Nonlinear Transmission and Solitons in Left-handed Metamaterials

Abstract

A number of theoretical studies and experimental results demonstrated the existence of a novel type of microstructured materials, which can be characterized, for some value of the parameters, by a negative real part of the magnetic permeability and a negative real part of the dielectric permittivity in the microwave frequency range. Such materials were first mentioned as a theoretical curiosity a long time ago [1]. Recently, it has also been noticed that the left-handed metamaterials may possess quite complicated nonlinear magnetic response [2]. We study numerically, with the help of the finite-difference time-domain (FDTD) method, one-and two-dimensional wave transmission through a slab of the left-handed metamaterial assuming that it possesses a hysteresis nonlinear response [2]. We observe two types of nonlinear effects associated with a change of the metamaterial properties: (i) nonlinearity-induced suppression of the wave transmission, and (ii) the nonlinearity-induced transmission and the generation of spatiotemporal electromagnetic solitons. In the later case, the nonlinearity-induced transmission of the slab for larger input powers is shown to take place for the slab, which is opaque and totally reflecting for low-amplitude wave scattering, In addition, in the case of the overcritical transmission we observe that the spatiotemporal dynamics is characterized by the generation and propagation of spatiotemporal solitons. In the case of overcritical power of the incident beam, the stationary state of the scattering cannot be reached (see Fig. 1) due to the generation of the temporal solitons inside the slab. Figure 2 shows the field structure (top) and the formation of a region of transparency, the effective left-handed region (bottom), in an initially opaque metamaterial slab by a large-amplitude electromagnetic wave, As we observe in simulations, an initially opaque slab [see Fig. 2(bottom)] becomes transparent [see black area inside the slab in Fig. 2(bottom)] for the high enough field intensities. The shift of the transparent domain to the left indicates the negative refraction of the beam in the left-handed slab.