| The study of electromagnetic waves in nonlinear gyromagnetic materials is mainly focused on the properties and potential applications of nonlinear waves. In the past few years, the availability of high-quality gyromagnetic crystals has led to a growing interest in nonlinear magnetic waves. The interactions of gyromagnetic crystals with infrared waves or microwaves have drawn much attention.In this paper, we theoretically investigated the properties of electromagnetic waves propagating in gyromagnetic waveguides with a plane interface, and the spatio-temporal characteristics of nonlinear waves in gyromagnetic materials. Ferromagnetic and antiferromagnetic crystals are considered in this paper, and three kinds of configarations are investigated: nonlinear antiferromagnet/linear ferromagnet, nonlinear antiferromagnet/linear dielectric, nonlinear antiferrornagnet/nonlinear antiferromagnet.The main results obtained are as follows:(1) Properties of surface waves in microwave frequency range on a plane interface between a nonlinear antiferromagnet and a linear ferromagnet are studied, (a) For transverse magnetic (TM) waves, the analytical dispersion relation and magnetic field distributions in space are obtained. On the basis of the dispersion relation, we investigated the properties of nonlinear surface waves. It is shown that there exist backward surface waves, with the phase velocity and group velocity opposite in direction, (b) For transverse electric (TE) waves, the nonlinear wave equation is transformed intoBernoulli equation, and the exact solutions of magnetic fields are obtained. It is found that there are two different field distributions corresponding to the large power and small power cases. We obtained the power-dependent dispersion equation and further investigated the frequency characteristics. It is revealed that, both for TM and TE waves, there exist passbands and stopbands, which can be controlled by varying the power of the wave.(2) Propagation properties of infrared waves on the interface between a nonlinear antiferromagnet and a linear dielectric are investigated, (a) For TM waves, the dispersion relation is obtained, and the variation of magnetic peak field positions with power is studied. The frequency characteristics of surface waves are analyzed. It is revealed that there exist frequency passbands and stopbands. The bandwidths can be controlled by varying the power, (b) For TE waves, we analyzed the frequency characteristics with the help of dispersion relation and boundary conditions, and found that there is a critical frequency, below which the TE wave can be backward surface waves. The results show that power and the ratio of permittivities influence the bandwidths.(3) Characteristics of stable electromagnetic surface waves propagating along the interface between two different nonlinear antiferromagnets are studied. For stable surface waves, there exist a frequency threshold, a power threshold and two cross-jumping powers. The frequency threshold is dependent on the permittivities of two antiferromagnets. All the incident waves satisfying the frequency and power thresholds can propagate steadily in this waveguide. When the power threshold is exceeded, surface magnetic waves will form. The peak field appears in one of theantiferromagnets at first. When the power is increased to the cross-jumping power, the peak field will jump into another antiferromagnet, crossing the interface. The maximum jumping distance is in the range from 100 microns to 200 microns, depending on the incident frequencies. Investigating the variation of the peak field position with the power, we found that two cross-jumping powers appear during the courses of power increasing and decreasing. It is noted that frequency and magnetic parameters are the factors which influence the magnetic field amplitude on the interface.(4) We analyzed the properties of spatio-temporal solitons in gyromagnetic materials, (a) The spatio-temporal instabilities of nonlinear gyromagnetic waves are studied...
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