Nonlinear All-Optical Switching Device by Using the Spatial Soliton Collision

We propose a new nonlinear all-optical switching device by using the spatial solitons collision. This is 1 × N switching device controlled by two control beams. The numerical results show that this device could really function as a 1 × N all-optical switching device. This device is a potential key component in the application of optical signal processing and optical computing systems.     

New Criterion for Designing Silica Multimode Interference Power Splitters

We introduce a new criterion for designing 1 × N silica multimode interference power splitters using overlapping-image multimode interference analysis. This criterion requires that widths of multimode waveguides in the devices should be greater than 2 times the product of port number N and effective widths of output waveguides. Better device uniformity can be achieved when the new criterion is satisfied.     

Branes, geometry and N = 1 duality with product gauge groups of SO and Sp

We study N = 1 dualities in four-dimensional supersymmetric gauge theories as the world volume theory of D4 branes with one compact direction in type IIA string theory. We generalize the previous work for SO(N_c1) × Sp(N_c2) with the superpotential W = TrX⁴ to the case of W = TrX^4(k+1) in terms of brane configuration. We conjecture that the new dualities for the product gauge groups of SO(N_c1) × Sp(N_c2) × SO(N_c3), SO(N_c1) × Sp(N_c2) × SO(N_c3) × Sp(N_c4) and higher multiple product gauge groups can be obtained by reversing the ordering of NS5 branes and D6 branes while preserving the linking numbers. We also describe the above dualities in terms of wrapping D6 branes around 3-cycles of Calabi-Yau threefolds in type IIA string theory. The theory with adjoint matter can be regarded as taking multiple copies of NS5 brane in the configuration of brane or geometric approaches.     

N=2 6-dimensional supersymmetric E6 breaking

We study the N=2 supersymmetric E₆ models on the 6-dimensional space–time where the supersymmetry and gauge symmetry can be broken by the discrete symmetry. On the space–time M⁴×S¹/(Z₂×Z₂′)×S¹/(Z₂×Z₂′), for the zero modes, we obtain the 4-dimensional N=1 supersymmetric models with gauge groups SU(3)×SU(2)×SU(2)×U(1)², SU(4)×SU(2)×SU(2)×U(1), and SU(3)×SU(2)×U(1)³ with one extra pair of Higgs doublets from the vector multiplet. In addition, considering that the extra space manifold is the annulus A² and disc D², we list all the constraints on constructing the 4-dimensional N=1 supersymmetric SU(3)×SU(2)×U(1)³ models for the zero modes, and give the simplest model with Z₉ symmetry. We also comment on the extra gauge symmetry breaking and its generalization.     

Duality and quantum-algebra symmetry of the AN−1 open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

Quenched master field equations for unitary matrix models

We derive the quenched master field equations for constrained systems such as the O(N) non-linear sigma model, U(N)×U(N) chiral models, and U(N) lattice gauge theory. The master equations are algebraic, and involve quenching in both the space and “fifth” (Langevin) time directions. The quenched master field for the O(N) nonlinear sigma model is found exactly. The 0-dimensional unitary matrix model is solved perturbatively, and we recover the Gross-Witten result. The master equation for the U(N)×U(N) chiral model is set up for non-perturbative approximation methods, and some qualitative results are obtained.     

Surface reconstructions of the Si(100)–Ge system

The surface reconstruction of epitaxial Ge layer on Si(100) was studied with ultrahigh vacuum scanning tunneling microscopy. The surface with 0.8 ML Ge grown in the presence of a hydrogen surfactant reveals the same structures as found in chemical-vapor-deposited Ge on Si(100): (i) defective (2×1) structure at 290°C, (ii) irregular (2×N) in Ge layer and defective (2×1) in bare Si regions at 420°C, and (iii) (2×N) in Ge-covered regions and c(4×4) in bare Si regions at 570°C. The morphology of step edges does not change with temperature, implying that the c(4×4) reconstruction is anisotropic in nature.     

