On the bond breaking model of polyatomic ion emission in secondary ion mass spectrometry

The cluster size distribution (number of clusters versus number of atoms in the cluster) resulting from a simple nearest neighbor Bond Breaking Model (BBM) of Secondary Ion Mass Spectroscopy (SIMS) is studied for one- and two-dimensional and Bethe lattices. In one dimension, the distribution is monotonic. In two dimensions, however, irregularities can occur as a function of the probability β of breaking any given bond. These irregularities differentiate between square, honeycomb, and triangular lattices and are most pronounced if the overall probability of breaking any bond in the lattice is small.     

Absolute band gap properties in two-dimensional photonic crystals composed of air rings in anisotropic tellurium background

We analyze the band gap spectra of two-dimensional photonic crystals created by square, triangular and honeycomb lattices of air rings with different geometrical shapes and orientations in anisotropic tellurium background. Specifically, five different shapes of rings (circular, hexagonal, elliptical, rectangular and square) are considered. Using the numerical plane wave method, we discuss the maximization of the absolute photonic band gap width as a function of air ring parameters with different shapes and orientations in three types of lattices.     

Coherent transmission and reflection of a two-dimensional planar photonic crystal

A method for modeling the radial distribution function for particles of a two-dimensional planar photonic crystal in the form of a monolayer of spatially ordered monodisperse spherical particles is proposed. The coherent transmission and reflection coefficients for layers under normal illumination are calculated in the quasi-crystalline approximation of the multiple wave scattering theory. The dependence of the coherent transmission and reflection of the layer on the degree of ordering of the spherical particles is investigated. The influence of the long-range order on the coherent transmission and reflection coefficients for layers with triangular, square, and hexagonal lattices is estimated. Monolayers of weakly absorbing dielectric and strongly absorbing metallic particles are considered.     

Wide angularly isotropic photonic bandgaps obtained from two-dimensional photonic crystals with Archimedean-like tilings

We present a theoretical study of new two-dimensional photonic crystals based on Archimedean-like tilings. Three structures are considered: a square lattice with a 4-atom unit cell and triangular lattices with 7- and 13-atom unit cells. A 12-fold local rotational symmetry is obtained for the triangular lattices and is approached for the square lattice. Wide photonic bandgaps can then be achieved, with very weak bandwidth dependence (~1%) on the wave-propagation direction. The complete bandgap frequency is shown to depend on the atomic bond length and not on the crystal period. This new class of periodic photonic crystals is a simple and attractive alternative to photonic quasi crystals.     

Creation of tunable absolute bandgaps in a two-dimensional anisotropic photonic crystal modulated by a nematic liquid crystal

Photonic crystals (PCs) have many potential applications because of their ability to control light-wave propagation. We have investigated the tunable absolute bandgap in a two-dimensional anisotropic photonic crystal structures modulated by a nematic liquid crystal. The PC structure composed of an anisotropic-dielectric cylinder in the liquid crystal medium is studied by solving Maxwell's equations using the plane wave expansion method. The photonic band structures are found to exhibit absolute bandgaps for the square and triangular lattices. Numerical simulations show that the absolute bandgaps can be continuously tuned in the square and triangular lattices consisting of anisotropic-dielectric cylinders by infiltrating nematic liquid crystals. Such a mechanism of bandgap adjustment should open up a new application for designing components in photonic integrated circuits.     

Disorder-induced localization of light near edges of nonlinear photonic lattices

We investigated the influence of edges and corners on the Anderson localization of light in disordered two-dimensional photonic lattices that are optically induced in nonlinear saturable photorefractive media. A systematic quantitative study of gradual transition from corner to bulk Anderson localization in truncated two-dimensional photonic lattices was carried out. We analyzed numerically the localization at several corners and edges of the square and triangular photonic lattices and compared them with the localization in bulk medium. We found that, for strong disorder, corners and edges effectively suppress Anderson localization, as compared to the bulk, but to a varying degree.     

