A (1+1)-dimensional integrable system with fifth order spectral problems and four dispersion relations

A new (1+1)-dimensional integrable model is investigated, of which the Lax integrability is shown by the existence of its fifth order spectral problems. Its bilinear form is obtained via introducing an auxiliary variable. The multiple soliton solutions are obtained by solving its bilinear system. It is shown that there are four different dispersion relations for multiple solitons. The amplitudes of the solitons are only wave number dependent while the velocities of the solitons are not only wave number dependent but also dispersion relation dependent. Because of the existence of four dispersion relations, the interactions among solitons are much more abundant because for any fixed wave number there are four different velocities including two left moving and two right moving. Especially, the existence of the multiple velocities makes the velocity resonant conditions can be readily satisfied to form many types of bound states including soliton molecules, soliton-breather molecules and breather molecules.     

The effect of the spontaneously generated coherence on the dynamical behaviors of the dispersion and the absorption

This paper investigates the effects of the spontaneously generated coherence (SGC) and incoherent pumping field on the dynamical behaviors of the dispersion and the absorption. Using a three-level Λ-type atomic medium, the influence of the relative phase between the applied fields on the transient dispersion and absorption is discussed. It is shown that the phase dependence of the dispersion and the absorption not only depend on the existence of SGC, but they depend on the existence of the incoherent pumping field as well. We show that the medium can be used as an optical switch in which the propagation of the laser pulse can be controlled by another laser field.     

The scale-breaking contributions of the Pauli-Jordan functions and of the Feynman propagators

Proofs have been given that the underlying background of the scale-breaking contributions of the Pauli-Jordan functions and of the Feynman propagators is the existence of an energy dependent dispersion of the canonical scale dimension, respectively. The energy dependence of these dispersions can be established by taking into account the existence of the time dispersion, too. For the interacting fields the above functions are subject to the scale invariance restoration around the underlying proper-time dispersions, in so far as the short space-like space-time region is considered.     

Light propagation in anisotropic metamaterials. I. Dispersion surfaces

The peculiarities of solutions of the wave dispersion equation in an unbounded indefinite medium for arbitrarily oriented optical axes are considered. All possible dispersion surfaces arising in such media are described, and the conditions of their existence are obtained. It is shown that only some specific pairs of surfaces are possible. The dispersion equation for the boundary problem is obtained, as well as the dependence of dispersion curves on the orientation of optical axis is investigated. The nonreciprocity of the wave refraction is shown.     

空间诱导群速度色散的数值研究

利用数值模拟方法研究了超短脉冲Bessel光束传输过程中的空间诱导群速度色散-数值模拟的结果证实了对于实验中有限宽度的Bessel光束，只要其衍射距离大于空间诱导群速度色散的距离，空间诱导群速度色散的理论就可以很好地描述脉冲的演化过程- 关键词： 脉冲光束 时空耦合 空间诱导群速度色散     

Parametric Analysis of Complex Dispersion Curves for Flexural Lamb Waves in Layered Plates in the Low-Frequency Range

A combined asymptotical and iteration method is used to study dispersion curves for the case of dynamic bending of isotropically layered plates. Based on the explicit limit formulation of dispersion equation, asymptotics of roots are derived in closed form for large values of root moduli. The influence of elastic and geometric parameters of layers are analyzed. The existence of critical values of geometric parameters that correspond to change of the type of asymptotics is demonstrated. The errors of asymptotics are estimated, and an iterative method is proposed for calculating the exact values of roots in statics. A low-frequency long-wave asymptotics of complex dispersion curves is derived; its accuracy is the higher the lower the frequency and the greater the number of the curve are. It is also proved that each complex curve has a long flat segment, the length of which increases simultaneously with the number of curve. The dispersion curves themselves are also calculated by another specific iterative procedure. The fundamental bending mode is analyzed together with its purely imaginary sister. The existence of the additional purely imaginary curve at low frequency is proved. Examples of calculating the static roots and the dispersion curves for subcritical and supercritical values of geometrical parameters are presented, and the efficiency of the algorithm is estimated.     

Low frequency resonant dispersion of sound in bubble media

Presented is a theory of a new type of resonant dispersion of sound in a gas-liquid bubble media based on the use of effective dynamic density. We show that because of spheroidal-translational oscillations of the bubbles the dynamic density of the gas-liquid media has a resonance dependence on the frequency, which is manifested in wave process as a low-frequency resonant dispersion of sound. This dispersion is significantly different from the known high-frequency resonant dispersion, which is due to resonance in the volume oscillations of the bubbles. The results of the experiments confirming the existence of the resonant dispersion of sound at a frequency equal to half the natural frequency of the spheroidal oscillations of bubbles are provided.     

Self—Steepening and Thired—Order Dispersion Induced Optical Solitons in Fiber

Usually,one considers only the group velocity dispersion(GVD)-and self-phase modulation(SPM)-induced solitons in optic soliton communication while other higher order effects such as the third-order dispersion(TOD),self-steepening(SS),and stimulated Raman scattering are considered only perturbatively,In this paper,we study the existence of the TOD-and SS-induced soliton solutions.The existence conditions of the TOD-and SS-induced bright and dark solitons are quite different from those of the GVD-and SPM-induced solitons.     

