Electromagnetic unidirectionality and frozen modes in magnetic photonic crystals

Magnetic photonic crystals are periodic arrays of lossless materials, at least one of which being magnetically polarized. Magnetization, either spontaneous or induced, is associated with nonreciprocal effects, such as Faraday rotation. Magnetic photonic crystals of certain configuration can also display strong spectral asymmetry, implying that light propagates in one direction much faster or slower than in the opposite direction. This essentially nonreciprocal phenomenon can result in electromagnetic unidirectionality. A unidirectional medium, being perfectly transmissive for electromagnetic waves of certain frequency, freezes the radiation of the same frequency propagating in the opposite direction. The frozen mode has zero group velocity and drastically enhanced amplitude. The focus of our investigation is the frozen mode regime. Particular attention is given to the case of weak nonreciprocity, related to the infrared and optical frequencies. It appears that even if the nonreciprocal effects become vanishingly small, there is still a viable alternative to the frozen mode regime that can be very attractive for a variety of practical applications.     

Spiking in an activator-inhibitor model for elements with S-shaped negative differential conductivity

Self-organized spatio-temporal dynamics of electrical transport is described by a simple noncubic activator-inhibitor system derived for layered semiconductor structures. The model exhibits a novel mode of self-sustained oscillations due to current filaments switching on and off (spiking) which may be periodic or chaotic. Additionally, we obtain complex multifilamentary spatio-temporal patterns. As such phenomena have been observed in various devices exhibiting S-shaped negative differential conductivity, our model is suggested to describe a generic mechanism.     

Periodic orbits and binary collisions in the classical three-body Coulomb problem

In the helium case of the classical three-body Coulomb problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. Focusing our attention on binary collisions with these tools, a sequence of periodic orbits are predicted and are actually found numerically. A family of periodic orbits found has regularity in their actions. For this family of periodic orbits, it is shown that thanks to its regularity, a partial summation of the Gutzwiller trace formula with a daring approximation gives a Rydberg series of energy levels.     

Resonant nonlinear intrachannel interactions in strongly dispersion-managed transmission systems

Nonlinear intrachannel interactions in a transmission system with strong periodic dispersion management are studied. The ghost pulse at the zero bit is shown to grow resonantly as a result of periodic forcing and temporal phase matching with the signal pulses. The growth rate depends on the degree of overlap between the signals. The analysis agrees with direct numerical simulation of the full system. Growth rates for various bit patterns as a function of map strength are obtained.     

New types of periodic structures in laser-induced chemical vapor deposition

New types of periodic structures that occur in laser-induced chemical vapor deposition have been investigated, mainly for polycrystalline Si deposited on glass substrates covered with a thin amorphous Si layer. These periodic structures, which are believed to be a general phenomenon in pyrolytic laser-induced processing, limit the resolution obtainable in direct writing of patterns.On leave from Fudan University, Department of Electronic Engineering, Shanghai, People's Republic of China     

Bound states and band structure—A unified treatment through the quantum Hamilton-Jacobi approach

We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate the bound and periodic states, once the problem is mapped to the zero energy sector of another quasi-exactly solvable quantum problem. The energy eigenvalues are obtained without having to solve for the corresponding eigenfunctions explicitly. We also demonstrate how to find the eigenfunctions through this method.     

Atomic layer molecular beam epitaxy (Almbe) of III–V compounds: Growth modes and applications

A new development of molecular beam epitaxy (MBE) for III–V compounds is described, based on cyclic perturbation of the growth front at atomic layer level by periodic pulsing, alternating or interrupting the molecular beams. The modification of the growth mechanism caused by this perturbations is discussed and related to periodic changes of surface stoichiometry which induce 2D growth mechanism by enhanced layer nucleation.Under appropriate modulation conditions, an atomic layer by layer growth mode can be achieved. A practical implementention of this mode, that we denote atomic layer MBE (ALMBE), is considered in which only group V beams are pulsed in a specially designed effusion cell. A number of growth applications of ALMBE are presented, including growth of highly mismatched heterostructures and short period superlattices containing two different group V elements such as arsenic and phosphorous.     

