of pump-probe experiments where knowledge of the relative polarization is also needed. The example of ER is illustrative. In that method for isotropic materials, due to symmetry, there are three unknown susceptibility elements. The key in an ER experiment is to create an elliptically polarized beam of well-known orientation. This can be done, e.g., by starting with a linearly polarized beam and introducing a quarter-wave plate, and then carefully measuring the transmission of the beam through a polarizer as a function of orientation, both before and after propagation through the NLO medium.

For pump-probe experiments, the optical Kerr gate is a good example. Starting with linearly polarized pump and probe beams with a relative polarization at 45 degrees, the pump induces a birefringence in the nonlinear sample that rotates the transmitted polarization. Monitoring the transmittance of the probe through a polarizer crossed to give zero transmittance without the pump gives a sensitive method for measuring the induced refractive index or absorption changes [Stegeman2012, Duguay1969, McMorrow1998]. Again, careful attention to the polarization is needed in these experiments.

#### References of Section 2.2.2.3

[Duguay1969] Duguay M. A. and Hansen J. W., 1969, An Ultrafast Light Gate, Appl. Phys. Lett, 15, 192-194.

[Maker1964] Maker P. D., Savage C. M., and Terhune R. W., 1964, Intensity-Dependent Changes in The Refractive Index of Liquids, Phys. Rev. Lett. 12, 507.

[McMorrow1988] McMorrow D., Lotshaw W. T., and Kenney-Wallace G. A., 1988, Femtosecond Optical Kerr Studies on the Origin of the Nonlinear Responses in Simple Liquids, IEEE J. Quantum Electronics 24, 443-454.

[Miguez2014] Miguez M. L., Barbano E. C., Zilio S. C., and Misoguti L., 2014, Accurate measurement of nonlinear ellipse rotation using a phase-sensitive method, Opt. Express 22, 25530-25538.

[Owyoung1972] Owyoung A., Hellwarth R. W., and George N., 1972, Intensity-Induced Changes in Optical Polarizations in Glasses, Phys. Rev. B 5, 628.

[Stegeman2012] Stegeman G I and Stegeman R A, 2012, *Nonlinear Optics: Phenomena, Materials and Devices* (John Wiley & Sons, Hoboken, NJ).

### 2.2.2.4 Beam distortion/absorption

In beam distortion measurements, one quantifies the spatial variation of the beam due to a NLO process by measuring the power that passes through a fixed reference (e.g., pin-hole) or using a spatially resolved detector (e.g., quad-cell). For beam absorption measurements, one seeks to measure the nonlinearity-dependent power reflected/transmitted (also referred to as “nonlinear R/T”) from the material, with the transmission dependent on both nonlinear absorption and scattering. In either case, it is possible to utilize single-beam or pump-probe style measurements. While more complex, the latter case provides more versatility to explore the temporal, polarization, and angular dependences of the nonlinearity as well as degenerate and non-degenerate spectral dependences.

Beam distortion and absorption refer to techniques such as Z-scan [Sheik-Bahae 1989, Sheik-Bahae 1990, Balu 2004, de Araújo 2016], I-scan [Taheri 1996], nonlinear reflection/transmission (loss) [Bloembergen 1962, Clays 1991, Sutherland 2003, Cheng 2018, Dong 2018, da Silva-Neto 2020], beam deflection [Ferdinandus 2013, Ferdinandus 2017,], and power limiting [Siegman 1962, Smirl 1975,
Soileau 1983, Gu 2006, Maas 2008, Liaros 2013, Riggs 2000]. Note that the I-scan technique had previously been used before being named as such (see, for example, [Bechtel 1976, Van Stryland 1985]). As these techniques involve spatial distortion/pointing and/or loss of the beam, they are generally used for the extraction of nonlinear parameters in free space. As a result, bulk materials, 0D-1D-2D materials, and metamaterials are commonly evaluated using these techniques. However, nonlinear loss measurements can also be used in waveguides and fibers, and is common for characterizing, e.g., 2PA and saturable absorption [Sorin 1984, Colin 1996, Set 2004, Jiang 2018].

In addition to the general best practices listed in Section 2.1, beam distortion techniques are the simplest to analyze using clean Gaussian beam profiles as this is currently an assumption of many subsequent analysis techniques [Sheik-Bahae 1990, Gu 2005] to extract the NLO coefficients; however, by using reference samples of known nonlinearity, such techniques can be calibrated for non-Gaussian beams [Bridges 1995]. Furthermore, for thick samples and/or short pulses, it is useful to characterize the pulse chirp to correct for modifications in the temporal response of the nonlinearity due to varying group velocities. We also note that nonlinear beam distortion and loss, when used together, provide a complete methodology for characterizing lossy and/or lossless materials, enabling accurate evaluation of the magnitude, sign, and dispersion of the nonlinear refractive index $n_2$, $n_{2,eff}$, $\alpha_2$, $\alpha_{2,eff}$, thermal index (dn/dT and dk/dT), etc. through the fitting of experimental quantities. With subsequent analysis [del Coso 2004, Christodoulides 2010], the complex value and sign of, e.g., a pure $\chi^{(3)}$ can be determined as well. When only one of the techniques is used the information is often restricted. Beam distortion alone is sometimes sufficient to discern the sign and magnitude of the complex nonlinear index and susceptibility in the case of lossless (or low-loss) materials. However, in the case of very lossy materials (Im($\varepsilon$) ~ Re($\varepsilon$)), the terms of the complex susceptibility are inextricably coupled in measurements of both nonlinear losses and nonlinear refraction. The use of beam distortion (Z-scan or other methods) alone results in an effective coefficient which combines contributions from both nonlinear absorption and refraction [Del Coso 2004].

In general, it can be difficult to separate the different contributions using a single methodology (e.g., Z-scan requires both open and closed aperture experiments), although information on the sign of the respective nonlinearities can often be obtained. Beam absorption alone is typically sufficient to discern the sign and magnitude of nonlinear absorption but does not give information on the nonlinear refraction, although in some cases the sign of the nonlinear refraction can be predicted [Smith 1999] (here negative absorption would correspond to either absorption saturation or gain depending on circumstances). Since both components cannot be individually interpreted, absorption alone also cannot provide complete information on the $\chi^{(3)}$ although it may be possible to discern the sign of the terms. Pump-probe experiments such as beam deflection [Ferdinandus 2013] again require simultaneous transmittance and deflection signals to determine both absorptive and refractive components [Ferdinandus 2017]. These restrictions can be easily understood by comparing the number of unknowns (nonlinear refraction and absorption coefficients) for a given material with the constraints (distortion and absorption measurements) imposed by the experimental information. In the case of an under-constrained problem such as when attempting to extract two coefficients with a single measurement, the sign can be argued based on Kramers-Kronig causality if one knows the underlying mechanism(s) and/or the spectral response of one of the nonlinear terms. Lastly, we reiterate that although in some cases a singular technique is sufficient to obtain information on the nonlinearity of a material, if one assumes a pure $\chi^{(3)}$ process, it is rare for this assumption to be absolutely accurate (e.g., higher-order processes may provide non-negligible contributions). In this scenario, a single measurement will return only an effective nonlinear response, comprising multiple underlying physical mechanisms. Thus, the use of several analysis techniques is highly encouraged. This will provide more data to constrain analysis and elucidate the response of various contributing effects.
[Bechtel1976] Bechtel, J., and Smith, W., 1976, Two-photon absorption in semiconductors with picosecond laser pulses. *Physical Review B*, **13**, 3515-3522.

[Bloembergen1962] Bloembergen, N., and Pershan, P. S., 1962, Light waves at the boundary of nonlinear media. *The Physical Review*, **128**, 606-622.

[Bridges1995] Bridges R.E., Fischer G.L., and Boyd R.W., 1995, Z-scan measurement technique for non-Gaussian beams and arbitrary sample thicknesses, *Opt. Lett.* **17**, 1821-3.

[Cheng2018] Cheng, J.-X., and Xie, X. S. (Eds.), 2018, *Coherent Raman scattering microscopy* (London, England: CRC Press).

[Christodoulides2010] Christodoulides, D. N., Khoo, I. C., Salamo, G. J., Stegeman, G. I., and Van Stryland, E. W., 2010, Nonlinear refraction and absorption: mechanisms and magnitudes. *Advances in Optics and Photonics*, **2**, 60-200.

[Clays1991] Clays, K., and Persoons, A., 1991, Hyper-Rayleigh scattering in solution. *Physical Review Letters*, **66**, 2980-2983.

[Colin1996] Colin, S., Contesse, E., Boudec, P. L., Stephan, G., and Sanchez, F., 1996, Evidence of a saturable-absorption effect in heavily erbium-doped fibers. *Optics Letters*, **21**, 1987-1989.

[Da Silva-Neto2020] Da Silva-Neto, M. L., Barbosa-Silva, R., de Araújo, C. B., de Matos, C. J. S., Jawaid, A. M., Ritter, A. J., Vaia, R. A., and Gomes, A. S. L., 2020, Hyper-Rayleigh scattering in 2D redox exfoliated semi-metallic ZrTe2 transition metal dichalcogenide. *Physical Chemistry Chemical Physics: PCCP*, **22**, 27845-27849.

[De Araújo2016] De Araújo, C. B., Gomes, A. S. L., and Boudebs, G., 2016, Techniques for nonlinear optical characterization of materials: a review. *Reports on Progress in Physics. Physical Society (Great Britain)*, **79**, 036401, 30 pages. doi:10.1088/0034-4885/79/3/036401

[Del Coso2004] Del Coso, R., and Solis, J., 2004, Relation between nonlinear refractive index and third-order susceptibility in absorbing media. *Journal of the Optical Society of America. B, Optical Physics*, **21**, 640-644.

[Dong2018] Dong, Y., Chertopalov, S., Maleski, K., Anasori, B., Hu, L., Bhattacharya, S., Rao, A. M., Gogotsi, Y., Mochalin, V. N., and Podila, R., 2018, Saturable absorption in 2D Ti3 C2 Mxene thin films for passive photonic diodes, *Advanced Materials*, **30**, 1705714, 8 pages. DOI:10.1002/adma.201705714

[Ferdinandus2013] Ferdinandus, M. R., Hu, H., Reichert, M., Hagan, D. J., and Van Stryland, E. W., 2013, Beam deflection measurement of time and polarization resolved ultrafast nonlinear refraction. *Optics Letters*, **38**, 3518-3521.

[Ferdinandus2017] Ferdinandus, M. R., Reed, J. M., Averett, K. L., Hopkins, F. K., and Urbas, A., 2017, Analysis of beam deflection measurements in the presence of linear absorption, *Optical Materials Express* **7**, 1598-1605. https://doi.org/10.1364/OME.7.001598

[Gu2005] Gu, B., Chen, J., Fan, Y.-X., Ding, J., and Wang, H.-T., 2005, Theory of Gaussian beam Z scan with simultaneous third- and fifth-order nonlinear refraction based on a Gaussian decomposition method, *Journal of the Optical Society of America B* **22**, 2651-9. doi:10.1364/JOSAB.22.002651

[Gu2006] Gu, B., Fan, Y.-X., Wang, J., Chen, J., Ding, J., Wang, H.-T., and Guo, B., 2006, Characterization of saturable absorbers using an open-aperture Gaussian-beam Z scan. *Physical Review A*, **73**, 065803-1-4.

[Jiang2018] Jiang, X., Gross, S., Withford, M. J., Zhang, H., Yeom, D.-I., Rotermund, F., and Fuerbach, A., 2018, Low-dimensional nanomaterial saturable absorbers for ultrashort-pulsed waveguide lasers. *Optical Materials Express*, **8**, 3055.

[Liaros2013] Liaros, N., Aloukos, P., Kolokithas-Ntoukas, A., Bakandritsos, A., Szabo, T., Zboril, R., and Couris, S., 2013, Nonlinear optical properties and broadband optical power limiting action of graphene oxide colloids. *The Journal of Physical Chemistry. C, Nanomaterials and Interfaces*, **117**, 6842-6850.

[Maas2008] Maas, D. J., Rudin, B., Bellancourt, A.-R., Iwaniuk, D., Marchese, S. V., Südmeyer, T., and Keller, U., 2008, High precision optical characterization of semiconductor saturable absorber mirrors. *Optics Express*, **16**, 7571-7579.

[Riggs2000] Riggs, J. E., Walker, D. B., Carroll, D. L., and Sun, Y.-P., 2000, Optical limiting properties of suspended and solubilized carbon nanotubes. *The Journal of Physical Chemistry. B*, **104**, 7071-7076.

[Set2004] Set, S. Y., Yaguchi, H., Tanaka, Y., and Jablonski, M., 2004, Laser Mode Locking Using a Saturable Absorber Incorporating Carbon Nanotubes. *Journal of Lightwave Technology*, **22**, 51-56.

[Sheik-Bahae1989] Sheik-Bahae, M., Said, A. A., and Van Stryland, E. W., 1989, High-sensitivity, single-beam $n_2$ measurements. *Optics Letters*, **14**, 955-957.

[Sheik-Bahae1990] Sheik-Bahae, M., Said, A. A., Wei, T.-H., Hagan, D. J., and Van Stryland, E. W., 1990, Sensitive measurement of optical nonlinearities using a single beam. *IEEE Journal of Quantum Electronics*, **26**, 760-769.

[Siegman19962] Siegman, A. E., 1962, Nonlinear optical effects: An optical power limiter. *Applied Optics*, **1**, 739-744. doi:10.1364/AO.1.000739

[Šiškins2019] Šiškins, M., Lee, M., Alijani, F., van Blankenstein, M. R., Davidovikj, D., van der Zant, H. S. J., and Steeneken, P. G., 2019, Highly anisotropic mechanical and optical properties of 2D layered As2S3 membranes. *ACS Nano*, **13**, 10845-10851.

[Smirl1975] Smirl, A. L., 1975, *Measurement Of Ultrafast Relaxation Times In Semiconductors Using Picosecond Pulses*. University of Arizona.

[Smith1999] Smith, D. D., Yoon, Y., Boyd, R. W., Campbell, J. K., Baker, L. A., Crooks, R. M., and George, M., 1999, Z-scan measurement of the nonlinear absorption of a thin gold film. *Journal of Applied Physics*, **86**, 6200-6205.

[Soileau1983] Soileau, M. J., Williams, W. E., and Van Stryland, E. W., 1983, Optical Power Limiter with Picosecond Response Time. *IEEE Journal of Quantum Electronics*, **19**, 731-735.
[Sorin1984] Sorin, W. V., Youngquist, R. C., Cutler, C. C., and Shaw, H. J., 1984, Single-mode-fiber saturable absorber. *Optics Letters, 9*, 315-317.

[Sutherland2003] Sutherland, R. L., 2003, *Handbook of nonlinear optics, 2nd edition* (Boca Raton, FL, CRC Press).

[Taheri1996] Taheri, B., Liu, B. J., Appling, D., Powell, R. C., and Song, J. J., 1996, Intensity scan and two photon absorption and nonlinear refraction of C60 in toluene. *Applied Physics Letters, 68*, 1317.

[Van Stryland1985] Van Stryland, E., Woodall, M. A., Vanherzeele, H., and Soileau, M. J., 1985, Energy Band-Gap Dependence of Two-Photon Absorption. *Optics Letters, 10*, 490-492.

### 2.2.2.5 Nonlinear interferometry

The purpose of NLO interferometry is usually to measure the real part of the nonlinear susceptibility ($\chi^{(2,3)}$), but this technique can also be used to measure both the real and imaginary parts by suitable experimental modifications [Chang 1965, Sutherland 2003]. When using a wavelength of operation at which the NLO material is transparent, the most important part is the non-resonant $Re(\chi^{(n)})$. In contrast, if we are interested in the enhancement of $\chi^{(n)}$ by resonance effects, information on both $Re(\chi^{(n)})$ and $Im(\chi^{(n)})$ spectra is needed. Although dispersion relations similar to the Kramers-Kronig relations hold for NLO coefficients [Sheik-Bahae 1990, Bassani 1991, Sheik-Bahae 1991, Hutchings 1992], it is practically impossible to strictly apply the Kramers-Kronig relations and there are restrictive conditions under which the Kramers-Kronig relations hold in time-resolved spectroscopy [Tokunaga 1995]. Thus, direct measurement of the real and imaginary parts is often required. NLO interferometry is most often used for bulk materials, but can be applied to other material categories as well. Although interferometric methods are also modified as heterodyne detection to be employed in SFG [Ostroverkhov 2005, Nihonyanagi 2013, Wang 2017] (otherwise only $|\chi^{(2)}|$ is obtained), most of the targeted nonlinearities measured by NLO interferometry are third-order nonlinearities in a pump-probe setup. In this case, a NLO interferometer is often based on pump, probe (signal), and reference beams. There are multiple interferometric configurations possible. They can be categorized in two-arm types (Michelson, Mach-Zehnder, Sagnac, etc., or two-beam interference) and resonator types (Fabry-Perot, or multiple-beam interference), and hybrids of them, e.g., Laser Interferometer Gravitational-Wave Observatory (LIGO) combining Michelson and Fabry-Perot [Abbott 2016]. There are also other classifications such as common path (Sagnac) and non-common path (Michelson) for the two arms, and also beam division methods are specified (space, time, direction, polarization, etc.).

In addition to the general best practices outlined in Section 2.1, it is important to evaluate the measurement sensitivity of the NLO interferometric method used and to account for a possible surface reflectance change due to changes in both the $Re(\chi^{(3)})$ and $Im(\chi^{(3)})$ parts. The bulk nonlinear refraction can also change the propagation time of pulses. With pulsed lasers, it is convenient to use time division (i.e., in the same sample path, reference, pump, and probe pulses arrive at the sample in that order) and spectral interference [Tokunaga 1995, Chen 2007]. In addition to time division, common path interferometry such as division by direction [Misawa 1995] or by polarization [van Dijk 2007] (where the reference and probe share a common optical path) is advantageous for obtaining stable interference, but otherwise active control to stabilize the optical path length is often required [Cotter 1989]. In order to cancel instabilities of the laser irradiance, balanced detection can also be employed by dividing the probe beam in two to be detected with an identical detector for subtractive detection [Waclawek 2019]. Resonance cavity effects with Fabry-Perot interferometers are also useful for enhancing the NLO effects by increasing the light-matter interaction [Birnbaum 2005, Fryett 2018, Wang 2021].