Phase separation and flux quantization in the doped quantum dimer model on square and triangular lattices

The doped two-dimensional quantum dimer model is investigated by numerical techniques on the square and triangular lattices, with significantly different results. On the square lattice, at small enough doping, there is always a phase separation between an insulating valence-bond solid and a uniform superfluid phase, whereas on the triangular lattice, doping leads directly to a uniform superfluid in a large portion of the resonating-valence-bond (RVB) phase. Under an applied Aharonov-Bohm flux, the superfluid exhibits quantization in terms of half-flux quanta, consistent with Q=2e elementary charge quanta in transport properties.     

Discrete breathers in a two-dimensional Morse lattice with an on-site harmonic potential

Two-dimensional discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials are investigated. Under the harmonic approximation, the linear dispersion relations for the triangular and the square lattices are discussed. The existence of discrete breathers in a two-dimensional Morse lattice with on-site harmonic potentials is proved by using local inharmonic approximation and the numerical method. The localization and amplitude of two-dimensional discrete breathers correlate closely to the Morse parameter a and the on-site parameter κ.     

Critical behavior in a model of correlated percolation

We study the critical behavior of certain two-parameter families of correlated percolation models related to the Ising model on the triangular and square lattices, respectively. These percolation models can be considered as interpolating between the percolation model given by the + and – clusters and the Fortuin-Kasteleyn correlated percolation model associated to the Ising model. We find numerically on both lattices a two-dimensional critical region in which the expected cluster size diverges, yet there is no percolation.     

Nonlinear soliton-like excitations in two-dimensional lattices and charge transport

We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation. Adding electrons to the lattice we find solectron bound states and offer computational evidence of how electrons can be controlled and transported by such acoustic waves and how electron-surfing occurs at the nanoscale. We also offer computational evidence of the possibility of long lasting, fast lattice soliton and corresponding supersonic, almost loss-free transfer or transport of electrons bound to such lattice solitons along crystallographic axes.     

Entropic rigidity of randomly diluted two- and three-dimensional networks

In recent work, we presented evidence that site-diluted triangular central-force networks, at finite temperatures, have a nonzero shear modulus for all concentrations of particles above the geometric percolation concentration p(c). This is in contrast to the zero-temperature case where the (energetic) shear modulus vanishes at a concentration of particles p(r)>p(c). In the present paper we report on analogous simulations of bond-diluted triangular lattices, site-diluted square lattices, and site-diluted simple-cubic lattices. We again find that these systems are rigid for all p>p(c) and that near p(c) the shear modulus mu approximately (p-p(c))(f), where the exponent f approximately 1.3 for two-dimensional lattices and f approximately 2 for the simple-cubic case. These results support the conjecture of de Gennes that the diluted central-force network is in the same universality class as the random resistor network. We present approximate renormalization group calculations that also lead to this conclusion.     

A new method for calculation of the magnetic properties in one- and two-dimensional spin systems with anisotropic Heisenberg exchange

A new approximation method is proposed for the calculation of the magnetic susceptibility of one-dimensional assembly of spins and the critical temperature of two-dimensional one both with the anisotropic Heisenberg exchange. In a linear chain system, every spins are grouped into pairs of adjacent spins (pair-approximation) or clusters of adjacent three spins ((q+1)-approximation), and the partition function of the total spin system is approximated as a sum of products of the partitions functions for the pairs or the clusters. Then the partition function of the anisotropic Heisenberg spin system is shown to reduce into a form of the Ising spin system with modified coupling constants. The exact result for the Ising chain system enables us to obtain an analytical expression for the magnetic susceptibility of anisotropic Heisenberg chain system. The same approximations are also applied to two-dimensional lattices, and the critical temperatures of the square, triangular, and honeycomb lattices with anisotropic Heisenberg exchange are calculated as a function of anisotropy parameter. The results are compared with those of the existing theories and shown to be quite excellent.     

