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In the continuously evolving realm of nonlinear optics, epsilon near zero (ENZ) materials have captured significant scientific interest, becoming a compelling focal point over the past decade. During this time, researchers have shown extraordinary demonstrations of nonlinear processes such as unity order index change via intensity dependent refractive index, enhanced second harmonic generation, saturable absorption in ultra-thin films and more recently, frequency shifting via time modulation of permittivity. More recently, remarkable strides have also been made in uncovering the intricacies of ENZ materials' nonlinear optical behavior. This review provides a comprehensive overview of the various types of nonlinearities commonly observed in these systems, with a focus on Drude based homogenous materials. By categorizing the enhancement into intrinsic and extrinsic factors, it provides a framework to compare the nonlinearity of ENZ media with other nonlinear media. The review emphasizes that while ENZ materials may not significantly surpass the nonlinear capabilities of traditional materials, either in terms of fast or slow nonlinearity, they do offer distinct advantages. These advantages encompass an optimal response time, inherent enhancement of slow light effects, and a broadband characteristic, all encapsulated in a thin film that can be purchased off-the shelf. The review further builds upon this framework and not only identifies key properties of transparent conducting oxides that have so far made them ideal test beds for ENZ nonlinearities, but also brings to light alternate material systems, such as perovskite oxides, that could potentially outperform them. We conclude by reviewing the upcoming concepts of time varying physics with ENZ media and outline key points the research community is working toward. 

On the occasion of 60 years of nonlinear-optical research, we present new data tables listing nonlinear- optical properties for different material categories as reported in the literature since 2000, and provide best practices for performing experiments. 

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.