Magnetoplasma modes of a spatially periodic two-dimensional electron gas

We examine the magnetoplasma dispersion of a two-dimensional electron gas with a spatially periodic charge density. The system studied is a periodic array of two-dimensional electron gas strips with constant equilibrium density. The integral equation describing the charge fluctuations on the strips, has been derived and solved numerically. The spatial dependence of the form of either propagating or evanescent waves. The latter are associated with the edge modes, recently discovered in electrons on liquid⁴ He. For a periodic array of two-dimensional strips, the modes in different strips, interact and form bands.     

Influences of the Current Transverse Profile on the Transverse Mode Competition of VCSELs Diodes

A spatially independent model of vertical-cavity surface-emitting lasers (VCSELs) is derived by integrating the spatially dependent rate equations over the cross section of the cavity of a VCSEL. The angular and radial non-uniformities of the injection current are taken into account. The well-known LP modes of a weakly-guiding cylindrical waveguide are employed to describe the transverse modal structure in the VCSEL cavity. This model is solved in a self-consistent way by using the 4th order Runge-Kutta method. The dependence of transverse mode competition on the current intensity, the angular and radial non-uniformities of the injection current, and the geometrical parameters of the electrical contact are thoroughly investigated and analyzed. The results are useful to the optimum design of the optical transverse modal structure of VCSELs.     

Quantum effects in the Gowdy T3 cosmology

The Gowdy T³ Cosmology is an exact solution to the vacuum Einstein equations interpreted to be a single polarization of gravitational waves propagating in an anisotropic, spatially inhomogeneous background. The classical behavior is reviewed and related to standard cosmological parameters. Canonical quantization of the dynamical degrees of freedom is reviewed. An adiabatic vacuum state is constructed. Adiabatic regularization is used to obtain non-divergent stress-energy tensor vacuum expectation values. Casimir energy terms due to T³ imposed discrete modes are evaluated. The vacuum expectation values are analyzed in early and late time limits and evaluated numerically. The regularized expectation value is used as a source for the classical background spacetime in the spirit of semi-classical gravity. An entirely vacuum expectation value source term produces essentially the time reverse of the classical evolution. Classical stress-energy added to the source restores the classical behavior at late times only. The combined system collapses from infinite to small but non-zero volume and reexpands. The classical singularity is replaced by a symmetric bounce.     

A novel numerical synthetic technique for determination of the TMon dispersion relation in a coaxial corrugated cylindrical waveguide

A novel, highly accurate numerical synthetic technique for determining the complete dispersive characteristics of electromagnetic modes in a spatially periodic structure is presented. The numerical method based on the coupling of the finite difference method in time domain with the discrete fourier transform is applied to calculate the eigenfrequencies and eigenfield distribution of a resonant cavity which is an appropriately shorted periodic slow wave circuit of N periods at both ends. The analytical synthetic technique, which is based on the intrinsic characteristic of spatially periodic structure, is used to derive the complete dispersion relation using the numerically measured resonances. The method was successfully applied for the case of TM_on modes in a coaxial corrugated waveguide and is applicable to slow wave structures of arbitrary geometry.     

Micromagnetic phase transitions and spin wave excitations in a ferromagnetic stripe

Magnetic excitations of micrometer-wide ferromagnetic stripes subjected to a transverse applied field have been measured between 1 and 20 GHz. The complexity of the observed response is attributed to the spatially nonuniform equilibrium spin distribution. This one is modeled analytically and numerically, which allows one to distinguish two micromagnetic phases governing the ground state. The nucleation-related phase transitions are evidenced by soft modes, while the different observed resonances are attributed to spin wave modes localized in the two phases and at their interface.     

Controlling intracellular Ca2+ spiral waves by the local agonist in the cell membrane

A modified spatially extended Tang-Othmer Ca2+ model is used to study intracellular Ca2+ spiral waves numerically.It is found that,as a local stimulation,the local agonist-binding on the cell membrane,which enhances the local concentration of the messenger molecule inositol 1,4,5-trisphosphate(IP 3),can influence the dynamics of the spiral waves.1) Strong enough stimuli can change the spiral wave from a meandering to a rigidly rotating one.2) On the other hand,strong enough stimuli can suppress the spiral wave from the system.It provides the theoretical clue for controlling the spiral waves by stimulating the cell membrane.     

