The paper presents the experimental results that demonstrate the formation of spatiotemporal parametric patterns in active ring resonators based on one-dimensional single- and bicomponent magnonic quasicrystals (MQCs). Such patterns are formed through the nonlinear parametric three-wave decay of a magnetostatic surface spin wave (MSSW). It is shown that in the active ring resonator based on the single-component MQC made from a ferrite film, the spatial patterns of magnetization are localized in the grooves at a MSSW frequency and in the crests at a frequency of parametrically excited spin waves (SWs). In the active ring resonator based on the bicomponent MQC (the ferromagnetic permalloy strips located on a ferrite film surface), the magnetization localization is observed in free parts of the ferrite film both at the MSSW frequency and at the frequency of parametrically excited SWs.

The research experimentally demonstrates the direct electric current control of hyperchaotic packets of dissipative dark envelope solitons that are self-generated in a microwave active ring resonator containing two nonlinear elements: a one-dimensional magnonic crystal (MC) with dynamic line defect and a transistor amplifier. The hyperchaotic packets of dissipative dark envelope solitons are formed at a magnetostatic surface spin wave (MSSW) propagating in the MC and taking part both in three-wave nonlinear spin-wave processes of decay and confluence. The transistor amplifier operates in output-power saturation mode. The direct electric current flowing through a copper wire placed along the longitudinal axis of the MC creates the dynamic line defect that effectively controls a duty factor of dissipative dark envelope soliton packets and their hyperchaotic properties at the MC band gap only. The hyperchaotic nature of dissipative soliton packets is confirmed by an estimation of the two highest Lyapunov exponents from the experimental time series. The modified Vyshkind-Rabinovich model demonstrates the self-generation of a dark pulse train at a decaying wave (MSSW) and a bright pulse train at the parametrically excited waves (the exchange spin waves) due to two saturation mechanisms. One of them is connected with the parametric instability, whereas the other one is caused by the increment nonlinearity. The developed self-generator may be of great interest to reservoir-computing that is based on the concept of ``computation at the edge of chaos.''

The paper presents the theoretical results that demonstrate the bright envelope soliton formation on a backward electromagnetic wave existing in a double negative medium based on a magnetized thin film of ferromagnetic semiconductor (FM SC). An analytical model of a magnetized ferromagnet containing magnetized cold and collisionless electron plasma is constructed based on the use of Maxwell's equations and material expressions including tensor functions of dielectric permittivity and magnetic permeability. The nonlinearity of the FM SC is due to the dependence of magnetization on the amplitude of the high-frequency magnetic field. It is shown that one of the solutions of the nonlinear Schrodinger equation with coefficients depending on the electromagnetic properties of the BEMW has a form of a bright envelope soliton. The duration of such nonlinear pulses is controlled by the change of thickness of a FM SC film, strength of a magnetic bias field and electron concentration in plasma.

In this paper, we consider a normally magnetized nonlinear ferromagnetic metamaterial (FM MM) layer possessing simultaneously negative effective permittivity and magnetic permeability in some microwave frequency range, where a backward electromagnetic wave (BEMW) exists. The FM MM is a nonconductive FM host containing a square two-dimensional array of thin conductive wires cladded with a nonmagnetic dielectric layer. The nonlinearity of the FM MM is due to the dependence of magnetization on the amplitude of the high-frequency magnetic field. It is shown, that bright envelope solitons can be formed on the BEMW in relatively thick FM MM layers and at relatively small wave numbers.

Left-handed (LH) metamaterials are generally structured materials possessing abnormal electromagnetic properties due to both negative permittivity and permeability. One of these properties is a backward wave (BW) propagation, in which the phase and group velocities are opposite to each other. Here we investigate the electrodynamic (dispersion and energy) characteristics of the BW existing in a magnetic LH metamaterial that is controlled by the external uniform magnetic field. Such a metamaterial is a host made from a mu-negative (ferromagnetic) nonconductive medium that contains a two-dimensional periodic structure of thin and isolated wires placed in the bias field directed either transversely or longitudinally to the electromagnetic wave propagation. A finite-difference time-domain-Landau-Lifshits-Gilbert (LLG) electromagnetic solver MaxLLG is used for the BW numerical simulations. This solver is based on the simultaneous usage of the Maxwell and LLG equations. By operating this software, the authors validate the existence of the BWs in the investigated LH metamaterial for two bias field orientations for various values of magnetic LH layer thickness and wire conductivity as well as for two connection types of wires with metallic planes that are placed on both sides of the metamaterial layer.

In this work, a theoretical study of the backward electromagnetic waves (BEMWs) existing in the bigyrotropic left-handed media controlled by a magnetic bias field is presented. The bigyrotropic media are both longitudinally and transversely magnetized ferromagnetic (FM) or antiferromagnetic (AFM) semiconductors (SCs) with electric and magnetic loss. It is shown that the BEMWs are observed both in the microwave and terahertz frequency ranges, in which the effective material parameters of the FM or AFM SCs are double negative. We demonstrate the control of the BEMW dispersion characteristics not only by changing the magnetic bias field direction and strength, but also by variation a material magnetization and thickness, an electron concentration in a solid-state plasma, as well as the electric and magnetic loss.

Congratulations to Yuri Pavlovich Sharayevsky on his anniversary.

We demonstrate the dissipative spatiotemporal patterns that are generated by an active ring resonator based on a magnonic quasicrystal (MQC) with Fibonacci-type structure. The dissipative patterns are formed through the magnetostatic surface spin-wave (MSSW) parametric decay into exchange spin waves (SWs), temporal dispersion of the ring resonator and amplification. In the spatial domain, the MSSW and SW parametric patterns measured with the help of Brillouin light spectroscopy have the quasiperiodic spatial localization in crests and grooves of the MQC, respectively. In contrast to the optical quasiperiodic parametric spatial conservative solitons, the amplitude profiles of the magnonic quasiperiodic parametric spatial dissipative patterns correspond to the profiles of the crests and grooves of the MQC. In the time domain, the packets of the chaotic parametric pulses, which are analogs of temporal solitons, are generated at each point of the spatial patterns. The chaotic nature of such pulses is confirmed by an estimate of a highest Lyapunov exponent from the experimental time series. The pulse packets are formed through the time-filtering technique using the external microwave (MW) pulses to control a ring gain. It is shown that at a certain duty factor of the external MW pulses, the parametric MSSW pulses have the amplitude and phase profiles corresponding to the profiles of a conservative bright envelope soliton.

We report on the self-generation of ultrashort hyperchaotic dark multisoliton sequences with two positive large Lyapunov exponents in an active ring resonator consisting of a multifunctional L-shaped magnonic waveguide and a saturable amplifier. The irregular magnonic waveguide supports the converting of backward volume magnetostatic spin waves with negative dispersion to magnetostatic surface spin waves with positive dispersion that is accompanied by a transition from four-wave to three-wave nonlinear spin-wave interactions. Each multisoliton complex consists of four dark parametric pulses containing the soliton trains of four dark incoherent spin-wave envelope solitons possessing a subnanosecond duration. Such patterns are formed due to the dispersion and nonlinearity management, the nonlinear transformation of the pulse signal in the saturable amplifier and the partial chaotic synchronization of both the ring eigenmodes and the spin wave automodulation frequencies. We also demonstrate a new intermittency type of "hyperchaotic multisoliton complexes-hyperchaotic multisoliton gas" with the increase of the signal power level.