Chao-Qing Dai

Controllable Akhmediev breather and Kuznetsov-Ma soliton trains in PT-symmetric coupled waveguides.

The PT-symmetric and PT-antisymmetric Akhmediev breather (AB) and Kuznetsov-Ma (KM) soliton train solutions of a (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in PT-symmetric coupled waveguides with gain and loss are derived via the Darboux transformation method. From these analytical solutions, we investigate the controllable behaviors of AB and KM soliton trains in a diffraction decreasing system with exponential profile. By adjusting the relation between the maximum Zm of effective propagation distance and the peak locations Zi of AB and KM soliton trains, we can control the restraint, maintenance and postpone excitations of AB and KM soliton trains.

Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform

A discussion and a cryptanalysis of the optical phase-truncated Fourier-transform-based cryptosystem are presented in this paper. The concept of an optical asymmetric cryptosystem, which was introduced into the optical image encryption scheme based on phase-truncated Fourier transforms in 2010, is suggested to be retained in optical encryption. A new method of attack is also proposed to simultaneously obtain the main information of the original image, the two decryption keys from its cyphertext, and the public keys based on the modified amplitude-phase retrieval algorithm. The numerical results illustrate that the computing efficiency of the algorithm is improved and the number of iterations is much less than that by the specific attack, which has two iteration loops.

Ultrashort self-similar solutions of the cubic-quintic nonlinear Schrödinger equation with distributed coefficients in the inhomogeneous fiber

By means of the similarity transformation, we obtain exact self-similar solutions (similaritons) of the generalized cubic-quintic (CQ) nonlinear Schrodinger equation with spatially inhomogeneous group velocity dispersion, CQ nonlinearity and amplification or attenuation. Exact balance conditions between the dispersion, nonlinearity and the gain/loss have been obtained. As an example, we investigate their propagation dynamics in the dispersion decreasing fiber (DDF). Considering the fluctuation of the fiber parameter in real application, the exact balance conditions do not satisfy, and so we perform direct numerical analysis with initial 10% white noise for the bright similariton in both the DDF and the periodic distributed amplification system. Numerical calculations indicate stable propagation of the bright similariton over tens of dispersion lengths. These ultrashort self-similar optical waves are potentially useful for all-optical data-processing schemes and the design of beam compressors and amplifiers.

Superposed Kuznetsov-Ma solitons in a two-dimensional graded-index grating waveguide

This work was supported by the National Natural Science Foundation of China (grants 11375007 and 11375079) and the Zhejiang Provincial Natural Science Foundation of China (grant LY13F050006).

Multi-rogue wave and multi-breather solutions in PT-symmetric coupled waveguides

Abstract The coupled nonlinear Schrodinger equation in parity-time symmetric coupled waveguides is studied by means of the modified Darboux transformation method. The hierarchies of rational solutions and breather solutions are generated from the plane wave solution. Some basic properties of multi-rogue waves and multi-breathers including the superposed Kuznetsov–Ma solitons, Akhmediev breathers and their combined structures are discussed. Our results might provide useful information for potential applications of synthetic parity-time symmetric systems in nonlinear optics and condensed matter physics.

Spatial solitons with the odd and even symmetries in (2+1)-dimensional spatially inhomogeneous cubic-quintic nonlinear media with transverse W-shaped modulation

We firstly investigate analytical spatial soliton solutions with the odd and even symmetries in (2+1)-dimensional spatially inhomogeneous cubic-quintic nonlinear media considering transverse W-shaped modulation. The power of localized states increases one by one along the line y = x when the soliton order number n increases. The stability analysis and numerical calculations show that stable fundamental solitons exist while higher order solitons are unstable in three nonlinear media, i.e. the defocusing cubic and focusing quintic nonlinear medium, focusing cubic and defocusing quintic nonlinear medium, and focusing cubic and focusing quintic nonlinear medium. While all solitons (even fundamental solitons) are unstable and ultimately decay into noise in the defocusing cubic and defocusing quintic nonlinear medium.

Controllable behaviours of rogue wave triplets in the nonautonomous nonlinear and dispersive system

A similarity transformation connecting the variable coefficient nonlinear Schrodinger equation with the standard nonlinear Schrodinger equation is constructed. The self-similar rogue wave triplet solutions (rational solutions) are analytically obtained for the nonautonomous nonlinear and dispersive system. The controllable behaviours of rogue wave triplets in two typical soliton management systems are discussed. In the exponential dispersion decreasing fibre, three kinds of rogue wave triplets with controllable behaviours are analysed. In the periodic distributed system, the rogue wave triplets recur periodically in the form of a cluster.

Three-dimensional structures of the spatiotemporal nonlinear Schrodinger equation with power-law nonlinearity in PT-symmetric potentials.

The spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in -symmetric potentials is investigated, and two families of analytical three-dimensional spatiotemporal structure solutions are obtained. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results indicate that solutions are stable below some thresholds for the imaginary part of -symmetric potentials in the self-focusing medium, while they are always unstable for all parameters in the self-defocusing medium. Moreover, some dynamical properties of these solutions are discussed, such as the phase switch, power and transverse power-flow density. The span of phase switch gradually enlarges with the decrease of the competing parameter k in -symmetric potentials. The power and power-flow density are all positive, which implies that the power flow and exchange from the gain toward the loss domains in the cell.

Multi-soliton solutions to the modified nonlinear Schrödinger equation with variable coefficients in inhomogeneous fibers

Multi-soliton solutions to the modified nonlinear Schr?dinger equation (MNLSE) with variable coefficients (VCs) in inhomogeneous fibers are obtained with the help of mapping transformation, which reduces the VC MNLSE into a constant-coefficient MNLSE. Based on the analytical solutions, one- and two-soliton transmissions in the proper dispersion management systems are discussed. The sustainment of solitons and the disappearance of breathers for the VC MNLSE are first reported here.

A bright 2D spatial soliton in inhomogeneous Kerr media with PT-symmetric potentials

The nonlinear Schrodinger equation with inhomogeneous diffraction and nonlinearity in the presence of PT-symmetric potentials is investigated, and an analytical bright 2D spatial soliton is obtained. The positive and negative signs in the parameters of the PT-symmetric potentials lead to four permutation and combination cases. The dynamical evolutions of the spatial soliton in the periodic modulated system and the diffraction decreasing waveguide are discussed. Dynamical characteristics of the form factors for the spatial soliton including the amplitude, width and phase are studied. Moreover, two kinds of nonlinear PT phase change are presented. These results may provide alternative methods in potential applications of synthetic PT-symmetric systems.