Vortex lattice solitons supported by localized gain

We show that localized gain supports the existence of dissipative vortex solitons in periodic Kerr media with strong two-photon absorption. Vortex solitons exist in both focusing and defocusing media, with their propagation constants emerging from semi-infinite or finite gaps in the lattice spectrum. Coincidence of the discrete rotational symmetries of the gain landscape and refractive index distribution is a necessary condition for exciting vortex solitons, which otherwise transform into stable dissipative multipoles.     

Stationary wave packets in the Kerr nonlinear media with imaginary harmonic potential and linear gain

The existence of stationary wave packets in the nonlinear Kerr media with an imaginary harmonic potential and a linear gain is investigated. By employing a variational approach the existence of stable bright solitons is shown for the case of a defocusing nonlinearity. In focusing nonlinear media, the bright solitons have been shown to be unstable. The predictions of variational approach are confirmed by numerical simulations of the full modified NLS equation. The predicted stationary localized wave packets can be observed in a quasi-one-dimensional BEC with an imaginary optical potential and atoms feeding.     

Two-dimensional dissipative solitons supported by localized gain

We show that the balance between localized gain and nonlinear cubic dissipation in the two-dimensional nonlinear Schr?dinger equation allows for the existence of stable localized modes that we identify as solitons. Such modes exist only when the gain is strong enough and the energy flow exceeds certain threshold value. Above the critical value of the gain, symmetry breaking occurs and asymmetric dissipative solitons emerge.     

Beam propagation in gain–loss balanced waveguides

Linear and nonlinear localized modes of a slab waveguide with distributed gain and loss are studied. The structure is an optical analog of parity-time symmetric potentials in quantum mechanics. Such waveguide structures support stable localized modes. The explicit equation for the propagation constant of linear modes is obtained. The existence of stable nonlinear modes in such waveguides is demonstrated. Bend losses in such structures are analyzed.     

本征态的局域化与增益介质中局域态的放大

用时域有限差分方法(FDTD)模拟了二维增益、非增益随机介质中的光学现象。在非增益介质中，观察到了局域态空间分布及其频率特征。在增益介质中，观察到局域态的放大过程。模拟结果显示非增益介质中的局域态相当于传统激光腔的腔模，随机激光是由局域态谐振产生的。     

Rotating vortex solitons supported by localized gain

We show that ringlike localized gain landscapes imprinted in focusing cubic (Kerr) nonlinear media with strong two-photon absorption support new types of stable higher-order vortex solitons containing multiple phase singularities nested inside a single core. The phase singularities are found to rotate around the center of the gain landscape, with the rotation period being determined by the strength of the gain and the nonlinear absorption.     

活性无序介质中泵浦功率对局域模发射的影响

基于具有局域-非周期-类结构的活性无序介质中的复杂局域模与合适泵浦光的相互作用模型,研究活性无序介质中泵浦功率对局域模发射的影响,定性解释了泵浦功率对局域模发射的影响.结果表明,局域-非周期-类结构的无序介质的透射谱只与介质的结构有关,而与介质的损耗和增益无关,不同的激发模具有不同的泵浦功率阈值.     

Solitons pinned to hot spots

We generalize a recently proposed model based on the cubic complex Ginzburg-Landau (CGL) equation, which gives rise to stable dissipative solitons supported by localized gain applied at a “hot spot” (HS), in the presence of the linear loss in the bulk. We introduce a model with the Kerr nonlinearity concentrated at the HS, together with the local gain and, possibly, with the local nonlinear loss. The model, which may be implemented in laser cavities based on planar waveguides, gives rise to exact solutions for pinned dissipative solitons. In the case when the HS does not include the localized nonlinear loss, numerical tests demonstrate that these solitons are stable/unstable if the localized nonlinearity is self-defocusing/focusing. Another new setting considered in this work is a pair of two symmetric HSs. We find exact asymmetric solutions for it, although they are unstable. Numerical simulations demonstrate that stable modes supported by the HS pair tend to be symmetric. An unexpected conclusion is that the interaction between breathers pinned to two broad HSs, which are the only stable modes in isolation in that case, transforms them into a static symmetric mode.     