Dynamics of the mixmaster-type vacuum universe with geometryR×S 3×S 3×S 3

A model of a spatially homogeneous and anisotropic, vacuum universe with geometryR×S ³×S ³×S ³ is studied using a hamiltonian formalism. The formalism is developed by first deriving the hamiltonian for aD-dimensional, mixmaster-type, vacuum universe. The model evolves from an initial Kasner-like state to a final Kasner-like state upon irreversible collapse. The collapse is predicted to be inevitable based on qualitative analysis and numerical calculations verify this behavior. A lower bound of 0.286 is found for the ratio of the contraction rate of the universe long after a Kasner phase transition to the contraction rate long before the transition. Seven of the seventeen theoretically possible qualitatively different compactification schemes are found numerically and tabulated. A subset of all the constraint satisfying initial conditions which leads to three isotropically expanding dimensions and six contracting dimensions is found.     

Towards the transverse mode-locking of oxide-confined VCSELs

We have investigated the lasing modes of oxide-confined vertical-cavity surface emitting lasers (VCSELs). The individual Laguerre–Gaussian modes have been spectrally and spatially resolved with scanning confocal microscope with time resolution of 4 ps. Subject to the injection of ultrafast laser pulses, the VCSEL showed irregular pulsed emission which indicates the potential for transverse mode-locking of the VCSEL.     

Anisotropy‐assisted non‐scattering coherent absorption of surface plasmon‐polaritons

The ability to control propagation of electromagnetic guided modes lies at the heart of integrated nanophotonics. Surface plasmon‐polaritons are a class of guided modes which can be employed in integrated optical systems. Here, we present a theoretical design of a coherent surface plasmon absorber which can perfectly harvest energy of coherently incident surface plasmons without parasitic scattering into free space modes. Excitation of free space modes which usually accompanies scattering of a surface plasmon by an interface boundary is avoided due to specially tailored anisotropy of the absorber. The concept of coherent SPP absorber is analyzed numerically for spatially non‐uniform and finite‐size structures. We believe that our results will be important for the development of integrated nanoplasmonic systems.     

Taming Random Lasers through Active Spatial Control of the Pump

Active control of the spatial pump profile is proposed to exercise control over random laser emission. We demonstrate numerically the selection of any desired lasing mode from the emission spectrum. An iterative optimization method is employed, first in the regime of strong scattering where modes are spatially localized and can be easily selected using local pumping. Remarkably, this method works efficiently even in the weakly scattering regime, where strong spatial overlap of the modes precludes spatial selectivity. A complex optimized pump profile is found, which selects the desired lasing mode at the expense of others, thus demonstrating the potential of pump shaping for robust and controllable single mode operation of a random laser.     

Collective electronic excitations in clusters in the vicinity of metal surfaces

We study the collective excitations of metal clusters approaching a metal surface. Using a simple model for the frequency-dependent dielectric constant ε(ω) and the multiple scattering method, we numerically investigate the shift in the plasmon resonance due to the coupling of the collective modes of the sphere with those of its mirror image. Results of the model calculation are verified by means of ab initio theory. As a prototype system we study Na₉ ⁺ cluster on the Cu(100) surface. The representation of the solid surface by a cluster of several, typically 54 substrate atoms, is used in combination with a high level configuration interaction (CI) calculation. PACS 31.15.Dv; 36.40.Gk; 73.20.-f     

Excitation of defect modes from the extended photonicband-gap structures of 1D photonic lattices

This paper stuides numerically the model equation in a one dimensional defective photonic lattice by modifying the potential function to a periodic function. It is found that defect modes (DMs) can be regarded as Bloch modes which are excited from the extended photonic band-gap structure at Bloch wave-numbers with k x = 0. The DMs for both positive and negative defects are considered in this method.     

Propagation of light in(2+1)-dimensional nonlinear optical media with spatially inhomogeneous nonlinearities

The(2 1)-dimensional nonlinear Schr(o)dinger(NLS)equation with spatially inhomogeneous nonlinearities is investigated,which describes propagation of light in(2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities.New types of optical modes and nonlinear effects in optical media are presented numerically.The results reveal that the regular split of beam can be obtained in (2 1)-dimensional nonlinear optical media with inhomogeneous nonlinearities,by adjusting the guiding parameter.Furthermore,the stability of beam regular split is discussed numerically,and the results reveal that the beam regular split is stable to the finite initial perturbations.     

Localized chemical wave emission and mode switching in a patterned excitable medium

Chemical waves are initiated from complex geometries in the excitable Belosouv-Zhabotinsky medium using a wet stamping technique. Because of the coupling between the system's chemical kinetics and geometry, waves are emitted only from selected locations. By varying the nature of the wave-triggering reagent (here formaldehyde or methanol), it is possible to switch between two spatially distinct modes of wave emission. The system's dynamics is studied numerically, and the results of modeling agree with experimental observations.     

