Wave Processes in Moderately and Strongly Nonlinear and Active Hyperbolic Metamaterials and Potential Applications

Two approaches to the moderately and strongly nonlinear active planar hyperbolic metamaterials, with and without an averaging over a unit cell are applied. For the proper sign of the nonlinearity of the layers included into the elementary cell of the metamaterial, the hotspots can be formed in IR range. Hypothetically, the hot spot formation is a rather common feature of the strongly nonlinear media with the interfaces between linear and nonlinear layers. The new evolution equations for the envelope amplitude of the nonlinear wave packets propagating in active hyperbolic media under an arbitrary angle to the optical axis are derived in the parabolic approximation. The mixed derivative in the evolution equation disappears and the equations reduce to the Nonlinear Schrodinger Equation (NSE) form for the waves propagating along an optical axis. The nonlinear quantum optics approach to the waves in hyperbolic active metamaterials is outlined.