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- A nonlinear metamaterial is an artificially constructed material that can exhibit properties not found in nature. Its response to electromagnetic radiation can be characterized by its permittivity and material permeability. The product of the permittivity and permeability results in the refractive index. Unlike natural materials, nonlinear metamaterials can produce a negative refractive index. These can also produce a more pronounced nonlinear response than naturally occurring materials. Nonlinear metamaterials are a periodic, nonlinear, transmission medium. These are a type of negative index metamaterial where the nonlinearity is available because the microscopic electric field of the inclusions can be larger than the macroscopic electric field of the electromagnetic (EM) source. This then becomes a useful tool which allows for enhancing the nonlinear behavior of the metamaterial. A dominant nonlinear response, however, can be derived from the hysteresis-type dependence of the material's magnetic permeability on the magnetic component of the incident electromagnetic wave (light) propagating through the material. Furthermore, the hysteresis-type dependence of the magnetic permeability on the field intensity allows changing the material from left to right-handed and back. Nonlinear media are essential for nonlinear optics. However most optical materials have a relatively weak nonlinear response, meaning that their properties only change by a small amount for large changes in intensity of the electromagnetic field. Nonlinear metamaterials can overcome this limitation, since the local fields of the resonant structures can be much larger than the average value of the field - in this respect metamaterials are similar to other composite media, such e.g. as random metal-dielectric composites, including fractal clusters and semicoutinouos/percolation metal films, where the areas with enhanced local light fields - “hot spots” - produce giant linear and non-linear optical responses. (en)
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