#### References of Section 2.2.2.5

[Abbott 2016] Abbott BP, Abbott R, Abbott TD, Abernathy MR, Acernese F, Ackley K et al. Observation of Gravitational Waves from a Binary Black Hole Merger. 2016 *Phys Rev Lett* **116**, 061102.

[Bassani 1991] Bassani F and Scandolo S. Dispersion relations and sum rules in nonlinear optics. 1991 *Phys Rev B* **44**, 8446.

[Birnbaum 2005] Birnbaum KM, Boca A, Miller R, Boozer AD, Northup TE, and Kimble HJ. Photon blockade in an optical cavity with one trapped atom. 2005 *Nature* **436**, 87.

[Chang1965] Chang J, Ducuing J, and Bloembergen N. Relative phase measurement between fundamental and second-harmonic light. 1965 *Phys Rev Lett* **15**, 6-8.
[Chen 2007] Chen Y-H, Varma S, Alexeev I, and Milchberg HM. Measurement of transient nonlinear refractive index in gases using xenon supercontinuum single-shot spectral interferometry. *2007 Opt Express* **15**, 7458.

[Cotter 1989] Cotter D, Ironside CN, Ainslie BJ, and Girdlestone HP. Picosecond pump-probe interferometric measurement of optical nonlinearity in semiconductor-doped fibers. *1989 Opt Lett* **14**, 317.

[Fryett 2018] Fryett T, Zhan A, and Majumdar A. Cavity nonlinear optics with layered materials. *2018 Nanophotonics* **7**, 355.

[Hutchings 1992] Hutchings DC, Sheik-Bahae M, Hagan DJ, and Van Stryland EW. Kramers-Krönig relations in nonlinear optics. *1992 Opt Quant Electron* **24**, 1.

[Misawa 1995] Misawa K and Kobayashi T. Femtosecond Sagnac interferometer for phase spectroscopy. *1995 Opt Lett* **20**, 1550.

[Nihonyanagi 2013] Nihonyanagi S, Mondal JA, Yamaguchi S, and Tahara T. Structure and Dynamics of Interfacial Water Studied by Heterodyne-Detected Vibrational Sum-Frequency Generation. *2013 Annual Review of Physical Chemistry* **64**, 579.

[Ostroverkhov 2005] Ostroverkhov V, Waychunas GA, and Shen YR. New Information on Water Interfacial Structure Revealed by Phase-Sensitive Surface Spectroscopy. *2005 Phys Rev Lett* **94**, 046102.

[Sheik-Bahae 1990] Sheik-Bahae M, Hagan DJ, and Van Stryland EW. Dispersion and band-gap scaling of the electronic Kerr effect in solids associated with two-photon absorption. *1990 Phys Rev Lett* **65**, 96.

[Sheik-Bahae 1991] Sheik-Bahae M, Hutchings DC, Hagan DJ, and Van Stryland EW. Dispersion of bound electron nonlinear refraction in solids. *1991 IEEE Journal of Quantum Electronics* **27**, 1296.

[Sutherland 2003] Sutherland R L, 2003, *Handbook of nonlinear optics, 2nd edition* (Boca Raton, FL, CRC Press).

[Tokunaga 1995] Tokunaga E, Terasaki A, and Kobayashi T. Femtosecond phase spectroscopy by use of frequency-domain interference. *1995 J Opt Soc Am B* **12**, 753.

[van Dijk 2007] Dijk MA van, Lippitz M, Stolwijk D, and Orrit M. A common-path interferometer for time-resolved and shot-noise-limited detection of single nanoparticles. *2007 Opt Express* **15**, 2273.

[Waclawek 2019] Waclawek JP, Kristament C, Moser H, and Lendl B. Balanced-detection interferometric cavity-assisted photothermal spectroscopy. *2019 Opt Express* **27**, 12183.

[Wang 2017] Wang J, Bisson PJ, Marmolejos JM, and Shultz MJ. Nonlinear interferometer: Design, implementation, and phase-sensitive sum frequency measurement. *2017 J Chem Phys* **147**, 064201.

[Wang 2021] Wang K, Seidel M, Nagarajan K, Chervy T, Genet C, and Ebbesen T. Large optical nonlinearity enhancement under electronic strong coupling. *2021 Nat Commun* **12**, 1486.

### 2.2.2.6 Third-order nonlinear imaging

Third-order nonlinear imaging techniques, most notably THG imaging [Squier1999, Woodward2016, Karvonen2017], can be meaningfully applied to material categories exhibiting spatially varying third-order nonlinear parameters (0D-1D-2D materials, metamaterials, on-chip waveguiding materials, and hybrid waveguiding systems). Third-order nonlinear imaging allows one to characterize the magnitude of $\chi^{(3)}$ along with the conversion efficiency associated with the material and the performed experiments. While the general best practices listed in Section 2.1 also apply for third-order nonlinear imaging, we further stress the importance of carefully characterizing the NLO excitation parameters (the peak power/irradiance/energy, beam size, pulse width and polarization) inside the material. This is particularly important, because optical components such as microscope objective lenses may considerably modify the properties of incident pulses.

#### References of Section 2.2.2.6

[Karvonen2017] Karvonen L., Säynätjoki A., Huttunen M. J., Autere A., Amirsolaimani B., Li S., Norwood R. A., Peyghambarian N., Lipsanen H., Eda G., Kieu K., and Sun Z., Rapid visualization of grain boundaries in monolayer MoS$_2$ by multiphoton microscopy. *Nature Communications* **8**, 15714.

[Squier1999] Squier J. A. and Müller M., 1999, Third-harmonic generation imaging of laser-induced breakdown in glass, Applied Optics **38**, 5789-5794.

[Woodward2016] Woodward R. I., Murray R. T., Phelan C. F., de Oliveira R. E. P., Runcorn T. H., Kelleher E. J. R., Li S., de Oliveira E. C., Fechine G. J. M., Eda G. and de Matos C. J. S., 2016, Characterization of the second-and third-order nonlinear optical susceptibilities of monolayer MoS$_2$ using multiphoton microscopy, 2D Materials **4**, 011006.

### 2.2.3 Remarks on choice of NLO technique

The technique-specific best practices listed above combined with the general best practices in Section 2.1 should form a solid basis to obtain high-quality NLO measurement data and appropriate analysis results. When selecting a technique for characterizing a given NLO coefficient, it should be noted that
for single-wavelength experiments only a specific frequency component of this nonlinearity will be
revealed. For example, when applying both THG and SPM with pump frequency ω to characterize the
χ⁽³⁾ of a given material, THG will yield χ⁽³⁾ (3ω: ω, ω, ω) whereas SPM will provide information about
χ⁽³⁾ (ω: -ω, ω, ω) plus permutations [Bloembergen1996, Shen2002, Sutherland2003, Stegeman2012,
Boyd2020]. This underlines the importance of including the technique used in each entry of the data
tables presented below. And, as we have previously stated, it is highly desirable to use multiple
techniques and/or multiple wavelengths and/or multiple pulse widths etc., as this both helps to
distinguish different nonlinearities (with perhaps multiple being present simultaneously) and yields
more physical insight into the NLO response(s) of the material under study.

References of Section 2.2.3

[Bloembergen1996] Bloembergen N., 1996, *Nonlinear Optics, 4th Edition* (World Scientific Printing)

[Boyd2020] Boyd R, 2020, *Nonlinear Optics, 4th Edition* (Academic Press)

[Shen2002] Shen Y. R., 1992, *The Principles of Nonlinear Optics* (John Wiley & Sons, Hoboken, NJ)

[Stegeman2012] Stegeman G. I. and Stegeman R. A., 2012, *Nonlinear Optics: Phenomena, Materials and Devices* (John Wiley & Sons, Hoboken, NJ)

[Sutherland2003] Sutherland R. L., 2003, *Handbook of nonlinear optics, 2nd Edition* (CRC Press, Boca Raton, FL)
## 3 Data tables and discussion

After having listed the most common NLO technique families and their best practices, we present here the actual data tables for bulk materials, 0D-1D-2D materials, metamaterials, fiber waveguiding materials, on-chip waveguiding materials, and hybrid waveguiding systems. The tables contain NLO data of representative experimental papers published since 2000 that we selected after verifying both the general best practices and the best practices specifically for the NLO techniques used in these works. In some cases, publications missing just one important parameter as specified in the best practices could not be included, although they seemed technically sound. The NLO coefficients that we searched for in the literature since 2000 are: $\chi^{(2)}$, $d_{\text{eff}}$, $\chi^{(3)}$, $n_{2,\text{eff}}$, $\gamma_{\text{eff}}$, $\alpha_2$, $\alpha_3$, $I_{\text{sat}}$, $g_{\text{Raman}}$, and $g_{\text{Brillouin}}$. We particularly looked for works that provide the most extensive NLO information, such as the dependence of the NLO coefficients on wavelength, on pulse duration, on doping level, on material composition, etc. For some recently developed materials in the data tables such extensive studies are yet to be performed; in those cases we selected papers that provide at least some quantitative NLO information, e.g., a single NLO coefficient and/or conversion efficiency, while complying with all (or almost all) the best practices. Note that no hyperpolarizabilities have been listed in the tables as these are typically only characterized at the molecular level, and that all the considered nonlinearities are of the second or third order, except for the three-photon absorption (3PA) coefficient $\alpha_3$. However, nonlinearities from, e.g., 2PA-induced free carriers, appear as effective fifth-order nonlinearities and may possibly contribute to some values reported in the literature. Note also that we have not included photorefractive effects, electro-optic effects, stimulated polariton scattering, nor cascaded second-order nonlinearities. The latter can very closely mimic bound-electronic nonlinearities but require propagation [DeSalvo1992, Torruellas1995, Stegeman1996]. These can sometimes be difficult to separate from other NLO responses. It is also important to keep in mind that some nonlinearities cannot properly be classified as either second or third order. As an example, we cite absorption saturation which in principle contains all orders of nonlinearities; however, it is often discussed as third order since at the lowest inputs it behaves that way. Furthermore, for several NLO coefficients the ‘effective’ values are often reported in the literature. When taking the example of the nonlinear index $n_2$, strictly speaking it originates only from the Kerr-nonlinear response of bound electrons (BEs) in the material, but in practice the measured value can also comprise the nonlinear response from free electrons, electrostriction, thermal effects, etc. so that the terminology of an ‘effective’ nonlinear index $n_{2,\text{eff}}$ is more appropriate [Christodoulides2010, Buckland1996]. Also, some $\chi^{(3)}$ values in the literature are in fact ‘effective’ $\chi^{(3)}$ values containing multiple nonlinearity contributions rather than just the bound-electronic contribution. Finally, we point out that, besides tabulating NLO coefficients, the tables also contain NLO conversion efficiencies and bandwidths specified in works based on, e.g., SHG, THG or FWM. This way we also pay attention to those materials for which the NLO coefficients were reported before 2000 but that witnessed strong progress after 2000 in terms of attainable conversion efficiencies and bandwidths.

The general approach used for filling out the data tables has been to have a single entry per paper. For example, for a paper where the wavelength dependence of a given material nonlinearity is reported, there is typically only a single table entry, specifying a prominent nonlinearity value (in many cases the highest value) and the corresponding wavelength, but with a special annotation in this entry that shows the paper also contains information on the wavelength dependence. Note that a paper reporting on multiple materials is documented in the table with multiple entries, i.e., one entry per material. Another general policy has been to include only those parameter values that are explicitly specified in the paper. In other words, conversions from one physical quantity to another have been avoided to rule out calculation errors from our side. As such, when for a given entry in the tables there is no value for, e.g., pump peak power or irradiance, the paper under consideration might have specified the pump excitation in terms of fluence or average power rather than peak power or irradiance.

The data tables in the following subsections (Sections 3.1 – 3.8) are presented per material category (bulk materials, solvents, 0D-1D-2D materials, metamaterials, fiber waveguiding materials, on-chip
waveguiding materials, and hybrid waveguiding systems) and include those parameters that are most important for the material category under consideration. The entries in these tables present NLO data at optical excitation wavelengths, and some of the tabulated works report on THz generation through, e.g., DFG of two optical excitation beams. However, for those papers where THz radiation was used as the excitation source, we added a dedicated THz table<fnref n="2" /> at the end of the manuscript (see Section 3.8). The different data tables are accompanied by an introductory text addressing relevant background information prior to 2000, followed by a discussion of the general trends seen in the data tables (e.g., how the new post-2000 data represent an advancement) and some recommendations for future NLO research. Each of the subsections (Section 3.1 – 3.8) starts with the names of the contributing co-authors in alphabetical order (“team”) and the team leader.

We would like to emphasize again that it has not been our goal to include a comprehensive overview of papers but rather a representative set of works in these data tables. The current version of the tables contains papers with a publication date up to May 2021. Also, we point out that the existing literature already provides very valuable review papers that give an overview of NLO works for a specific material or material category, with a detailed discussion of the underlying physics. We refer to several of these recent review papers in the introductory texts and discussions below.

### References of Section 3

[Buckland1996] Buckland E. L. and Boyd R. W., 1996, Electrostrictive contribution to the intensity-dependent refractive index of optical fibers, Opt. Lett. 21, 1117-1119.

[Christodoulides2010] Christodoulides D. N., Choon Khoo I., Salamo G. J., Stegeman G. I., and Van Stryland E. W., 2010, Nonlinear refraction and absorption: mechanisms and magnitudes, Advances in Optics and Photonics 2, 60-200.

[DeSalvo1992] DeSalvo R. J., Hagan D. J., Sheik-Bahae M., Stegeman G., Vanherzeele H. and Van Stryland E. W., 1992, Self-Focusing and Defocusing by Cascaded Second Order Effects in KTP, Opt. Lett. 17, 28-30.

[Stegeman1996] Stegeman G. I., Hagan D. J. and Torner L., 1996, Chit(2) cascading phenomena and their applications to all-optical signal processing, mode-locking, pulse compression and solitons, Optical and Quantum Electronics 28, 1691-1740.

[Torruellas1995] Torruellas W. E., Wang Z., Hagan D. J., Van Stryland E. W., Stegeman G. I., Torner L. and Menyuk C., 1995, Observation of Two-Dimensional Spatial Solitary Waves in a Quadratic Medium, Phys. Rev. Lett., 74, 5036-9.

<footnote n="2">² The focus of the THz table is on the intrinsic THz NLO properties of various materials. It is useful to note that active electronic devices, such as Schottky diodes, high electron mobility transistors, resonant tunneling diodes, etc. can also generate (sub-)THz radiation when paired with appropriate in- and out-coupling structures. However, due to the fundamentally different nonlinear mechanisms of these devices, they are not included in this manuscript.</footnote>
# 3.1 Bulk materials: data table and discussion

**Team:** Adam Ball, Philippe Boucaud, Georges Boudebs, Ksenia Dolgaleva, Daniel Espinosa, Anderson Gomes, Nathaniel Kinsey (team leader), Rich Mildren, Ray Secondo, Eiji Tokunaga, Eric Van Stryland

## 3.1.1 Introduction

### 3.1.1.1 Bulk materials and their NLO applications

The bulk materials category is a highly diverse segment that presents NLO data on macroscopic 3D-material samples (ranging from thin films of ~100 nm thickness to crystalline material samples on the scale of cm's), where material structuring (see metamaterials category in Section 3.4) and quantum size effects (see 0D-1D-2D materials category in Section 3.3) are not important. The properties of bulk materials are typically measured using free-space diffracting beams (usually 1 or 2-beam experiments). Most experiments are performed with sample lengths less than the diffraction length (Rayleigh range) to allow for simple analysis.

Many bulk materials themselves are key for applications including frequency synthesis, stimulated scattering, ultrafast pulse characterization, and lasers. In addition, bulk materials generally serve as a starting point for the investigation of new materials before they are integrated into devices for applications across fields such as optoelectronics and fiber optics including uses in sensing, optical communications, and fiber lasers, as well as other types of active fibers and integrated photonics technology.

The listed materials, which include high-purity as well as impurity-doped materials, have been grouped into three sub-categories of insulators, semiconductors, and conductors. Within these groups, we focus our efforts on the development of inorganic materials only. Solvents are included in a separate section of this article (see Section 3.2), and we also draw attention to Section 3.8 on the characterization of material nonlinearities in the THz regime, many of which are bulk materials. These works have been separated to account for their unique considerations and in view of the rising area of THz NLO. However, works which utilize optical beams to generate THz waves remain in this section.

In keeping with this article's focus on post-2000 developments, the listed NLO materials emphasize those featured in research since 2000 but is not all-inclusive, giving priority to those publications that contain the most experimental information (see best practices in Section 2).

