Dynamics of weakly localized waves

We develop a transport theory to describe the dynamics of (weakly) localized waves in a quasi-1D tube geometry both in reflection and in transmission. We compare our results to recent experiments with microwaves and to other theories, such as random matrix theory and supersymmetric theory.     

Maximum visibility in interferometers illuminated by vectorial waves

The maximum visibility achievable in arbitrary lossless linear interferometers illuminated with two vectorial transversal electromagnetic beams is determined.     

Modulation of coherence of vectorial electromagnetic waves in the Young interferometer

We show the modulation of coherence for vectorial electromagnetic waves taking place in the interference plane of a Young interferometer. The amplitude of modulation is determined by the polarization properties at the slits.     

Reconstruction of protein structures from a vectorial representation

We show that the contact map of the native structure of globular proteins can be reconstructed starting from the sole knowledge of the contact map's principal eigenvector, and present an exact algorithm for this purpose. Our algorithm yields a unique contact map for all 221 globular structures of PDBselect25 of length N相似文献   

Threshold energy of vectorial spatial solitary waves in non-linear quadratic crystals

Excitation and propagation of spatial solitary waves due to three-wave mixing in quadratic non-linear media lead to a rich variety of interesting phenomena some of which have already experimental evidence. Analytical and numerical modelling plays a key role in gaining insight in the experimental data, in completing the theoretical understanding of the process and in predicting new possible applications. In this context, we present an extensive analytical and numerical study on the multi-parameter family of vectorial spatial solitary waves in bulk quadratic crystals. We focus our attention particularly on the threshold energy necessary to drive solitary waves on available crystals exhibiting a second order non-linearity and in describing how this threshold depends on the crystal parameters.     

Relation of vectorial structures of diffracted plane waves with the elliptical aperture configuration and the light polarization in the far field

The analytical vectorial structure of a linearly polarized plane wave diffracted by an elliptical aperture is studied in detail based on the vector angular spectrum representation. It is found that the energy flux density spot sizes and the energy fluxes of the TE and TM term depend on the elliptical aperture configuration and the polarization direction of the incident plane wave. And the far fields can have smaller spots and larger energy fluxes for an elliptical aperture compared to a circular aperture with the same input wave amplitude. And its potential application in information encoding and transmission for free space communications is proposed apart from re-focusing to enhance the optical storage density. This encoding scheme has the benefit of easy implementation without modulating any properties of the light source.     

Nonparaxial diffraction of vectorial plane waves at a small aperture

By using the vectorial Rayleigh diffraction integrals, a nonparaxial propagation equation of vectorial plane waves diffracted at a small rectangular aperture is derived analytically and some special cases are discussed. Numerical calculation results are given to illustrate the applicability and validity of our theoretical formulae. It is shown that for the apertured case the ratio of the aperture width and wavelength affects the beam nonparaxiality. The nonparaxial approach presented in this paper has to be used for diffracted plane waves if the aperture width is comparable with or less than the wavelength.     

Intensity-controlled interactions between vectorial spatial solitary waves in quadratic nonlinear media

We numerically investigate the interaction of vectorial solitary waves propagating in a bulk crystal with a phase-matchable quadratic nonlinearity. We obtain coalescence, steering, crossing, or repulsion by controlling the launched intensities in two orthogonal polarizations without any coherent seed at the second harmonic.     

First laboratory observation of freely propagating electrostatic waves produced by intense, localized field structures

Freely propagating electrostatic waves (free modes) are observed to be produced by intense, localized field structures in laboratory measurements performed in an unmagnetized plasma in a state of strong Langmuir turbulence. The freely traveling waves conform to the Langmuir dispersion relation and have an average frequency which is approximately 11% higher than the average frequency of the localized field structures. The observations are consistent with the predictions of strong Langmuir turbulence theory.     

Nonlinear localized waves in a periodic medium

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.     

Interactions of Type II vectorial spatial solitary waves in materials with quadratic non-linearity

We present analytical, numerical and experimental results of the interactions between Type II vectorial spatial solitary waves (QSSW) in second-order non-linear media. We show that the outcome of the interaction can be changed from beam coalescence to steering, crossing or repulsion through a non-coherent control (i.e. the control does not rely on the relative phase between the interacting QSSW). We also provide experimental evidence that both quasi-elastic and inelastic collision between QSSW are feasible in second order non-linear media, depending on the relative velocity of the interacting QSSW. We determine (analytically, numerically and experimentally) the critical transverse velocity for elastic collision to be observed, when the fundamental frequency component of the two interacting beams are orthogonally polarized at the input face of the non-linear crystal.     

Nonisospectral effects on generating localized waves

In this paper we explain how space-time localized waves can be generated by introducing nonisospectral effects which are usually related to non-uniformity of media. The nonisospectral Korteweg–de Vries, modified Korteweg–de Vries and the Hirota equations are employed to demonstrate the idea. Their solutions are presented in terms of Wronskians and double Wronskians and space-time localized dynamics are illustrated.     

Dynamics of localized waves with large amplitude in a weakly dispersive medium with a quadratic and positive cubic nonlinearity

The dynamics of localized waves is analyzed in the framework of a model described by the Korteweg-de Vries (KdV) equation with account made for the cubic positive nonlinearity (the Gardner equation). In particular, the interaction process of two solitons is considered, and the dynamics of a “breathing” wave packet (a breather) is discussed. It is shown that solitons of the same polarity interact as in the case of the Korteweg-de Vries equation or modified Korteweg-de Vries equation, whereas the interaction of solitons of different polarity is qualitatively different from the classical case. An example of “unpredictable” behavior of the breather of the Gardner equation is discussed.     

Speckle evolution of diffusive and localized waves

We show that while the statistics of static speckle patterns are generic, fluctuations in the change within speckle patterns are greatly enhanced in the localization transition. The probability distributions of the displacement of phase singularities and the standard deviations of the changes of phase and intensity with frequency shift of incident microwave radiation are given in terms of the same expression which describes the probability distribution of total transmission. This function depends only upon a single parameter, the variance of the corresponding variable. The changing statistics in the localization transition reflects the number of underlying electromagnetic modes with which the incident wave interacts.     

Desynchronization waves and localized instabilities in oscillator arrays

We consider a ring of identical or near-identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the desynchronization transition that occurs as the coupling strengths are increased. We demonstrate Anderson localization of the modes of instability and show that such localized instability generates waves of desynchronization that spread to the whole array. Similar results should apply to other networks with regular topology and heterogeneous connection strengths.