Theoretical Research Of Bright Soliton In Left-Handed Material

Left-handed material (LHM) is a new type of artificial materials. LHM have the property of effective permittivity and permeability are both negative. This results in an effective negative index of the refraction. Compare with the normal material, LHM have some unusual properties, such as negative index of the refraction, perfect imaging, inversion of the Doppler shift effect, etc. Nowadays, with the further study of LHM, the research of nonlinear effect in LHM will be more abundant.In this thesis, firstly, we study the structure of the composite materials, especially study the composite materials which created by arrays of single split-ring resonators and wires. In addition, we study the Ba0.5Sr0.5TiO3(BST) material, which have the property of negative index of the refraction. This material is fabricated by the method of photonic crystal. We also add BST medium in directional coupler to study the property of the coupler.After have the knowledge of the structure of LHM, for isotropic and homogeneous nonlinear LHM, the dynamics of plane electromagnetic wave transmit in LHM are governed by a set of coupled nonlinear Schrodinger equation (CNLS). Under certain condition, nonlinear effect balance with dispersion, the electric and magnetic field envelopes can form solitons. In this thesis, theoretically, we use Hirota method to solve CNLS. A bright soliton solution is possible existing in isotropic and homogeneous nonlinear LHM. Afterward, we use split-step Fourier method to study the bright soliton solution of the CNLS. Under different conditions, we get some pictures of the space-time evolution of bright soliton in LHM. The result of the numerical simulation indicates that it is possible to exist stable bright soliton in LHM when some condition is satisfied.