M-theory on AdS4 × M: the complete Osp(2|4) × SU(3) × SU(2) spectrum from harmonic analysis

We reconsider the Kaluza-Klein compactifications of D = 11 supergravity on AdS₄ × (G/H)₇ manifolds that were classified in the eighties, in the modern perspective of AdS₄/CFT₃ correspondence. We focus on one of the three N = 2 cases: (G/H)₇ = M¹¹¹ = SU(3) × SU(2) × U(1) /SU(2) × U(1)′ × U(1)′'. Relying on the systematic use of the harmonic analysis techniques developed in the eighties by one of us (P. Fré) with R. D'Auria, we derive the complete spectrum of long, short and massless Osp(2|4) × SU(3) × SU(2) unitary irreducible representations obtained in this compactification. Our result also provides a general scheme for the other N = 2 compactifications. Furthermore, it is a necessary comparison term in the AdS₄/CFT₃ correspondence: the complete AdS/CFT match of the spectra that we obtain will provide a much more stringent proof of the ACS/CFT correspondence than in the S⁷ case, since the structure of the superconformal field theory on the M2-brane world volume must be such as to reproduce, at the level of composite operators, the flavor group representations, the conformal dimensions and the hyperchanges that we obtain in the present article. The investigation of this match is left to future publications. Here we provide an exhaustive construction of the Kaluza-Klein side of our spectroscopy.     

Does the quenched reduced U(∞) chiral model break spontaneously in weak coupling?

The U(N) chiral model, when quenched using Parisi's rule, has a [U(1) × U(1)]^N/U(1) global invariance. To determine whether this symmetry breaks spontaneously in weak coupling for N=∞, a one-loop calculation of the distribution of eigenvalues of the single U(N) matrix of the model is performed. This distribution is shown to be uniform on the unit circle and hence, no symmetry breaking occurs. Further, the order parameter | tr U|²/N², which should be zero at N=∞ in the absence of spontaneous symmetry breaking, is evaluated in the weak coupling phase for one, two and three dimensions for N varying from 2 to 50 by Monte Carlo simulation of the quenched model. The data indicate that this parameter indeed goes to zero as N→∞ implying that the symmetry does not break.     

Heterogeneous catalytic reaction on a 2×2 lattice

We study a model proposed by Fichthorn, Gulari and Ziff for the kinetics of a generic heterogeneous catalytic reaction, A+B→AB. This reaction includes the steps of adsorption and desorption of reactants A and B, surface reaction through the Langmuir–Hinshelwood mechanism, and desorption of product AB. We solve the model exactly and without any restriction on a 2×2 lattice.

Despite the reduced number of sites employed, the solution shows some of the general features observed by simulating the mechanism on a large N×N lattice.

The rate of reaction depends on the rate of desorption of reactants with a maximum at a value similar to those found by performing heavy simulations. Also, on a 2×2 lattice, we have coverage of fluctuations of reactants as a function of their rate of desorption, as found on large N×N lattices.     

Universal ZN-graded differential calculus

We investigate the propeties of differential algebras generated by an operator d satisfying the property d^N = 0 instead of d² = 0 as in the usual case. Several examples of realizations of such differential algebras are given, either in the context of Z_N-graded N × N matrix algebras, or as a generalized differential calculus on manifolds.     

All-optical serial switcher

We present a device that is capable of switching a sequence of equally spaced pulses between two or more outputs, according to the switching information carried from the first pulse, that behaves as an addresser. The device acts as an all-optical serial switcher and it is based on the properties of a soliton beam in a transverse refractive index profile. We further study the interaction force between solitons.     

光致异构聚合物中光学空间孤子的垂直全光调控

用数值方法研究了在具有光致异构非线性的聚合物中光学空间孤子的垂直全光调控.结果表明，对于调控光和信号光是相干的情况，被调控的信号光会产生散射甚至坍塌、微偏转等现象，其作用强弱依赖于两束光的初始相位之差、调控光光强、调控光入射位置等.这种垂直全光调控效应有望应用于全光开光、光集成等方面. 关键词： 光折变空间孤子 孤子相互作用 垂直调控 光致异构     

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N_f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N_f → Sp (2N_f) and SU (N_f → O (N_f), respectively, rather than the symmetry breaking pattern SU (N_f) × SU (N_f) → SU (N_f) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ Λ_QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 1/L₂ Λ_QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.     

