**5. Conclusions**

We considered the interaction of the optical waves with free electrons in metals. The theoretical analysis in such a case is based on Maxwell's equations and the equation of motion of a free electron in an external electric field. As a result, plasmonic excitations emerge. The dielectric function of a free electron gas with plasmonic oscillations is described by the dielectric function (22) known as the Drude model. The longitudinal plasma oscillations excited at the plasma frequency *ω* ¼ *ω<sup>p</sup>* are called the volume plasma oscillations, and the quasi-particles related to these oscillations are called the volume plasmons. SPPs may exist at the interface of the metal described by the Drude dielectric function and the dielectric medium. SPPs are the TM waves. They are characterized by the limited propagation length in the dielectric and the spatial confinement in the direction perpendicular to the propagation direction. The subwavelength confinement of the optical field is possible for SPPs. The nonlinear optical effects in plasmonic structures are significantly enhanced. The nonlinear optical phenomena such as modulation, switching, harmonic generation, FWM are possible in plasmonic nano-structures. Highly efficient all-optical switching and all-optical modulation can be realized in nonlinear plasmonic metamaterials based on nano-particles, split-ring resonators, and LCs.

Plasmonics plays an essential role in modern nonlinear optics. The nonlinear optical effects can be achieved at the reduced optical power due to enhanced effective nonlinearity in plasmonic nanostructures. The size of the nonlinear components can be scaled down which is important for the development of functional nanophotonic circuits. The ultrafast optical signal processing on the femtosecond scale can be realized due to the small response time of the plasmonic excitations.
