Coupled tapered/uptapered optical beams

For the first time we propose the phenomenon of coupled tapering and uptapering in two mutually incoherent beams coaxially co-propagating in a nonlinear medium with small gain or loss. During tapering or uptapering, the widths and powers of the beams evolve in such a manner that they always satisfy the condition of soliton pairing. It is shown that under certain condition one beam can taper/uptaper, while, other uptaper/taper during coupled tapering/uptapering which is quite counterintuitive.     

Mutual-focusing of two co-propagating beams and formation of trapped spatial breather pair in saturable nonlinear media

In this paper, using parabolic equation approach, coupled propagation of two coaxially co-propagating and mutually incoherent bright cylindrical beams in saturable nonlinear medium has been investigated. Considering the coupling coefficient equal to unity (κ=1), a detailed account of formation of spatial soliton pair (i.e. both beams are stationary trapped) and spatial breather pair (i.e. width of each beam oscillates with the propagation distance) has been provided and existence of spatially trapped breather pair (i.e. average width of each breather of the pair does not change with the propagation distance) has been shown. Conditions of formation of trapped spatial breather pair and their existence line has also been revealed for arbitrary beam width ratio of the beams. It is revealed that spatial soliton pairs are just a special case of trapped breather pair. The regions (conditions) of mutual-focusing and mutual-defocusing of spatial soliton pair/breather pair have also been identified. Lastly, the law of trapped breather pair formation is proposed.     

Spatial optical solitons in inhomogeneous elliptic core saturating nonlinear fiber

We have investigated the propagation characteristics of spatial optical solitons in saturating nonlinear waveguide employing JWKB and paraxial ray approximation. We have obtained two second-order coupled nonlinear differential equations for transverse soliton widths of solitons. Threshold power for stable propagation of the beam has been calculated from these coupled equations. We have undertaken stability analysis, which predicts robustness of these solitons. Both guiding as well as antiguiding cases have been considered and shown that stable spatial soliton propagation is possible in both cases.     

Incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media

We theoretically investigate the propagation of incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media. It is found that multipole-mode soliton pairs with arbitrary different orders of Hermite-Gaussian shape can exist when the total power of two beams equals the critical power and the ratio of the beam widths for the Gaussian part is inversely proportional to the square root of the ratio of the wave numbers. When the total power does not equal the critical power, the Hermite-Gaussian breather pair exists and their beam widths evolve analogously. For general cases where the ratio of the beam widths is arbitrary, soliton-breather pairs or breather-breather pairs can be formed and their beam widths evolve synchronously in-phase or out-of-phase. Numerical simulations directly based on the nonlocal nonlinear Schrödinger equation are conducted for comparison with our theoretical predictions. The numerical stability analysis shows the higher-order Hermite-Gaussian solitons can not be stable for small nonlocality or for some media like liquid crystals.     

FDTD analysis of out-of-plane propagation in 12-fold photonic quasi-crystals

The out-of-plane propagation characteristics of an infinitely extended 12-fold photonic quasi-crystal structure is modeled using the FDTD technique. The quasi-crystal pattern is designed using the dual beam multiple exposure holographic lithography system previously reported. Simulations indicate that two types of mode families are possible; “bandgap guided” and; “index guided”. Results are presented showing mode profiles; effective index versus propagation constant and wavelength plots; and modal attenuation due to power leakage. Potential applications include a new novel micro-structured optical fiber.     

强非局域介质中1+1维高斯型损耗空间双孤子的相互作用

研究了1+1维高斯型双光束在含小损耗的强非局域非线性介质中的传输特性。通过对该介质中光束传输遵循的非局域非线性薛定谔方程进行近似简化,得到了含小损耗强非局域非线性介质中1+1维高斯型双光束传输模型。在此基础上运用解析的方法研究了双光束传输的演化规律,得到了准双孤子解。经过进一步分析发现,在传输过程中两光束中心的轨迹为艾里函数;两光束会准周期性地碰撞、分离;随着传输距离的增大,两光束中心之间的最大距离会越来越大。另一方面,当损耗逐渐增大时,两光束的碰撞空间周期将变短,同时两光束中心之间的最大距离也越来越大。     

Composite optical vortices in noncollinear Laguerre--Gaussian beams and their propagation in free space

Taking two Laguerre-Gaussian beams with topological charge 1 = ±1 as an example, this paper studies the composite optical vortices formed by two noncollinear Laguerre-Gaussian beams with different phases, amplitudes, waist widths, off-axis distances, and their propagation in free space. It is shown by detailed numerical illustrative examples that the number and location of composite vortices at the waist plane are variable by varying the relative phase β, amplitude ratio η, waist width ratio ξ, or off-axis distance ratio μ. The net topological charge lnet is not always equal to the sum lsum of charges of the two component beams. The motion, creation and annihilation of composite vortices take place in the free-space propagation, and the net charge during the propagation remains unchanged and equals to the net charge at the waist plane.     

