Conservation laws of the generalized nonlocal nonlinear Schrodinger equation

The derivations of several conservation laws of the generalized nonlocal nonlinear Schrodinger equation are presented. These invaxiants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.

The solutions of the strongly nonlocal spatial solitons with several types of nonlocal response functions

The fundamental and second order strongly nonlocal solitons of the nonlocal nonlinear Schrodinger equation for several types of nonlocal responses are calculated by Ritz＇s variational method. For a specific type of nonlocal response, the solutions of the strongly nonlocal solitons with the same beam width but different degrees of nonlocality are identical except for an amplitude factor. For a nonlocal case where the nonlocal response function decays in direct proportion to the mth power of the distance near the source point, the power and the phase constant of the strongly nonlocal soliton are in inverse proportion to the （m ＋ 2）th power of its beam width.

Elliptic Function Waves of Spinor Bose-Einstein Condensates in an Optical Lattice

An improved nonlinear Schrodinger equation different from usual one of spinor Bose-Einstein condensates （BECs） in an optical lattice are obtained by taking into account a nonlinear term in the equation of motion for probability amplitude of spins carefully. The elliptic function wave solutions of the model are found under specific boundary condition, for example, the two ends of the atomic chain are fixed. In the case of limit the elliptic function wave solutions are reduced into spin-wave-like or solitons.

Interaction of Nonlocal Incoherent White-Light Solitons

The propagation and interaction of nonlocal incoherent white-light solitons in strongly nonlocal kerr media is investigated. Numerical simulations show that the interaction properties of nonlocal incoherent white-light solitons are different from the case in local media. The interactions of nonlocal incoherent white-light solitons are always attractive independent of their relative phase, while the other parameters such as the extent of nonlocality and the input power have a great impact on the soliton interactions. Pertinent numerical examples are presented to show their propagation and interaction behaviour further.

Influence of Deviation on Optical Transmission through Aperiodic Superlattices

We propose a deviation model and study the influences of the relative error and sensitivity of a machine on the transmission coefficients （TCs） of Fibonacci superlattices. It is found that for a system with fewer layers, the influence of deviation can be ignored. When superlattices become more complicated, they may be fabricated by a machine with suitable relative error and possess the designed value of TO. However, when the number of system layers exceeds some critical value, superlattices should be manufactured only by precise machines. The influence of the sensitivity is also discussed.

A Formula of Propagating Beams Driven by Few-Cycle Gaussian Pulse in Dispersive Media

A formula is developed to describe the propagation of beams driven by few-cycle Gaussian pulse in a media with group velocity dispersion （GVD）. With the method, the spatiotemporal evolution of the pulsed beam can be straightforwardly quantified as long as the monochromatic beam solutions in free space, which have been widely investigated in previous works, are known. The method makes it possible to analytically deal with the few-cycle pulsed beams with transverse profiles other than the Gaussian one, which is, to our knowledge, the one mainly investigated previously, in GVD media.

Rotating soliton clusters in nonlocal nonlinear media

From the study of the dynamics for the ring-like soliton clusters, we find that there exists a critical value of the ring radius, dcr, for the stationary rotation of the clusters with respect to the beam centre even in the presence of the relatively strong noise, and that the soliton clusters will not rotate but only undergo periodic collisions in the form of simple harmonic oscillator if the ring radius is large enough. We also show that the direction of the rotation can be opposite to the direction of phase gradient when the relative phase difference is within the domain 0 〈 ｜θ｜ 〈 π, while along the direction of phase gradient when the relative phase difference is within the domain π 〈｜θ｜ 〈 2π

Long-Range Interactions between Nematicons

We theoretically and experimentally investigate the long-range interaction between nematicons. It is demonstrated that the interaction becomes strongest when the pretilt angle of liquid crystal molecules is nearly π/4 for a given single-beam input power P0, and that the interaction becomes stronger when the incident power Po increases at a given pretilt angle. In this way, the interaction is still observed when the initial separation is 43 times of the soliton width, much larger than that implemented in lead glasses [Nature Phys. 2 （2006） 769].

