Research On The Propagation And Control Of Light And Electromagnetic Waves In Metamaterials

Light is an electromagnetic wave, composed by the electric field and magnetic field components. Figuratively speaking, light has "two handed"-electric and magnetic "hand". When the light interacts with atoms of conventional materials, its behaviour is’one-handed’due to only the electric’hand’efficiently probing the atoms of a material, whereas the magnetic component is normally weak and remains relatively unused. However, the metamaterials (MMs), that is, artificial materials are engineered to have properties that may not be found in nature, can allow both field components of light to be coupled to "meta-atoms". Magnetic response of MMs makes the magnetic field component become very important, even has the equally importance with electric field component. The magnetic field provides another manipulated "handed" for the light and electromagtitic wave, and enables entirely new optical properties and excites applications with such’two-handed’light. MMs usually gain their properties from structure rather than composition, using small inhomogeneities to create effective macroscopic behavior. The resonant magnetic permeability and controllable electromagnetic characteristics of MMs open the door of hope for developing new types of optical components, many of which are unthinkable in the past and break through the "limit" binding and bottleneck of conventional devices. These include, for example, optical waveguide, optical cloaking, transformation optic, subwavelength image and all-optical switches.Moreover, the electromagnetic response characteristics of the artificial MMs can be designed artificially according to the people’s demand, and which are primarily determined by the geometry, size, arrangement pattern, and composed materials. These properties provide us more freedom to harness the propagation of light and electromagnetic wave at will. This dissertation focuses on the magnetic response characteristics and the controllable electromagtic properties of MMs, investigates the propagation and control of light and electromagnetic wave in MMs, reveals the novel phenomena of light and electromagnetic wave propagating in MMs, and presents some new structures or devices for controlling the light and electromagnetic wave. Our results can not only expand the research field of the conventional optics, but also improve the performance of existing photonic devices and develop new and unprecedented photon devices in the future. The main innovative ideas are described as below: (1)Generalized nonlinear Schrodinger equation (NLSE) suitable for few-cycle pulse propagation in the MMs is derived; the role of the magnetic response of MMs in ultrashort pulse propagation is disclosed. The controllable and anomalous self-steepening effect and high-order nonlinear dispersive terms are porposed and demonstracted, and the novel nonlinear phenomena related to these effects are demonstracted.Based on the principle of nonlinear optics and combined with the magnetic resonance of MMs, the theoretical models for ultrashort pulse propagation in nonlinear MMs are built. Then the models are extended to the NLSEs with Raman delay response, linear loss, and the cross phase modulation when two or more pulses propagating inside the MMs. These models will provide the theoretical foundation for soliton, MI, soliton self-frequency shift (SSFS) and supercontinuum generation, and so on. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and polarization, respectively, resulting in controllable self-steepening (SS) effects and higher-order dispersively nonlinear terms in the propagation models. By using the NLSEs in the Drude dispersive model as an example, we identify the role of the dispersive permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is found that the negative SS moves the center of generated pulse toward the leading side, and shifts a part of energy of the generated pulse towards the red side, opposite to the case of positive SS. And the negative second-order nonlinear dispersion (SOND) may act as the role of the anomalous group velocity dispersion (GVD), which makes the otherwise impossible phenomena possible, such as, soliton and MI.