Four examples of laterally coupled semiconductor lasers with different waveguiding structures have been studied using coupled mode theory and allowing for frequency detuning between the lasers. The structures include purely real index guiding, pure gain-guiding, and combinations of index guiding and antiguiding with gain-guiding. The dynamics of these four systems have been explored using AUTO software (standard numerical continuation package), linear stability analysis, and direct integration of the rate equations. Convincing agreement between results obtained by these three methods has been demonstrated, including effects due to variation of laser pumping rate, detuning, and linewidth enhancement factor. A periodicity of behavior with laser separation has been revealed that was previously overlooked. This periodicity has increasing influence on the bifurcations of the system as the structures develop from those with purely real guidance to a combination of index antiguiding and gain-guiding. The laser design and operating parameters used are realistic for a wide range of edge-emitting and surface-emitting lasers of practical importance, so that the dynamics studied here are relevant to real systems of coupled lasers.

The coupled discrete linear and Kerr nonlinear Schrödinger equations with gain and loss describing transport on dimers with parity-time (PT ) symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase-portraits of the system. A pendulum equation with a linear potential and a constant force for the phase-difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behaviour of all solutions of the system, including changes in the topological structure of the phase-plane, is then discussed. arXiv:1307.2788v2 [physics.optics]

In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them with those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent experimental developments in the former context. The stability properties of the fundamental waves, for both on-site and inter-site modes, are examined analytically and corroborated by numerical results. Furthermore, their dynamical evolution when they are found to be unstable is obtained through appropriately crafted numerical experiments.

We study the mobility of solitons in lattices with quadratic (chi(2), alias second-harmonic-generating) nonlinearity. Using the notion of the Peierls-Nabarro potential and systematic numerical simulations, we demonstrate that, in contrast with their cubic (chi(3)) counterparts, the discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D), in any direction. We identify parametric regions where an initial kick applied to a soliton leads to three possible outcomes: staying put, persistent motion, or destruction. On the 2D lattice, the solitons survive the largest kick and attain the largest speed along the diagonal direction.

We consider inhomogeneous non-linear wave equations of the type u =u +V (u, x)-αu (α≥0). The spatial real axis is divided in intervals I , i=0,..., N+1 and on each individual interval the potential is homogeneous, i.e., V(u, x)=V (u) for x∈I . By varying the lengths of the middle intervals, typically one can obtain large families of stationary front or solitary wave solutions. In these families, the lengths are functions of the energies associated with the potentials V . In this paper we show that the existence of an eigenvalue zero of the linearisation operator about such a front or stationary wave is related to zeroes of the determinant of a Jacobian associated to the length functions. Furthermore, the methods by which the result is obtained is fully constructive and can subsequently be used to deduce the stability and instability of stationary fronts or solitary waves, as will be illustrated in examples. © 2012 Elsevier Inc

We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three dynamical regimes: when both components are subcritical, we do not observe nucleation of coherent structures; when both components are supercritical they both form dark solitons in one dimension (1D) and vortices or rotating vortex dipoles in two dimensions (2D); in the intermediate regime, we observe the nucleation of a structure in the form of a dark-antidark soliton in 1D; the 2D analog of such a structure, a vortex-lump, is also observed.Introduction. In the past few years, there has been an increasing number of studies of multi-component Hamiltonian systems. This has been triggered primarily by the development of theoretical and experimental results in coupled atomic Bose-Einstein condensates (BECs) At the same time, many theoretical and experimental studies deal with the dragging of an "impurity" (e.g., a blue-detuned laser beam) through a one-component condensate. This setting has been demonstrated to be prototypical for dark soliton formation in 1D [16,17], and for vortex formation in 2D [18]. These nonlinear waves can be thought of as a type of nonlinear Cerenkov radiation that is emitted, when the motion of the impurity is supercritical with respect to the local speed of sound of the BEC. Recently, a combined experimental and theoretical study of the Cerenkov emission of phonons by a laser obstacle was reported [19]; in a different study [20], it has been shown that in the case of large obstacles (and for a supersonic flow of the BEC), the Cerenkov cone transforms into a spatial shock wave consisting of a chain of dark solitons [20]. In fact, this setting has been particularly relevant for the study of the breakdown of

Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX This paper reports on time-domain modeling of an optical switch based on the PT-Symmetric Bragg grating. The switching response is triggered by suddenly switching on the gain in the Bragg grating to create a PT-Symmetric Bragg grating. Transient and dynamic behavior of the PT Bragg gratings is analyzed using the time-domain numerical Transmission Line Modeling (TLM) method including a simple gain saturation model. The on/off ratio and the switching time of the PT-Bragg grating optical switch are analyzed in terms of the level of gain introduced in the system and the operating frequency. The paper also discusses the effect the gain saturation has on the operation of the PT-Symmetric Bragg gratings.

Received Month X, XXXX; revised Month X, XXXX; accepted Month X, XXXX; posted Month X, XXXX (Doc. ID XXXXX); published Month X, XXXX We report on the impact of realistic gain and loss models on the bistable operation of nonlinear parity-time Bragg gratings. In our model we include both dispersive and saturable gain and show that levels of gain/loss saturation can have significant impact on the bistable operation of a nonlinear PT Bragg grating based on GaAs material. The hysteresis of the nonlinear PT Bragg grating is analyzed for different levels of gain and loss and different saturation levels. We show that high saturation levels can improve the nonlinear operation by reducing the intensity at which the bistability occurs. However when the saturation intensity is low, saturation inhibits the PT characteristics of the grating.