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

We present eight types of spatial optical solitons which are possible in a model of a planar waveguide that includes a dual-channel trapping structure and competing (cubic-quintic) nonlinearity. The families of trapped beams include “broad” and “narrow” symmetric and antisymmetric solitons, composite states, built as combinations of broad and narrow beams with identical or opposite signs (“unipolar” and “bipolar” states, respectively), and “single-sided” broad and narrow beams trapped, essentially, in a single channel. The stability of the families is investigated via the computation of eigenvalues of small perturbations, and is verified in direct simulations. Three species-narrow symmetric, broad antisymmetric, and unipolar composite states-are unstable to perturbations with real eigenvalues, while the other five families are stable. The unstable states do not decay, but, instead, spontaneously transform themselves into persistent breathers, which, in some cases, demonstrate dynamical symmetry breaking and chaotic internal oscillations. A noteworthy feature is a stability exchange between the broad and narrow antisymmetric states: in the limit when the two channels merge into one, the former species becomes stable, while the latter one loses its stability. Different branches of the stationary states are linked by four bifurcations, which take different forms in the model with the strong and weak coupling between the channels.     

Study of mutual information multimodality medical image registration based on modified simplex optimization method

Because of a different imaging mechanism and highly complexity of body tissues and structures. Different modality medical images provide non-overlay complementary information. This has very important significance for multimodal medical image registration. Image registration is the first and key part of problem to be solved in the integrations. When the spatial position of two medical images is same, the registration could be achieved. For two CT and PET images, the principal axis method is adopted to achieve the rough registration. The modified simplex algorithm is employed to implement global search using the mutual information as similarity measure. The initial registration parameters are achieved through principal axis Based on the results of test, improved simplex method can adjust reflecting distance. Stepped-up optimization algorithm on the new experimental points through the methods of “reflection”, “enlargement”, “shrinkage” or “global systolic”. A mutual information registration based on modified simplex optimization method is presented in this paper to improve the speed of medical image registration.Results indicate that the proposed registration method prevents the optimizing process from falling into local extremum and improves the convergence speed while keeping the precision. The accurate registration of multimodal image with different resolutions is achieved.     

Nonlinear massive spin-2 field generated by higher derivative gravity

We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein’s gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called “(Helmholtz-)Jordan frame” and “Einstein frame.” In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected.     

Numerical modeling of spatio-temporal solitons using an adaptive spherical Fourier Bessel split-step method

We present a novel technique to numerically solve pulsed optical beam or “light bullet” propagation in bulk nonlinear media based on the scalar nonlinear Schrödinger (NLS) equation in three dimensions with spherical symmetry. Using fast algorithms for spherical Fourier Bessel transforms along with adaptive longitudinal stepping and transverse grid management in a symmetrized split-step technique, it is possible to accurately study many nonlinear effects, including the possibility of spatio-temporal collapse, or the collapse-arresting mechanism due to saturable nonlinearity.     

Change of thermotropic properties in liquid crystal with multiple phase transitions: Surface “aging” effect

The effect of surface “aging” on thermotropic properties of polymorphic mesogen, 4-butoxyphenylester of 4-decyloxybenzoic acid (BPEDBA) which exhibits the smectic G, smectic C, smectic A, and nematic mesophases has been investigated. Temperatures of direct and reverse phase transitions and temperature widths of the heterophase regions have been determined with high accuracy. The shift of the phase transition temperatures and change of the temperature widths of the heterophase regions under the influence of surface “aging” have been reported.     

Low-frequency breathers in polyethylene crystal

It is shown both analytically and numerically that three-dimensional low-frequency (acoustic) breathers identified as localized coupled bend and twist nonlinear waves can exist in polyethylene (PE) crystal. Their motion along the chain is accompanied by the simultaneous excitation of both (“zig” and “zag”) sub-chains forming PE macromolecule.In the region of a breather one can observe intensive out-of-plane motion of carbon atoms and relatively small displacements in the plane of the zigzag. In spite of this smallness, the “secondary” nonlinear effects turn out to be crucial for the existence of breathers.Both the existence and stability of low-frequency breathers in free motion are confirmed by computer simulation, using the Molecular Dynamics (MD) procedure. The stability of breathers with respect to thermal excitations as well as to mutual collisions and collisions with optical breathers is also discussed. We study also the breathers’ formation in different conditions. It turns out that the frequencies and extensions of the breathers can be varied in very narrow regions predicted by our analytical solution.     

On the numerical integration of FPU-like systems

This paper concerns the numerical integration of systems of harmonic oscillators coupled by nonlinear terms, like the common FPU models. We show that the most used integration algorithm, namely leap-frog, behaves very gently with such models, preserving in a beautiful way some peculiar features which are known to be very important in the dynamics, in particular the “selection rules” which regulate the interaction among normal modes. This explains why leap-frog, in spite of being a low order algorithm, behaves so well, as numerical experimentalists always observed. At the same time, we show how the algorithm can be improved by introducing, at a low cost, a “counterterm” which eliminates the dominant numerical error.     