### 3.1.1.2 Background prior to 2000

#### 3.1.1.2.1 Background for insulators/dielectrics

When the laser was invented in 1960 electro-optic (EO) crystals were already in use. Nevertheless, the terminology of “nonlinear optics” was not typically employed in this context. The first use of dielectrics for NLO is considered to be the wavelength conversion experiment in the seminal work of [Franken1961]. Some of the most important NLO materials are insulating crystals such as lithium niobate [Midwinter1968; Schaufele1966; Smith1965], beta-barium borate [Chen1987], and potassium titanyl phosphate [Bierlein1989], to name a few. Works from the earliest days of NLO have demonstrated efficient nonlinear actions accompanied by well-developed theories of nonlinear light-matter interaction and crystal optics [Boyd2020; Stegeman2012; Sutherland2003]. Thus, these nonlinear crystals have been key enablers for many past and current technologies including harmonic generators, and OPO/OPG/OPA, optical modulators and switches making use of numerous second- and third-order nonlinear phenomena such as the Pockels effect, parametric mixing, and Raman scattering. In addition, efforts worked to improve the efficiency limits of phase matching by introducing periodically poled crystals with QPM [Lim1989; Myers1997; Wang1999]. In this regard lithium niobate is by far the most developed. Of course, much work went into the study of glasses as well. For example, the laser fusion program developed low nonlinear index glasses to prevent optical damage from catastrophic self-focusing in laser host glasses as well as other glass optical elements [Agrawal2013;
Tollefson2021]. Another interesting development was the measurement of third-order effects in popular second-order NLO crystals [Sheik-Bahae1997a] using Kerr lens autocorrelation [Sheik-Bahae1997b]. While third-order nonlinearities are generally masked by second-order processes, and thus might be neglected, certain applications can be limited by third-order effects such as self-focusing within the nonlinear crystal. Thus, understanding and correcting for these higher-order nonlinearities is a key feature for high-power applications or scenarios requiring especially large crystals.

Another key advance occurred during the late 1960s to 1970s with the invention of the laser diode, and the development of optical fibers. Together these opened new avenues to pursue all-optical devices aimed at applications in communications [Willner2019], and motivated studies of the nonlinearities in fused silica and other optical glasses [Agrawal2013]. Despite the small nonlinearity of silica-based glasses, the low propagation loss in fused silica fibers provided a platform to explore various nonlinear phenomena with appreciable efficiency including pulse compression [Dietel1983; Palfrey1985], temporal soliton propagation [Agrawal2013; Boyd2020; Stegeman2012], and all-optical switching [Agrawal2013; Boyd2020; Mollenauer1980; Stegeman2012] that have led to applications in fiber lasers [Ter-Mikirtychev2014] and communication systems [Willner2019] (see fiber waveguiding materials category in Section 3.5 for more information). Similarly, efforts also focused on increasing the typically weak nonlinearity of glasses by employing doped glasses [Alekseev1980; Ekimov1988; Kityk2002], photorefractive glasses [Hall1985] (not included in the table), and more recently chalcogenide glasses (ChGs) [Asobe1997]. Models to describe the nonlinearities in these dielectrics also evolved alongside experimental studies [Agrawal2013; Boyd2020; Stegeman2012]. The linear dispersion can be used in a semi-empirical way to predict nonlinear index changes in low-loss optical glasses. This so-called “BGO” model [Boling1978] was found to be valid to estimate $n_2$ of many glasses. This includes chalcogenide glasses [Fedus2010] despite the presence of NLA. It was also noted that for dielectrics, the bandgap determines the NLA spectrum as well as the dispersion of the NLR [DeSalvo1996; Sheik-Bahae1990; Sheik-Bahae1991]. Thus, the BGO model and bandgap scaling are complementary.

### 3.1.1.2.2 Background for semiconductors

Bulk semiconductors from groups II-VI, III-V, or IV, like ZnSe, GaAs, or Si, respectively, have been a mainstay in NLO since the invention of the laser. While the study of such materials in their bulk form has been a key starting point for the study of new semiconductors, structuring and combining semiconductors in novel ways has continually ignited many unique and important technologies such as detectors, lasers, and amplifiers. Much of this research excitement in semiconductors originated from the near-gap resonant nonlinearities which produced large NLO responses, with potential application in all-optical switching, and all-optical computing etc. albeit with limited bandwidth and recovery times [Hardy2007; Miller2010]. Applications involving resonant nonlinearities have included semiconductor optical amplifiers [Olsson1989; Urquhart2011], laser diodes [Bhattacharya1997], and more recently the generation of broadband infrared and THz waves [Krotkus2010; Shan2004]. Additionally, the introduction of quantum well structures provided large second-order nonlinearities, able to be engineered by altering the layer stack [Schmitt-Rink1989] (see the 0D-1D-2D materials category in Section 3.3 for more information). Such approaches have led to several useful technologies including semiconductor saturable absorbing mirrors (SESAMs) [Jung1997; Keller1996; Kim1989], which have directly enabled ultrashort mode locked laser technologies, and self-electro-optic effect devices (SEEDs) [Miller1989]. Theoretical descriptions for the response of resonant nonlinearities in semiconductors evolved similarly, encompassing effects such as band-filling, saturation, bandgap renormalization, and exciton resonance [Garmire1998].

Similarly, below-gap non-resonant nonlinearities including harmonic generation, and wave mixing were also studied [Boyd2020; Stegeman2012], and while they provide nearly an instantaneous response, these were noted as being weaker than their resonant counterparts and challenging to phase match due to their limited anisotropy. Through fabrication advances, these challenges were addressed via the use of QPM approaches [Armstrong1962; Gordon1993; Thompson1976; Hum2007]. Another key advance in semiconductor nonlinearities came from a unified model of the nonlinear refractive
index. In the case of direct bandgap semiconductors in their transparency range, they were understood in terms of nonlinear Kramers-Kronig relations [Hutchings1992; Sheik-Bahae1991] as a consequence of the NLA mechanisms of 2PA, Raman, and AC-Stark effects. Through this, it was noted that as the incident photon energy moves from resonant linear absorption saturation near the bottom of the conduction band to a non-resonant transition, the nonlinearity smoothly transitions from real saturation to “virtual” saturation otherwise known as the AC-Stark effect. Scaling rules and nonlinear dispersion relations based on the material bandgap were subsequently developed which supplied theoretical models to predict NLO coefficients, and to analyze the variety of reported NLO data [Hutchings1992; Sheik-Bahae1990; Sheik-Bahae1991; Wherrett1984]. Since 2000, Dinu's [Dinu2003a] and Garcia's [Garcia2012] models have been widely used for similar descriptions of indirect bandgap semiconductors.

### 3.1.1.2.3 Background for conductors

Nonlinearities in metals and conducting materials have been studied for nearly as long as NLO with early works examining harmonic generation in thin films [Bloembergen1968, Bloembergen1969; Sipe1980] as well as in percolated or random films [Shalaev1998]. The majority of research focused on elemental metals such as Au [C. K. Sun1994], Ag [Bloembergen1968], Cu [Elsayed-Ali1987], etc., and was closely tied with the fields of transient thermoreflectance to measure the thermal properties of metals [Brorson1990; Hohlfeld2000]. While bulk metals have exhibited large nonlinearities, they have not led to many applications in large part due to their high loss and propensity to be damaged under the high irradiances needed for NLO. One key exception to this has been surface enhanced nonlinearities, useful for achieving large improvement in processes such as Raman scattering [Wang2020]. Yet due to their limitations, the study of bulk metals was largely relegated to fundamental measurements and understanding of various light-induced effects such as so-called “Fermi-smearing,” interband transitions, and free-electron photoionization [Allen1987; Anisimov1974]. More recently, metals are finding great interest in areas including plasmonics [Maier2007; Maradudin2014], metamaterials and nanoparticles embedded in dielectrics [Cai2009] (see metamaterials category in Section 3.4), as well as in the closely related area of epsilon-near-zero (ENZ) effects [Liberal2017; Reshef2019] (see Section 3.1.2.1.2).

### 3.1.1.3 Considerations for bulk materials when performing NLO measurements

For solid materials, attention should be paid to thermal effects when using high-repetition-rate lasers or with materials showing linear absorption. Thermal effects may build up collectively over many pulses or arise within the pulse width depending upon the loss of the material. As a result, one must clearly identify the different roles of thermal and non-thermal nonlinearities [Bautista2021; Falconieri1999]. Also, the role of the pulse duration is very important in determining the origin of the nonlinearity being exploited [Christodoulides2010; De Araújo2016] and should be considered accordingly. Additionally, in many cases, bulk materials are explored as thin films grown on substrates. In this scenario, researchers should carefully characterize and remove the response of the substrate. Works should contain a detailed description of how the substrate contribution was removed as well as a report of the substrate-only response for comparison. In addition to these specific considerations for bulk materials, also the best practices described in Section 2 should be taken into account when performing NLO measurements.

### 3.1.1.4 Description of general table outline

Tables 2A and 2B show a representative list of, respectively, the second- and third-order NLO properties reported since 2000 for our range of bulk materials, across our 3 subcategories. The works included in Tables 2A and 2B were selected based upon the best practices in Section 2 and the considerations
outlined above. Table 2B lists, besides third-order nonlinearities, also 3PA coefficients. Each entry in the Tables contains information about the material and its properties, linear optical properties, NLO technique used, the excitation parameters, and the resulting NLO parameter(s).

The entries are arranged in alphabetical order, and within each material, entries are ordered by NLO technique (referred to as “Method” in the tables). The works that report dispersive datasets or dependences of the NLO parameter on multiple parameters (e.g., thickness, doping, composition, etc.) are denoted by “a b” respectively, in the Tables. The papers included in the Tables nominally report data obtained at room temperature, unless denoted otherwise by “c”. The works reporting different compositions or material variations are split into different entries where applicable. For papers with multiple thicknesses of the same material, the thickest material is reported. The data is sub-divided into “Material properties,” “Measurement details,” and “Nonlinear properties.” Measurements using two beams have the properties of the pump and probe beam listed separately, where provided, while single beam measurements are contained within the pump column. Units are contained within the table unless noted in the header. 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. If dispersive values for the NLO parameter were provided, the cited value represents the peak value for the material within the stated measurement range. For works that report tensor components, the component is shown as a leading number followed by a colon and the value (e.g., $\chi^{(2)}_{15} = 1E-12 [m/V] \rightarrow 15: 1E-12 [m/V]$). Indices are shown as listed in the original paper. Lastly, some papers relied on non-standard NLO measurement techniques (e.g., method listed as “Other”) or have notes associated with their measurement/analysis (e.g., identifying the definition used for the conversion efficiency $\eta$). These values and information are listed within the “Comments” column with the value and unit identified.

## 3.1.2 Discussion

### 3.1.2.1 Advancement since 2000 and remaining challenges

#### 3.1.2.1.1 Advancement and challenges for insulators/dielectrics

Dielectrics are one of the most well-developed and well-understood NLO material platforms. While several works have continued to refine the understanding of nonlinearities in dielectrics such as fused silica (see Section 1.1) and sapphire [Nikolakakos2004] due to their use as reference materials, post-2000 most of the advancement has been focused on applications, providing new devices and enhancing performance of existing methods, including pushing the efficiency of cascaded NLO processes (not included in table). While new material research is still ongoing, it has been more focused. In particular, advance in IR NLO materials such as chalcogenide glasses (ChGs), pnictide, and oxides has been realized, driven by emerging lasers, spectroscopy, sensing, and imaging applications in the mid- to far-IR. Among them, ChGs have received attention due to their ability to be integrated with optical and photonic-crystal fibers (PCFs) [Dudley2009; Knight2003]. When doped with rare earth elements such as Er, Nd, Pr, etc. or undoped, many applications of active and passive optical devices have been proposed [Mairaj2002; Sanghera2009; Ta'eed2005; Yan2016]. The high optical nonlinearities of these glasses have been studied over a wide range of wavelengths to optimize their compositions for applications related to all-optical switching or optical limiting [Chen2020; Cherukulappurath2004; Ensley2019; Fedus2010; Petit2009]. Furthermore, experiments have been made on mid-IR supercontinuum generation (SCG) by pumping bulk or fiber chalcogenide with fs pulses [Gattass2012; Granzow2011; Marandi2012; Møller2015; Petersen2018; Yu2013, Yu2014]. Similar advances in bulk form have been realized for cm-scale materials such as CdSiP$_2$ and lead oxyhalides, wherein lead oxides demonstrate both high transparency and strong SHG [Abudurusuli2021].

We also note the continued expansion of organic and organic-crystal materials for NLO applications from the mid-1990s and well into the 2000s [Bosshard2020; Nalwa1997]. While our effort here focuses on the development of inorganic materials, advances in organic nonlinearities have nonetheless
constituted a major effort since 2000. For more information we direct the reader to reviews on organic NLO [Wang2012; Yesodha2004].

### 3.1.2.1.2 Advancement and challenges for semiconductors

Major advancements in semiconductor nonlinearities have been made largely due to improved fabrication and characterization methods. New measurements were completed on many semiconductors, such as Si, diamond, GaN, AlN, GaAs, GaP, InN, and InSb over a wide range of wavelengths, and compared to existing models of the NLR and NLA coefficients, leading to better understanding of the 3rd-order NLO coefficient's spectral behavior [Almeida2019; Bristow2007a; Chen2017; Fishman2011; Hurlbut2007; Lin2007; Oishi2018a, Oishi2018b; Olszak2010; Wang2013]. A unifying theory of 3PA has also been reported and compared to Wherrett's scaling model for most binary II-VI and III-V semiconductors [Wherrett1984; Benis2020].

Due to these advances in fabrication and characterization, new potential applications of semiconductors have begun to emerge. For example, QPM techniques in orientation-patterned (OP) GaAs and GaP have surpassed the strict constraint of birefringent phase-matching to produce efficient SHG, DFG, OPO, and OPG. As a result, a wide range of IR (wavelengths from 2500 nm to 14200 nm) [Feaver2013; Kuo2006; O'Donnell2019; Smolski2018; Vodopyanov2014] and THz (from 0.4 THz to 4.5 THz) frequencies [Kiessling2013; Schaar2008] can be generated.

Spurred by parallel advancements in plasmonics and metamaterials, in the last 5 years, another key area of advancement has been in the study of semiconductors that exhibit epsilon-near-zero (ENZ) or near-zero-index (NZI) properties [Kinsey2019; Liberal2017; Reshef2019] occurring from either free-electrons or phononic resonances (see also the metamaterials category in Section 3.4). Although optically lossy, which must be carefully considered for its impact upon applications, homogeneous ENZ materials have demonstrated extraordinarily large index modification (Δn ~ 0.5 – 1) [Alam2016; Benis2019; Caspani2016; Clerici2017; Kinsey2015a], enhanced harmonic generation [Capretti2015a, Capretti2015b], negative refraction [Bruno2020], optically defined surfaces [Saha2020], and recently temporal interfaces and interactions such as frequency shifting [Khurgin2020; Shaltout2016; Zhou2020]. While initial works demonstrated effects through experimental efforts, more recently theory has followed to provide a deterministic and predictive explanation of nonlinearities in popular ENZ materials [Khurgin2021; Secondo2020; Solis2021]. Currently, efforts have focused on the exploration of doped oxides such as Dy:CdO, Al:ZnO, and Sn:InO in the near-IR (~1300 – 1600 nm) but undoubtedly other materials will be explored in the future expanding into the mid- and far-IR spectral ranges.

### 3.1.2.1.3 Advancement and challenges for conductors

Since 2000, the growth of NLO research in plasmonics, metamaterials, metal nanoparticles, and nanophotonics [Maier2007; Maradudin2014] has brought a renewed interest in the study of nonlinearities in bulk metals and conducting materials [Kauranen2012]. The ability to nanostructure metals with ultra-tight light confinement has led to studies that make use of the inherent metal nonlinearity [MacDonald2009; Mayer2011; Mesch2016] as well as for enhancing the NLO response of an external material [Lee2014]. One key application has been in the enhancement of Raman interactions for sensing and material study [Jiang2010]. This has been the primary advance in the study, application, and understanding of metals in NLO since 2000 (see metamaterials category in Section 3.4 for more information). Ignited by materials exploration within the field of plasmonics, another advancement in conductors was the expansion of studied materials for optical applications, with many heavily doped semiconductors, conducting ceramics, and alloys being investigated [Saha2020]. These compound metallic materials provided additional benefits such as robustness, tunability of the NLO response, and new potential applications in sensing [Golubev2018; Robert2016] while exhibiting similar NLO responses to previously explored materials.
Similarly, the rise of topological materials and topological photonics has also affected NLO in the 21st century. While the area is closely linked to low dimensional materials (see 0D-1D-2D materials category in Section 3.3), some multilayer or bulk variants have also been studied. In particular, large second-order NLO effects have been reported in Weyl semimetals such as TaAs, TaP, and NbAs [Osterhoudt2019; Patankar2018; Wu2017; Yan2017], as well as enhanced surface nonlinearities in Dirac nodal-line ZrSiS semi-metals [Chi2020].

While the losses that occur in conducting materials and their propensity for damage remain a primary concern for the broad adoption of bulk conductors in NLO applications, the expansion of available materials combined with new physical understanding and physics may provide the ingredients for metals to make a contribution to the NLO field. Regardless, they remain key supporting materials for various fields of photonics, and understanding their inherent nonlinearities remains an important task for the field of NLO.

### 3.1.2.2 Recommendations for future works on bulk materials

As lasers and various methods of measurement continue to advance, our ability to characterize materials evolves in parallel. Systems with several tunable excitation beams, supercontinuum probes, variable repetition rates, etc. are expanding characterization capabilities and allowing more flexibility, which before 2000 was difficult to put into practice. We encourage future NLO works to embrace these new capabilities, exploring characterization and datasets which include more than just single wavelengths and pulse widths. Among various parameters, temporal and spectral information are perhaps the most useful information to be added for bulk materials, although this depends upon the application area of the material. In addition, the more thorough characterization will support an improved understanding of the NLO interactions at play, helping to delineate the roles of unwanted effects such as thermal nonlinearities and nonlinear scattering and improving the reliability of results.

Another area of recommendation for the community is in the reporting of key experimental metrics. In many cases, papers are missing certain parameters of the experiment (peak/average power, beam waist, repetition rate, pulse width, etc., see tables) or do not report the method for calculation (flat top, Gaussian, full-width-half-max, etc.). This can lead to difficulty when interpreting the results as well as invoke questions as to the experimental rigor. By meticulously reporting the metrics of experiments, we can improve the trust in the results, aid in reproducibility, and help to avoid errors.