Secondary instabilities of interfacial waves due to coupling with a long wave mode in a two-layer Couette flow

We report experiments on the stability of interfacial waves in a two-layer Couette flow. As the shear rate is increased, the periodic wave train arising from the primary instability undergoes a secondary instability which results in wave coalescence or nucleation, after a long transient. This secondary instability crucially involves the coupling with a long wave mode, which corresponds to variations of the mean interface level. These observations are favourably compared to stability results on travelling wave solutions for a set of two coupled equations, one for the envelope of a weakly unstable wave packet, and the other for the marginal long wave mode with zero wave number. A physical mechanism for this instability is proposed, as well as an interpretation for the onset of chaos.     

Polarization-Independent Guided-Mode Resonance Filters under Oblique Incidence

We present the dispersion relation of guided-mode resonances in planar periodic waveguides, both for s-polarized （TF, mode） and p-polarized （TM mode） incident waves. For a fixed homogeneous planar waveguide, dispersion curves of the TE eigenmode cannot cross that of the TM eigenmode at all. That is to say, at a certain wavelength, TE and TM modes cannot be excited with the same propagation constant. Due to Bragg reflection in the planar periodic waveguide, dispersion curves of the TE leaky mode may intersect with that of the TM leaky mode in the first Brillouin zone. We employ these intersections to achieve polarization-independent guided-mode resonance filters.     

Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling

In this paper, we study a system of three coupled van der Pol oscillators that are coupled through the damping terms. Hopf bifurcations and amplitude death induced by the coupling time delay are first investigated by analyzing the related characteristic equation. Then the oscillation patterns of these bifurcating periodic oscillations are determined and we find that there are two kinds of critical values of the coupling time delay: one is related to the synchronous periodic oscillations, the other is related to eight branches of asynchronous periodic solutions bifurcating simultaneously from the zero solution. The stability of these bifurcating periodic solutions are also explicitly determined by calculating the normal forms on center manifolds, and the stable synchronous and stable phase-locked periodic solutions are found. Finally, some numerical simulations are employed to illustrate and extend our obtained theoretical results and numerical studies also describe the switches of stable synchronous and phase-locked periodic oscillations.     

Analytical study of the splitting process of a multiply-quantized vortex in a Bose–Einstein condensate and collaboration of the zero and complex modes

We study the dynamics of a trapped Bose–Einstein condensate with a multiply-quantized vortex, and investigate the roles of the fluctuations in the dynamical evolution of the system. Using the perturbation theory of the external potential, and assuming the situation of the small coupling constant of self-interaction, we analytically solve the time-dependent Gross–Pitaevskii equation. We introduce the zero mode and its adjoint mode of the Bogoliubov–de Gennes equations. Those modes are known to be essential for the completeness condition. We confirm how the complex eigenvalues induce the vortex splitting. It is shown that the physical role of the adjoint zero mode is to ensure the conservation of the total condensate number. The contribution of the adjoint mode is exponentially enhanced in synchronism with the exponential growth of the complex mode, and is essential in the vortex splitting.     

Transmitted interference effect of double metallic nanoslits composed of a slit and a square-funnel slit

The transmitted interference characteristics for double metallic nanoslits, which are composed of a slit and a square funnel, are investigated by the finite-difference time-domain method. Two types of interference patterns, i.e., the periodic single peak or the periodic double peaks profile, are observed by varying the geometric parameters of the square-funnel slit. The fringe period crucially depends on the exit layer thickness of the square-funnel slit. The near-field field intensity can be enhanced three times that in symmetric slit-doublet structure by selecting specific parameters. We also find that surface plasmon waves can creep along the interface between metal and dielectric, even though the interface possesses orthogonal corners.     

Synchronization and Pattern Dynamics of Coupled Chaotic Maps on Complex Networks

The synchronization and pattern dynamics of coupled logistic maps on a certain type of complex network, constructed by adding random shortcuts to a regular ring, is investigated. For parameters where an isolated map is fully chaotic, the defect turbulence, which is dominant in the regular network, can be tamed into ordered periodic patterns or synchronized chaotic states when random shortcuts are added, and the patterns formed on the complex network can be grouped into two or three branches depending on the coupling strength.     

