No abstract

We demonstrate that solitary pulses in linearly coupled nonlinear Schrödinger equations with gain in one mode and losses in another one, which is a model of an asymmetric erbium-doped nonlinear optical coupler, exist and are stable, as was recently predicted analytically. Next, we consider interactions between the pulses. The in-phase pulses attract each other and merge into a single one. Numerical and analytical consideration of the repulsive interaction between -out-of-phase pulses reveals the existence of their robust pseudobound state, when a final separation between them takes an almost constant minimum value, as a function of the initial separation, T in , in a certain interval of T in . In the case of the phase difference /2, the interaction is also repulsive. ͓S1063-651X͑96͒12210-8͔ PACS number͑s͒: 42.81.Dp; 42.81.Qb; 52.35.Sb; 03.40.KfLocalized pulses ͑solitons͒ play a central role in numerous physical systems that have attracted a lot of interest ͓1,2͔. Real systems must contain an active element providing for a loss-compensating gain. In nonlinear optical fibers ͑NOF's͒ the losses can be compensated by the erbium-doped amplifiers ͓2͔. However, if the active element is uniformly distributed in the system, it makes the zero solution unstable, thus lending instability to the solitary pulse. A well-known model with this property is the cubic Ginzburg-Landau ͑GL͒ equation ͓3͔. In the application to NOF's, it may be regarded as a perturbed nonlinear Schrödinger ͑NLS͒ equation:where u(z,) is an envelope of the electromagnetic waves in the fiber, z and are the propagation distance and the socalled reduced time, ␥ 0 is gain, and ␥ 1 and ␥ 2 are coefficients of the dispersive and nonlinear losses. Equation ͑1͒ has an exact solitary-pulse solution ͓3͔, which can form bound states ͓4͔. However, at ␥ 0 Ͼ0 the solution uϭ0 is unstable in this model, hence an isolated pulse is unstable too. A problem of fundamental interest is to find a tractable physical model that can support stable pulses. Recently, it was proposed in ͓5͔ in the form of a dual-core NOF ͑cou-pler͒, in which one core is active while the other one is pure lossy. The model gives rise to two solitons, one stable and one unstable, the unstable one being a separatrix between attraction domains of the stable soliton and the stable zero solution.In Ref. ͓5͔, only analytical results were presented. It remains necessary to check those results numerically, which is the first objective of the present work. It will be demonstrated that the pulses indeed exist and are stable. The shape of the numerically obtained pulses proves to be so close to the analytically predicted form that one virtually cannot distinguish between them. The other objective of this work is to consider collisions between the pulses. We will arrive at a simple concept of a ''pseudo-bound state'' of two pulses.The model put forward in ͓5͔ is a system of two linearly coupled perturbed NLS equations for amplitudes of electromagnetic waves in an asymmetric twin-core NOF, only one core being acti...

We investigate the existence and stability of solitons in an optical waveguide equipped with a Bragg grating (BG) in which nonlinearity contains both cubic and quintic terms. The model has straightforward realizations in both temporal and spatial domains, the latter being most realistic. Two different families of zero-velocity solitons, which are separated by a border at which solitons do not exist, are found in an exact analytical form. One family may be regarded as a generalization of the usual BG solitons supported by the cubic nonlinearity, while the other family, dominated by the quintic nonlinearity, includes novel "two-tier" solitons with a sharp (but nonsingular) peak. These soliton families also differ in the parities of their real and imaginary parts. A stability region is identified within each family by means of direct numerical simulations. The addition of the quintic term to the model makes the solitons very robust: simulating evolution of a strongly deformed pulse, we find that a larger part of its energy is retained in the process of its evolution into a soliton shape, only a small share of the energy being lost into radiation, which is opposite to what occurs in the usual BG model with cubic nonlinearity.

In this paper, we present the design and analysis of a novel hybrid porous core octagonal lattice photonic crystal fiber for terahertz (THz) wave guidance. The numerical analysis is performed using a full-vector finite element method (FEM) that shows that 80% of bulk absorption material loss of cyclic olefin copolymer (COC), commercially known as TOPAS can be reduced at a core diameter of 350 μm. The obtained effective material loss (EML) is as low as 0.04  cm^-1 at an operating frequency of 1 THz with a core porosity of 81%. Moreover, the proposed photonic crystal fiber also exhibits comparatively higher core power fraction, lower confinement loss, higher effective mode area, and an ultra-flattened dispersion profile with single mode propagation. This fiber can be readily fabricated using capillary stacking and sol-gel techniques, and it can be used for broadband terahertz applications.

No abstract

We investigate the existence and stability of gap solitons in a double-core optical fiber, where one core has the Kerr nonlinearity and the other one is linear, with the Bragg

We study the stability and interactions of chirped solitary pulses in a system of nonlinearly coupled cubic Ginzburg-Landau (CGL) equations with a group-velocity mismatch between them, where each CGL equation is stabilized by linearly coupling it to an additional linear dissipative equation. In the context of nonlinear fiber optics, the model describes transmission and collisions of pulses at different wavelengths in a dual-core fiber, in which the active core is furnished with bandwidth-limited gain, while the other, passive (lossy) one is necessary for stabilization of the solitary pulses. Complete and incomplete collisions of pulses in two channels in the cases of anomalous and normal dispersion in the active core are analyzed by means of perturbation theory and direct numerical simulations. It is demonstrated that the model may readily support fully stable pulses whose collisions are quasielastic, provided that the group-velocity difference between the two channels exceeds a critical value. In the case of quasielastic collisions, the temporal shift of pulses, predicted by the analytical approach, is in semiquantitative agreement with direct numerical results in the case of anomalous dispersion (in the opposite case, the perturbation theory does not apply). We also consider a simultaneous collision between pulses in three channels, concluding that this collision remains quasielastic, and the pulses remain completely stable. Thus, the model may be a starting point for the design of a stabilized wavelength-division-multiplexed transmission system.

The existence and stability of solitons in a dual-core optical waveguide, in which one core has Kerr nonlinearity while the other one is linear with a Bragg grating written on it, are investigated. The system's spectrum for the frequency omega of linear waves always contains a gap. If the group velocity c in the linear core is zero, it also has two other, upper and lower (in terms of omega) gaps. If c not equal to 0, the upper and lower gaps do not exist in the rigorous sense, as each overlaps with one branch of the continuous spectrum. When c=0, a family of zero-velocity soliton solutions, filling all the three gaps, is found analytically. Their stability is tested numerically, leading to a conclusion that only solitons in an upper section of the upper gap are stable. For c not equal to 0, soliton solutions are sought for numerically. Stationary solutions are only found in the upper gap, in the form of unusual solitons, which exist as a continuous family in the former upper gap, despite its overlapping with one branch of the continuous spectrum. A region in the parameter plane (c,omega) is identified where these solitons are stable; it is again an upper section of the upper gap. Stable moving solitons are found too. A feasible explanation for the (virtual) existence of these solitons, based on an analytical estimate of their radiative-decay rate (if the decay takes place), is presented.