Research On Spatiotemporal Electromagnetic Soliton Formations And Propagation Characteristics In Metamaterials

Soliton is a very fundamental and important nonlinear phenomenon in nature and its occurrence is due to the balance between linear and nonlinear effects. The optical or electromagnetic solitons promise some potential applications for optical communication, optical computing and all-optical information processing, et al. In the past few years, a new artificially-constructed electromagnetic materials, i.e., metamaterials (MMs) exhibits intriguing linear and nonlinear electromagnetic properties not found in naturally occurring materials, meaning that soliton physics and phenomena in such materials will be more interesting and much richer; in the meanwhile, the electromagnetic properties of MMs are designed at will, and so these provide us an alternative approach to actively manipulate solitons. In this paper, we will combine the basic theory and method of conventional soliton and the novel properties of MMs to investigate the formation and propagation properties of spatiotemporal electromagnetic soliton in MMs, focusing on the new soliton phenomena. In addition, we will apply engineerable electromagnetic properties of MMs to further explore the principle and project for manipulating soliton at will. Our results will not only enrich and develop conventional soliton theorey, but also lay the theoretical foundation for designing relevant photon devices and optical-controlled optical technologies related to MMs. The main innovative research results are listed below:Firstly, we for the first time present a systematic investigation of spatiotemporal electromagnetic soliton formation and pulse splitting in nonlinear MMs. The theoretical predictions demonstrate that spatiotemporal electromagnetic solitons may exist in the positive-index region of a MM with focusing nonlinearity and anomalous group velocity dispersion (GVD), as well as in the negative-index region of the MM with defocusing nonlinearity and normal GVD. As a result, this counterintuitive result for higher-dimensional soliton formation to some extent breaks the conventional viewpoint. In particular, we can engineer the balance among dispersion, diffraction, nonlinearity by adjusting the sizes of the typical constitutive elements of MMs, indicating the experimental circumstances for generating and manipulating spatiotemporal electromagnetic solitons can be created by elaborating appropriate MMs. In addition, we find that, in the negative-index region of a MM, a spatial ring may be formed as the electromagnetic pulse propagates for focusing nonlinearity and anomalous GVD; while the phenomenon of temporal splitting of electromagnetic pulse may appear for the same case except for the defocusing nonlinearity. Finally, we discuss the switchable sign of nonlinearity and its role in the propagation of electromagnetic pulses. It is found that the extra nonlinear magnetization makes the sign of effective nonlinear effect engineerable by varying the relative ratio between electric and magnetic frequencies. This makes us manipulate the dynamical behaviors of electromagnetic pulses in MMs more freely.Secondly, we further investigate the influences of higher-order nonlinear effects originating from the dispersive magnetic permeability on the dynamic behavior of spatiotemporal electromagnetic pulse splitting, focusing on the anomalous propagation properties not occurred in conventional materials. It is well known that the most noticeable difference between a MM and a conventional material is that the former have a dispersive magnetic permeability. This difference leads to the fact that the model for describing ultrashort pulse propagation in MMs includes a controllable self-steepen (SS) effect which can be positive or negative, and a series of extra higher-order nonlinear dispersive terms. Nowadays, the evolution of ultrashort pulse optics has arrived at a point where light pulses with durations comparable to the carrier oscillation cycle have become available. As a result, we predict that such higher-order nonlinear effects will exert a very strong influence on the propagation of ultrashort electromagnetic pulse in MMs. Our further analysis shows that, like the case of ordinary materials, the inclusion of SS with positive value gives rise to the asymmetry between the leading and trailing pulses, but the relative magnitudes of the two peaks are reversed, namely, the leading pulse being higher than the trailing pulse. However, the negative SS does opposition. In addition, we investigate the influences of second-order nonlinear dispersion (SND) not found in conventional materials on the pulse splitting. The results show that, unlike the SS effect, the SND effect brings about the symmetric pulse splitting. Moreover, it is demonstrated that SND with positive value will enhance the pulse spreading; while SND with negative value does opposition.Finally, we in detail investigate modulation instability (MI) in nonlinear MMs, and disclosed some new instability phenomena. These works are of very important significance for generation of ultrashort pulses and soliton formation. The conditions for spatial and spatiotemporal instabilities in MMs are reserved due to the role of negative index; while the condition for temporal MI is the same that in ordinary material. In addition, special attention is paied to the general features of instability induced by arbitrary high-order nonlinear dispersion effects originating from the combination of dispersive magnetic permeability and nonlinear polarization. It is shown that, just like their linear counterparts, all even-order nonlinear dispersions not only deform the original instability regions, but also may lead to the appearance of new instability regions. However, all odd-order nonlinear dispersions always suppress MI irrespective of their signs, quite different from their linear counterparts which exert no influence on instability. The role of SS and SND in temporal and spatiotemporal instabilities is particularly analyzed to exemplificatively demonstrate the general results. In particular, we find that SND with appropriate value opens up a new instability window with an unlimited temporal range and the gain value increases monotonically with increasing repetition rate. Such phenomena have never arisen in conventional materials.