This book provides readers with a detailed overview of second- and third-order nonlinearities in various nanostructures, as well as their potential applications. Interest in the field of nonlinear optics has grown exponentially in recent years and, as a result, there is increasing research on novel nonlinear phenomena and the development of nonlinear photonic devices. Thus, such a book serves as a comprehensive guide for researchers in the field and those seeking to become familiar with it.This text focuses on the nonlinear properties of nanostructured systems that arise as a result of optical wave mixing. The authors present a review of nonlinear optical processes on the nanoscale and provide theoretical descriptions for second and third-order optical nonlinearities in nanostructures such as carbon allotropes, metallic nanostructures, semiconductors, nanocrystals, and complex geometries. Here, the characterization and potential applications of these nanomaterials are also discussed. The factors that determine the nonlinear susceptibility in these systems are identified as well as the influence of physical mechanisms emerging from resonance and off-resonance excitations. In addition, the authors detail the effects driven by important phenomena such as quantum confinement, localized surface plasmon resonance, Fano resonances, bound states, and the Purcell effect on specific nanostructured systems. Readers are provided with a groundwork for future research as well as new perspectives in this growing field.

Prof. Carlos Torres-Torres's main research is in nonlinear optics exhibited by nanostructures and thin films. Most of his publications involve the ultrafast optical Kerr effect, laser ablation, and the nonlinear optical absorption in metallic nanoparticles nucleated by ion-implantation, grown by sol-gel methods or prepared by spray pyrolysis processing routes. His research on 2D materials was awarded by the 2013 MRS Spring Congress in San Francisco, California. He is currently a full professor at the Instituto Politécnico Nacional Mexico where he is responsible for the Laboratory of Vectorial Optical Instrumentation. He was awarded best reviewer in 2015 by the Journal of Optics and Laser Technology, Elsevier and also has been awarded outstanding reviewer by various prestigious journals such as the Journal of Physics: Applied Physics, Molecular Liquids, Sensors & Actuators B, Materials Science & Semiconductor Processing, Materials Chemistry and Physics, Applied Surface Science and Optical Materials, Physical Chemistry Chemical Physics, RSC Advances and Physica Scripta. He has published over 100 scientific papers with more than 1000 citations. He is currently a coordinator of a group in the Nanoscience and Micro Nanotechnology Network and head of the group of Instrumentation of Signals in Nanostructures at the Instituto Politécnico Nacional Mexico.Geselle García-Beltrán is a PhD student at the Instituto Politécnico Nacional Mexico. She received her M.S. in Mechanical Engineering with a thesis related to the nonlinear optics and mechanic phenomena exhibited by nanofluids at the Escuela Superior de Ingeniería Mecánica y Eléctrica Unidad Zacatenco del Instituto Politécnico Nacional Mexico. During her time as a PhD student, she has deepened her knowledge of the nonlinear optical effects of plasmonic carbon/metal nanofluids and nanostructures. Her research has focused on the development of probabilistic logic gates based on third-order nonlinear optical effects