Tsitsas, NL; Rompotis, N; Kourakis, I; Kevrekidis, PG; and Frantzeskakis, DJ, "Higher-order effects and ultrashort solitons in lefthanded metamaterials" (2009). PHYSICAL REVIEW E. 55. Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/55

We consider short pulse propagation in nonlinear metamaterials characterized by a weak Kerr-type nonlinearity in their dielectric response. In the frequency "band gaps" (where linear electromagnetic waves are evanescent) with linear effective permittivity ǫ < 0 and permeability µ > 0, we derive two short-pulse equations (SPEs) for the high-and lowfrequency band gaps. The structure of the solutions of the SPEs is also briefly discussed, and connections with the soliton solutions of the nonlinear Schrödinger equation are presented. . The frequency dependence of the effective permittivity ǫ and permeability µ of these media is such that there exist frequency bands where the medium displays either a right-handed (RH) behavior (ǫ > 0, µ > 0) or a left-handed (LH) behavior (ǫ < 0, µ < 0), thus exhibiting negative refraction at microwave [2,3,4] or optical frequencies [5]. Frequency band gaps, i.e., frequency domains where linear EM waves are evanescent (e.g., for ǫ < 0 and µ > 0), also exist in metamaterials. Hence, when a nonlinearity occurs, say in the dielectric response of the medium (a physically relevant situation in nonlinear metamaterials [6,7,8,9,10,11,12]), then nonlinearity-induced localization of EM waves is possible. Such localization is indicated by the formation of gap solitons, which occur mainly in nonlinear optics [13] and Bose-Einstein condensates (BECs) [14], by means of the nonlinear Schrödinger (NLS) equation with a periodic potential. Gap solitons were also predicted to occur in nonlinear metamaterials [15]. There, the approximation of slowly varying electric and magnetic field envelopes, led to a nonlinear Klein-Gordon (NKG) equation supporting gap solitons.Nonlinear models describing localization of wave packets in periodic media, e.g., the NLS equation in optics [13] and NKG equation in metamaterials [15] are usually derived in the framework of the slowly-varying envelope approximation. However, as far as ultra-short pulse propagation is concerned, i.e, for pulse widths of the order of a few cycles of the carrier

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Diffraction of electromagnetic waves by periodic grating waveguides is investigated by using a rigorous integral equation method, which combines semianalytical techniques and the Method of Moments with entire domain basis functions. The electric field integral equation is employed with unknown function the electric field on the grooves. This equation is subsequently solved by applying an entire domain Galerkin's technique. The proposed analysis provides high numerical stability and controllable accuracy. All the involved computations are analytically carried out, leading to an analytic solution with the sole approximation of the final truncation of the expansion functions sets. The computed results exhibit superior accuracy and numerical efficiency compared with those already derived by applying different methods. The effect of the incident field's and grating's characteristics on the diffraction process as well as the grating structure's efficient operation as a narrow band reflection filter are thoroughly investigated. The numerical results obtained provide design guidelines, which may be exploited appropriately in the development of millimeter and optical waveguide structures.

Eliminating the electromagnetic interaction of a device with its background is a topic which attracts considerable attention both from a theoretical as well as from an experimental point of view. In this work, we analyze an infinite two‐dimensional planar microstrip antenna, excited by an incident plane wave, and propose its potential operation as a low‐profile receiving antenna, by suitably adjusting the parameters of its cloaking superstrate. We impose a semi‐analytic integral equation method to determine the scattering characteristics of the microstrip antenna. The method utilizes the explicit expressions of the Green's function of the strip‐free microstrip and yields the surface strip's current as the solution of a suitable linear system. Subsequently, the antenna's far‐field response is obtained. Numerical results are presented for the achieved low profile of the receiving antenna, by choosing suitably the cloaking superstrate parameters. It is demonstrated that for specific cloaking parameters the scattered field by the antenna is considerably reduced, while the received signal from the antenna is maintained at sensible levels. We point out that the material values achieving this reduction correspond to a superstrate filled with anϵ‐near‐zero or a low‐index metamaterial. Finally, the variations of the device reaction for various superstrates are depicted, concluding that for optimized superstrate's parameters, the reaction values are significantly reduced, while at distinct scattering angles even approach zero.