Gap solitons in Ginzburg-Landau media

Beyond-band discrete soliton interaction in binary waveguide arrays

We investigate different scenarios of interaction between two beyond-band discrete solitons (BBDSs), which are a new class of solitons in binary waveguide arrays and have been investigated just recently. In the quasi-continuous regime when solitons intensity is low and, thus, solitons are broad, two BBDSs with the same envelope in binary waveguide arrays interact with each other practically like two well-known fundamental solitons governed by the nonlinear Schrödinger equation in a single optical fiber. However, this similarity disappears if the discrete nature of the system is enhanced by increasing the intensity of BBDSs. In that case, two initially in-phase BBDSs with the same detuning cannot periodically collide during propagation. We also show that single-peaked BBDSs are more robust and less mobile than double-peaked BBDSs with the same detuning. This robustness stops two identical single-peaked BBDSs from interaction even at initial separations when double-peaked BBDSs can still strongly interact with each other or with single-peaked BBDSs.

Interactions of the solitons in periodic driven-dissipative systems supporting quasibound states in the continuum

The paper is devoted to the dynamics of dissipative gap solitons in the periodically corrugated optical waveguides whose spectrum of linear excitations contains a mode that can be referred to as a quasi-bound state in the continuum. These systems can support a large variety of stable bright and dark dissipative solitons that can interact with each other and with the inhomogeneities of the pump. One of the focus points of this work is the influence of slow variations of the pump on the behavior of the solitons. It is shown that for the fixed sets of parameters the effect of pump inhomogeneities on the solitons is not the same for the solitons of different kinds. The second main goal of the paper is systematic study of the interaction between the solitons of the same or different kinds. It is demonstrated that various scenarios of intersoliton interactions can occur: The solitons can repulse each other or get attracted. In the latter case, the solitons can annihilate, fuse in a single soliton, or form a new bound state depending on the kinds of the interacting solitons and on the system parameters.

Pulse propagation in a 1D array of excitable semiconductor lasers

Nonlinear pulse propagation is a major feature in continuously extended excitable systems. The persistence of this phenomenon in coupled excitable systems is expected. Here, we investigate theoretically the propagation of nonlinear pulses in a 1D array of evanescently coupled excitable semiconductor lasers. We show that the propagation of pulses is characterized by a hopping dynamics. The average pulse speed and bifurcation diagram are characterized as a function of the coupling strength between the lasers. Several instabilities are analyzed such as the onset and disappearance of pulse propagation and a spontaneous breaking of the translation symmetry. The pulse propagation modes evidenced are specific to the discrete nature of the 1D array of excitable lasers.

Self-localization of polariton condensates in periodic potentials

We predict the existence of novel spatially localized states of exciton-polariton Bose-Einstein condensates in semiconductor microcavities with fabricated periodic in-plane potentials. Our theory shows that, under the conditions of continuous nonresonant pumping, localization is observed for a wide range of optical pump parameters due to effective potentials self-induced by the polariton flows in the spatially periodic system. We reveal that the self-localization of exciton-polaritons in the lattice may occur both in the gaps and bands of the single-particle linear spectrum, and is dominated by the effects of gain and dissipation rather than the structured potential, in sharp contrast to the conservative condensates of ultracold alkali atoms.

Pulse propagation in a fiber Bragg grating written in a slow saturable fiber amplifier

We have developed a model to study nonlinear pulse propagation in a fiber Bragg grating written in an erbium-doped fiber amplifier. The saturation effect in such amplifiers depends on the accumulated energy along the pulse rather than on the pulse instantaneous power. We have shown that the gain saturation effect cannot be neglected when Bragg solitons are amplified by erbium-doped fiber amplifiers. The slow saturation of the amplifier limits the output pulse power, and it tends to split the amplified pulse into several pulses. We have shown that when the propagation velocity of the amplified pulses decreases, the amplifier gain per unit length increases.

Two-dimensional dissipative gap solitons

We introduce a model which integrates the complex Ginzburg-Landau equation in two dimensions (2Ds) with the linear-cubic-quintic combination of loss and gain terms, self-defocusing nonlinearity, and a periodic potential. In this system, stable 2D dissipative gap solitons (DGSs) are constructed, both fundamental and vortical ones. The soliton families belong to the first finite band gap of the system's linear spectrum. The solutions are obtained in a numerical form and also by means of an analytical approximation, which combines the variational description of the shape of the fundamental and vortical solitons and the balance equation for their total power. The analytical results agree with numerical findings. The model may be implemented as a laser medium in a bulk self-defocusing optical waveguide equipped with a transverse 2D grating, the predicted DGSs representing spatial solitons in this setting.