Near band centre states for one-dimensional off-diagonal disordered systems

We study and characterize the eigenstates near the centre of the band of a one-dimensional tight binding model with off-diagonal disorderW _T . We report a new exponent for the localization length on an energy-dependent range of disorderW _T . We correlate this feature with a change of structure of the wave-function displayed by the behaviour of its density-density correlation function.     

Relativistic electronic states in disordered systems

The energy spectrum of relativistic electrons in one-dimensional disordered systems is investigated. Using an approximate solution to the one-dimensional Dirac equation as given by Steslicka and Davison and following a method reported earlier by the author for nonrelativistic cases, an equation connecting the wave functions at three consecutive atomic sites is derived. This “connection equation” is then analysed with the help of (1) Worpitzky's theorem and (2) a perturbational approach due to Phariseau. With the help of these approaches, explicit equations are derived for electronic energies in disordered systems with small deviations from periodicity. These explicit equation indicate that, in general, a band structure of electronic energies exists in each region of the system; they reveal further that there occur energies in addition to those characterising the local bands and these extra energies constitute a disturbance to the (local) band structures.     

Complete band gaps in one-dimensional left-handed periodic structures

Artificially fabricated structures with periodically modulated parameters such as photonic crystals offer novel ways of controlling the flow of light due to the existence of a range of forbidden frequencies associated with a photonic band gap. It is believed that modulation of the refractive index in all three spatial dimensions is required to open a complete band gap and prevent the propagation of electromagnetic waves in all directions. Here we reveal that, in sharp contrast to what was known before and contrary to the accepted physical intuition, a one-dimensional periodic structure containing the layers of transparent left-handed (or negative-index) metamaterial can trap light in three-dimensional space due to the existence of a complete band gap.     

Commensurate-incommensurate transition in one-dimensional disordered systems

Commensurate-incommensurate transition in the one-dimensional disordered system is investigated and the soliton density near commensurability at high and low temperatures is obtained.     

Extension of photonic band gaps in one-dimensional photonic crystals

A method is proposed for extending photonic band gaps by constructing periodic structures from two or more consecutively located photonic crystals with different lattice constants or filling factors. The photonic band gaps with a maximum extension are predicted by superposing the photonic band gap maps on one another. It is demonstrated that both the lowest and higher order band gaps can be merged in photonic crystals with a high refractive index contrast.     

Control of photonic band gaps in one-dimensional photonic crystals

The photonic band gaps in one-dimensional photonic crystals (PCs) are theoretically investigated. A new method to broaden the photonic band gaps is introduced. Based on the similar method, a kind of photonic crystals is constructed to generate photonic band gaps with proportioned central frequencies. This technology can be used for designing nonlinear PCs for harmonic generation.     

Theories of electrons in one-dimensional disordered systems

A critical survey of the literature on the theory of electronic states in, and electron transmission through, models of one-dimensional disordered solids and liquids is given in the first part. Reference to work on three-dimensional systems is included, especially where exact results have been obtained. The relationship between this subject and the problem of elastic vibrations in disordered solids is pointed out. A complete exposition of the authors' work on one-dimensional conductivity is then presented. It provides a rigorous solution of the problem of average resistance, and of the variance (fluctuations) of resistance, for important classes of disorder which are carefully and precisely defined. Conclusions regarding the role of disorder with respect to the transmission properties are presented and discussed. It is also pointed out that, with appropriate modifications, the results apply generally to wave propagation in inhomogeneous media.     

Pancharatnam and total phases for one-dimensional photonic band gaps

We study the time evolution of the total and Pancharatnam phase of four-level atoms in the presence of a one-dimensional photonic-band-gap material. We obtain analytical and numerical results under certain parametric conditions and analyze the effect of a Kerr-like medium and the detuning parameter on the dynamics of the Pancharatnam phase for the initial atomic position. We observe an interesting feature of the Pancharatnam phase for the one-dimensional photonic-band-gap material.     

Effective equations for disordered one-dimensional systems

Using the method of supersymmetry, effective equations are derived for the one-particle Green's function of various one-dimensional disordered models. As an example, explicit expressions for the density of states and the localization length are derived for the two-band model of a one-dimensional semiconductor.     

Optical properties of high-order band gaps in one-dimensional photonic crystal

Plane wave expansion method and transfer matrix method have been used to study the optical properties of eighty ninth photonic band gaps (PBGs) in one dimensional photonic crystal (1DPCs) with a form of Si (air|Si)₈. The results show that high order PBGs (HR-PBGs) in normalize dispersion curves have slower convergence speed than low order PBGs (LR-PBGs) and appear periodic detergency phenomena with the increasing of Λ/λ values (where Λ is the constant of one dimensional lattice and λ is wavelength) and their band widths and central wavelengths are more sensitive to fabrication errors than that of LR-PBG. Finally, some special forms of Si (air|Si)₈ structure with input and output rib waveguides are fabricated on Silicon-on-Insulator (SOI) materials by semiconductor micromachining technology. By measuring and analyzing their insertion loss spectra, we demonstrate that the HR-PBGs of 1DPCs also have the potential application in integration optics.     