Lastly, the new millennium has seen an explosion in new materials available for study. In many cases, it can be observed that works jump directly to the demonstration of example applications without performing rigorous characterization of the material's NLO response. While such studies are useful, we remind the community that carefully conducted experiments and reporting of inherent NLO coefficients ($\chi^{(2,3)}$, $n_2$, $g_{Raman}$, etc.) is of key importance to the field as new materials and applications continue to be explored.
### 3.1.3 Data table for bulk materials

<table><caption>**Table 2A.** Second-order NLO properties of bulk 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="3">Material Properties</th><th colspan="2">Measurement Details</th><th colspan="3">Nonlinear Properties</th><th rowspan="2">Comments<br>Reference</th></tr><tr><th>Thickness<br>Fabrication<br>Substrate</th><th>Index<br>Abs. Coeff.<br>Wavelength</th><th>Crystallinity<br>Bandgap<br>Doping Level</th><th>Pump<br>Wavelength<br>Peak Power<br>or<br>Irradiance<br>Pulse Width<br>Rep. Rate</th><th>Probe<br>Wavelength<br>Peak Power<br>or<br>Irradiance<br>Pulse Width</th><th>χ<sup>(2)</sup> [m/V]*</th><th>d [m/V]*</th><th>η [%]*,†</th></tr></thead><tbody><tr><td colspan="12" style="text-align: center; font-weight: bold;">Conductors</td></tr><tr><td>NbAs<sup>a</sup></td><td>SHG</td><td>-<br>Vapor<br>Transport<br>-</td><td>-<br>5 [1/μm]<br>800 [nm]</td><td>Monocrys.</td><td>800 [nm]<br>-<br>100 [fs]<br>-</td><td>-<br>-<br>-</td><td>-</td><td>33: 2.7E-9</td><td>-</td><td>-<br>[Wu2017]</td></tr><tr><td>TaAs<sup>a</sup></td><td>SHG</td><td>-<br>Vapor<br>Transport<br>-</td><td>-<br>5 [1/μm]<br>-</td><td>Monocrys.</td><td>800 - 2500<br>[nm]<br>-<br>50 [fs]<br>-</td><td>-<br>-<br>-<br>-</td><td>-</td><td>-</td><td>-</td><td>Nonlinear conductivity σ = 5E-3<br>[1/Ω-V]<br><br>[Patankar2018]</td></tr><tr><td>TaAs<sup>a,c</sup></td><td>SHG</td><td>-<br>Vapor<br>Transport<br>-</td><td>-<br>5 [1/μm]<br>800 [nm]</td><td>Monocrys.</td><td>800 [nm]<br>-<br>100 [fs]<br>-</td><td>-<br>-<br>-<br>-</td><td>-</td><td>33: 3.6E-9</td><td>-</td><td>-<br>[Wu2017]</td></tr><tr><td>TaAs</td><td>Other (see<br>comments)</td><td>-<br>Chemical<br>Vapor<br>Transport<br>-</td><td>-<br>-<br>-<br>-</td><td>Monocrys.<br>N<sub>e</sub> = 8.08E+23<br>N<sub>h</sub> = 9.35E+23<br>[1/m<sup>3</sup>]</td><td>10600 [nm]<br>-<br>CW<br>-</td><td>-<br>-<br>-<br>-</td><td>-</td><td>-</td><td>-</td><td>Method: Bulk Photovoltaic Effect<br>Nonlinear conductivity σ<sub>aac</sub> = 154 ± 17 [μA/V<sup>2</sup>]<br><br>[Osterhoudt2019]</td></tr><tr><td>TaP<sup>a</sup></td><td>SHG</td><td>-<br>Vapor<br>Transport<br>-</td><td>-<br>5 [1/μm]<br>800 [nm]</td><td>Monocrys.</td><td>800 [nm]<br>-<br>100 [fs]<br>-</td><td>-<br>-<br>-<br>-</td><td>-</td><td>33: 3.2E-9</td><td>-</td><td>-<br>[Wu2017]</td></tr></tbody></table>
<table><tbody><tr><td>ZrSiS</td><td>SHG</td><td>-<br>Chemical Vapor Transport</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>1300 [nm]<br>7.6 [MW/m²]<br>120 [fs]<br>1 [kHz]</td><td>4780E-12</td><td>-</td><td>0.011</td><td>-<br>[Chi2020]</td></tr><tr><td colspan="10" style="background-color: #D9EAD3; text-align: center; font-weight: bold;">Semiconductors</td></tr><tr><td>Al<sub>0.08</sub>Ga<sub>0.92</sub>N<sup>b</sup></td><td>SHG</td><td>980 [nm]<br>MOCVD (0001) c-Sapphire</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>1064 [nm]<br>360 [kW]<br>5 [ns]<br>14 [Hz]</td><td>-</td><td>31: 1.45E-12<br>15: 1.45E-12<br>33: -2.9E-12</td><td>-</td><td>-<br>[Passeri2004]</td></tr><tr><td>Al<sub>0.5</sub>Ga<sub>0.5</sub>N</td><td>SHG</td><td>63 [nm]<br>MOCVD (0001) c-Sapphire</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>1064 [nm]<br>-<br>5 [ns]<br>13 [Hz]</td><td>-</td><td>33: 1.20e-12</td><td>-</td><td>-<br>[Larciprete2006]</td></tr><tr><td>Al<sub>x</sub>Ga<sub>1-x</sub>N<sup>b</sup></td><td>SHG</td><td>2.13 [µm]<br>MOCVD and HVPE (0001) c-Sapphire</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>1064 [nm]<br>-<br>1.25 [ms]<br>82 [MHz]</td><td>-<br>-<br>-</td><td>31: 5.3E-12<br>33: -7.4E-12</td><td>-</td><td>-<br>[Sanford2005]</td></tr><tr><td>AlN</td><td>SHG</td><td>340 [nm]<br>MBE<br>Sapphire</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>800 [nm]<br>-<br>7 [fs]<br>80 [MHz]</td><td>-</td><td>3.22E-12</td><td>-</td><td>-<br>[Kobayashi2007]</td></tr><tr><td>AlN<sup>b</sup></td><td>SHG</td><td>620 [µm]<br>PVT<br>-<br>-</td><td>60 [1/m]<br>1030 [nm]</td><td>Monocrys.</td><td>1030 [nm]<br>2.2 [TW/m²]<br>10 [ns]<br>1 [kHz]</td><td>-</td><td>31: 9.55E-14<br>15: 5.48E-12<br>33: 4.3E-12</td><td>-</td><td>-<br>[Majkić2017]</td></tr><tr><td>OC-GaAs<sup>a,b</sup></td><td>DFG</td><td>1 [mm]<br>-<br>-<br>-</td><td>-<br>-<br>-<br>-</td><td>-</td><td>2100-2130 [nm]<br>-<br>6 [ps]<br>50 [MHz]</td><td>2130-2160 [nm]<br>-<br>-<br>-</td><td>-</td><td>0.012<br>1.2</td><td>Optical-to-THz Conversion Eff.<br>Quantum Eff.<br>[Schaar2008]</td></tr><tr><td>DB-GaAs<sup>a</sup></td><td>DFG</td><td>5.05 [mm]<br>-<br>-<br>-</td><td>-<br>-<br>-<br>-</td><td>-</td><td>2100-2130 [nm]<br>-<br>6 [ps]<br>50 [MHz]</td><td>2130-2160 [nm]<br>-<br>-<br>-</td><td>-</td><td>0.012<br>1.2</td><td>Optical-to-THz Conversion Eff.<br>Quantum Eff.<br>[Schaar2008]</td></tr></tbody></table>
<table><tbody><tr><td>OP-GaAs<sup>a</sup></td><td>DFG</td><td>800 [µm]<br>MBE and<br>HVPE</td><td>-<br>-<br>-</td><td>2100-2130 [nm]<br>6 [ps]<br>50 [MHz]</td><td>2130-2160 [nm]<br>-<br>-</td><td>-</td><td>0.012<br>1.2</td><td>Optical-to-THz Conversion Eff.<br>Quantum Eff.<br>[Schaar2008]</td></tr><tr><td>PI-GaAs</td><td>DFG</td><td>653 [µm]<br>-<br>-</td><td>-<br>-<br>-</td><td>2119.6 [nm]<br>4.6 [ns]<br>24 [kHz]</td><td>2138.4 [nm]<br>-<br>4.6 [ns]</td><td>-</td><td>4.31E-5<br>0.0103</td><td>DFG Conversion Eff.<br>Quantum Eff.<br>[Mei2016]</td></tr><tr><td>OP-GaAs</td><td>DFG</td><td>1.8 [mm]<br>-<br>-</td><td>-<br>-<br>-</td><td>1053 [nm]<br>17 [ns]<br>2 [kHz]</td><td>-<br>-<br>-</td><td>-</td><td>0.6<br>4.2</td><td>DFG Energy / Pump Energy<br>Quantum Conversion Eff.<br>[Boyko2018]</td></tr><tr><td>GaAs<sup>b</sup></td><td>SHG</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>Monocrys.<br>1.42 [eV]<br>-</td><td>852 [nm]<br>14 [ps]<br>-</td><td>7.5E-10</td><td>-</td><td>-<br>[Bergfeld2003]</td></tr><tr><td>OP-GaAs</td><td>SHG</td><td>500 [µm]<br>MBE and<br>HVPE</td><td>8 [1/m]<br>4135 [nm]</td><td>4135 [nm]<br>63 [ns]<br>25 [Hz]</td><td>-<br>-<br>-</td><td>-</td><td>1.0857E-10</td><td>33<br>[Skauli2002]</td></tr><tr><td>OP-GaAs<sup>b</sup></td><td>Other (see comments)</td><td>1 [mm]<br>-<br>-</td><td>-<br>-<br>-</td><td>1952 [nm]<br>46 [ps]<br>1 [MHz]</td><td>-<br>-<br>-</td><td>-</td><td>22.5</td><td>Method: Optical parametric<br>generation<br>OPA Power Conversion Eff.<br>[Qiang Fu2018]</td></tr><tr><td>OP-GaAs<sup>b</sup></td><td>Other (see comments)</td><td>1 [mm]<br>-<br>-</td><td>-<br>-<br>-</td><td>1992 [nm]<br>150<br>[GW/m<sup>2</sup>]<br>95 [ps]<br>100 [MHz]</td><td>-<br>-<br>-</td><td>-</td><td>32.6</td><td>Method: Optical Parametric<br>Oscillation<br>[Qiand Fu2020]</td></tr><tr><td>DB-GaAs<sup>b</sup></td><td>Other (see comments)</td><td>-<br>MBE and<br>HVPE</td><td>3.33<br>4400 [nm]</td><td>4400 [nm]<br>100<br>[TW/m<sup>2</sup>]<br>100 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-</td><td>0.087<br>3.3</td><td>Method: Optical Rectification<br>Internal Optical-to-THz<br>Conversion Eff.<br>Internal Photon Conversion Eff.<br>[Vodopyanov2006]</td></tr></tbody></table>
<table><tbody><tr><td>OP-GaAs</td><td>Other (see comments)</td><td>500 [µm]<br>MBE and<br>HVPE<br>-</td><td>-</td><td>-</td><td>3250 [nm]<br>-<br>1 [ps]<br>-</td><td>-</td><td>-</td><td>51<br>15</td><td>Method: Optical parametric<br>generation<br><br>Slope Eff.<br>External Conversion Eff.<br><br>[Kuo2006]</td></tr><tr><td>OP-GaAs</td><td>Other (see comments)</td><td>400 [µm]<br>MBE and<br>HVPE<br>-</td><td>-</td><td>-</td><td>1980 [nm]<br>-<br>120 [fs]<br>100 [MHz]</td><td>-</td><td>-</td><td>1.6E-4<br>4.7E-4</td><td>Method: Parametric down<br>conversion<br><br>Optical-to-THz Conversion Eff.<br>Internal Optical-to-THz<br>Conversion Eff.<br><br>[Imeshev2006]</td></tr><tr><td>OP-GaAs</td><td>Other (see comments)</td><td>250 [µm]<br>-<br>-<br>4200 [nm]</td><td>3.01<br>-<br>-</td><td>-</td><td>1000 [nm]<br>-<br>70 [fs]<br>250 [MHz]</td><td>-</td><td>-</td><td>25</td><td>Method: Half-Harmonic<br>Generation<br><br>Slope Conversion Eff.<br><br>[Sorokin2018]</td></tr><tr><td>GaN<sup>b</sup></td><td>SHG</td><td>229.67<br>[µm]<br>MOCVD<br>and HVPE<br>Free-standing</td><td>-<br>-<br>-<br>-</td><td>Monocrys.<br>-</td><td>1064 [nm]<br>-<br>1.25 [ms]<br>82 [MHz]</td><td>31: 5.7E-12<br>33: -9.2E-12</td><td>-</td><td>-</td><td>-<br><br>[Sanford2005]</td></tr><tr><td>GaN<sup>b</sup></td><td>SHG</td><td>4.2 [µm]<br>-<br>Sapphire</td><td>2.2978<br>-<br>1064 [nm]</td><td>Monocrys.<br>-</td><td>1064 [nm]<br>-<br>10 [ns]<br>10 [Hz]</td><td>zxx: 15.3E-12<br>xzx: 14.8E-12<br>zzz: 30.3E-12</td><td>-</td><td>-</td><td>-<br><br>[Fujita2000]</td></tr><tr><td>GaN</td><td>SHG</td><td>3.5 [µm]<br>MBE<br>(0001) c-Sapphire</td><td>-<br>-<br>-</td><td>-</td><td>1980 [nm]<br>-<br>6 [ns]<br>30 [Hz]</td><td>2.8E-11</td><td>-</td><td>-</td><td>-<br><br>[Nevou2006]</td></tr><tr><td>GaN</td><td>SHG</td><td>2 [µm]<br>MOCVD<br>(0001) c-Sapphire</td><td>-<br>-<br>-</td><td>Monocrys.<br>3.42 [eV]</td><td>1064 [nm]<br>-<br>5 [ns]<br>14 [Hz]</td><td>-</td><td>31: 2.4E-12<br>15: 1.8E-12<br>33: -3.7E-12</td><td>-</td><td>-<br><br>[Passeri2004]</td></tr><tr><td>GaN</td><td>SHG</td><td>302 [nm]<br>MOCVD<br>(0001) c-Sapphire</td><td>-<br>-<br>-</td><td>Monocrys.<br>3.42 [eV]</td><td>1064 [nm]<br>360 [kW]<br>5 [ns]<br>13 [Hz]</td><td>-</td><td>33: 4.82e-12</td><td>-</td><td>-<br><br>[Larciprete2006]</td></tr></tbody></table>
<table><tbody><tr><td>GaN</td><td>SHG</td><td>340 [nm]<br>MBE<br>Sapphire</td><td>-<br>-<br>-</td><td>Monocrys.<br>-<br>-</td><td>800 [nm]<br>-<br>7 [fs]<br>80 [MHz]</td><td>-<br>-<br>-</td><td>1.59E-11</td><td>-</td><td>-<br>[Kobayashi2007]</td></tr><tr><td>GaN</td><td>SHG</td><td>1 [µm]<br>MOCVD<br>(0001) c-Sapphire</td><td>2.29<br>-<br>1064 [nm]</td><td>Monocrys.<br>3.4 [eV]<br>-</td><td>1064 [nm]<br>-<br>7 [ns]<br>10 [Hz]</td><td>-<br>-<br>-</td><td>31: 5.45E-12<br>33: -1.107E-11</td><td>-</td><td>-<br>[Kravetsky2000]</td></tr><tr><td rowspan="2">GaN</td><td rowspan="2">SHG<br>Imaging</td><td>2.5 [µm]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>1230 [nm]<br>-<br>150 [fs]<br>125 [MHz]</td><td>-<br>-<br>-</td><td>3E-12</td><td>-</td><td>-</td><td>-<br>[Sun2000]</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ITO<sup>a</sup></td><td>SHG</td><td>37 [nm]<br>Sputtering<br>Silicon</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>1100 [nm]<br>420<br>[GW/m<sup>2</sup>]<br>150 [fs]<br>81 [MHz]</td><td>-<br>-<br>-<br>-</td><td>xzx: 5E-14<br>zzz: 1.8E-13</td><td>-</td><td>3.00E-13</td><td>Photon Conversion Eff.<br>[Capretti2015a]</td></tr><tr><td>(110)-GaP<sup>b</sup></td><td>DFG</td><td>663 [µm]<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>1074 [nm]<br>1.3 [TW/m<sup>2</sup>]<br>5 [ns]<br>10 [Hz]</td><td>1064 [nm]<br>1.5 [MW]<br>10 [ns]</td><td>-</td><td>-</td><td>0.182<br>39.6</td><td>THz/Input<br>Photon Conversion Eff.<br>[Jiang2011]</td></tr><tr><td>(110)-GaP</td><td>DFG</td><td>663 [µm]<br>-<br>-</td><td>3.217<br>220 [1/m]<br>120000<br>[nm]</td><td>-<br>-<br>-</td><td>1064 [nm]<br>5 [kW]<br>10 [ns]<br>-</td><td>-<br>1.2 [TW/m<sup>2</sup>]<br>5 [ns]</td><td>-</td><td>-</td><td>0.22<br>25</td><td>Internal Eff.<br>Photon Conversion Eff.<br>[Jiang2010]</td></tr><tr><td>OP-GaP<sup>a</sup></td><td>DFG</td><td>1 [mm]<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>1550 [nm]<br>-<br>110 [fs]<br>93.4 [MHz]</td><td>1800-1960 [nm]<br>-<br>60 [fs]</td><td>-</td><td>-</td><td>19</td><td>Photon Conversion Eff.<br>[Lee2017]</td></tr><tr><td>OP-GaP<sup>b</sup></td><td>DFG</td><td>1.7 [mm]<br>-<br>-</td><td>-<br>32 [1/m]<br>1064 [nm]</td><td>-<br>-<br>-</td><td>1064 [nm]<br>-<br>23 [ns]<br>80 [kHz]</td><td>1748 [nm]<br>-<br>-</td><td>-</td><td>-</td><td>1<br>2.5</td><td>Pump-to-DFG Eff.<br>Photon Conversion Eff.<br>[Wei2018]</td></tr><tr><td>OP-GaP</td><td>DFG</td><td>1.7 [mm]<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>1064 [nm]<br>-<br>23 [ns]<br>80 [kHz]</td><td>1748 [nm]<br>-<br>16 [ns]</td><td>-</td><td>1.3E-11</td><td>1.2</td><td>-<br>[Wei2017]</td></tr></tbody></table>
<table><tbody><tr><td>OP-GaP</td><td>Other (see comments)</td><td>1 [mm]<br/>-<br/>-</td><td>-<br/>-<br/>-<br/>2.27 [eV]</td><td>1048 [nm]<br/>-<br/>140 [fs]<br/>80 [MHz]</td><td>-</td><td>-</td><td>8.6<br/>28.9</td><td>Method: Optical Parametric Oscillation<br/>Idler Slope Conversion Eff.<br/>Quantum Eff.</td></tr><tr><td>OP-GaP</td><td>Other (see comments)</td><td>500 [µm]<br/>-<br/>-<br/>4200 [nm]</td><td>3.3<br/>-<br/>-<br/>2.26 [eV]</td><td>1000 [nm]<br/>-<br/>70 [fs]<br/>250 [MHz]</td><td>-</td><td>-</td><td>59</td><td>[O'Donnell2019]<br/>Method: Half-Harmonic Generation<br/>Slope Conversion Eff.</td></tr><tr><td>4H SiC</td><td>SHG</td><td>-<br/>-<br/>SiC</td><td>2.54<br/>-<br/>1064 [nm]</td><td>Monocrys.<br/>-<br/>-<br/>1064 [nm]</td><td>3.71<br/>[GW/m²]<br/>100 [ns]<br/>5 [kHz]</td><td>-<br/>-<br/>-<br/>1064 [nm]</td><td>31: 6.5E-12<br/>15: 6.7E-12<br/>33: -11.7E-12</td><td>-<br/>-<br/>-<br/>[Sato2009]</td></tr><tr><td>6H SiC</td><td>SHG</td><td>-<br/>-<br/>SiC</td><td>2.54<br/>-<br/>1064 [nm]</td><td>Monocrys.<br/>-<br/>-<br/>1064 [nm]</td><td>3.71<br/>[GW/m²]<br/>100 [ns]<br/>5 [kHz]</td><td>-<br/>-<br/>-<br/>1064 [nm]</td><td>31: 6.7E-12<br/>15: 6.5E-12<br/>33: -12.5E-12</td><td>-<br/>-<br/>-<br/>[Sato2009]</td></tr></tbody></table>