Separate Polarization Modes Synchronization and Synchronization Switches between Vertical-Cavity Surface-Emitting Lasers

For vertical-cavity surface-emitting lasers (VCSELs) with polarization-rotated feedback, there exist several synchronization types such as synchronizations between total powers and synchronizations between separate polarization modes. Based on the two-mode rate equations, we study and compare numerically the performances of different synchronization types. Our results show that three synchronization types exhibit good performances when their synchronization conditions are satisfied. They are the complete synchronization between total powers, complete synchronization between x-polarized modes, and generalized synchronization between x-polarized and y-polarized modes. The former two types are sensitive to the injection rate and spontaneous emission, while the third type is contrary. Synchronization type with the best performance may switch from one to another, with changing of injection rate and spontaneous emission factor.     

Massless and quantized modes of kinks in the phase space of superconducting gaps

We investigated quantized modes of kinks in the phase space of superconducting gaps in a superconductor with multiple gaps. The kink is described by the sine-Gordon model in a two-gap superconductor and by the double sine-Gordon model in a three-gap superconductor. A fractional-flux vortex exists at the edge of the kink, and a fractional-flux vortex will be stable in a three-gap superconductor with time-reversal symmetry breaking. The kink and fractional-flux vortex exhibit massless modes as a sliding motion. We show further that there are one zero-energy mode (massless mode) and quantized excitation modes in kinks, which are characteristic features of multi-gap superconductors. The equation of quantized modes for the double sine-Gordon model is solved numerically. The correction to the ground-state energy is calculated based on the renormalization theory.     

理论研究电流注入对垂直腔面发射激光器多横模行为的影响

从包含时空变量的速率方程出发,针对弱折射率导引垂直腔面发射激光器(VCSELs),利用空间积分法分析了典型电注入参数对VCSELs多横模行为的影响,在不降低模型准确性的前提下提高了仿真效率。仿真结果表明,注入盘孔径和注入环越小、注入强度越低以及电流扩散越弱时,VCSELs更易实现单横模工作;反之,VCSELs高阶横模开始出现并呈现较强的模式竞争,引发了载流子空间烧孔效应,并导致基模强度降低。进一步得出,在环形注入方式下,高阶模式更容易出现且彼此间的竞争较盘形注入时强。     

Formula for the absorption coefficient for multi-wall nanotubes

We present a formalism for calculating the absorption coefficient of a pair of coaxial tubules. A spatially nonlocal, dynamical self-consistent field theory is obtained by calculating the electrostatic potential produced by the charge density fluctuations as well as the external electric field. There are peaks in the absorption spectrum arising from plasma excitations corresponding either to plasmon or particle-hole modes. In this Letter, we numerically calculate the plasmon contribution to the absorption spectrum when an external electric field is applied. The number of peaks depends on the radius of the inner as well as outer tubule. The height of each peak is determined by the plasmon wavelength and energy. For a chosen wave number, the most energetic plasmon has the highest peak corresponding to the largest oscillator strength of the excited modes. Some of the low-frequency plasmon modes have such weak coupling to an external electric field that they are not seen on the same scale as the modes with larger energy of excitation. We plot the peak positions of the plasmon excitations for a pair of coaxial tubules. The coupled modes on the two tubules are split by the Coulomb interaction. The energies of the two highest plasmon branches increase with the radius of the outer tubule. On the contrary, the lowest modes decrease in energy as this radius is increased. No effects due to inter-tubule hopping are included in these calculations.     

Polarization modulation of light in an optical waveguide under lateral compression

It is shown that a lateral pressure applied to a circular single-mode optical waveguide changes the phase difference between two orthogonally polarized modes and thereby modulates the polarization state of light (elastooptic effect). The efficiency of polarization modulation is characterized by a strain-to-phase difference conversion factor as applied to polarization modes of the fiber. An expression relating the phase difference between the modes and the displacement of squeezing plates is obtained and checked in real experiments and numerically. The efficiency of conversion of lateral pressure to phase difference between the polarization modes is shown to be fairly high, on the order of 10⁴ rad/(μm m).     

Dynamics of a nonlinear field

A systematic study is made of the plane wave modes of a nonlinear c-number field (λφ⁴ model) and interesting features of the behavior of such fields, which do not seem to have been observed before, are brought out. These relate to the case λ < 0, wherein there are different regimes characterized by different kinds of elliptic-function forms for the waves. We show that when the amplitude of the elliptic function waves approaches critical values corresponding to “phase transition” from one regime to another, the energy density in the field increases without limit (though the amplitude is finite). In two of the regimes which are “tachyonic” in nature, there are frozen wave modes which are spatially periodic but time independent. These turn out however to be unstable against perturbations. Finally we observe that in one of these regimes there exist a lower bound on the energy density in the wave field. The case of fields with higher nonlinearities is briefly considered.