Hole Wave Research Articles

Chaotic pattern, bifurcation, sensitivity and traveling wave solution of the coupled Kundu–Mukherjee–Naskar equation

In this paper, the coupled Kundu–Mukherjee–Naskar equation is considered, which is usually used to describe the oceanic rogue waves, hole waves and Bragg grating fibers. Firstly, the traveling wave transformation is applied to convert the coupled Kundu–Mukherjee–Naskar equation into two-dimensional planar dynamic system. Secondly, bifurcation and two-dimensional phase portrait of the coupled Kundu–Mukherjee–Naskar equation are discussed by using the plane dynamics system. What is more, after adding periodic perturbation term, two-dimensional phase portrait, three-dimensional phase portrait, Poincaré section and sensitivity of its perturbed system are plotted by the Maple software. Finally, the optical soliton solutions of the coupled Kundu–Mukherjee–Naskar equation are obtained by using planar dynamical system method.

On the Eigen Frequencies of Rectangular Resonator with a Hole in the Wall

The rectangular waveguide is attached to a hole in a wall of rectangular resonator and the corresponding to the hole part of the waveguide boundary is cross-section of the waveguide. The problem of excitation of the resonator by an eigen wave of the waveguide is investigated. The condition on a hole is obtained from the condition defining the wave in the waveguide, outgoing from cross-section. The initial diffraction problem is reduced to some infinite set of linear algebraic equations. Numerical experiment shows that the dependence of expansion coefficients of the field in the resonator on frequency of exciting wave has resonant nature. We propose to use the real values of the resonance frequencies of the running on the hole wave as the initial approximations for eigen frequencies of the resonator with a hole in the wall.

Symmetries and conservation laws of some asymptotically symmetric spacetimes of interest in gravitational waves

In this paper, we discuss symmetries and the corresponding conservation laws of certain exact solutions of the Einstein field equations (EFEs) representing a Schwarzschild black hole and gravitational waves in asymptotically flat space times. Of particular interest are symmetries of asymptotically flat spacetimes because they admit a property that identifies them for the existence of gravitational waves there. In the light of this fact, we discuss symmetry algebras of a few recently published solutions of Einstein equations in asymptotically flat metrics. Given the fact that gravitational waves are of great interest in relativity, we focus in this paper on finding the type of symmetries they admit and their corresponding conservation laws. We also show how these symmetries are radically different from the other well-known symmetries and present necessary condition that distinguishes them.

Superconducting electron and hole lenses

We show how a superconducting region (S) sandwiched between two normal leads (N), in the presence of barriers, can act as a lens for propagating electron and hole waves by virtue of the so- called crossed Andreev reflection (CAR). The CAR process which is equivalent to the Cooper pair splitting into the two N electrodes provides a unique possibility of constructing entangled electrons in solid state systems. When electrons are locally injected from an N lead, due to the CAR and normal reflection of quasiparticles by the insulating barriers at the interfaces, sequences of electron and hole focuses are established inside another N electrode. This behavior originates from the change of momentum during electron-hole conversion beside the successive normal reflections of electrons and holes due to the barriers. The focusing phenomena studied here is fundamentally different from the electron focusing in other systems like graphene pn junctions. In particular due to the electron-hole symmetry of superconducting state, the focusing of electrons and holes are robust against thermal excitations. Furthermore the effect of superconducting layer width, the injection point position, and barriers strength is investigated on the focusing behavior of the junction. Very intriguingly, it is shown that by varying the barriers strength, one can separately control the density of electrons or holes at the focuses.

Phase study of the generated surface plasmon waves in light transmission through a subwavelength aperture

Interference of surface plasmon (SP) waves plays a key role in light transmission through a subwavelength aperture surrounded by groove structures. In order to characterize interference of the hole and groove-generated SP waves, their phase information was carefully investigated using finite difference time domain simulations. In a structure with only one groove, constructive interference of the generated SP waves will enhance transmitted light by a factor of 5.4 compared with that of a single hole. Increasing the groove number to 3 in the design, which supports constructive interference of SP waves, will enhance the transmission coefficient to 10.5 times that for the single-hole transmission coefficient.

Structure Parameters and Electric Field Effects on Exciton Binding Energies of CdTe/ZnTe Quantum Rings

We study the effects of the structural parameters such as the wetting layer thickness and the size of self-assembled CdTe/ZnTe quantum rings (QRs) under an external electric field on the exciton binding energies due to Coulomb interaction between electrons and holes with a finite-element method based on the linear elasticity theory of solids and the eight-band k·p Hamiltonian. The exciton binding energies are shown to decrease linearly with increasing the outer diameter of QRs and to decrease with increasing the wetting layer thickness, agreeing with the results of the truncated quantum dots (QDs). It is shown that the isotropic probability density distribution of the electron and the hole waves is strongly affected by the static electric field and shifts in opposite directions with increasing electric field intensity, i.e., by the quantum Stark effect, similar to the case of truncated QDs. However, it is demonstrated that both the exciton binding energies with different QR heights decrease linearly but saturate to a constant value, compared to those of truncated QDs which decrease parabolically with increasing electric field intensity.

