Transmission Property Of Light In One-dimensional Photonic Crystals Containing Indefinite Metamaterials With Nonlinearity

With the development of artificial electromagnetic media, in particular, the emergence of metamaterials has greatly expanded the study of electromagnetic materials. It is notable that anisotropic metamaterials, that's indefinite metamaterials, were firstly discovered by D. R. Smith et al. in 2003. Since such materials have extraordinary electromagnetic characteristics and have been realized experimentally, indefinite metamaterials have received increasing attention over the past few years. Recently, various applications of indefinite metamaterials have been proposed and investigated in the frequency range of microwaves. Up till now, the investigations of indefinite metamaterials have been extended to multilayered periodic structures from single layer, especially in photonic crystals. This thesis deals nonlinear transmission property for new type of one-dimensional photonic crystals consisting of indefinite metamaterials, negative-index materials, and Kerr-type nonlinear indefinite metamaterials. It's expcted that the research results can further complete the nonlinearity for one-dimensional photonic crystals and provide valuable information for the design of new parts of apparatus. The main works involved are follows as:1. Modulation of bistable lateral shifts in a one-dimensional nonlinear photonic crystal consisting of indefinite metamaterials has been studied theoretically. It is found that optical bistability can be achieved at very low threshold values of normalized input intensity in this composite structure when the indefinite metamaterial is a cut-off, anticut-off and never cut-off medium. It is also found that there exists corresponding bistable lateral shift which is strongly dependent on the parameters of indefinite metamaterials.2. According to the dispersion relation of indefinite metamaterials, electromagnetic wave can be divided into five distinct frequency intervals. Nonlinear propagation characteristics are investigated theoretically in a one-dimensional photonic band-gap structure doped with a nonlinear indefinite metamaterial defect for five distinct frequency intervals. It is found from the electric field distribution that there exists the bright gap solitonlike when the nonlinear indefinite metamaterial defect is a cut-off medium, while the dark gap solitonlike can appear in the nonlinear never cut-off defect layer. It is also found that there exists corresponding bistable lateral shift the properties of which are strongly dependent on the permittivity and permeability of nonlinear indefinite metamaterials. Moreover, in contrast to the switch-down threshold value, the switch-up threshold value is more sensitive to the incident frequency.3. Based on transfer matrix method and stationary-phase method, nonlinear propagation characteristics are investigated theoretically in a one-dimensional photonic band-gap structure containing left-handed materials and a nonlinear indefinite metamaterial defect for five distinct frequency intervals. It is found that there exists a typical S-shape curve of the normalized input-output intensity when the nonlinear indefinite metamaterial defect is a cutoff and never cutoff medium. It is also found that there exists corresponding bistable lateral shift which is strongly dependent on the incident frequency.Our study will lead to potential applications in integrated optics and optical switches.