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تسجيل مستخدم جديدNonlinear anti-directional couplers with gain and loss
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Following the concept of $mathcal{PT}$-symmetric couplers, we propose a linearly coupled system of nonlinear waveguides, made of positive- and negative-index materials, which carry, respectively, gain and loss. We report novel bi- and multi-stability states pertaining to transmitted and reflective intensities, which are controlled by the ratio of the gain and loss coefficients, and phase mismatch between the waveguides. These states offer transmission regimes with extremely low threshold intensities for transitions between coexisting states, and very large amplification ratio between the input and output intensities leading to an efficient way of controlling light with light.
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Families of coupled solitons of $mathcal{PT}$-symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions modulation (CIM), are reported. Profiles, powers, stability areas, and propagation
dynamics of the obtained $mathcal{PT}$-symmetric coupled solitons are investigated. By comparing the results of the models with and without CIM, we find that the stability area of the model with CIM is much broader than the one without CIM. Remarkably, oscillating $mathcal{PT}$-symmetric coupled solitons can also exist in the model of CIM with the same coefficients of the self- and cross-interactions modulations. In addition, the period of these oscillating coupled solitons can be controlled by the linear coupling coefficient.
We produce transmission and reflection spectra of the anti-directional coupler (ADC) composed of linearly-coupled positive- and negative-refractive-index arms, with intrinsic Kerr nonlinearity. Both reflection and transmission feature two highly ampl
ified peaks at two distinct wavelengths in a certain range of values of the gain, making it possible to design a wavelength-selective mode-amplification system. We also predict that a blend of gain and loss in suitable proportions can robustly enhance reflection spectra which are detrimentally affected by the attenuation, in addition to causing red and blue shifts owing to the Kerr effect. In particular, ADC with equal gain and loss coefficients, is considered in necessary detail.
We discuss the finite-time collapse, also referred as blow-up, of the solutions of a discrete nonlinear Schr{o}dinger (DNLS) equation incorporating linear and nonlinear gain and loss. This DNLS system appears in many inherently discrete physical cont
exts as a more realistic generalization of the Hamiltonian DNLS lattice. By using energy arguments in finite and infinite dimensional phase spaces (as guided by the boundary conditions imposed), we prove analytical upper and lower bounds for the collapse time, valid for both the defocusing and focusing cases of the model. In addition, the existence of a critical value in the linear loss parameter is underlined, separating finite time-collapse from energy decay. The numerical simulations, performed for a wide class of initial data, not only verified the validity of our bounds, but also revealed that the analytical bounds can be useful in identifying two distinct types of collapse dynamics, namely, extended or localized. Pending on the discreteness /amplitude regime, the system exhibits either type of collapse and the actual blow-up times approach, and in many cases are in excellent agreement, with the upper or the lower bound respectively. When these times lie between the analytical bounds, they are associated with a nontrivial mixing of the above major types of collapse dynamics, due to the corroboration of defocusing/focusing effects and energy gain/loss, in the presence of discreteness and nonlinearity.
We consider the asymptotic behavior of the solutions of a nonlinear Schrodinger (NLS) model incorporating linear and nonlinear gain/loss. First, we describe analytically the dynamical regimes (depending on the gain/loss strengths), for finite-time co
llapse, decay, and global existence of solutions in the dynamics. Then, for all the above parametric regimes, we use direct numerical simulations to study the dynamics corresponding to algebraically decaying initial data. We identify crucial differences between the dynamics of vanishing initial conditions, and those converging to a finite constant background: in the former (latter) case we find strong (weak) collapse or decay, when the gain/loss parameters are selected from the relevant regimes. One of our main results, is that in all the above regimes, non-vanishing initial data transition through spatiotemporal, algebraically decaying waveforms. While the system is nonintegrable, the evolution of these waveforms is reminiscent to the evolution of the Peregrine rogue wave of the integrable NLS limit. The parametric range of gain and loss for which this phenomenology persists is also touched upon.
We introduce a discrete lossy system, into which a double hot spot (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic waveguides, with a
pair of amplified nonlinear cores embedded into it. We focus on the case of the self-defocusing nonlinearity and cubic losses acting at the HSs. Symmetric localized modes pinned to the double HS are constructed in an implicit analytical form, which is done separately for the cases of odd and even numbers of intermediate sites between the HSs. In the former case, some stationary solutions feature a W-like shape, with a low peak at the central site, added to tall peaks at the positions of the embedded HSs. The special case of two adjacent HSs is considered too. Stability of the solution families against small perturbations is investigated in a numerical form, which reveals stable and unstable subfamilies. The instability of symmetric modes accounting for by an isolated positive eigenvalue leads to their spontaneous transformation into co-existing stable antisymmetric modes, while the instability represented by a pair of complex-conjugate eigenvalues gives rise to persistent breathers.
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