<footnote>a Multiple wavelengths reported, b Multiple Parameters (e.g., thickness, crystal orientation) reported, c Measurement taken at a temperature other than room temperature. *Units as illustrated unless otherwise indicated in table, † See Comments for a description of conversion efficiencies</footnote>
<table><caption>**Table 2B.** Third-order NLO properties of bulk materials from representative works since 2000. In addition, 3PA coefficients are provided at the end of the table. Legend for superscripts: see below the table.</caption><thead><tr><th rowspan="2">Material</th><th rowspan="2">Method</th><th colspan="3">Material Properties</th><th colspan="2">Measurement Details</th><th colspan="2">Nonlinear Properties</th><th rowspan="2">Comments<br>Reference</th></tr><tr><th>Thickness<br>Fabrication<br>Substrate</th><th>Index<br>Abs. Coeff.<br>Wavelength</th><th>Crystallinity<br>Bandgap<br>Doping Level</th><th>Pump<br>Wavelength<br>Peak Power or<br>Irradiance<br>Pulse Width<br>Rep. Rate</th><th>Probe<br>Wavelength<br>Peak Power or<br>Irradiance<br>Pulse Width</th><th>χ<sup>(3)</sup> [m<sup>2</sup>/V<sup>2</sup>]*</th><th>n<sub>2</sub> [m<sup>2</sup>/w]<br>α<sub>2</sub> [m/W]<sup>†</sup><br>α<sub>3</sub> [m<sup>3</sup>/W<sup>2</sup>]</th></tr></thead><tbody><tr><th colspan="10" style="text-align: center;">Conductors</th></tr><tr><td>TiN</td><td>Z-Scan</td><td>52 [nm]<br>Sputtering<br>Fused Silica</td><td>2.66<br>35 [1/μm]<br>1550 [nm]</td><td>Polycrys.</td><td>1550 [nm]<br>14.1 [TW/m<sup>2</sup>]<br>150 [fs]<br>1 [kHz]</td><td>-</td><td>-5.9E-17-i1.7E-16</td><td>-3.70E-15<br>-6.60E-09<sup>†</sup><br>-</td><td>-<br>[Kinsey2015b]</td></tr><tr><td>TiN</td><td>Beam Defl.</td><td>30 [nm]<br>Sputtering<br>Fused Silica</td><td>-<br>54.8 [1/μm]<br>650 [nm]</td><td>Polycrys.<br>5 [eV]<br>-</td><td>800 [nm]<br>-<br>55 [fs]<br>1 [kHz]</td><td>650 [nm]<br>-<br>110 [fs]</td><td>-</td><td>4.70E-13<br>2.15E-07<br>-</td><td>-<br>[George2019]</td></tr><tr><th colspan="10" style="text-align: center;">Insulators</th></tr><tr><td>Al<sub>2</sub>O<sub>3</sub><sup>a</sup></td><td>Z-Scan</td><td>1 [mm]<br>-<br>-</td><td>-<br>-<br>-</td><td>Monocrys.<br>7.3 [eV]</td><td>550 [nm]<br>-<br>1[ps]<br>1 [kHz]</td><td>-<br>-<br>-<br>-</td><td>-</td><td>3.30E-20<br>-<br>-<br>-</td><td>[Major2004]</td></tr><tr><td>As<sub>2</sub>S<sub>3</sub></td><td>Z-Scan</td><td>-<br>Amorphous<br>Mat. Inc.<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2000 [nm]<br>20 [TW/m<sup>2</sup>]<br>90 [fs]<br>26 [Hz]</td><td>-<br>-<br>-<br>-</td><td>-</td><td>2.50E-18<br>-<br>-<br>-</td><td>-<br>[Ensley2019]</td></tr><tr><td>AsSe</td><td>Z-Scan</td><td>-<br>Amorphous<br>Mat. Inc.<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2000 [nm]<br>20 [TW/m<sup>2</sup>]<br>90 [fs]<br>26 [Hz]</td><td>-<br>-<br>-<br>-</td><td>-</td><td>6.20E-18<br>-<br>-<br>-</td><td>-<br>[Ensley2019]</td></tr><tr><td>(Bi<sub>2</sub>O<sub>3</sub>)<sub>0.25</sub>(ZnO)<sub>0.375</sub><br>(B<sub>2</sub>O<sub>3</sub>)<sub>0.375</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>532 [nm]<br>-<br>80 [ps]<br>10 [Hz]</td><td>-<br>-<br>-<br>-</td><td>-</td><td>3.00E-18<br>5.50E-11<br>-</td><td>-<br>[Gomes2007]</td></tr></tbody></table>
<table><tbody><tr><td>Ge<sub>0.18</sub>Ga<sub>0.05</sub><br>Sb<sub>0.07</sub>S<sub>0.3</sub>Se<sub>0.4</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>-<br>1.66 [eV]<br>-</td><td>1064 [nm]<br>20 [TW/m<sup>2</sup>]<br>15 [ps]<br>10 [Hz]</td><td>-<br>-<br>-<br>-</td><td>4.60E-18<br>9.00E-12<br>-<br>[Petit2006]</td><td>-</td></tr><tr><td>Ge<sub>0.1</sub>As<sub>0.1</sub>Se<sub>0.6</sub> Te<sub>0.2</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.9<br>317 [1/m]<br>1064 [nm]</td><td>-<br>1.23 [eV]<br>-</td><td>1064 [nm]<br>14 [TW/m<sup>2</sup>]<br>15 [ps]<br>10 [Hz]</td><td>2.00E-17<br>8.00E-11<br>-<br>[Cherukulappurath2004]</td><td>-</td></tr><tr><td>Ge<sub>0.115</sub>As<sub>0.24</sub> Se<sub>0.645</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.265<br>-<br>1550 [nm]</td><td>-<br>1.75 [eV]<br>-</td><td>1550 [nm]<br>10 [TW/m<sup>2</sup>]<br>260 [fs]<br>1 [kHz]</td><td>7.90E-18<br>1.00E-13<br>-<br>[Wang2014]</td><td>-</td></tr><tr><td>Ge<sub>0.15</sub>Sb<sub>0.1</sub> Se<sub>0.75</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.598<br>-<br>1550 [nm]</td><td>-<br>1.72 [eV]<br>-</td><td>1550 [nm]<br>10 [TW/m<sup>2</sup>]<br>260 [fs]<br>1 [kHz]</td><td>7.50E-18<br>1.00E-13<br>-<br>[Wang2014]</td><td>-</td></tr><tr><td>Ge<sub>0.16</sub>Sb<sub>0.14</sub>S<sub>0.7</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.31<br>-<br>1064 [nm]</td><td>-<br>2.1 [eV]<br>-</td><td>1064 [nm]<br>20 [TW/m<sup>2</sup>]<br>15 [ps]<br>10 [Hz]</td><td>2.10E-18<br>1.00E-12<br>-<br>[Petit2009]</td><td>-</td></tr><tr><td>Ge<sub>0.23</sub>Sb<sub>0.07</sub> Se<sub>0.7</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.58<br>-<br>1064 [nm]</td><td>-<br>1.66 [eV]<br>-</td><td>1064 [nm]<br>5 [TW/m<sup>2</sup>]<br>15 [ps]<br>10 [Hz]</td><td>1.03E-17<br>2.40E-11<br>-<br>[Petit2007]</td><td>-</td></tr><tr><td>Ge<sub>0.33</sub>As<sub>0.12</sub> Se<sub>0.55</sub></td><td>Z-Scan</td><td>-<br>Amorphous<br>Mat. Inc.<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2000 [nm]<br>20 [TW/m<sup>2</sup>]<br>90 [fs]<br>26 [Hz]</td><td>3.80E-18<br>-<br>-<br>[Ensley2019]</td><td>-</td></tr><tr><td>Ge<sub>0.33</sub>As<sub>0.12</sub> Se<sub>0.55</sub></td><td>Z-Scan</td><td>-<br>Amorphous<br>Mat. Inc.<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>3900 [nm]<br>20 [TW/m<sup>2</sup>]<br>240 [fs]<br>10 [Hz]</td><td>7.50E-18<br>-<br>-<br>[Ensley2019]</td><td>-</td></tr><tr><td>(GeS<sub>2</sub>)<sub>0.1</sub>(Sb<sub>2</sub>S<sub>3</sub>)<sub>0.75</sub><br>(CsI)<sub>0.15</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.8<br>-<br>1064 [nm]</td><td>-<br>-<br>-</td><td>1064 [nm]<br>20 [TW/m<sup>2</sup>]<br>17 [ps]<br>0.1 [Hz]</td><td>8.10E-18<br>1.20E-11<br>-<br>[Fedus2010]</td><td>-</td></tr><tr><td>(NaPO<sub>3</sub>)<sub>0.4</sub>(BaF<sub>2</sub>)<sub>0.1</sub><br>(WO<sub>3</sub>)<sub>0.5</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>532 [nm]<br>-<br>80 [ps]<br>10 [Hz]</td><td>6.00E-19<br>5.00E-12<br>-<br>[Falcão-Filho2004]</td><td>-</td></tr></tbody></table>
<table><tbody><tr><td>(Pb(PO<sub>3</sub>)<sub>2</sub>)<sub>0.4</sub><br>(WO<sub>3</sub>)<sub>0.6</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>1.93<br>116 [1/m]<br>1064 [nm]</td><td>-<br>-<br>-</td><td>1064 [nm]<br>50 [TW/m<sup>2</sup>]<br>17 [ps]<br>10 [Hz]</td><td>-<br>-<br>-<br>-</td><td>4.50E-19<br>2.00E-13<br>-<br>[Oliveira2010]</td></tr><tr><td>(PbO)<sub>0.46</sub>(Ga<sub>2</sub>O<sub>3</sub>)<sub>0.1</sub><br>(Bi<sub>2</sub>O<sub>3</sub>)<sub>0.426</sub><br>(BaO)<sub>0.014</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.3<br>-<br>1064 [nm]</td><td>-<br>-<br>-</td><td>1064 [nm]<br>30 [TW/m<sup>2</sup>]<br>15 [ps]<br>10 [Hz]</td><td>-<br>-<br>-<br>-</td><td>1.60E-18<br>1.00E-12<br>-<br>[De Araújo2005]</td></tr><tr><td>(TeO<sub>2</sub>)<sub>0.7</sub>(GeO<sub>2</sub>)<sub>0.15</sub><br>(K<sub>2</sub>O)<sub>0.05</sub>(Bi<sub>2</sub>O<sub>3</sub>)<sub>0.1</sub></td><td>Z-Scan</td><td>-<br>Melt Quench<br>-</td><td>2.1<br>11 [1/m]<br>1064 [nm]</td><td>-<br>3.08 [eV]<br>-</td><td>1064 [nm]<br>50 [TW/m<sup>2</sup>]<br>17 [ps]<br>10 [Hz]</td><td>-<br>-<br>-<br>-</td><td>7.50E-20<br>2.00E-13<br>-<br>[Oliveira2014]</td></tr><tr><td colspan="8" style="text-align: center; font-weight: bold;">Semiconductors</td></tr><tr><td>Al:ZnO</td><td>Nonlin.<br>R/T</td><td>900 [nm]<br>PLD<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>785 [nm]<br>13000 [TW/m<sup>2</sup>]<br>100 [fs]<br>100 [Hz]</td><td>1258 [nm]<br>-<br>100 [fs]</td><td>8E-20+i2E-20<br>-<br>-</td></tr><tr><td>Al:ZnO<sup>b</sup></td><td>Nonlin.<br>R/T</td><td>900 [nm]<br>PLD<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>787 [nm]<br>900 [TW/m<sup>2</sup>]<br>100 [fs]<br>100 [Hz]</td><td>1120-1550 [nm]<br>-<br>-<br>-</td><td>3.5E-19-i2E-19<br>-<br>-</td></tr><tr><td>Diamond</td><td>Brillouin<br>Laser<br>Threshold</td><td>5 [mm]<br>CVD<br>-</td><td>-<br>-<br>-</td><td>Monocrys.<br>40 [ppb]</td><td>532 [nm]<br>-<br>CW<br>-</td><td>-<br>-<br>-<br>-</td><td>g<sub>Brillouin</sub> = 6.0E-10 [m/W]<br>Shift = 167 [GHz]<br>[Bai2020]</td></tr><tr><td>Diamond</td><td>I-scan</td><td>100 [µm]<br>Natural<br>-</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>250 [nm]<br>500 [TW/m<sup>2</sup>]<br>100 [fs]<br>-</td><td>-<br>-<br>-<br>-</td><td>2.20E-11<br>-<br>-<br>-</td></tr><tr><td>Diamond</td><td>Nonlin.<br>R/T</td><td>100 [µm]<br>Type IIa<br>-</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>273 [nm]<br>90 [TW/m<sup>2</sup>]<br>150 [fs]<br>1 [kHz]</td><td>410 [nm]<br>-<br>-<br>-</td><td>2.40E-11<br>-<br>-<br>-</td></tr><tr><td>Diamond</td><td>Nonlin.<br>R/T</td><td>300 [µm]<br>CVD<br>-</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>800 [nm]<br>-<br>40 [fs]<br>100 [kHz]</td><td>-<br>-<br>-<br>-</td><td>7.30E-21<br>9.00E-13<br>-<br>[Motojima2019]</td></tr></tbody></table>
<table><tbody><tr><td rowspan="3">Diamond</td><td rowspan="3">Nonlin.<br>R/T</td><td>300 [µm]</td><td>-</td><td>Monocrys.</td><td>800 [nm]</td><td>-</td><td>1.20E-20</td><td>-</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.75E-12</td><td>[Motojima2019]</td></tr><tr><td>-</td><td>-</td><td>N<sub>ion flux</sub> = 2E+11<br>[1/cm<sup>2</sup>]</td><td>40 [fs]<br>100 [kHz]</td><td>-</td><td>-</td><td></td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">Nonlin.<br>R/T</td><td>300 [µm]</td><td>-</td><td>Monocrys.</td><td>800 [nm]</td><td>-</td><td>2.42E-19</td><td>-</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.01E-12</td><td>[Motojima2019]</td></tr><tr><td>-</td><td>-</td><td>N<sub>ion flux</sub> = 1E+12<br>[1/cm<sup>2</sup>]</td><td>40 [fs]<br>100 [kHz]</td><td>-</td><td>-</td><td></td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">SRS Pump-<br>Probe</td><td>8 [mm]</td><td>-</td><td>Monocrys.</td><td>1864 [nm]<br>100 [kW]</td><td>2480 [nm]<br>3.75 [kW]</td><td>-</td><td>g<sub>Raman</sub> = 3.8E-11 [m/W]<br>Shift = 1.33E+5 [1/m]</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td></td></tr><tr><td>-</td><td>-</td><td>-</td><td>4 [ns]<br>4 [ns]</td><td>-</td><td>-</td><td>[Sabella2015]</td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">THG</td><td>1 [µm]</td><td>-</td><td>Nanocrystalline</td><td>1055 [nm]<br>150 [GW/m<sup>2</sup>]</td><td>-</td><td>5E-22</td><td>Conversion Eff. = 5.6E-6<br>[%]</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>90 [fs]</td><td>-</td><td>-</td><td></td></tr><tr><td>Si</td><td>-</td><td>-</td><td>1 [kHz]</td><td>-</td><td>-</td><td>[Trojánek2010]</td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">Z-Scan</td><td>300 [µm]</td><td>-</td><td>Monocrys.</td><td>800 [nm]</td><td>-</td><td>4.16E-20</td><td>-</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>9.93E-14</td><td>[Motojima2019]</td></tr><tr><td>-</td><td>-</td><td>-</td><td>40 [fs]<br>100 [kHz]</td><td>-</td><td>-</td><td></td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">Z-Scan</td><td>300 [µm]</td><td>-</td><td>Monocrys.</td><td>800 [nm]</td><td>-</td><td>5.50E-20</td><td>-</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>1.61E-13</td><td>[Motojima2019]</td></tr><tr><td>-</td><td>-</td><td>N<sub>ion flux</sub> = 1E+12<br>[1/cm<sup>2</sup>]</td><td>40 [fs]<br>100 [kHz]</td><td>-</td><td>-</td><td></td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">Z-Scan</td><td>1 [µm]</td><td>-</td><td>Nanocrystalline</td><td>580 [nm]<br>2500 [TW/m<sup>2</sup>]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>90 [fs]</td><td>-</td><td>-</td><td>[Trojánek2010]</td></tr><tr><td>Si</td><td>-</td><td>-</td><td>1 [kHz]</td><td>-</td><td>-</td><td></td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">Z-Scan</td><td>-</td><td>-</td><td>Monocrys.</td><td>310 [nm]<br>700 [TW/m<sup>2</sup>]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>9.00E-12</td><td>[Kozák2012]</td></tr><tr><td>-</td><td>-</td><td>-</td><td>100 [fs]<br>1 [kHz]</td><td>-</td><td>-</td><td></td></tr><tr><td rowspan="3">Diamond</td><td rowspan="3">Z-Scan</td><td>-</td><td>-</td><td>Monocrys.</td><td>350 [nm]</td><td>-</td><td>9.00E-20</td><td>-</td></tr><tr><td>CVD</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>[Kozák2012]</td></tr><tr><td>-</td><td>-</td><td>-</td><td>100 [fs]<br>1 [kHz]</td><td>-</td><td>-</td><td></td></tr></tbody></table>