The Ising Susceptibility Scaling Function

We have dramatically extended the zero field susceptibility series at both high and low temperature of the Ising model on the triangular and honeycomb lattices, and used these data and newly available further terms for the square lattice to calculate a number of terms in the scaling function expansion around both the ferromagnetic and, for the square and honeycomb lattices, the antiferromagnetic critical point.     

Tunable full band gap in two-dimensional anisotropic photonic crystals infiltrated with liquid crystals

We analyze the tunability of full band gap in two-dimensional photonic crystals created by square and triangular lattices of anisotropic tellurium rods in air background, considering that the rods are infiltrated with liquid crystal. Using the plane-wave expansion method, we study the variation of full band gap by changing the optical axis orientation of liquid crystal.     

Tunable out-of-plane band gap of two-dimensional anisotropic photonic crystals infiltrated with liquid crystals

We analyze the tunability of out-of-plane band gap in two-dimensional photonic crystals created by square and triangular lattices of air holes in anisotropic tellurium background, considering that the rods are infiltrated with liquid crystal. Using the plane wave expansion method, we study the variation of out-of-plane band gap by changing the optical axis orientation of liquid crystal.     

Vortices in quantum spin systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices. Received 2 October 1998     

Neél order in square and triangular lattice Heisenberg models

We show that the density matrix renormalization group can be used to study magnetic ordering in two-dimensional spin models. Local quantities should be extrapolated with the truncation error, not with its square root. We introduce sequences of clusters, using cylindrical boundary conditions with pinning fields, which provide for rapidly converging finite-size scaling. We determine the magnetization for both the square and triangular Heisenberg lattices with errors comparable to the best alternative approaches.     

Breakdown of universality in directed spiral percolation

Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated in this model are generally rarefied and have chiral dangling ends on both the square and triangular lattices. It is found that the clusters are more compact and less anisotropic on the triangular lattice than on the square lattice. The elongation of the clusters is in a different direction than the imposed directional constraint on both the lattices. The values of some of the critical exponents and fractal dimension are found considerably different on the two lattices. The DSP model then exhibits a breakdown of universality in 2D between the square and triangular lattices. The values of the critical exponents obtained for the triangular lattice are not only different from that of the square lattice but also different form other percolation models.Received: 12 March 2004, Published online: 23 July 2004PACS: 02.50.-r Probability theory, stochastic processes, and statistics - 64.60.-i General studies of phase transitions - 72.80.Tm Composite materials     

Fabrication of two-dimensional infrared photonic crystals by deep reactive ion etching on Si wafers and their optical properties

We report the fabrication and characterization of two-dimensional silicon-based photonic crystal structures realized by deep reactive ion etching. Photonic crystals with square and triangular lattices with very high aspect ratios up to 33 have been achieved. Photonic bandgap behaviors are identified by the transmission and reflection spectra measured by using a Fourier transform infrared spectrometer. The experimental results are in good agreement with the calculated band structures.     

Wave radiation in lattice fracture

The square and triangular lattices are considered, where the uniform crack growth is accompanied by the wave radiation. The radiation energy and structure are studied. The energy radiated to the bulk of the lattice is found in a direct way. The radiation structure is described based on the crack problem solution and by means of the analysis of two-dimensional dispersion relations for the intact lattice. The mode III problem for square lattice is discussed in detail, whereas, in the case of the plane problem for the triangular lattice, the only those results are derived which follow from the two-dimensional dispersion relations. It is shown that there exists a finite crack-speed-dependent region of wavenumbers corresponding to the waves radiated to the bulk of the lattice. In the case of the triangular-cell lattice, in addition, one or several lattice Rayleigh waves are radiated. For the square lattice a complete solution for the wave field is presented with the crack-speed-dependent far-field asymptote. The latter is characterized by the wave amplitude asymptotically decreasing as the distance from the crack front in power −1/3. The asymptotically significant crack-speed-dependent direction of the radiation is determined. Such asymptotic results are also valid for the triangular lattice.