Nonlinear optics is the study of all effects that can be described as multi-photon interactions in various material systems, including cases where the frequency of one or more photons tends to zero. This feature issue is dedicated to works on both second-order nonlinear optics (three-photon interactions) and third-order nonlinear optics (four-photon interactions) that focus on understanding the fundamental mechanisms of the nonlinear optical response when the nonlinearity is large and approaches the fundamental quantum limit—a regime required by applications and characterized by interesting physics. Slightly more than half of the papers focus on theoretical analysis, with a strong emphasis on understanding model systems in view of the fundamental limits to the nonlinear optical response, which are dictated by quantum mechanics, and with several discussions of new theoretical approaches to understand and model the nonlinear optical response. The remaining papers provide an experimental counterpoint that includes examples of nonlinear optical responses in a variety of systems, an overview of how the fundamental limits can be approached in real materials, and of how the nonlinear response scales with spatial dimensions. The latter is quantified by identifying scale-invariant intrinsic quantities such as the dimensionless ratios between experimental results and the quantum limits.
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