(2)Relations between the properties of the light and electromagnetic wave propagating in MMs and the electromagnetic parameters of MMs are investigated systematically. The abnormal MI phenomena are revealed, and the novel nonlinear optical phenemona and their controllability, including the MI and soliton, are demonstrated. These results subvert the conventional conditions for generating Mis in conventional materials.Some unusual phenomena for MIs in MMs are disclosed. Firstly, it is shown that MI is irrespective of the sign of SS parameter, although the SS parameter can be either positive or negative. The SS effect will lead to the reduction of the gain and movement of the positions of the critical frequency and the fastest growing frequency to lower frequencies. Secondly, MI may occur even in the normal GVD regime or in the case of no GVD in MMs with a nonlinear electric polarization. These results subvert the conventional conditions for generating MIs in conventional materials. Thirdly, it is shown that negative refraction not only brings some new features to MI, but also makes MI possible in ordinary material in which it is otherwise impossible. For example, spatial MI can occur in the defocusing regime, while it only occurs in the focusing regime in ordinary material. Spatiotemporal MI can appear in negative-index MMs (NIMs) in the case of anomalous GVD and defocusing nonlinearity, while it cannot appear in ordinary material in the same case. Fourth, we find that SS and saturable nonlinearity suppress the MI generation, but SOND promotes the MI in the anomalous GVD region. And the existing range of the MI in SS parameter expands with the increasing saturation parameter, however, in the anomausly GVD, the existing range of the MI in SOND expands with the increasing saturation parameter, and the existing range of the MI in SOND becomes narrow with the increasing saturation parameter in the normal GVD. Fifth, we study MI in the nonlinear optical coupler with a NIM channel, trying to identify the different MI properties from those in conventional couplers. It is found that MI is significantly influenced by the nonlinear parameters and the ratio of the forward to backward-propagating wave’s power. And the threshold condition for the power ratio and input power can exist only in the normal dispersion regime.(3)The nonlinear absorption effect of electric field and the enhanced nonlinear refraction in a lossy MM induced by the active linear magnetic permeability and nonlinear magnetization are found. The typical nonlinear optical phenemona, including the SSFS and dispersive wave (DW) generation and their controllability, are disclosed. These suggest that the nonlinear MMs have valuable potentials for supercontinuum generation and broadband source.Firstly, we develop the nonlinear absorption and refraction for fields propagating in materials with both electric and magnetic dispersion and nonlinearity. For the electric field, it is shown theoretically that the nonlinear refraction index and nonlinear absorption become depending on the linear absorption and third-order nonlinear magnetization strongly. Especially, it is found that the active linear magnetic permeability induces a nonlinear absorption (refraction) of electric field in a lossy metamaterial even when the imaginary (real) part of the nonlinear polarization is absent. Secondly, we present a theory to investigate the SSFS in nonlinear MMs. It is found that the negative SS term enhances SSFS and the positive SS term suppresses SSFS within a long propagation distance. Moreover, we discuss the influence of third-order dispersion (TOD) on SSFS and show that TOD decelerates the SSFS. For high-order solitons, it is shown that even relatively small values of the negative SS parameter can achieve relatively large frequency shifts. Numerical calculations indicate that the negative SS coefficient leads to wider spectrum width, meaning that the nonlinear MMs are valuable candidates for supercontinuum generation and broadband sources. Thirdly, we discuss the controllability of the DW generation in the MMs, and identify the combined effects of the anomalous SS and TOD on the DW generation. It is demonstrated that SS effects have a great impact on the peak power of the DW with only a small impact on the frequency shift. For the positive TOD, the negative SS effect broadens the DW’s spectrum, shifts the DW to blue side, and enhances the peak power, opposite to the case of positive SS;however, for the negative TOD, the negative SS effect narrows the DW’s spectrum, shifts the DW to red side, and enhances the peak power, also opposite to the case of positive SS. The important difference between negative and positive SS effects in DW generation suggests that we can manipulate DWs in a new way. The controllable SSFS and DW generation indicates that the nonlinear MMs are valuable candidates for supercontinuum generation and broadband sources.