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We study discrete surface solitons in semi-infinite, one-dimensional, nonlinear (Kerr), quasiperiodic waveguide arrays of the Fibonacci and Aubry-André types, and explore different families of localized surface modes, as function of optical power content ("nonlinearity") and quasiperiodic strength ("disorder"). We find a strong asymmetry in the power content of the mode as a function of the propagation constant, between the cases of focusing and defocusing nonlinearity, in both models. We also examine the dynamical evolution of a completely localized initial excitation at the array surface. We find that, in general, for a given optical power, a smaller quasiperiodic strength is required to effect localization at the surface than in the bulk. Also, for fixed quasiperiodic strength, a smaller optical power is needed to localize the excitation at the edge than inside the bulk. [ABSTRACT FROM AUTHOR]

Abstract: We study the formation of nonlinear localized modes and discrete surface solitons near the edges or interfaces of weakly coupled nonlinear optical waveguides, one-dimensional photonic crystals. We draw an analogy between the staggered nonlinear surface optical modes and the surface Tamm states known in the electronic theory. We discuss the crossover between discrete solitons inside the array and surface solitons at the edge of the array by analyzing the families of even and odd nonlinear localized modes located at finite distances from the edge of a waveguide array. Then, we study the formation of guided modes localized at an interface separating two different periodic photonic lattices. Employing the effective discrete model, we analyze linear and nonlinear interface modes and also predict the existence of stable interface solitons including the hybrid staggered/unstaggered lattice solitons with the tails belonging to the spectral gaps of different types. Finally, we discuss briefly the recent experimental observation of discrete surface solitons and nonlinear Tamm states. [Copyright &y& Elsevier]

By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions have a symmetric amplitude profile and two different topological charges. We also observe the dynamical formation of a variety of "bound-state" solutions composed of two or more of these vortex solitons. All of these stable composite structures persist in the conservative cubic Umit for high values of their power content. [ABSTRACT FROM AUTHOR]

We have found several families of vortex soliton solutions in two-dimensional discrete dissipative systems governed by the cubic-quintic complex Ginzburg-Landau equation. There are symmetric and asynunetric solutions, and some of them have simultaneously two different topological charges for two different closed loops encircling, i.e., centered at, the singularity. Their regions of existence and stability are determined. Additionally, we have analyzed the relationship between dissipation and stability for a number of solutions, finding that dissipation favors the stability of the vortex soliton solutions. [ABSTRACT FROM AUTHOR]

We examine the switching dynamics of discrete solitons propagating along two coupled discrete arrays which are twisted to form a Möbius strip. We analyze the potential of the topological switches by comparing the differences between the Möbius strip and untwisted discrete arrays. We employ the Ablowitz-Ladik (AL) model and reveal a nontrivial Berry phase associated with the monopole spectra in parameter space. We study the dynamical evolution of the AL soliton launched into one of the chains and observe its switching behavior. While in the untwisted discrete case, the soliton splits in nearly identical portions as the interchain coupling is increased, in the Möbius case and for weak coupling, we observe a well-defined "switching time" where the soliton switches completely from one chain to the other. [ABSTRACT FROM AUTHOR]