The (1+1)-dimensional spatial solitons in media with weak nonlinear nonlocality

We study the propagation of （l＋l）-dimensional spatial soliton in a nonlocal Kerr-type medium with weak non- locality. First, we show that an equation for describing the soliton propagation in weak nonlocality is a nonlinear Schr6dinger equation with perturbation terms. Then, an approximate analytical solution of the equation is found by the perturbation method. We also find some interesting properties of the intensity profiles of the soliton.

Hollow Gaussian beams in strongly nonlocal nonlinear media

The propagation of hollow Gaussian beams in strongly nonlocal nonlinear media is studied in detail. Two analytical expressions are derived. For hollow Gaussian beams, the intensity distribution always evolves periodically. However the second-order moment beam width can keep invariant during propagation if the input power is equal to the critical power. The interaction of two hollow Gaussian beams and the vortical hollow Gaussian beams are also discussed. The vortical hollow Gaussian beams with an appropriate topological charge can keep their shapes invariant during propagation.

Defect solitons supported by parity-time symmetric defects in superlattices

The existence and stability of defect solitons supported by parity-time （PT） symmetric defects in superlattices are investigated. In the semi-infinite gap, in-phase solitons are found to exist stably for positive defects, zero defects, and negative defects. In the first gap, out-of-phase solitons are stable for positive defects or zero defects, whereas in-phase solitons are stable for negative defects. For both the in-phase and out-of-phase solitons with the positive defect and in-phase solitons with negative defect in the first gap, there exists a cutoff point of the propagation constant below which the defect solitons vanish. The value of the cutoff point depends on the depth of defect and the imaginary parts of the PT symmetric defect potentials. The influence of the imaginary part of the PT symmetric defect potentials on soliton stability is revealed.

Teleporting an Unknown Two-qubit Entangled State via Ion-Trap Systems

We propose a scheme for teleportation of an unknown two-qubit entangled state via trapped ions. In this scheme, we use the GHZ state as a quantum channel and the success probability can reach 1. The distinct advantage of our scheme is insensitive to the heating of the vibrational mode. In addition, Bell-state measurement is not required.

Dipole Solitons in Nonlinear Media with an Exponential-Decay Nonlocal Response

By applying the variational approach,the analytical expression of dipole solitons is obtained in nonlinear media with an exponential-decay nonlocal response.The relations of the soliton power versus the propagation constant and the soliton width are given.Some numerical simulations are carried out.The results show that the analytical expression is in excellent agreement with the numerical results for the strongly nonlocal case.

The contrast between defect solitons in parity-time symmetric superlattice and simple-lattice complex potentials

The existence and stability of defect superlattice solitons in parity-time （PT） symmetric superlattice and simplelattice complex potentials are reported. Compared with defect simple-lattice solitons in similar potentials, the defect soliton in superlattice has a wider stable range than that in simple-lattice. The solitons＇ power increases with increasing propagation constant. For the positive defect, the solitons are stable in the whole region where solitons exist in the semi-infinite gap. For the zero defect, the solitons are unstable at the edge of the band. For the negative defect, the solitons propagate with the shape of Y at low propagation constant and propagate stably at the large one.

Study on the approximative formula for the far-field of a Gaussian beam under circular aperture diffraction and its divergence

The approximative formula for the far-field diffraction of a Gaussian beam through a circular aperture is obtained by using the superposition of Gaussian beams instead of the aperture function, and the explicit expression for calculating the beam divergence is also gained. Using the formula, the influences of the aberrations on the far-field wavefront and the beam＇s divergence are researched, and the results show that the large aberrations badly affect the far-field wavefront and the divergence. It is suggested that the aberrations and the diffractions should be avoided when designing the transmitter.