随机激光器中准态腔的阈值与其局域化程度的关系

基于光波在有限随机介质中的局域化理论，利用有限时域差分法数值求解Maxwell方程 组，研究了随机介质中的激光现象，分析了准态模的放大与其 空间局域性的关系. 通过研究二维非增益随机介质中光波的局域化，确定了准态模的空间分 布和频谱特征. 通过引入增益，研究了准态模的放大过程和阈值特性. 结果表明空间局域化 强的准态模在增益介质中被优先放大，且有较低的阈值. 关键词： 随机激光器 准态模 随机介质中的光学特性     

Localized modes in a finite-size open disordered microwave cavity

We present measurements of the spatial intensity distribution of localized modes in a two-dimensional open microwave cavity randomly filled with cylindrical dielectric scatterers. We show that each of these modes displays a range of localization lengths, and we successfully relate the largest value to the measured leakage rate at the boundary. These results constitute unambiguous signatures of the existence of strongly localized electromagnetic modes in two-dimensional open random media.     

Higher-order solitons in amplitude-disordered waveguide arrays

We investigate the existence and stability of different families of spatial solitons in optical waveguide arrays whose amplitudes obey a disordered distribution. The competition between focusing nonlinearity and linearly disordered refractive index modulation results in the formation of spatial localized nonlinear states. Solitons originating from Anderson modes with few nodes are robust during propagation. While multi-peaked solitons with in-phase neighboring components are completely unstable, multipole-mode solitons whose neighboring components are out-of-phase can propagate stably in wide parameter regions provided that their power exceeds a critical value. Our findings, thus, provide the first example of stable higher-order nonlinear states in disordered systems.     

Asymmetrical surface soliton trains

We elucidate the existence, stability and propagation dynamics of multi-spot soliton packets in focusing saturable media. Such solitons are supported by an interface beside which two harmonically photonic lattices with different modulation depths are imprinted. We show that the surface model can support stable higher-order structures in the form of asymmetrical surface soliton trains, which is in sharp contrast to homogeneous media or uniform harmonic lattice modulations where stable asymmetrical multi-peaked solitons do not exist. Surface trains can be viewed as higher-order soliton states bound together by several different lowest order solitons with appropriate relative phases. Their existence as stable objects enriches the concept of compact manipulation of several different solitons as a single entity and offers additional freedom to control the shape of solitons by adjusting the modulation depths beside the interface.     

Dynamics of bright discrete staggered solitons in photovoltaic photorefractive media

Theoretical results on spatial optical bright solitons excited in arrays of nonlinear defocusing waveguides, that result from the photovoltaic effect in a photorefractive material, are presented. The existence of four types of stationary discrete bright staggered solitons, on-site, inter-site, twisted inter-site, and twisted on-site solitons, is shown both analytically and numerically, and their stability properties are investigated. The maximum Hamiltonian of staggered solitons with the same total power corresponds to stable modes. It is shown that for low total power the on-site mode is stable while in the high power regime the inter-site mode is stable. These results are confirmed numerically. In addition, steering properties of localized modes are investigated by introducing a transversal translational shift. Because of the translational symmetry between on-site and inter-site localized modes they are considered as two dynamical realizations of the same moving mode, and the formalism of the Peierls-Nabarro effective potential is applied to interpret the exchange between trapping and steering of these modes. This critically depends on the mode’s total power and the introduced phase difference. On the other hand, steering of twisted inter-site and on-site localized modes is not numerically observed. Instead, transversal perturbation leads to a transformation of twisted modes either into a trapped on-site mode of smaller power and radiation, or into two trapped on-site modes.     