<table><tbody><tr><td>Diamond</td><td>Z-Scan</td><td>530 [µm]<br/>CVD<br/>-</td><td>-</td><td>Monocrys.</td><td>260 [nm]<br/>400 [TW/m²]<br/>120 [fs]<br/>1 [kHz]</td><td>-</td><td>-</td><td>2.30E-12</td><td>[Almeida2017]</td></tr><tr><td>Diamond</td><td>Z-Scan</td><td>530 [µm]<br/>CVD<br/>-</td><td>-</td><td>-</td><td>Monocrys.</td><td>427.5 [nm]<br/>400 [TW/m²]<br/>120 [fs]<br/>1 [kHz]</td><td>-</td><td>-</td><td>1.70E-19</td><td>-</td></tr><tr><td>Diamond</td><td>Other (see Comments)</td><td>700 [µm]<br/>CVD<br/>-</td><td>-</td><td>Polycrys.</td><td>351 [nm]<br/>200 [fs]<br/>-</td><td>515 [nm]<br/>200 [fs]</td><td>2.7E-21</td><td>-</td><td>1.40E-19</td><td>Method: Phase Object Pump-Probe<br/>[Zhang2017]</td></tr><tr><td>Diamond</td><td>Raman Linewidth (TCUPS 1/2)</td><td>500 [µm]<br/>CVD<br/>-</td><td>-</td><td>Monocrys.<br/>&lt;1 [ppm] N₂</td><td>808 [nm]<br/>80 [fs]<br/>78 [MHz]</td><td>-</td><td>-</td><td>-</td><td>Raman Linewidth = 150 [1/m]<br/>[Lee2010]</td></tr><tr><td>Diamond</td><td>Raman Linewidth (TCUPS 1/2)</td><td>250 [µm]<br/>Natural<br/>-</td><td>-</td><td>Monocrys.<br/>&lt;1 [ppm] N₂</td><td>808 [nm]<br/>80 [fs]<br/>78 [MHz]</td><td>-</td><td>-</td><td>-</td><td>Raman Linewidth = 190 [1/m]<br/>[Lee2010]</td></tr><tr><td>Diamond</td><td>Raman Linewidth (TCUPS 1/2)</td><td>420 [µm]<br/>HPHT<br/>-</td><td>-</td><td>Monocrys.<br/>10-100 [ppm] N₂</td><td>808 [nm]<br/>80 [fs]<br/>78 [MHz]</td><td>-</td><td>-</td><td>-</td><td>Raman Linewidth = 190 [1/m]<br/>[Lee2010]</td></tr><tr><td>Diamond</td><td>Raman (Pump-Probe)</td><td>6.5 [mm]<br/>CVD<br/>-</td><td>-</td><td>Monocrys.</td><td>532 [nm]<br/>8 [ns]<br/>-</td><td>573 [nm]<br/>8 [ns]</td><td>-</td><td>-</td><td>gRaman = 4.2E-10 [m/W]<br/>Shift = 1.33E+5 [1/m]<br/>[Savitski2013]</td></tr><tr><td>GaAs</td><td>Nonlin. R/T</td><td>-</td><td>-</td><td>1.42 [eV]</td><td>8700 [nm]<br/>10 [ps]<br/>10 [Hz]</td><td>900 [nm]<br/>10 [ps]</td><td>-</td><td>5.00E-09</td><td>-<br/>[Fishman2011]</td></tr><tr><td>(001)-GaAs</td><td>Nonlin. R/T</td><td>425 [µm]<br/>-</td><td>-</td><td>Monocrys.</td><td>1305 [nm]<br/>1.09 [TW/m²]<br/>68.1 [fs]<br/>1 [kHz]</td><td>0.5, 1, 2 [THz]<br/>-</td><td>-</td><td>4.25E-10</td><td>-<br/>[Tiedje2007]</td></tr><tr><td>GaAs</td><td>SPM/XPM</td><td>1 [mm]<br/>-</td><td>-</td><td>-</td><td>1064 [nm]<br/>53 [ps]<br/>100 [MHz]</td><td>-</td><td>-</td><td>-</td><td>-<br/>[Garcia2000]</td></tr></tbody></table>
<table><tbody><tr><td></td><td>(100)-GaP<sup>a,b</sup></td><td>Z-Scan</td><td>500 [µm]<br/>-<br/>-</td><td>3.1<br/>-<br/>1040 [nm]</td><td>-<br/>-<br/>-</td><td>1040 [nm]<br/>-<br/>61 [fs]<br/>52 [MHz]</td><td>-<br/>-<br/>-</td><td>7.00E-18<br/>-<br/>-<br/>-<br/>[Liu2010]</td></tr><tr><td></td><td>(100)-GaP<sup>a,b</sup></td><td>Z-Scan</td><td>500 [µm]<br/>-<br/>-</td><td>-<br/>4 [1/mm]<br/>800 [nm]</td><td>-<br/>2.27 [eV]<br/>-</td><td>800 [nm]<br/>-<br/>37 [fs]<br/>100 [MHz]</td><td>-<br/>-<br/>-</td><td>4.16E-11<br/>-<br/>-<br/>[Liu2010]</td></tr><tr><td></td><td>InN<sup>a,b</sup></td><td>FWM</td><td>-<br/>PAMBE<br/>GaN-on-<br/>sapphire</td><td>2.78<br/>1.2 [1/µm]<br/>1400 [nm]</td><td>-<br/>0.82 [eV]<br/>-</td><td>1400 [nm]<br/>35 [TW/m<sup>2</sup>]<br/>100 [fs]<br/>1 [kHz]</td><td>-<br/>-<br/>-</td><td>4.20E-10 [esu]<br/>-<br/>-</td></tr><tr><td></td><td>InN<sup>b</sup></td><td>FWM</td><td>-<br/>PAMBE<br/>GaN-on-<br/>sapphire or<br/>Si</td><td>2.95<br/>870 [1/mm]<br/>1500 [nm]</td><td>Monocrys.<br/>0.75 [eV]<br/>1E+25 [1/m<sup>3</sup>]</td><td>1500 [nm]<br/>-<br/>100 [fs]<br/>1 [kHz]</td><td>-<br/>-<br/>-</td><td>8.00E-10 [esu]<br/>-3.40E+10<br/>-</td></tr><tr><td></td><td>InN</td><td>Nonlin.<br/>R/T</td><td>750 [nm]<br/>Sputtering<br/>GaN-on-<br/>Sapphire</td><td>-<br/>-<br/>-</td><td>Polycrys.<br/>1.74 [eV]<br/>1E+26 [1/m<sup>3</sup>]</td><td>1550 [nm]<br/>153 [TW/m<sup>2</sup>]<br/>100 [fs]<br/>100 [MHz]</td><td>1550 [nm]<br/>15.3 [TW/m<sup>2</sup>]<br/>100 [fs]</td><td>-<br/>1.67E-09<br/>-</td></tr><tr><td></td><td>InN</td><td>Z-Scan</td><td>250 [nm]<br/>MBE<br/>AlN on c-<br/>Sapphire</td><td>2.45<br/>8.7 [1/µm]<br/>790 [nm]</td><td>-<br/>0.8 [eV]<br/>5.5E+24 [1/m<sup>3</sup>]</td><td>790 [nm]<br/>26 [TW/m<sup>2</sup>]<br/>200 [fs]<br/>80 [MHz]</td><td>-<br/>-</td><td>-<br/>-<br/>-</td></tr><tr><td></td><td>InN</td><td>Z-Scan</td><td>-<br/>PAMBE<br/>AlN/GaN on<br/>R-sapphire</td><td>-<br/>-<br/>-</td><td>Monocrys.<br/>0.65 [eV]<br/>1.4E25 [1/m<sup>3</sup>]</td><td>1500 [nm]<br/>20 [TW/m<sup>2</sup>]<br/>120 [fs]<br/>-</td><td>-<br/>-</td><td>1.90E-14<br/>4.75E-08<br/>-</td></tr><tr><td></td><td>InP<sup>a,b</sup></td><td>I-Scan</td><td>2 [mm]<br/>-<br/>-</td><td>-<br/>-<br/>-</td><td>-<br/>-</td><td>1064 [nm]<br/>6 [TW/m<sup>2</sup>]<br/>10 [ps]<br/>-</td><td>-<br/>-</td><td>2.55E-10<br/>-</td></tr><tr><td></td><td>InP:Fe<sup>a</sup></td><td>I-Scan</td><td>2 [mm]<br/>-<br/>-</td><td>-<br/>-<br/>-</td><td>-<br/>-</td><td>1064 [nm]<br/>6 [TW/m<sup>2</sup>]<br/>10 [ps]<br/>-</td><td>-<br/>-</td><td>2.55E-10<br/>-</td></tr></tbody></table>
<table><tbody><tr><td>InSb</td><td>Nonlin.<br>R/T</td><td>1 [mm]<br>-<br>-</td><td>-<br>-<br>10600 [nm]</td><td>-<br>0.18 [eV]<br>-</td><td>10600 [nm]<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>Nonlinear Free Carrier<br>Refraction Cross Section:<br>4.5E-19 [m²]<br>[Dubikovskiy2008]</td></tr><tr><td>InSb</td><td>Z-Scan</td><td>540 [µm]<br>-<br>-</td><td>-<br>-<br>Monocrys.<br>0.18 [eV]<br>9.00E+19 [1/m³]</td><td>9000 [nm]<br>-<br>370 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>1050 [nm]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2.90E-08<br>-<br>-<br>[Olszak2010]</td></tr><tr><td>InSn:O</td><td>Beam Defl.</td><td>310 [nm]<br>-<br>Float Glass</td><td>-<br>-<br>-</td><td>1242 [nm]<br>-<br>100 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>1050 [nm]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>5.50E-17<br>-<br>-<br>[Benis2017]</td></tr><tr><td>InSn:O</td><td>THG</td><td>37 [nm]<br>Sputtering<br>Silicon</td><td>-<br>-<br>1550 [nm]</td><td>-<br>400 [GW/m²]<br>150 [ns]<br>81 [MHz]</td><td>-<br>-<br>-</td><td>3.5E-18</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-<br>[Capretti2015a]</td></tr><tr><td>Silicon<sup>a,b</sup></td><td>Z-Scan</td><td>675 [µm]<br>-<br>-</td><td>-<br>-<br>Monocrys.<br>p = 1E+21 [1/m³]</td><td>2600 [nm]<br>570 [TW/m²]<br>150 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2.50E-18<br>-<br>2.00E-27<br>-<br>[Wang2013]</td></tr><tr><td>Silicon</td><td>Z-Scan</td><td>125 [µm]<br>-<br>-</td><td>-<br>-<br>Monocrys.<br>1.12 [eV]<br>Intrinsic</td><td>1220 [nm]<br>78 [TW/m²]<br>200 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>4.70E-18<br>2.10E-11<br>-<br>-<br>[Bristow2007b]</td></tr><tr><td>Silicon</td><td>Z-Scan</td><td>480 [µm]<br>-<br>-</td><td>-<br>-<br>Monocrys.<br>10 [Ω-cm]</td><td>1540 [nm]<br>7 [TW/m²]<br>130 [fs]<br>76 [MHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>4.50E-18<br>7.90E-12<br>-<br>-<br>[Dinu2003b]</td></tr><tr><td>Silicon</td><td>Z-Scan</td><td>500 [µm]<br>-<br>-</td><td>-<br>-<br>Monocrys.<br>Intrinsic</td><td>1550 [nm]<br>-<br>190 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>5.00E-18<br>1.03E-11<br>-<br>-<br>[Gai2013]</td></tr><tr><td>Silicon</td><td>Z-Scan</td><td>500 [µm]<br>-<br>-</td><td>-<br>-<br>Monocrys.<br>20 [Ω-cm]</td><td>1501 [nm]<br>-<br>-<br>500 [Hz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2.20E-18<br>4.80E-12<br>-<br>-<br>[Lin2007]</td></tr></tbody></table>
<table><tbody><tr><td rowspan="3">4H SiC<sup>a</sup></td><td rowspan="3">Z-Scan</td><td>498 [µm]</td><td>-</td><td>Monocrys.</td><td>530 [nm]</td><td>-</td><td>3.19E-19</td><td>-</td></tr><tr><td>-</td><td>-</td><td>3.25 [eV]</td><td>-</td><td>-</td><td>2.00E-12</td><td>-</td></tr><tr><td>-</td><td>-</td><td>-</td><td>123 [fs]</td><td>-</td><td>-</td><td>-</td><td>[Guo2021]</td></tr><tr><td rowspan="3">6H SiC<sup>a</sup></td><td rowspan="3">Z-Scan</td><td>258 [µm]</td><td>-</td><td>Monocrys.</td><td>800 [nm]</td><td>-</td><td>3.88E-19</td><td>-</td></tr><tr><td>-</td><td>-</td><td>2.99 [eV]</td><td>-</td><td>-</td><td>3.95E-13</td><td>-</td></tr><tr><td>-</td><td>-</td><td>-</td><td>176 [fs]</td><td>-</td><td>-</td><td>-</td><td>[Guo2021]</td></tr><tr><td rowspan="3">6H SiC<sup>b</sup></td><td rowspan="3">Z-Scan</td><td>340 [µm]</td><td>-</td><td>Monocrys.</td><td>780 [nm]</td><td>-</td><td>4.75E-19</td><td>-</td></tr><tr><td>-</td><td>-</td><td>3.10 [eV]</td><td>-</td><td>-</td><td>6.40E-13</td><td>-</td></tr><tr><td>-</td><td>-</td><td>1.00E15</td><td>-</td><td>-</td><td>-</td><td>[DesAutels2008]</td></tr><tr><td rowspan="3">6H SiC<sup>b</sup></td><td rowspan="3">Z-Scan</td><td>220 [µm]</td><td>-</td><td>Monocrys.</td><td>780 [nm]</td><td>-</td><td>4.00E-19</td><td>-</td></tr><tr><td>-</td><td>-</td><td>3.10 [eV]</td><td>-</td><td>-</td><td>5.20E-13</td><td>[DesAutels2008]</td></tr><tr><td>-</td><td>-</td><td>2.50E17</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td colspan="9" style="text-align: center; font-weight: bold;">Three Photon Absorption</td></tr><tr><td rowspan="3">Al<sub>2</sub>Se<sub>1.5</sub>S<sub>1.5</sub></td><td rowspan="3">Z-Scan</td><td>-</td><td>2.7</td><td>-</td><td>1550 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>-</td><td>-</td><td>1.74 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>-</td><td>1550 [nm]</td><td>-</td><td>150 [fs]</td><td>-</td><td>-</td><td>5.50E-26</td><td>[Shabahang2014]</td></tr><tr><td rowspan="3">CdS</td><td rowspan="3">Nonlin.<br>R/T</td><td>-</td><td>2.34</td><td>-</td><td>1064 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>-</td><td>-</td><td>2.42 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>-</td><td>1064 [nm]</td><td>-</td><td>30 [ps]</td><td>-</td><td>-</td><td>1.50E-26</td><td>[Benis2020]</td></tr><tr><td rowspan="3">CdS</td><td rowspan="3">Z-Scan</td><td>-</td><td>2.34</td><td>-</td><td>1200 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>-</td><td>-</td><td>2.42 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>-</td><td>1200 [nm]</td><td>-</td><td>150 [fs]</td><td>-</td><td>-</td><td>1.10E-26</td><td>[Benis2020]</td></tr></tbody></table>
<table><tbody><tr><td>CdSe</td><td>Z-Scan</td><td>-<br>-<br>-</td><td>2.5<br>-<br>1500 [nm]</td><td>-<br>-<br>-</td><td>1.9 [eV]</td><td>-<br>-<br>-</td><td>1500 [nm]<br>-<br>150 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2.40E-25</td><td>[Benis2020]</td></tr><tr><td>CdTe</td><td>Z-Scan</td><td>-<br>-<br>-</td><td>2.7<br>-<br>1750 [nm]</td><td>-<br>-<br>-</td><td>1.44 [eV]</td><td>-<br>-<br>-</td><td>1750 [nm]<br>-<br>150 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>1.20E-24</td><td>[Benis2020]</td></tr><tr><td>GaAs<sup>a</sup></td><td>Z-Scan</td><td>-<br>-<br>-</td><td>3.4<br>-<br>2300 [nm]</td><td>-<br>-<br>-</td><td>1.42 [eV]</td><td>-<br>-<br>-</td><td>2600 [nm]<br>-<br>15 [ps]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>9.00E-25</td><td>[Benis2020]</td></tr><tr><td>GaAs<sup>a</sup></td><td>Z-Scan</td><td>-<br>-<br>-</td><td>3.4<br>-<br>2300 [nm]</td><td>-<br>-<br>-</td><td>1.42 [eV]</td><td>-<br>-<br>-</td><td>2600 [nm]<br>-<br>150 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>7.50E-25</td><td>[Benis2020]</td></tr><tr><td>GaAs</td><td>Z-Scan</td><td>-<br>-<br>-</td><td>3.4<br>-<br>2300 [nm]</td><td>-<br>-<br>-</td><td>1.42 [eV]</td><td>-<br>-<br>-</td><td>2300 [nm]<br>-<br>100 [fs]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>3.50E-25</td><td>[Hurlbut2007]</td></tr><tr><td>InSb<sup>c</sup></td><td>Z-Scan</td><td>-<br>-<br>-</td><td>3.95<br>-<br>12000 [nm]</td><td>-<br>-<br>-</td><td>0.228 [eV]</td><td>-<br>-<br>-</td><td>12000 [nm]<br>-<br>10 [ps]<br>1 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2.50E-20</td><td>[Benis2020]</td></tr><tr><td>4H SiC</td><td>Z-Scan</td><td>-<br>-<br>-</td><td>498 [µm]</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>-<br>-<br>-</td><td>990 [nm]<br>-<br>177 [fs]<br>50 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>1.9E-27</td><td>[Guo2021]</td></tr><tr><td>6H SiC</td><td>Z-Scan</td><td>-<br>-<br>-</td><td>258 [µm]</td><td>-<br>-<br>-</td><td>Monocrys.</td><td>-<br>-<br>-</td><td>990 [nm]<br>-<br>177 [fs]<br>50 [kHz]</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>4.0E-28</td><td>[Guo2021]</td></tr><tr><td>ZnO</td><td>Nonlin.<br>R/T</td><td>-<br>-<br>-</td><td>1.94<br>-<br>1064 [nm]</td><td>-<br>-<br>-</td><td>3.27 [eV]</td><td>-<br>-<br>-</td><td>1064 [nm]<br>-<br>30 [ps]<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>-<br>-<br>-</td><td>2.20E-26</td><td>[Benis2020]</td></tr></tbody></table>
<table><tbody><tr><td>ZnO</td><td>Z-Scan</td><td>-</td><td>1.95</td><td>-</td><td>900 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>3.27 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>900 [nm]</td><td>-</td><td>100 [fs]</td><td>-</td><td>5.40E-27</td><td>[He2005]</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>1 [kHz]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ZnS<sup>a</sup></td><td>Z-Scan</td><td>-</td><td>2.3</td><td>-</td><td>960 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>3.54 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>800 [nm]</td><td>-</td><td>30 [ps]</td><td>-</td><td>1.60E-27</td><td>[Benis2020]</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>1 [kHz]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ZnS</td><td>Z-Scan</td><td>-</td><td>2.3</td><td>-</td><td>800 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>3.54 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>800 [nm]</td><td>-</td><td>100 [fs]</td><td>-</td><td>1.70E-27</td><td>[He2005]</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>1 [kHz]</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ZnSe<sup>a</sup></td><td>Nonlin.<br>R/T</td><td>-</td><td>2.48</td><td>-</td><td>1064 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>2.67 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>1064 [nm]</td><td>-</td><td>30 [ps]</td><td>-</td><td>1.50E-26</td><td>[Benis2020]</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ZnSe</td><td>Nonlin.<br>R/T</td><td>-</td><td>2.48</td><td>-</td><td>1350 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>2.67 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>1064 [nm]</td><td>-</td><td>30 [ps]</td><td>-</td><td>9.10E-27</td><td>[Cirloganu2008]</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>ZnTe</td><td>Z-Scan</td><td>-</td><td>2.8</td><td>-</td><td>1200 [nm]</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>2.28 [eV]</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td></td><td></td><td>-</td><td>1200 [nm]</td><td>-</td><td>150 [fs]</td><td>-</td><td>2.00E-26</td><td>[Benis2020]</td></tr><tr><td></td><td></td><td>-</td><td>-</td><td>-</td><td>1 [kHz]</td><td>-</td><td>-</td><td>-</td></tr></tbody></table>

