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We study nonlinear wave phenomena in hyperbolic and plasma-like dielectric isotropic metamaterials, dielectric-graphene (DG), dielectric-semiconductor (DS) and dielectric-metal (DM) plasma-like media (PM) (DGPM, DSPM, DMPM, respectively). When a THz beam passes through a layered DGPM in the presence of external magnetic field, we show the ability to effectively control the resonant complex nonlinear conductivity of graphene and modulation of the beam amplitude. In the hyperbolic nonlinear active IR field concentrator, the possibilities of (i) forming three types of focused nonlinear wave structures and (ii) the quasi-chaotic behaviour of the field amplitude inside the region of focusing in the above-threshold regime are demonstrated. Non-stationary regime for incident beam is included into consideration. When pulses in the IR range impinge a layer of a planar hyperbolic metamaterial with gain-active inclusions providing resonant nonlinear dissipation, the formed wave beam demonstrates pronounced synergistic behaviour with both “absorption” and “survival” phenomena. In a multilayer DMPM operating in the THz range, the transmission of a wave beam happens with the nonlinear medium transparency, whereas the medium nonlinearity is manifested via the nonlinear conductivity/nonlinear losses. In this case, quantum effects in thin metal layers were taken into account. They led, in particular, to nonlocality of the medium response. These and other theoretically revealed effects are experimentally realizable, provided with estimates for the parameters of structures and materials, and can be useful in creating effectively controllable nonlinear modulators, limiters, concentrators, sensors, devices with harmonic generation and frequency mixing, and other devices.
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