Highly engineered mesoporous structures for optical processing

Arranging periodic, or quasi-periodic, regions of differing refractive index in one, two, or three dimensions can form a unique class of mesoporous structures. These structures are generally known as photonic crystals, or photonic quasicrystals, and they are the optical analogue of semiconducting materials. Whereas a semiconductor's band structure arises from the interaction of electron or hole waves with an arrangement of ion cores, the photonic crystal band structure results from the interaction of light waves with an arrangement of regions of differing refractive index. What makes photonic crystals highly attractive to the optical engineer is that we can actually place the regions of differing refractive index in a pattern specifically tailored to produce a given optical function, such as an extremely high dispersion, for example. That is, we can define the geometrical arrangement of the dielectric foam to provide us with the form of band structure we require for our optical functionality. In this paper, the optical properties and applications of these highly engineered mesoporous dielectrics will be discussed.

Microscopic Description of Nanostructures Grown on (N11) Surfaces

We report on a theoretical study of GaAs/InGaAs based nanostructures grown along the [N11] direction. The elastic deformations of the structures were calculated by means of the continuum elasticity theory, taking into account commensurability constraints at the interfaces. The strained atomic positions were derived, as well as the strain induced piezoelectric polarizations and electric fields. These data were used as an input for the calculation of the fundamental electronic transitions of our systems within the empirical tight-binding approach. These results are compared with the envelope function methods. We applied our approach to a (211) oriented InAs quantum dot embedded in a GaAs matrix, and to a (311) oriented InGaAs quantum wire, embedded in AlGaAs barriers. In both cases, we obtained a non-symmetric elastic deformation due to the lower symmetry of (N11)-oriented structures. Moreover, the atomic displacements and the strain induced piezoelectric potential induce a separation of the hole and electron wave functions, which are shifted from the dot center.

Resonant Reflections in a Particle Conducting Through a Normal-Conductor–Superconductor Interface in Magnetic Fields

A quantum resonance in the conduction through the normal-conductor–superconductor junction is investigated in the presence of a magnetic field using a numerical transfer matrix method. It is shown that dip-pairs in the conductance curve occur at a certain geometry of the system owing to the resonant reflection caused by the interference of the reflected electron and hole waves under a finite magnetic field. By examining a local density of quasiparticles, we found that the feature of the resonant state giving the dip-pair in the conductance (in a magnetic field) is very different from that in a finite bias voltage.

Renormalized Schr�dinger Equation for Excitons in Graded Quantum Dot

A simple method for calculating the ground-state energy of excitons confined in spherical quantum dots is presented. The exciton trial wave function is taken as a product of the ground-state wave functions of the unbound electron and hole in the QD, with a correlation function that depends only on electron-hole separation. A renormalized Schrodinger equation for the correlation function is deduced by using the variational principle. Both the differential equations for the unbound electron (hole) wave function in the QD and for the correlation function are solved numerically by means of the trigonometric sweep method. The ground state binding energies of an exciton in a GaAs-(Ga, Al)As spherical QD as a function of the dot radius are calculated for the models of square-well, soft-edge-barrier and double-step potentials.

C-V profiling of delta layers in silicon by quantum and classical approaches

The resolution of the capacitance-voltage profiling technique is known to be limited by the Debye length for classical structures. When very narrow layers exist in the sample quantum effects become important and the spatial extent of the electron (or hole) wave function can become a limiting factor. In this paper the interpretation of C-V profiles of structures containing delta-doped layers is discussed, concentrating on n-type layers in silicon. C-V profiles are calculated for a range of structures by solving Poisson's equation in one dimension, and results obtained from this classical model are compared with the electron wave function width as calculated from Schrodinger's equation.

Electronic structures of quantum wires formed by lateral strain.

The electronic structures of quantum wires formed by lateral strain are studied in the framework of the effective-mass envelope-function method. The hole energy levels, wave functions, and optical transition matrix elements are calculated for the real quantum-wire structure, and the results are compared with experiment. It is found that one-dimensional confinement effects exist for both electronic and hole states related to the n(001)=1 state. The lateral strained confinement causes luminescence-peak redshifts and polarization anisotropy, and the anisotropy is more noticeable than that in the unstrained case. The variation of hole energy levels with well widths in the [110] and [001] directions and wave vector along the [1\ifmmode\bar\else\textasciimacron\fi{}10] direction are also obtained.

Electron hole and electron wave excitation in a plasma with transverse effects

Excitation of electron holes and electron wave pulses is investigated numerically in a single-ended plasma by computer simulation using a particle model. The transverse effects are taken into account by introducing the perpendicular wavenumber in the Poisson equation. Increase in the plasma potential in front of a plasma source, resulting from propagation of the rarefaction pulse from an end boundary, gives rise to the excitation of electron holes, while the rarefaction pulse reflects back as the compression pulse toward the boundary. The qualitative properties are in good agreement with experiment.