<footnote><sup>a</sup> Multiple wavelengths reported, <sup>b</sup> Multiple Parameters (e.g., thickness, crystal orientation) reported, <sup>c</sup> Measurement taken at a temperature other than room temperature. *Units as illustrated unless otherwise indicated in table, <sup>†</sup> A negative value of α<sub>2</sub> represents saturable absorption, <sup>‡</sup> TCUPS: Transient Coherent Ultrafast Phonon Spectroscopy</footnote>
References of Section 3.1

[Abudurusuli2021] Abudurusuli, A., Li, J., and Pan, S. A review on the recently developed promising infrared nonlinear optical materials. 2021 *Dalton Transactions* **50**, 3155. https://doi.org/10.1039/D1DT00054C

[Agrawal2013] Agrawal, G. P. Nonlinear Fiber Optics (5th ed.). 2013 Academic Press.

[Ahn2014] Ahn, H., Lee, M. T., and Chang, Y. M. Spectral dependence of third-order nonlinear optical properties in InN. 2014 *Applied Physics Letters* **104**, 17. https://doi.org/10.1063/1.4878618

[Alam2016] Alam, M. Z., De Leon, I., and Boyd, R. W. Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region. 2016 *Science* **352**, 795. https://doi.org/10.1126/science.aae0330

[Alekseev1980] Alekseev, N. E., Gapontsev, V. P., Zhabotinskii, M. E., Kravchenko, V. B., and Rudnitskii, I. P. Laser Phosphate Glasses. 1980 *Izdatel'stvo Nauka*, 352.

[Allen1987] Allen, P. B. Theory of thermal relaxation of electrons in metals. 1987 *Physical Review Letters* **59**, 1460. https://doi.org/10.1103/PHYSREVLETT.59.1460

[Almeida2019] Almeida, G. F. B., Santos, S. N. C., Siqueira, J. P., Dipold, J., Voss, T., and Mendonça, C. R. Third-order nonlinear spectrum of GaN under femtosecond-pulse excitation from the visible to the near infrared. 2019 *Photonics* **6**, 69. https://doi.org/10.3390/photonics6020069

[Almeida2017] Almeida, J. M. P., Oncebay, C., Siqueira, J. P., Muniz, S. R., De Boni, L., and Mendonça, C. R. Nonlinear optical spectrum of diamond at femtosecond regime. 2017 *Scientific Reports* **7**, 1. https://doi.org/10.1038/s41598-017-14748-4

[Anisimov1974] Anisimov, S. I., Kapeliovich, B. L., and Perel'man, T. L. Electron emission from metal surfaces exposed to ultrashort laser pulses. 1974 *Journal of Experimental and Theoretical Physics* **39**, 375.

[Armstrong1962] Armstrong, J. A., Bloembergen, N., Ducuing, J., and Pershan, P. S. Interactions between Light Waves in a Nonlinear Dielectric. 1962 *Physical Review* **127**, 1918. https://doi.org/10.1103/PhysRev.127.1918

[Asobe1997] Asobe, M. Nonlinear Optical Properties of Chalcogenide Glass Fibers and Their Application to All-Optical Switching. 1997 *Optical Fiber Technology* **3**, 142. https://doi.org/10.1006/ofte.1997.0214

[Bai2020] Bai, Z., Williams, R. J., Kitzler, O., Sarang, S., Spence, D. J., Wang, Y., ... Mildren, R. P. Diamond Brillouin laser in the visible. 2020 *APL Photonics* **5**, 3. https://doi.org/10.1063/1.5134907

[Bautista2021] Bautista, J. E. Q., da Silva-Neto, M. L., Campos, C. L. A. V., Maldonado, M., de Araújo, C. B., and Gomes, A. S. L. Thermal and non-thermal intensity dependent optical nonlinearities in ethanol at 800 nm, 1480 nm, and 1560 nm. 2021 *Journal of the Optical Society of America B* **38**, 1104. https://doi.org/10.1364/josab.418635

[Benis2020] Benis, S., Cirloganu, C. M., Cox, N., Ensley, T., Hu, H., Nootz, G., ... Van Stryland, E. W. Three-photon absorption spectra and bandgap scaling in direct-gap semiconductors. 2020 *Optica* **7**, 888. https://doi.org/10.1364/OPTICA.396056

[Benis2019] Benis, S., Munera, N., Van Stryland, E. W., and Hagan, D. J. Z-scan and beam-deflection measurements of Indium-Tin-Oxide at epsilon-near-zero. 2019 *Nonlinear Optics* NTu3B.2. https://doi.org/10.1364/NLO.2019.NTu3B.2

[Benis2017] Benis, S., Zhao, P., Hagan, D. J., and Van Stryland, E. W. Nondegenerate, Transient Nonlinear Refraction of Indium Tin Oxide Excited at Epsilon-Near-Zero. 2017 *Nonlinear Optics*, NW1A.3. https://doi.org/10.1364/NLO.2017.NW1A.3

[Bergfeld2003] Bergfeld, S., Daum, W. Second-Harmonic Generation in GaAs: Experiment versus Theoretical Predictions of $\chi^{(2)}_{xyz}$. 2003 *Physical Review Letters* **90**, 036801. https://doi.org/10.1103/PhysRevLett.90.036801

[Bhattacharya1997] Bhattacharya, P. Semiconductor Optoelectronic Devices (2nd ed.). 1997 New York, Prentice-Hall.

[Bierlein1989] Bierlein, J. D., Vanherzeele, H. Potassium titanyl phosphate: properties and new applications. 1989 *Journal of the Optical Society of America B* **6**, 622. https://doi.org/10.1364/JOSAB.6.000622

[Bloembergen1969] Bloembergen, N., Burns, W. K., and Matsuoka, M. Reflected third harmonic generated by picosecond laser pulses. 1969 *Optics Communications* **1**, 195. https://doi.org/10.1016/0030-4018(69)90064-9

[Bloembergen1968] Bloembergen, N., Chang, R. K., Jha, S. S., and Lee, C. H. Optical second-harmonic generation in reflection from media with inversion symmetry. 1968 *Physical Review* **174**, 813. https://doi.org/10.1103/PHYSREV.174.813

[Boling1978] Boling, N. L., Glass, A. J., and Owyoung, A. Empirical Relationships for Predicting Nonlinear Refractive Index Changes in Optical Solids. 1978 *IEEE Journal of Quantum Electronics* **14**, 601. https://doi.org/10.1109/JQE.1978.1069847

[Bosshard2020] Bosshard, C., Sutter, K., Pretre, P., Hulliger, H., Florsheimer, M., Kaatz, P., and Gunter, P. Organic Nonlinear Optical Materials (1st ed.). 2020 London, CRC Press. https://doi.org/10.1201/9780429114090

[Boyd2020] Boyd, R. W. Nonlinear Optics. 2020 Oxford, Academic Press.

[Boyko2018] Boyko, A. A., Schunemann, P. G., Guha, S., Kostyukova, N. Y., Kolker, D. B., Panyutin, V. L., ... Petrov, V. Optical parametric oscillator pumped at ~1 µm with intracavity mid-IR difference-frequency generation in OPGaAs. 2018 *Optical Materials Express* **8**, 549. https://doi.org/10.1364/OME.8.000549

[Bristow2007] Bristow, A. D., Rotenberg, N., and Van Driel, H. M. Two-photon absorption and Kerr coefficients of silicon for 850-2200 nm. 2007 *Applied Physics Letters* **90**, 191104. https://doi.org/10.1063/1.2737359

[Brorson1990] Brorson, S. D., Kazeroonian, A., Moodera, J. S., Face, D. W., Cheng, T. K., Ippen, E. P., ... Dresselhaus, G. Femtosecond room-temperature measurement of the electron-phonon coupling constant in metallic superconductors. 1990 *Physical Review Letters* **64**, 2172. https://doi.org/10.1103/PhysRevLett.64.2172

[Bruno2020] Bruno, V., Devault, C., Vezzoli, S., Kudyshev, Z., Huq, T., Mignuzzi, S., ... Shalaev, V. M. Negative Refraction in Time-Varying Strongly Coupled Plasmonic-Antenna-Epsilon-Near-Zero Systems. 2020 *Physical Review Letters* **124**, 43902. https://doi.org/10.1103/PhysRevLett.124.043902

[Cai2009] Cai, W., and Shalaev, V. M. Optical Metamaterials: Fundamentals and Applications. 2009 Springer.
[Capretti2015a] Capretti, A., Wang, Y., Engheta, N., and Dal Negro, L. Comparative Study of Second-Harmonic Generation from Epsilon-Near-Zero Indium Tin Oxide and Titanium Nitride Nanolayers Excited in the Near-Infrared Spectral Range. 2015 *ACS Photonics* **2**, 1584. https://doi.org/10.1021/acsphotonics.5b00355

[Capretti2015b] Capretti, A., Wang, Y., Engheta, N., and Dal Negro, L. Enhanced third-harmonic generation in Si-compatible epsilon-near-zero indium tin oxide nanolayers. 2015 *Optics Letters* **40**, 1500. https://doi.org/10.1364/ol.40.001500

[Carnemolla2018] Carnemolla, E. G., Caspani, L., DeVault, C., Clerici, M., Vezzoli, S., Bruno, V., ... Ferrera, M. Degenerate optical nonlinear enhancement in epsilon-near-zero transparent conducting oxides. 2018 *Optical Materials Express* **8**, 3392. https://doi.org/10.1364/ome.8.003392

[Caspani2016] Caspani, L., Kaipurath, R. P. M., Clerici, M., Ferrera, M., Roger, T., Kim, J., ... Faccio, D. Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials. 2016 *Physical Review Letters* **116**, 1. https://doi.org/10.1103/PhysRevLett.116.233901

[Cirloganu2008] Cirloganu, C. M., Olszak, P. D., Padilha, L. A., Webster, S., Hagan, D. J., Van Stryland, E. W. Three-photon absorption spectra of zinc blende semiconductors: theory and experiment. 2008 *Optics Letters* **33**, 22. https://doi.org/10.1364/OL.33.002626

[Chen1987] Chen, C., Fan, Y. X., Eckardt, R. C., and Byer, R. L. Recent Developments In Barium Borate. 1987 *Proc. SPIE*, 0681. https://doi.org/10.1117/12.939612

[Chen2020]. Chen, F., Zhang, J., Cassagne, C., and Boudebs, G. Large third-order optical nonlinearity of chalcogenide glasses within gallium-tin-selenium ternary system. 2020 *Journal of the American Ceramie Society* **103**, 5050. https://doi.org/10.1111/JACE.17272

[Chen2017] Chen, H., Huang, X., Fu, H., Lu, Z., Zhang, X., Montes, J. A., and Zhao, Y. Characterizations of nonlinear optical properties on GaN crystals in polar, nonpolar, and semipolar orientations. 2017 *Applied Physics Letters* **110**, 1. https://doi.org/10.1063/1.4983026

[Cherukulappurath2004] Cherukulappurath, S., Guignard, M., Marchand, C., Smektala, F., and Boudebs, G. Linear and nonlinear optical characterization of tellurium based chalcogenide glasses. 2004 *Optics Communications* **242**, 313. https://doi.org/10.1016/j.optcom.2004.08.027

[Chi2020] Chi, S., Liang, F., Chen, H., Tian, W., Zhang, H., Yu, H., ... Zhang, H. Surface Nonlinear Optics on Centrosymmetric Dirac Nodal-Line Semimetal ZrSiS. 2020 *Advanced Materials* **32**, 1. https://doi.org/10.1002/adma.201904498

[Christodoulides2010]. Christodoulides, D. N., Khoo, I. C., Salamo, G. J., Stegeman, G. I., and Van Stryland, E. W. Nonlinear refraction and absorption: mechanisms and magnitudes. 2010 *Advances in Optics and Photonics* **2**, 60. https://doi.org/10.1364/aop.2.000060

[Clerici2017] Clerici, M., Kinsey, N., DeVault, C., Kim, J., Carnemolla, E. G., Caspani, L., ... Ferrera, M. Controlling hybrid nonlinearities in transparent conducting oxides via two-colour excitation. 2017 *Nature Communications* **8**, 15829. https://doi.org/10.1038/ncomms15829

[De Araújo2005] De Araújo, C. B., Falcão-Filho, E. L., Humeau, A., Guichaoua, D., Boudebs, G., and Kassab, L. R. P. Picosecond third-order nonlinearity of lead-oxide glasses in the infrared. 2005 *Applied Physics Letters* **87**, 1. https://doi.org/10.1063/1.2137457

[De Araújo2016] De Araújo, C. B., Gomes, A. S. L., and Boudebs, G. Techniques for nonlinear optical characterization of materials: A review. 2016 *Reports on Progress in Physics* **79**, 036401. https://doi.org/10.1088/0034-4885/79/3/036401

[DeAutels2008] DesAutels, G. L., Brewer, C., Walker, M., Juhl, S., Finet, M., Ristich, S., Whitaker, M., Powers, P. Femtosecond Laser Damage Threshold and Nonlinear Characterization in Bulk Transparent SiC Materials. 2008 *Proceedings of the SPIE* **6875**, https://doi.org/10.1117/12.765560.

