| Negative refraction mechanism can be divided into two types, namely localresonance and non-local Bragg scattering. The former doesn't impose a limit on thesizes of the lattice constants, the period of the structure could be much smaller than theworking wavelength. Left-handed material (LHM) with simultaneously ε<0and μ<0,which belongs to this mechanism, is approximated to be a isotropic homogeneous media.Photonic crystals (PhCs) are inhomogeneous materials whose lattice constants are inorder of the wavelength of light and Bragg scattering strength of each scatter is strong.The propagation of light waves inside such lattices will be modified by the photonicbandgap, and negative refraction will be realized in particular frequency ranges by finedesign the band structure. Currently negative refraction media promise a lot of interestsby the scientific community and are engineered materials functionality for applications.In this work, we study in detail the issue of negative refraction mechanism in bothisotropy and anisotropy metamaterials, typically in LHM and PhCs, the main works areas follows:(1) By using the effective media theory, negative refraction phenomena in LHM isinvestigated in detail. It is emphasised that in this kind of isotropic media backwardwaves will appear because of the Poynting vector direction is antiparallel to the phasevelocity direction and negative refraction is a consequence of a negative phase velocity.It has been investigated that the group velocity is always positive without the need ofconsideration of the refractive index. It is point out that the spatial aspect of an incidentwave refracts negatively, and the temporal nature of the wave refracts positively whichpreserves the Causality. It has been confirmed that ε′<0and μ′<0is only anecessary condition for the existence of backward wave, when losses are present,(?)is also required.(2) The richness properties of the surface waves generated at the surfaces ofnegative refraction index media is minutely elucidated. By analysising the dispersioncurves of TE and TM surface modes in the single interface configuration, it is fund thatwhen conditionsε1ε2<0andε1+ε2<0are satisfied, there exists surface wave on the interface between the air and semi-infinite non-magnetic media. Media withsimultaneouslyε2<0andμ2<0can support surface wave with both TE and TMpolarization. An interesting idea of controling the group velocity of the surface waves ispresented. Dispersion relationships of symmetric and anti-symmetric surface modesdistribution in the LHM slab interfaces configuration are discussed in detail, whichprovided an amplification factor ofexp(k2ω2c2xd)for the evanescent wave incidentfrom air, and the field distribution of the evanescent wave in the slab system is alsopresented. The attenuation factor of the evanescent wave is modified in the condition ofd→∞.(3) Negative refraction effects of light propagating in two-dimensional square,hexagonal and rhombus lattice silicon PhCs are demonstrated. Theoretical analyses andnumerical simulations are presented. Three different kinds of negative refractions,namely, negative refraction with effective negative index, all-angle negative refraction(AANR) without a negative index, and negative refraction as a result of the complexequal-frequency contour (EFC) shapes have been verified and compared. It is fund thatlight focusing effect occurs in both effective negative index PhC slab and AANR PhCslab. The negative refraction in former system has high angular dependence. The AANRPhC slab is more suitable for high-resolution superlensing application. Thepreferential-direction waveguide effect in hexagonal lattice PhCs and superprism effectof both Г-T and Г-M interface direction in rhombus lattice PhCs are also investigated.(4) The principles of subwavelength imaging in PhCs slab have been explained indetail. Propagation wave can focal in AANR PhCs without an effective negative index.For evanescent wave with large transverse vector component, PhCs permit existence ofspactial bound surface states which can used to amplify the evanescent wave thatexponentially decay in air. It is imposed an upper cutoff for superlensing using PhCs.The resolution limit of a PhC superlens is derived, and a high resolution PhCs superlensis designed, a full width at half maximum (FWHM) of0.35λ is obtained on the imageplane.
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