(4) Relations between the omnidirectional bandgap in the multilayer structures containing MMs and the electromagnetic parameters of MMs are established. The tunabilities of the zero-average-index bandgaps and zero-effective-phase bandgaps are disclosed. The effective methods to enlarge the bandwidth of the omnidirectional bandgap are presented. Moreover, two kinds of new omnidirectional and multiple-channeled filters based on the omnidirectional bandgap of IDPCs composed of MMs are designed and demonstrated.One-dimensional photonic crystals (1DPCs) composed of alternating layers of positive-index materials (PIMs) and NIMs possess zero-average-index bandgaps, and IDPCs formed by the alternating layers of single-negative materials lead to a zero-effective-phase bandgaps. Both bandgaps are omnidirectional bandgaps with weak dependence on the incident angle, which become a research hotspot these years. However, it is lack of an effective method to measure the width of the omnidirectional bandgaps and the frequencies of photonic band-edges, and there is also lack of an active method to control these two bandgaps. To resolve these problems, the band-edge formulas for both bandgaps are derived, and relations between the omnidirectional bandgap and the electromagnetic parameters of MMs are established. Especially, some novel methods to enlarge the zero-average-index bandgaps and zero-effective phase bandgap have been presented, which have potential applications in improving omnidirectional mirrors and omnidirectional optical filters, etc. Moreover, we propose an independently tunable omnidirectional multichannel filter by combining the advantages of the independently tunable filtering properties of fractal structures and the omnidirectional resonant modes of one-dimensional photonic crystals containing negative-index materials. Compared to the conventional multichannel filters, each channel of the proposed filter can be tuned separately, and the frequency position of the filter is insensitive to the incident angle of light, which provides a simple way to design omnidirectional multichannel filters with specific channels. Finally, the design and application of omnidirectional and multiple-channeled filters with high-quality (high-Q) factors applied by using photonic heterostructures containing single-negative materials are demonstrated. Through adjusting the period number of the heterostructures, the number of the resonance modes can be controlled, and results in the insensitiveness of the resonance modes on the incident angle. With perfect transmission, controllable mode, and omnidirectional channel, this structure opens a promising way to fabricate omnidirectional and multiplechanneled filters for future dense wavelength division multiplexing applications.(5)Relations between some propagating properties of the light and electromagnetic wave propagating in MMs and the electromagnetic parameters of the anisotropic MMs are established. The abnormal total reflection of light waves in the anisotropic MMs is revealed, the conditions for the negative Goos-Hanchen (GH) effect are presented, the enhanced methods of the negative photon tunneling times and lateral shifts are demonstrated, and the new omnidirectional bandgaps in the IDPCs containing anisotropic MMs are found.Firstly, the existence conditions for total reflection and the corresponding critical angle at the interface separating an isotropic medium and an indefinite MM for TE-and TM-polarized electromagnetic waves are obtained. For different kinds of indefinite MM, there appear different total reflection phenomena. Particularly, the anomalous total reflection can occur for anti-cutoff medium, in which the incident angle is smaller than the critical angle and the Brewster’s angle can be smaller than the critical angle. Especially, the omnidirectional total reflection exists for the always cutoff medium and anti-cutoff medium. Secondly, we study GH shifts of a light beam transmitted from an indefinite MM slab. The analytic expressions for the transmission coefficient and the lateral shift are obtained by using the stationary-phase method, and different conditions for the occurrence of a negative lateral shift are deduced. It is shown that the lateral shift at the transmitted resonance points is found to be enhanced greatly, and the sign of the lateral shift around the transmitted resonance points is strongly dependent on the permittivity and permeability of the indefinite MM. Thirdly, we study the phenomenon of photon tunneling through a frustrated total internal reflection structure with a dispersive lossy indefinite MM barrier. The tunneling coefficient, lateral shift, and tunneling time for different incident light waves through the barrier are obtained by employing the stationary-phase approximation. It is shown that negative lateral shift and tunneling time can appear in the cutoff indefinite MM, and they can be enhanced by the linear loss of the MMs. The negative tunnelling time indicates that superluminal propagation could be observed when a photon tunnels through the indefinite MM. Finally, the explicit dispersion relation and photonic bandgaps for lDPCs consisting of alternative layers of indefinite MM and ordinary PIM are obtained and analyzed in detail, and the roles of the anisotropic MMs in the frequencies of the band edges, the width of the bandgaps and defects are discussed.