A few points on omnidirectional band gaps in one-dimensional photonic crystals

The universal condition for the formation of omnidirectional band gaps (OBG) in photonic crystal (PC) was derived with consideration of permeability of the materials. And it was found that there are four kinds of PCs: one of them has no OBG, and one always possesses OBG. For the other two kinds of PCs, there are OBG for only TM or TE waves respectively. Moreover, in all PCs, the OBG can be broadened by decreasing the refractive index of the ambient medium or/and increasing the contrast between the wave impedances of the component materials of the PC. PACS 42.70.Qs; 71.20.Tx     

Localization properties of driven disordered one-dimensional systems

We generalize the definition of localization length to disordered systems driven by a time-periodic potential using a Floquet-Green function formalism. We study its dependence on the amplitude and frequency of the driving field in a one-dimensional tight-binding model with different amounts of disorder in the lattice. As compared to the autonomous system, the localization length for the driven system can increase or decrease depending on the frequency of the driving. We investigate the dependence of the localization length with the particle's energy and prove that it is always periodic. Its maximum is not necessarily at the band center as in the non-driven case. We study the adiabatic limit by introducing a phenomenological inelastic scattering rate which limits the delocalizing effect of low-frequency fields.     

Diffusion and hopping conductivity in disordered one-dimensional lattice systems

We investigate one-dimensional lattice systems with (symmetric) nearest neighbor transfer ratesW _{n, n+1} which are independently distributed according to a probability density(w). For two general classes of(w), we rigorously determine the asymptotic behavior of the relevant single site Green function ₀() near=0, and obtain exact results for the long time decay of the initial probability amplitude and for the low energy density of states. A scaling hypothesis, accurately confirmed by computer simulations, is used to relate the low frequency hopping conductivity() uniquely to ₀(–i), and we conjecture that the resulting asymptotic behavior for() is also exact. The critical exponents associated with the various asymptotic laws depend on(w) and show a crossover from universal to non-universal behavior. Comparison is made with the results of several approximate treatments.     

Symmetry and transport of waves in one-dimensional disordered systems

The transfer matrix approach to transport in one-dimensional systems is reviewed in detail with emphasis on the role of symmetrized products. First, the concept of a transfer matrix is introduced, and then generalized through the introduction of symmetrized products. The resulting formalism is successively applied to the problem of averaging: resistance, density of states, conductance (i.e. transmission coefficient), phases of transmission and reflection, and frequency response. Finally the problem of 1/f noise in disordered systems is addressed in the language of symmetrized transfer matrices.     

Direct current hopping conductance in one-dimensional diagonal disordered systems

Based on a tight-binding disordered model describing a single electron band, we establish a direct current (dc) electronic hopping transport conductance model of one-dimensional diagonal disordered systems, and also derive a dc conductance formula. By calculating the dc conductivity, the relationships between electric field and conductivity and between temperature and conductivity are analysed, and the role played by the degree of disorder in electronic transport is studied. The results indicate the conductivity of systems decreasing with the increase of the degree of disorder, characteristics of negative differential dependence of resistance on temperature at low temperatures in diagonal disordered systems, and the conductivity of systems decreasing with the increase of electric field, featuring the non-Ohm's law conductivity.     

Wavelet-based method for computing elastic band gaps of one-dimensional phononic crystals

A wavelet-based method was developed to compute elastic band gaps of one-dimensional phononic crystals. The wave field was expanded in the wavelet basis and an equivalent eigenvalue problem was derived in a matrix form involving the adaptive computation of integrals of the wavelets. The method was then applied to a binary system. For comparison, the elastic band gaps of the same one-dimensional phononic crystals computed with the wavelet method and the well-known plane wave expansion (PWE) method are both presented in this paper. The numerical results of the two methods are in good agreement while the computation costs of the wavelet method are much lower than that of PWE method. In addition, the adaptability of wavelets makes the method possible for efficient band gap computation of more complex phononic structures. Supported by the National Natural Science Foundation of China (Grant No. 10632020)     

Complete photonic band gaps in one-dimensional ternary photonic crystals containing single negative materials

Complete photonic band gaps (PBGs) are found in one-dimensional ternary photonic crystals (1D TPCs) composed of an ordinary dielectric and single negative metamaterials. The proposed TPC gives omni directional PBG completely independent of polarizations dependent weekly on angle of incidence. Here the choice of different parameters of TPC is done in such a way so that it eliminates the Brewster's-angle transmission resonance, thus allowing a complete 3D PBG. It exhibits a photonic band or gap near frequencies where either the magnetic permeability or the electric permittivity of the metamaterial changes sign, whose width increases with the increasing angle of incidence. These result from the dispersive properties of the metamaterials and disappear for the particular case of propagation along the stratification direction. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material for TE and TM polarizations.     

Experimental validation of band gaps and localization in a one-dimensional diatomic phononic crystal

The propagation of compressional ultrasonic pulses through a finite one-dimensional chain of various unit cells is investigated experimentally. The chain, initially compressed by an axially applied constant force, is excited by a periodic force, which acts in line with axis of bead chain. The experimental measurements giving the eigenfrequencies of the specimen are based on a Fourier analysis of the transmitted acoustic pulse. The results are compared with the numerical calculations and it is shown that the two approaches are well correlated. A phononic band structure is observed and under certain conditions, depending on the parity of the number and on the masses of the beads in the chain, it is shown that localized modes propagating in the forbidden band are exhibited. Much attention is devoted to the existence of these localized modes according to the mass ratio between two adjacent beads constituting the unit cell.     

Low-frequency band gaps in one-dimensional thin phononic crystal plate with periodic stubbed surface

Using supercell plane wave expansion method, the Lamb wave band structure of one-dimensional thin plate with periodic stubs is investigated. The numerical results show that flat bands will appear and band gap can exist in a low-frequency domain. The position of the flat bands and width of the low-frequency Lamb wave band gap can be tuned by the stub height, plate thickness and filling fraction. The band gap is obtained by opening the folding points of the same plate modes not the crossing point of different plate mode when the stub height is small.