利用空间诱导色散补偿介质色散

研究了超短脉冲贝塞尔光束在色散介质中的传输特性 ,指出空间诱导色散效应可以用来补偿介质色散作用 ,从而可以在色散介质中实现无衍射无色散的类时空孤子波的传输。用理论推导和数值模拟的方法得到的具有反常色散性质的空间诱导色散可以有效地补偿介质色散。数值模拟的结果表明 ,由于超短脉冲贝塞尔光束的无衍射无色散传输距离受到高阶色散效应和贝塞尔光束空间受限两方面的限制 ,无衍射无色散传输只能在有限距离内近似实现。通过增加脉冲长度可以减小高阶色散效应的影响。在传输距离小于衍射距离时 ,空间诱导色散效应可以很好地描述脉冲演化和色散补偿过程     

Potential Surface Waves in a Warm Nonisothermal Plasma Bounded by Metal

The dispersion properties of potential surface waves (SW), propagating at a warm nonisothermal plasma-metal boundary across the external magnetic field are studied in this paper. The existence of potential SW is shown to be possible in frequency ranges, where electromagnetic SW do not exist. The influence of transverse plasma density inhomogeneity on dispersion properties of the SW considered is studied as well.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

Discrepancy of dielectric constant between MHz region and Raman frequency region in tetragonal BaTiO3

A definite discrepancy of dielectric constant along a-axis of tetragonal BaTiO₃ between several MHz and Raman frequency region is found. By assuming a relaxational dispersion of Debye type, temperature dependence of relaxation time is obtained. This relaxational dispersion strongly suggests the existence of a central mode of which width decreases and height increases when the tetragonal-orthorhombic transition is approached.     

Power dependence of dispersion-managed solitons for anomalous, zero, and normal path-average dispersion

We determine the power dependence of dispersion-managed solitons on map strength and average dispersion, using a combination of numerical simulations and the variational approach. In particular, we investigate the behavior near zero dispersion and identify the region of existence of dispersion-managed solitons in the average normal-dispersion regime.     

Temporal correlation vortices and topological dispersion

Interference measurements of a polychromatic partially coherent light source verify the existence of a temporal correlation vortex. Topological dispersion is found to destabilize this singularity.     

Anomalous dispersion and group velocity properties in subwavelength uniaxial metamaterial waveguide with metal cladding

We investigate propagation behavior of electromagnetic waves in a slab uniaxial metamaterial waveguide with metal cladding and discuss the dispersion relation, group velocity and energy flux distribution of transverse electric guided modes in two kinds of uniaxial metamaterial waveguides with different orientations of optical axis in detail. The numerical results show that there exist anomalous dispersion properties such as backward modes existing in low-frequency range, and the group velocity can be negative or approach zero. If the orientation of optical axis is selected properly, each guided mode has two dispersion curves—one is normal dispersion and another belongs to anomalous dispersion and shows a transition from a backward mode to a forward one with the angular frequency increasing. In addition, the condition of the existence of cutoff frequency is clarified. These properties may have potential applications in optical information storage, optical communication, integrated optics and nanophotonic devices.     

Existence of negative dispersion and band gap in a helically inner cladded annular circular waveguide

Helical waveguide, a different type of waveguide structure, has been considered for analysis of modal dispersion characteristics. This paper deals with the study of a new type of annular waveguide, in which the inner cladding is made by the helical windings i.e. sheath helix and the outer cladding is as usual simple step-index cladding. Using vector approach, the general characteristic equation for the proposed waveguide has been derived. The modal dispersion characteristics for the lowest order modes for different pitch angles and thickness are determined and analyzed. We have found that there is an existence of the negative dispersion curve in the helically inner cladded annular circular waveguide. It means that the inner cladding is responsible for the negative dispersion which is generally obtained in a photonic band gap.     

Dispersion interactions between unexcited molecules having axial symmetry: Contributions of order six and eight

A study is made of the dominant terms of an earlier model-based formula describing the dispersion energy of axially symmetric interacting molecules. The existence of mixed-pole eighth-order terms is noted.     

Dispersion relations of surface phonons from atomic scattering

We show the existence of a spatial forbidden zone for one-phonon atomic scattering by surfaces. In case of scattering by surface modes, this region is bounded by sharp observable maxima of the scattering intensity, whose angular locations depend only on the dispersion relation of the modes involved. A method for obtaining the dispersion relation of surface modes needing no measurement of scattering energies then follows. The method is applied to the He-NaF system.     

Exact solution of the dispersion equation for cyclotron waves for a cylindrical Fermi-surface

An exact solution of the dispersion equation for extraordinary cyclotron waves propagating in a metal with a cylindrical Fermi-surface is presented. The existence of a hitherto unnoticed mode is pointed out.