Research On Nonlinear Propagation Of Light Waves In Periodically Microstructured Photonic Materials

It is a consensus to replace electron with photon as the carrier of information because photonic technology has several advantages, such as high transmission speed, high density and high fault tolerance. However, photons are not so prone to be controlled as electrons, and the photonic devices are far from mature compared to electronic component, which result in that optical information technonlogy has been only applied to information transmission, further more, the basic information function. Thus, the research on the interaction between light wave and new type photonic material and the exploration of technologies of controlling photon by using photonic material are the basis of the development of novel photonic devices and are very important in optical calculation and all optical communication, both theoretically and practically. Periodically microstructure photonic material as Bragg gratings, photonic crystal, optical lattice, and metamaterials et al, are ideal material for all-optical devices because of their ability in manipulating and controlling photons. In this thesis, we investigate the properties of nonlinear propagation in two kinds of new type periodically microstructure optical material, i.e. optical lattice and metamaterials. Our work and results are mainly follows:Firstly, optical lattice is an optical media with transverse periodic lattice modulation refractive index. Beams appear plenty of interesting phenomena when they propagate in the nonlinear optical lattice, especially periodic modulation with transverse refractive index can affect deeply the form and transmission characteristic of spacial solition. Using the variational principle and numerical method, we study the beam evolution of Kerr nonlinear optical lattice, and obtain the forms for the evolution during propagation of beam width, beam amplitude and frequency chirp, and post the influence of modulation period and modulation depth of optical lattice on the light-wave's nonlinear propagation. The following, we find the conditions for lattice soliton formation and stabile propagation. We find that solitions can propagate only if the ratio of beam width and modulation period are less than a certain numerical value. With the good characteristic similar to nonlinearity, periodic lattice can offer a better method to control the lattice soliton formation and propagation.Secondly, attenuation is an intrinsic property of any practical system, including optical lattice. Therefore, it is important to compensate the medium loss for maintaining the propagation of the spatial soliton in the system. We first propose and demonstrate a scheme to compensate medium loss for spatial soliton propagation, i.e., controlling the modulation depth of a Bessel lattice along the light propagation direction to compensate the loss effect. Here, we investigated the propagation of a spatial soliton in a dissipative modulated Bessel optical lattice, both analytically and numerically. The dynamic evolution equations for beam width, amplitude, and curvature wavefront are obtained by a variational approach. It is shown that by properly increasing the modulation depth of refractive index of the optical lattice, the loss effect can be compensated exactly to fulfill stable spatial soliton propagation.Thirdly, metamaterials are artificial materials which have anomalous properties not possessed by natural materials. The research about metamaterials is one of the important frontline in modern scientific domain. One of the most important differences between metamaterials and conventional materials is that the magnetic permeabilities of metamaterials are dispersive. Combining the properites of metamatirials and the related principles of nonlinear optics, we have investigated the propagation properties of light wave in metamatirals. It is shown that, under the Drude dispersive model, the dispersive permeability results in a self-steepening parameter which can be negative, positive or zero depending on the central frequency of the pulse, and a series of higher-order nonlinear dispersion terms in the propagation equation. Furthermore, the propagation equation is analyzed by using the moment method, an explicit expression for power conservation for the propagation equation is obtained, and the unique propagation properties of ultrashort pulse in metamaterials are disclosed. It is found that due to the role of the second-order nonlinear dispersion, the characteristic parameters of the ultrashort pulse, including energy, frequency shift, duration, center position, and chirp, all oscillate with propagation distance.Fourthly, on the basis of the propagation equation obtained for ultrashort pulse in nonlinear metamaterials we have investigated the modulational instability in metamaterials of the propagation of both coherent and incoherent ultrashort pulses. The combination of dispersive magnetic permeability with nonlinear polarization leads to a series of nonlinear dispersion terms in the propagation equations for ultrashort pulses in metamaterials. Here we present an investigation of modulation instability (MI) of both coherent and partially coherent ultrashort pulses in metamaterials to identify the role of nonlinear dispersion in pulse propagation. The Wigner–Moyal equation for partially coherent ultrashort pulses and the nonlinear dispersion relation for MI in metamaterials are derived. Combining the standard MI theory with the unique properties of the metamaterial, the influence of the controllable first-order nonlinear dispersion, namely self-steepening, and the second-order nonlinear dispersion on both coherent and partially coherent MI, in both negative-index and positive-index regions of the metamaterial for all physically possible cases is analyzed in detail. For the first time to our knowledge, we demonstrate that the role of the second-order nonlinear dispersion in MI is equivalent to that of group-velocity dispersion (GVD) to some extent, and thus due to the role of the second-order nonlinear dispersion, MI may appear in the otherwise impossible cases, such as in the normal GVD regime.