Theoretical modeling of hard X-ray surface modes in a periodic multilayer

The excitation of hard X-ray surface modes of a periodic multilayer is studied with the help of theoretical modeling. It is found that a hard X-ray surface mode can appear in a specific periodic multilayer coated with a high-density reflecting layer. The generation of the hard X-ray surface modes is shown to be effective only at a certain set of the structural parameters of the multilayer. A method for the calculation of the propagation (attenuation) length of the surface mode running in the periodic multilayer is described. The excitation of the hard X-ray surface modes is compared with that of optical surface modes in photonic crystals. The relationship between the surface modes and guided modes of periodic multilayers is discussed.     

Dynamics of a nonlinear parametrically excited partial differential equation

We investigate a parametrically excited nonlinear Mathieu equation with damping and limited spatial dependence, using both perturbation theory and numerical integration. The perturbation results predict that, for parameters which lie near the 2:1 resonance tongue of instability corresponding to a single mode of shape cos nx, the resonant mode achieves a stable periodic motion, while all the other modes are predicted to decay to zero. By numerically integrating the p.d.e. as well as a 3-mode o.d.e. truncation, the predictions of perturbation theory are shown to represent an oversimplified picture of the dynamics. In particular it is shown that steady states exist which involve many modes. The dependence of steady state behavior on parameter values and initial conditions is investigated numerically. (c) 1999 American Institute of Physics.     

Magnetoresistance of Electrons Channelled by Microscopic Magnetic Field Modulation

We report the magnetoresistance of two-dimensional electron gas, which is made of GaAs based epitaxial mul-tilayers and laterally subjected to a periodic magnetic field. The modulation field is produced by an array of submicrometre ferromagnets fabricated at the surface of the heterostructure. The magnetoresistance of about 20% is found at low temperature 80K. The measurement is in quantitative agreement with semiclassical simulations, which reveal that the magnetoresistance is due to electrons trapped in snake orbits along lines of zero magnetic field.     

Periodically structured X‐ray waveguides

The properties of X‐ray vacuum‐gap waveguides (WGs) with additional periodic structure on one of the reflecting walls are studied. Theoretical considerations, numerical simulations and experimental results confirm that the periodic structure imposes additional conditions on efficient propagation of the electromagnetic field along the WGs. The transmission is maximum for guided modes that possess sufficient phase synchronism with the periodic structure (here called `super‐resonances'). The field inside the WGs is essentially given at low incidence angle by the fundamental mode strongly coupled with the corresponding phased‐matched mode. Both the simulated and the experimental diffraction patterns show in the far field that propagation takes place essentially only for low incidence angles, confirming the mode filtering properties of the structured X‐ray waveguides.     

Responses of Hodgkin-Huxley Neuronal Systems to Spike-Train Inputs

We investigate responses of the Hodgkin-Huxley globally neuronal systems to periodic spike-train inputs. The firing activities of the neuronal networks show different rhythmic patterns for different parameters. These rhyth- mic patterns can be used to explain cycles of firing in real brain. These activity patterns, average activity and coherence measure are affected by two quantities such as the percentage of excitatory couplings and stimulus intensity, in which the percentage of excitatory couplings is more important than stimulus intensity since the transition phenomenon of average activity comes about.     

Dispersive elastodynamics of 1D banded materials and structures: analysis

The elastodynamics of 1D periodic materials and finite structures comprising these materials are studied with particular emphasis on correlating their frequency-dependent characteristics and on elucidating their pass-band and stop-band behaviors. Dispersion relations are derived for periodic materials and are employed in a novel manner for computing both pass-band and stop-band complex mode shapes. Through simulations of harmonically induced wave motion within a finite number of unit cells, conformity of the frequency band structure between infinite and finite periodic systems is shown. In particular, only one or two unit cells of a periodic material could be sufficient for “frequency bandedness” to carry over from the infinite periodic case, and only three to four unit cells are necessary for the decay in normalized transmission within a stop band to practically saturate with an increase in the number of cells. Dominant speeds in the scattered wave field within the same finite set of unit cells are observed to match those of phase and group velocities of the infinite periodic material within the most active pass band. Dynamic response due to impulse excitation also is shown to capture the infinite periodic material dynamical characteristics. Finally, steady-state vibration analyses are conducted on a finite fully periodic structure revealing a conformity in the natural frequency spread to the frequency band layout of the infinite periodic material. The steady-state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium, and it is shown that the maximum localized response under stop-band conditions could be significantly less than in an equivalent homogenous structure and the converse is true for pass-band conditions.