Plasmonic all-optical bistable device based on nematic liquid crystal

Low-power all-optical bistable liquid crystal (LC) devices are reported in which surface plasmons propagate along a metallic grating. The threshold switching illumination was 1.4 mW/mm² in the device with the twisted-nematic LC cell. This is a lower value than for all-optical bistable devices reported previously. This low-power bistability device can be used in two-dimensional optical memories or spatial light modulators.     

Ultrafast All-Optical Serial-to-Parallel Conversion and Its Application to Optical Label Processing

A novel scheme for all-optical serial-to-parallel conversion (SPC) is proposed for label recognition of ultrafast asynchronous burst optical packets. Compact SP converter modules were developed using a fiber array or a surfaceemitting planar lightwave circuit, and 1-Tbit/s and 40-Gbit/s SPC for 16-bit optical packets is demonstrated using the modules. The key device in the converter is a spin-polarized surface-reflection all-optical switch (LOTOS) with an ultrafast switching time (250 fs) and an extremely high on/off ratio (>30 dB). Label recognition of 40-Gbit/s 16-bit burst-mode optical packets is experimentally confirmed using an optical clock-pulse generator and a complementary metal-oxide-semiconductor (CMOS) electronics circuit as well as the all-optical SP converter. 1 x 4 self-routing is also demonstrated using 2-channel control signals generated from the CMOS circuit according to a routing table.     

Diffraction from reconstructed surfaces with incommensurate domain walls

The kinematic approximation method has shown that the peak intensity and the full width at half maximum (FWHM) of stepped surfaces exhibit an oscillatory behavior for changing incident energy. This paper generalizes the kinematic approximation to an (N × 1) reconstructed surface with a distribution of various types of lateral displacements at a step. A particular solution of this model we call the fixed point solution, yields a clear intuitive understanding of these oscillations as well as an exact solution for the step density of any surface. The specific examples of (5 × 1) and (2 × 1) reconstruction are examined to show the striking differences between the reconstructed surface diffraction patterns. These differences make an examination of the half-maximum (HM) intensity position a powerful tool to determine the surface structure for any incommensurate stepped surface.     

Branched polymers from a double-scaling limit of matrix models

Multicritical potentials and correlation functions are given for models of rectangular M × N matrices, in the limit that N goes to infinity. These models are soluble without using orthogonal polynomials, and describe filamentary random surfaces, or, equivalently, a phase of branched polymers. It is shown that the equations describing multicritical behaviour are obtained from the hierarchy of flows that preserve Burgers' equation. Instanton solutions are studied - they imply that only the k = 2 model is unitary, and that the coefficients (for arbitrary k) of g_st^l is the perturbative expansion of the specific heat grow as l!.     

Ring resonators with N × M couplers

Multiple-zero multiple-pole optical filter transfer functions may be implemented more efficiently in an integrated optics architecture if higher order N × M optical couplers are utilized. For example, a coherent ring resonator made from two 3×3 couplers offers some advantages over the three mirror Fabry-Perot etalon, which is its analog. To this end we develop the formalism for obtaining the transfer functions and scattering matrices of ring resonators made from two N × M couplers. We then present a methodology for analyzing serial and parallel systems of N × M optical coupler ring resonators.     

DNA-based organic-on-inorganic semiconductor Schottky structures

A sandwich device has been fabricated from DNA molecular film by solution processing located between Al and p-type silicon inorganic semiconductor. We have performed the electrical characteristics of the device such as current–voltage (I–V), capacitance–voltage (C–V) and capacitance–frequency (C–f) at room temperature and in dark. The DNA-based structure has showed the rectifying behavior. From its optical absorbance spectrum, it has been seen that DNA has been a semiconductor-like material with wide optical band energy gap of 4.12 eV and resistivity of 1.6 × 10¹⁰ Ω cm representing a p-type conductivity.