Study of interference in a double-slit without walls by plasmon tomography techniques

We investigate the free propagation of two parallel surface plasmon polaritons (SPP) beams using plasmon tomography. In the Fourier-plane images, we observed interference features that are not in correspondence with the images of SPPs on the sample's surface. We clearly observed that the interference maxima and minima are distributed over an arc of a circle. We explain the characteristics of the observed interference patterns assuming that each SPP beam can be considered as a “slit without walls”. We discuss important implications of this work for SPP tomography and interferometric plasmonic sensors.     

Identification of dynamic characteristics of nonlinear joint based on the optimum equivalent linear frequency response function

Identification of dynamic characteristics of local nonlinearities has been aimed in this paper. The spirit of the identification method is established on Optimum Equivalent Linear Frequency response function (OELF). Dynamic behavior of nonlinear elements in system is extracted from OELF using two different techniques. The first technique is “Direct Identification Method” (DIM) in which no pre-assumed model is considered for the nonlinearity's behavior and the second technique is “Model based Identification Method” (MIM). The second technique is introduced with two different formulations, in order to take into account the practical limits due to the inaccessibility of nonlinearity location and/or indeterminability of degree of freedom. Dynamic characteristics of common nonlinearity mechanisms like cubic stiffness, pure slip, and stick-slip have been identified using the proposed technique and it has been shown that, although the proposed identification technique is simple, it does not require any sophisticated measurement hardwares and techniques, as required by most of the identification methods proposed so far. Also, the relation of this technique to harmonic balance method is discussed.     

Effects of misalignments in the optical vortex transformation performed by holograms with embedded phase singularity

Spatial characteristics of diffracted beams produced by a “fork” hologram from an incident circular Laguerre-Gaussian beam whose axis differs from the hologram optical axis are studied theoretically. General analytical representations for the complex amplitude distribution of a diffracted beam are derived in terms of superposition of Kummer beams or hypergeometric-Gaussian beams. The diffracted beam structure is determined by combination of the “proper” topological charge m of the incident vortex beam and the topological charge l of the singularity “imparted” by the hologram. Evolution of the diffracted beam structure is studied in detail for several combinations of m and l and for various incident beam displacements with respect to the optical axis of the hologram. Variations of the intensity and phase distribution due to the incident beam misalignment are investigated and possible applications for the purposeful optical vortex beam generation and optical measurements are discussed.     

Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach

In this paper we study the quantum phase properties of “nonlinear coherent states” and “solvable quantum systems with discrete spectra” using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be applied to few special solvable quantum systems with known discrete spectrum as well as to some new classes of nonlinear oscillators with particular nonlinearity functions. Finally the associated phase distributions and their nonclasscial properties such as the squeezing in number and phase operators have been investigated, numerically.     

Dependence of magnetic field generation by thermal convection on the rotation rate: A case study

Dependence of magnetic field generation on the rotation rate is explored by direct numerical simulation of magnetohydrodynamic convective attractors in a plane layer of conducting fluid with square periodicity cells for the Taylor number varied from zero to 2000, for which the convective fluid motion halts (other parameters of the system are fixed). We observe 5 types of hydrodynamic (amagnetic) attractors: two families of two-dimensional (i.e. depending on two spatial variables) rolls parallel to sides of periodicity boxes of different widths and parallel to the diagonal, travelling waves and three-dimensional “wavy” rolls. All types of attractors, except for one family of rolls, are capable of kinematic magnetic field generation. We have found 21 distinct nonlinear convective MHD attractors (13 steady states and 8 periodic regimes) and identified bifurcations in which they emerge. In addition, we have observed a family of periodic, two-frequency quasiperiodic and chaotic regimes, as well as an incomplete Feigenbaum period doubling sequence of bifurcations of a torus followed by a chaotic regime and subsequently by a torus with 1/3 of the cascade frequency. The system is highly symmetric. We have found two novel global bifurcations reminiscent of the SNIC bifurcation, which are only possible in the presence of symmetries. The universally accepted paradigm, whereby an increase of the rotation rate below a certain level is beneficial for magnetic field generation, while a further increase inhibits it (and halts the motion of fluid on continuing the increase), remains unaltered, but we demonstrate that this “large-scale” picture lacks many significant details.     

Self-organization of five species in a cyclic competition game

Cyclic competition game models, particularly the “rock–paper–scissors” model, play important roles in exploring the problem of multi-species coexistence in spatially ecological systems. We propose an extended “rock–paper–scissors” game to model cyclic interactions among five species, and find that two of the five can coexistent when biodiversity disappears, which is different from the “rock–paper–scissors” game. As the number of fingers is five, we named the new model the “fingers” game, where the thumb, forefinger, middle finger, ring finger, and little finger cyclically dominate their subsequent species and are dominated by their former species. We investigate the “fingers” model in two ways: direct simulations and nonlinear partial differential equations. An important finding is that the number of species in a cyclic competition game has an influence on the emergence of biodiversity. To be specific, the “rock–paper–scissors” model is in favor of maintaining biodiversity in comparison with the “fingers” model when the variables (population size, reproduction rate, selection rate, and migration rate) are the same. It is also shown that the mobility and reproduction rate can promote or jeopardize biodiversity.