Wenhua Su

Modulation instability induced by nonlinear dispersion in nonlinear metamaterials

We show that modulation instability may occur even in the normal group-velocity dispersion regime, or in the case of no group-velocity dispersion in metamaterials with a nonlinear electric polarization. The physical origin of the modulation instability is the additional second-order nonlinear dispersion effect resulted from the combination of the linear dispersive magnetic permeability with the nonlinear electric polarization. Based on the Drude model, a numerical simulation is performed to confirm the theoretical predictions, and a detailed discussion on the role of the second-order nonlinear dispersion effect in modulation instability in both negative-index and positive-index regions of metamaterial is presented.

DARK SOLITON SOLUTIONS TO THE NONLINEAR SCHRÖDINGER EQUATION FOR ULTRASHORT PULSE PROPAGATION IN METAMATERIALS

The nonlinear Schrodinger equation for ultrashort pulse propagation in metamaterials with a nonlinear polarization is solved by an extended tanh function expansion method, and the dark solitary wave solutions for various conditions are obtained. The role of the dispersive magnetic permeability, which manifests itself as self-steepening and higher order nonlinear dispersion terms in the nonlinear Schrodinger equation in dark solitary wave propagation, is identified. It is found that the negative self-steepening effect in metamaterials makes the solitary wave move to the leading side, opposite to that in ordinary materials, in which the self-steepening effect is always positive. Most importantly, due to the role of the second order nonlinear dispersion, dark solitons can be formed in the absence of linear dispersion, or even in the case of anomalous linear group velocity dispersion, different from the conditions for dark soliton formation in ordinary materials.

Dark electromagnetic solitons in the anomalous group-velocity dispersion regime in metamaterials

Solitons have been found in many physical branches. Previous investigations on solitons mainly focused on various nonlinear dispersive media in nature. It is well known that in the nonlinear dispersive medium, soliton formation is due to the exact balance between the nonlinearity and the group velocity dispersion (GVD). When the signs of nonlinearity and GVD are the same, that is, the positive (focusing) nonlinearity vs. positive (normal) GVD, or the negative (defocusing) nonlinearity vs. negative (anomalous) GVD, the interaction between nonlinearity and GVD may lead to the generation of dark solitons. In this paper, we study the formation and propagation of dark electromagnetic solitons in the metamaterials, artificial structures that display properties beyond those available in naturally occurring materials. We use an extended Tanh-function expansion method to solve the nonlinear equation for ultrashort electromagnetic pulse propagation in metamaterial with a nonlinear polarization, and get dark solitary solutions under various conditions. It is found that, due to the role of the second-order nonlinear dispersion resulted from the dispersive magnetic permeability, dark solitons can be formed in the absence of linear dispersion, or even in the case of anomalous linear GVD for a focusing nonlinearity, challenging the traditional conditions for dark soliton formation.

Study of metamaterial-based nonlinear optics

Metamaterials (MMs) are artificial structures that display properties beyond those available in naturally occurring materials. The most notable MM is the negative-index material with simultaneously negative electric and magnetic responses. Recently, MMs exhibiting negative electric and magnetic properties in the infrared and optical frequencies have been realized, which will affect substantially the conventional optics and their applications in devices of compact cavities, adaptive lenses, tunable mirrors, isolators, converters, and so on. Moreover, MMs with nonlinear electric and/or magnetic response have also been demonstrated. This will further stimulate intense investigation in MM-based nonlinear optics due to the richness and the potential applications of the nonlinear property of MMs. In this paper, we report on our recent progress on investigation of some typical third-order nonlinear optical phenomena in MMs, such as modulation instability, soliton propagation, self-focusing, and so on. The controllability and the novel properties of the nonlinear phenomena in MMs are demonstrated.

Self-focusing and self-defocusing of the optical beam propagation in a nonlinear negative-refractive-index material

We study the phenomena of self-focusing and self-defocusing of an optical beam in a nonlinear negative-refractive-index material (NRM). It is shown that an optical beam propagating in NRM experiences self-focusing and self-defocusing for negative and positive nonlinear refractive index respectively. The critical power for self-focusing is the same as that in a conventional nonlinear positive-refractive-index material. Further, we show by numerical simulations that the nonlinear NRM can be used to compensate for self-focusing in the propagation of high power lasers in conventional nonlinear positive-refractive-index medium. The modulation generated by self-focusing in nonlinear positive-refractive-index medium can be reduced drastically by inserting a piece of nonlinear NRM.

Property of electromagnetic solitons in negative-index metamaterials

We study the propagation property of soliton pulses in negative-index metamaterials with a nonlinear polarization, and especially analyze the influence of the controllable self-steepening effect, which is resulted from the dispersive magnetic permeability in negative-index metamaterials, on soliton formation and propagation. The results indicate that the negative self-steepening effect also leads to the asymmetry of soliton pulse, the center shift and the decay of higher-order soliton. In addition, the controllable self-steepening effect can be used to counteract the shift of soliton pulse resulted from the third order dispersion effect to make the soliton pulse propagation without center shift to some extent.

The role of dispersive magnetic permeability in ultrashort electromagnetic pulse propagation in nonlinear metamaterials

Compared to the non-magnetic ordinary dielectrics, the negative-index metamaterials have not only a dispersive electric permittivity but also a dispersive magnetic permeability. The purpose of this paper is to identify the role of dispersive magnetic permeability in nonlinear propagation of ultrashort electromagnetic pulses in metamaterials. Firstly, we derived a generalized system of coupled three-dimensional nonlinear Schroedinger equations suitable for few-cycle pulse propagation in the metamaterial with both nonlinear electric polarization and nonlinear magnetization, which clearly demonstrates the role of dispersive permeability in nonlinear pulse propagation: In the linear propagation aspect, its contribution is buried in the ordinary dispersive terms; while in the nonlinear propagation aspect, the dispersive permeability manifests itself as a nonlinear polarization dispersion, although it is a linear parameter. Secondly, by exemplificatively using the coupled nonlinear Schroedinger equations in the Drude dispersive model, we quantitatively discussed the influence of dispersive permeability on pulse propagation in metamaterials.

Metamaterial-based low-pass spatial filters for high-power lasers

Two kinds of novel spatial filters constructed by metamaterials and their possible applications in high-power laser systems have been investigated. The first one can be constructed by forming a compensating bilayer of indefinite metamaterials. It is shown that the cutoff wave vector of the low-pass spatial filter can be adjusted desirably. The second kind of low-pass spatial filter is based on the controllable dispersion characteristics of photonic crystals. With proper design, the higher spatial frequency components, which are incident to the filter with angles exceed a critical value, are reflected totally because no Bloch waves of the photonic crystals can be excited. However, the lower spatial frequency components are coupled to the self-collimating modes and permeate with high transmission. The applications of the two novel kinds of metamaterials-based low-pass spatial filter in high-power lasers are discussed.