Analysis of ElectromagneticWave Propagation in Frequency Bands of Nonlinear Metamaterials - Tsitsas, Nikolaos L. (Applied Computational Electromagnetics Society Journal (ACES), 2022)
Electromagnetic wave propagation phenomena in nonlinear metamaterials are investigated for waves propagating either in the left-handed frequency band or in the frequency band gaps. In the left-handed band, we implement directly the reductive perturbation method to Faraday’s and Amp´ere’s laws and derive a second-and a thirdorder nonlinear Schr¨odinger (NLS) equation, describing solitons of moderate and ultra-short pulse widths, respectively. Then, we find necessary conditions and derive exact bright and dark soliton solutions of these equations. On the other hand, in the frequency band gaps with negative linear effective permittivity and positive permeability (where linear electromagnetic waves are evanescent), we derive two short-pulse equations (SPEs) for the high- and low-frequency band gaps. The structure of the SPEs solutions is discussed, and connections with the NLS soliton solutions are presented. Numerical simulations of the SPEs solutions are included and compared with those of the reduced wave equations. Directions towards the modelling of wave propagation in nonlinear chiral metamaterials are pointed out.