Varieties of stable vortical solitons in Ginzburg-Landau media with radially inhomogeneous losses

Using a combination of the variation approximation and direct simulations, we consider the model of the light transmission in nonlinearly amplified bulk media, taking into account the localization of the gain, i.e., the linear loss shaped as a parabolic function of the transverse radius, with a minimum at the center. The balance of the transverse diffraction, self-focusing, gain, and the inhomogeneous loss provides for the hitherto elusive stabilization of vortex solitons, in a large zone of the parameter space. Adjacent to it, stability domains are found for several novel kinds of localized vortices, including spinning elliptically shaped ones, eccentric elliptic vortices which feature double rotation, spinning crescents, and breathing vortices.     

Spatial solitons in linearly and nonlinearly amplitude-modulated optical lattices

We demonstrated that linearly and nonlinearly amplitude-modulated (chirped) harmonic lattices can support odd and even solitons in both focusing and defocusing saturable media. The modulated lattice modifies the profiles and enlarges the stability domains of solitons, comparing with the unchirped one. Twisted solitons, or “soliton trains” whose profiles exhibit multi-peak structures can also be supported by linearly and nonlinearly chirped lattices. In sharp contrast with periodic lattices, chirped lattices remarkably broaden the existence and stability domains of twisted solitons, especially for solitons with more components. While even solitons in focusing media and twisted solitons in defocusing media are unstable, odd and twisted solitons in focusing media are stable in relatively wide parameter windows. Chirped lattice can be used as a linear guidance to realize the oscillation of solitons which is impossible in unchirped lattice.     

Stationary one-dimensional dispersive shock waves

We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defects in defocusing media with linear gain and two-photon absorption. We found that, in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from a defect or generating beam, the competition between gain and two-photon absorption in a dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed a certain critical value.     

Fundamental solitons in discrete lattices with a delayed nonlinear response

The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are stable, and their broad intersite counterparts are marginally stable, featuring a virtually vanishing real instability eigenvalue. The solitons become unstable in the case of the slowly relaxing nonlinearity. The character of the instability alters with the increase of the delay time, which leads to a change in the dynamics of unstable discrete solitons. They form robust localized breathers in rapidly relaxing media, and decay into oscillatory diffractive pattern in the lattices with a slow nonlinear response. Marginally stable solitons can freely move across the lattice.     

Dark spatial solitons in discrete cubic media with self- and cross-phase modulation

We analytically study the background stability of dark strongly localized vectorial modes in discrete cubic media with self- and cross-phase modulation. The instability regions are identified as a function of the linear and non-linear coupling strength as well as the ratio between the background amplitudes of the two components. The respective instability gain is calculated. Approximate analytical solutions for vectorial discrete solitons of different topologies are derived. The analytical results obtained are confirmed by direct numerical simulations.     

Self-trapped spatially localized states in combined linear-nonlinear periodic potentials

We analyze the existence and stability of two kinds of self-trapped spatially localized gap modes,gap solitons and truncated nonlinear Bloch waves,in one-and two-dimensional optical or matter-wave media with self-focusing nonlinearity,supported by a combination of linear and nonlinear periodic lattice potentials.The former is found to be stable once placed inside a single well of the nonlinear lattice,it is unstable otherwise.Contrary to the case with constant self-focusing nonlinearity,where the latter solution is always unstable,here,we demonstrate that it nevertheless can be stabilized by the nonlinear lattice since the model under consideration combines the unique properties of both the linear and nonlinear lattices.The practical possibilities for experimental realization of the predicted solutions are also discussed.     

Discrete breathers in two-dimensional Josephson-junction arrays

We have proposed theoretically and studied numerically the existence of discrete breathers (intrinsic localized modes) in the dynamics of a two-dimensional Josephson-junction array biased by radio-frequency fields. The solutions are linearly stable in the framework of the Floquet theory and robust in the presence of thermal fluctuations. We have also discussed the conditions for realizing an experimental detection of these modes.