Studies On The Transmission Of Optical Solitons In Negative Index Materials Under Higher-order Effects

Negative index materials (NIMs) is a kind of artificial material with simultaneously negative dielectric permittivityεand negative magnetic permeabilityμelectromagnetic, which can exhibit different electromagnetic properties from conventional materials in nature. Recently, the rapid developing artificial electromagnetic materials have received great attentions including optics, electromagnetics, materials science, communications, etc. With the successful fabrication of NIMs over near-infrared and visible light frequencies, the abundant nonlinear properties of NIMs gradually attracts much attention, the transmission of ultrashort optical pulse in NIMs and the potential applications in optical device and all-optical control have become a new hotspot.In this paper, the transmissions of optical solitary waves in NIMs under the higher-order effects are studied. Starting from Maxwell equations, a normalized nonlinear Schrodinger equation has been derived, which can describe the propagation of femtosecond optical pulse in NIMs. Subsequently, the exact bright and gray (dark) solitary wave solutions of this model are obtained by ansatz method, and the influences of higher-order effects on propagation properties of the solitary wave solutions are analyzed in detail. The obtained results will have much significance for the numerical study of the stability of solitary waves in NIMs and the applications in optical devices.The main contents are as follows:(1) Firstly, we introduce the concept, development and different electromagnetic properties of NIMs from the conventional materials, as well as the realization of NIMs over the microwave, near-infrared and visible light frequencies, and the research progress of the optical solitary waves in NIMs.(2) Starting from Maxwell equations, on the base of Scalora's theoretical model describing the propagation of ultrashort pulse in NIMs with negatively dispersive permittivity and permeability, a normalized nonlinear Schrodinger equation is derived, which can govern the femtosecond optical pulses propagation in NIMs. The model includes the higher-order dispersion and nonlinear effects, especially the second-order nonlinear dispersion effect which does not exist in conventional materials, and all effects in the model are directly expressed by the negative permittivityεand negative permeabilityμin explicit. Under the Drude dispersion model, the parameter model is analyzed in detail and the results show that the dispersion and nonlinear effects can be controlled by adjusting the permittivity and permeability, namely, by engineering the structure of the NIMs, which will be of a momentous significance for the formation of solitons and all-optical control in NIMs.(3) Based on the derived nonlinear Schrodinger equation, three cases of bright solitary wave solutions under different higher-order effects are obtained through the ansatz method, and then the existence conditions and properties of bright solitary waves as well as the influence of the higher-order effects are analyzed in detail. The results show that bright solitary waves can exist in NIMs under certain conditions, and the high-order effects play an important role in the formation of bright solitary waves which can exhibit many particular features comparing to the conventional materials. As for the bright solitary wave in the presence of the fifth-order nonlinearity and second-order nonlinear dispersion effects, it is difficult to exist in NIMs, but can exist in artificial materials with normal dispersion.(4) Similarly, three cases of gray(dark) solitary wave solutions in NIMs under different higher-order effects are obtained by using ansatz method, and the characteristics of gray(dark) solitary waves in NIMs are analyzed in detailed. It can be found that all the three cases of gray (dark) solitary waves can exist in NIMs under proper conditions, and the higher-order effects have a great impact on the formation and propagation characteristics of the second and third cases of gray (dark) solitary waves. In particular, the fifth-order nonlinearity and the second-order nonlinear dispersion effects play a crucial role in the third case of gray (dark) solitary wave. Moreover, the gray (dark) solitary waves can be formed under the balance of the nonlinear effects without linear dispersion.