[DeSalvo1996] DeSalvo, R., Said, A. A., Hagan, D. J., Van Stryland, E. W., and Sheik-Bahae, M. (1996). Infrared to ultraviolet measurements of two-photon absorption and n/sub 2/ in wide bandgap solids. IEEE Journal of Quantum Electronics, 32(8). https://doi.org/10.1109/3.511545

[Dietel1983] Dietel, W., Fontaine, J. J., and Diels, J.-C. Intracavity pulse compression with glass: a new method of generating pulses shorter than 60 fsec. 1983 *Optics Letters* **8**, 1324. https://doi.org/10.1364/OL.8.000004

[Dinu2003a] Dinu, M. Dispersion of Phonon-Assisted Nonresonant Third-Order Nonlinearities. 2003 *IEEE Journal of Quantum Electronics* **39**, 1498.

[Dinu2003b] Dinu, M., Quochi, F., and Garcia, H. Third-order nonlinearities in silicon at telecom wavelengths. 2003 *Applied Physics Letters* **82**, 2954. https://doi.org/10.1063/1.1571665

[Dubikovskiy2008] Dubikovskiy, V., Hagan, D. J., and Van Stryland, E. W. Large nonlinear refraction in InSb at 10 µm and the effects of Auger recombination. 2008 *Journal of the Optical Society of America B* **25**, 223. https://doi.org/10.1364/josab.25.000223

[Dudley2009] Dudley, J. M., and Taylor, J. R. Ten years of nonlinear optics in photonic crystal fibre. 2009 *Nature Photonics* **3**, 85. https://doi.org/10.1038/nphoton.2008.285

[Ekimov1988] Ekimov, A. I., and Efros, A. L. Nonlinear Optics of Semiconductor-Doped Glasses. 1988 *Physica Status Solidi* (B) **150**, 627. https://doi.org/10.1002/pssb.2221500244

[Elsayed-Ali1987] Elsayed-Ali, H. E., Norris, T. B., Pessot, M. A., and Mourou, G. A. Time-resolved observation of electron-phonon relaxation in copper. 1987 *Physical Review Letters* **58**, 1212. https://doi.org/10.1103/PhysRevLett.58.1212

[Ensley2019] Ensley, T. R., and Bambha, N. K. Ultrafast nonlinear refraction measurements of infrared transmitting materials in the mid-wave infrared. 2019 *Optics Express* **27**, 37940. https://doi.org/10.1364/OE.380702
[Falcão-Filho 2004] Falcão-Filho, E. L., De Araújo, C. B., Bosco, C. A. C., Acioli, L. H., Poirier, G., Messaddeq, Y., ... Poulain, M. Nonlinear optical properties of tungstate fluorophosphate glasses. 2004 *Journal of Applied Physics* **96**, 2525. https://doi.org/10.1063/1.1758309

[Falconieri 1999] Falconieri, M., and Salvetti, G. (1999). Simultaneous measurement of pure-optical and thermo-optical nonlinearities induced by high-repetition-rate, femtosecond laser pulses: Application to CS2. 1999 *Applied Physics B: Lasers and Optics* **69**, 133. https://doi.org/10.1007/s003400050785

[Fang 2015] Fang, Y., Xiao, Z., Wu, X., Zhou, F., Yang, J., Yang, Y., and Song, Y. Optical nonlinearities and ultrafast all-optical switching of m-plane GaN in the near-infrared. 2015 *Applied Physics Letters* **106**, 251903. https://doi.org/10.1063/1.4923184

[Feaver 2013] Feaver, R. K., Peterson, R. D., & Powers, P. E. Longwave-IR optical parametric oscillator in orientation-patterned GaAs pumped by a 2 µm Tm:Ho:YLF laser. 2013 *Optics Express* **21**, 16104. https://doi.org/10.1364/oe.21.016104

[Fedus 2010] Fedus, K., Boudebs, G., Coulombier, Q., Troles, J., and Zhang, X. H. Nonlinear characterization of GeS2-Sb2S 3-CsI glass system. 2010 *Journal of Applied Physics* **107**, 023108. https://doi.org/10.1063/1.3289607

[Fishman 2011] Fishman, D. A., Cirloganu, C. M., Webster, S., Padilha, L. A., Monroe, M., Hagan, D. J., and Van Stryland, E. W. Sensitive mid-infrared detection in wide-bandgap semiconductors using extreme non-degenerate two-photon absorption. 2011 *Nature Photonics* **5**, 561. https://doi.org/10.1038/nphoton.2011.168

[Franken 1961] Franken, P. A., Hill, A. E., Peters, C. W., and Weinreich, G. Generation of Optical Harmonics. 1961 *Physical Review Letters* **7**, 118. https://doi.org/10.1103/PhysRevLett.7.118

[Fu 2020] Fu, Qiand, Xu, L., Liang, S., Shardlow, P. C., Shepherd, D. P., Alam, S.-U., and Richardson, D. J. High-average-power picosecond mid-infrared OP-GaAs OPO. 2020 *Optics Express* **28**, 5741. https://doi.org/10.1364/OE.380189

[Fu 2018] Fu, Qiang, Xu, L., Liang, S., Shepherd, D. P., Richardson, D. J., and Alam, S. U. Widely Tunable, Narrow-Linewidth, High-Peak-Power, Picosecond Midinfrared Optical Parametric Amplifier. 2018 *IEEE Journal of Selected Topics in Quantum Electronics* **24**, 1. https://doi.org/10.1109/JSTQE.2018.2789878

[Fujita 2000] Fujita, T., Hasegawa, T., Haraguchi, M., Okamoto, T., Fukui, M., and Nakamura, S. Determination of second-order nonlinear optical susceptibility of GaN films on sapphire. 2000 *Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers* **39**, 2610. https://doi.org/10.1143/jjap.39.2610

[Gagarskiï 2008] Gagarskiï, S. V., and Prikhod'ko, K. V. Measuring the parameters of femtosecond pulses in a wide spectral range on the basis of the multiphoton-absorption effect in a natural diamond crystal. 2008 *Journal of Optical Technology* **75**, 139. https://doi.org/10.1364/jot.75.000139

[Gai 2013] Gai, X., Yu, Y., Kuyken, B., Ma, P., Madden, S. J., Van Campenhout, J., ... Luther-Davies, B. Nonlinear absorption and refraction in crystalline silicon in the mid-infrared. 2013 *Laser and Photonics Reviews* **7**, 1054. https://doi.org/10.1002/lpor.201300103

[Garcia 2000] Garcia, H., Johnson, A. M., and Trivedi, S. Photorefractive beam-coupling measurement of the nonlinear refractive index of semiconductor films. 2000 *Physica Status Solidi (B) Basic Research* **220**, 47. https://doi.org/10.1002/1521-3951(200007)220:1<47::AID-PSSB47>3.0.CO;2-U

[Garcia 2012] Garcia, Hernando, and Avanaki, K. N. Direct and indirect two-photon absorption in Ge within the effective mass approximation. 2012 *Applied Physics Letters* **100**, 131105. https://doi.org/10.1063/1.3693389

[Garmire 1998] Garmire, E., Kost, A. Nonlinear Optics in Semiconductors I. 1998 Academic Press.

[Gattass 2012] Gattass, R. R., Brandon Shaw, L., Nguyen, V. Q., Pureza, P. C., Aggarwal, I. D., and Sanghera, J. S. All-fiber chalcogenide-based mid-infrared supercontinuum source. 2012 *Optical Fiber Technology* **18**, 345. https://doi.org/10.1016/j.yofte.2012.07.003

[George 2019] George, H., Reed, J., Ferdinandus, M., DeVault, C., Lagutchev, A., Urbas, A., ... Kinsey, N. Nonlinearities and carrier dynamics in refractory plasmonic TiN thin films. 2019 *Optical Materials Express* **9**, 345. https://doi.org/10.1364/OME.9.003911

[Golubev 2018] Golubev, A. A., Khlebtsov, B. N., Rodriguez, R. D., Chen, Y., and Zahn, D. R. T. Plasmonic Heating Plays a Dominant Role in the Plasmon-Induced Photocatalytic Reduction of 4-Nitrobenzenethiol. 2018 *Journal of Physical Chemistry C* **122**, 5657. https://doi.org/10.1021/acs.jpcc.7b12101

[Gomes 2007] Gomes, A. S. L., Falcão Filho, E. L., De Araújo, C. B., Rativa, D., De Araujo, R. E., Sakaguchi, K., ... Kazansky, P. G. Third-order nonlinear optical properties of bismuth-borate glasses measured by conventional and thermally managed eclipse Z scan. 2007 *Journal of Applied Physics* **101**, 033115. https://doi.org/10.1063/1.2434940

[Gonzalez 2009] Gonzalez, L. P., Murray, J. M., Krishnamurthy, S., and Guha, S. Wavelength dependence of two photon and free carrier absorptions in InP. 2009 *Optics Express* **17**, 8741. https://doi.org/10.1364/oe.17.008741

[Gordon 1993] Gordon, L., Woods, G. L., Eckardt, R. C., Route, R.,. Feigelson, R. S., Fejer, M. M., and Byer, R. L. Diffusion-bonded stacked GaAs for quasiphase- matched second-harmonic generation of a carbon dioxide laser. 1993 *Electronics Letters* **29**, 1942. https://doi.org/10.1049/el:19931293

[Granzow 2011] Granzow, N., Stark, S. P., Schmidt, M. A., Tverjanovich, A. S., Wondraczek, L., and Russell, P. S. J. Supercontinuum generation in chalcogenide-silica step-index fibers. 2011 *Optics Express* **19**, 21003. https://doi.org/10.1364/OE.19.021003

[Grinblat 2019] Grinblat, G., Nielsen, M. P., Dichtl, P., Li, Y., Oulton, R. F., and Maier, S. A. Ultrafast sub-30-fs all-optical switching based on gallium phosphide. 2019 *Science Advances* **5**, 1. https://doi.org/10.1126/sciadv.aaw3262

[Guo 2021] Guo, X., Peng, Z., Ding, P., Li, L., Chen, X., Wei, H., Tong, Z., Guo, L. Nonlinear optical properties of 6H-SiC and 4H-SiC in an extensive spectral range. 2021 *Optical Materials Express* **11**, 4. https://doi.org/10.1364/OME.415915
[Hall1985] Hall, T. J., Jaura, R., Connors, L. M., and Foote, P. D. The photorefractive effect—a review. 1985 *Progress in Quantum Electronics* **10**, 77. https://doi.org/10.1016/0079-6727(85)90001-1

[Hardy2007] Hardy, J., and Shamir, J. Optics inspired logic architecture. 2007 *Optics Express* **15**, 150. https://doi.org/10.1364/OE.15.000150

[He2005] He, J., Qu, Y., Li, H., Mi, J., Ji, W., Three-photon absorption in ZnO and ZnS crystals. 2005 *Optics Express* **13**, 23. https://doi.org/10.1364/OPEX.13.009235

[Hohlfeld2000] Hohlfeld, J., Wellershoff, S. S., Güdde, J., Conrad, U., Jähnke, V., and Matthias, E. Electron and lattice dynamics following optical excitation of metals. 2000 *Chemical Physics* **251**, 237. https://doi.org/10.1016/S0301-0104(99)00330-4

[Hum2007] Hum, D. S., Fejer, M. M. Quasi-phasematching. 2007 *Comptes Rendus Physique* **8**, 180. https://doi.org/10.1016/j.crhy.2006.10.022

[Hurlbut2007] Hurlbut, W. C., Vodopyanov, K. L., Kuo, P. S., Fejer, M. M., and Lee, Y. S. Multi-photon absorption and nonlinear refraction of GaAs in the mid-infrared. 2007 *Optics Letters* **32**, 668. https://doi.org/10.1364/ol.32.000668

[Hutchings1992] Hutchings, D. C., Sheik-Bahae, M., Hagan, D. J., and Van Stryland, E. W. Kramers-krönig relations in nonlinear optics. 1992 *Encyclopedia of Modern Optics*, Elsevier. https://doi.org/10.1016/B978-0-12-809283-5.00749-7

[Imeshev2006] Imeshev, G., Fermann, M. E., Vodopyanov, K. L., Fejer, M. M., Yu, X., Harris, J. S., ... Lynch, C. High-power source of THz radiation based on orientation-patterned GaAs pumped by a fiber laser. 2006 *Optics Express* **14**, 4439. https://doi.org/10.1364/OE.14.004439

[Jiang2010] Jiang, Y., Ding, Y. J., and Zotova, I. B. Power scaling of widely-tunable monochromatic terahertz radiation by stacking high-resistivity GaP plates. 2010 *Applied Physics Letters* **96**, 031101. https://doi.org/10.1063/1.3292585

[Jiang2011] Jiang, Y., Li, D., Ding, Y. J., and Zotova, I. B. Terahertz generation based on parametric conversion: from saturation of conversion efficiency to back conversion. 2011 *Optics Letters* **36**, 1608. https://doi.org/10.1364/ol.36.001608

[Jung1997] Jung, I. D., Kärtner, F. X., Matuschek, N., Sutter, D. H., Morier-Genoud, F., Shi, Z., ... Keller, U. Semiconductor saturable absorber mirrors supporting sub-10-fs pulses. 1997 *Applied Physics B: Lasers and Optics* **65**, 137. https://doi.org/10.1007/s003400050259

[Kadlec2004] Kadlec, F., Nemec, H., and Kužel, P. Optical two-photon absorption in GaAs measured by optical-pump terahertz-probe spectroscopy. 2004 *Physical Review B - Condensed Matter and Materials Physics* **70**, 125205. https://doi.org/10.1103/PhysRevB.70.125205

[Kauranen2012] Kauranen, M., and Zayats, A. V. Nonlinear plasmonics. 2012 *Nature Photonics* **6**, 737. https://doi.org/10.1038/nphoton.2012.244

[Keller1996] Keller, U., Weingarten, K. J., Kartner, F. X., Kopf, D., Braun, B., Jung, I. D., ... Aus der Au, J. Semiconductor saturable absorber mirrors (SESAM's) for femtosecond to nanosecond pulse generation in solid-state lasers. 1996 *IEEE Journal of Selected Topics in Quantum Electronics* **2**, 435. https://doi.org/10.1109/2944.571743

[Khurgin2020] Khurgin, J. B., Clerici, M., Bruno, V., Caspani, L., DeVault, C., Kim, J., ... Kinsey, N. Adiabatic frequency shifting in epsilon-near-zero materials: the role of group velocity. 2020 *Optica* **7**, 226. https://doi.org/10.1364/optica.374788

[Khurgin2021] Khurgin, J. B., Clerici, M., and Kinsey, N. Fast and Slow Nonlinearities in Epsilon-Near-Zero Materials. 2021 *Laser and Photonics Reviews* **15**, 2000291. https://doi.org/10.1002/lpor.202000291

[Kiessling2013] Kiessling, J., Breunig, I., Schunemann, P. G., Buse, K., and Vodopyanov, K. L. High power and spectral purity continuous-wave photonic THz source tunable from 1 to 4.5 THz for nonlinear molecular spectroscopy. 2013 *New Journal of Physics* **15**, 105014. https://doi.org/10.1088/1367-2630/15/10/105014

[Kim1989] Kim, B. G., Garmire, E., Hummel, S. G., and Dapkus, P. D. Nonlinear Bragg reflector based on saturable absorption. 1989 *Applied Physics Letters* **54**, 1095. https://doi.org/10.1063/1.100768

[Kinsey2015a] Kinsey, N., DeVault, C., Kim, J., Ferrera, M., Shalaev, V. M., and Boltasseva, A. Epsilon-near-zero Al-doped ZnO for ultrafast switching at telecom wavelengths. 2015 *Optica* **2**, 616. https://doi.org/10.1364/OPTICA.2.000616

[Kinsey2015b] Kinsey, Nathaniel, Syed, A. A., Courtwright, D., DeVault, C., Bonner, C. E., Gavrilenko, V. I., ... Boltasseva, A. Effective third-order nonlinearities in metallic refractory titanium nitride thin films. 2015 *Optical Materials Express* **5**, 2395.

[Kinsey2019] Kinsey, Nathaniel, DeVault, C., Boltasseva, A., and Shalaev, V. M. Near-zero-index materials for photonics. 2019 *Nature Reviews Materials* **4**, 742. https://doi.org/10.1038/s41578-019-0133-0

[Kityk2002] Kityk, I. V., Wasylak, J., Benet, S., Dorosz, D., Kucharski, J., Krasowski, J., and Sahraoui, B. Synthesized rare-earth doped oxide glasses for nonlinear optics. 2002 *Journal of Applied Physics* **92**, 2260. https://doi.org/10.1063/1.1498888

[Knight2003] Knight, J. C. Photonic crystal fibres. 2003 *Nature* **424**, 847. https://doi.org/10.1038/nature01940

[Kobayashi2007] Kobayashi, Y., Yoshitomi, D., Iwata, K., Takada, H., and Torizuka, K. Ultrashort pulse characterization by ultra-thin ZnO, GaN, and AlN crystals. 2007 *Optics Express* **15**, 9748. https://doi.org/10.1364/oe.15.009748

[Kozák2012] Kozák, M., Trojánek, F., Dzurňák, B., and Malý, P. Two- and three-photon absorption in chemical vapor deposition diamond. 2012 *Journal of the Optical Society of America B* **29**, 1141. https://doi.org/10.1364/josab.29.001141

[Kravetsky2000] Kravetsky, I. V., Tiginyanu, I. M., Hildebrandt, R., Marowsky, G., Pavlidis, D., Eisenbach, A., and Hartnagel, H. L. Nonlinear optical response of GaN layers on sapphire: The impact of fundamental beam interference. 2000 *Applied Physics Letters* **76**, 810. https://doi.org/10.1063/1.125592

[Krotkus2010] Krotkus, A. Semiconductors for terahertz photonics applications. 2010 *Journal of Physics D: Applied Physics* **43**, 273001. https://doi.org/10.1088/0022-3727/43/27/273001

[Kuo2006] Kuo, P. S., Vodopyanov, K. L., Fejer, M. M., Simanovskii, D. M., Yu, X., Harris, J. S., ... Weyburne, D. Optical