Nonlinear guided waves and symmetry breaking in left-handed waveguides

We analyze nonlinear guided waves in a planar waveguide made of a left-handed material surrounded by a Kerr-like nonlinear dielectric, and predict that such a waveguide can support fast and slow symmetric and antisymmetric nonlinear modes. We study the symmetry breaking bifurcation and asymmetric modes in such a symmetric structure. The analysis of nonlinear dispersion properties of the guided waves shows that the modes can be either forward or backward.     

Optical vortex solitons and soliton clusters in photonic crystal fibres

We study higher-order nonlinear modes in the form of vortex solitons and soliton clusters propagating in the waveguides created in photonic crystal fibers made of a material with the focusing Kerr nonlinearity. We find numerically different families of such nonlinear modes with a nontrivial topology and study their bifurcations. We also study the soliton stability to propagation. We demonstrate that waveguides in photonic crystal fibers may support a variety of soliton clusters with the symmetries that may differ from the lattice symmetry. We also discuss briefly the case of a dual-core coupler created by two neighboring cores in a photonic crystal fiber and find numerically the profiles of symmetric and asymmetric nonlinear modes.     

The surface plasmon polariton dispersion relations in a nonlinear-metal-nonlinear dielectric structure of arbitrary nonlinearity

The analytic surface plasmon polaritons(SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach.We consider both asymmetric and symmetric structures.Especially,in the symmetric system,two possible modes can exist:the odd mode and the even mode.The dispersion relations of the two modes are obtained.Due to the nonlinear dielectric,the magnitude of the electric field at the interface appears and alters the dispersion relations.The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.     

Dispersion relation for surface plasmon polaritons in metal/nonlinear-dielectric/metal slot waveguides

We present the first (to our knowledge) exact dispersion relation for the transverse-magnetic surface plasmon polariton (SPP) modes of a plasmonic slot waveguide, which is formed by a nonlinear Kerr medium sandwiched between two metallic slabs. The obtained relation is then simplified to the case of small field intensities, while retaining nonlinear terms, to derive approximate dispersion equations for the symmetric and antisymmetric SPP modes.     

Nonclassical light in symmetric nonlinear directional coupler

We examine the quantum-statistical properties of light beams in a directional symmetric nonlinear coupler composed of one linear waveguide and two nonlinear waveguides operating by the second-harmonic generation. Linear and nonlinear mismatches are taken into account. Non-classical behaviour of single and compound modes in such a device is investigated. This work was partially supported by the Grant 202/96/0421 of the Czech Grant Agency and by the Complex Grant VS96028 of Czech Ministry of Education.     

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.     

Surface solitons in trilete lattices

Fundamental solitons pinned to the interface between three semi-infinite one-dimensional nonlinear dynamical chains, coupled at a single site, are investigated. The light propagation in the respective system with the self-attractive on-site cubic nonlinearity, which can be implemented as an array of nonlinear optical waveguides, is modeled by the system of three discrete nonlinear Schrödinger equations. The formation, stability and dynamics of symmetric and asymmetric fundamental solitons centered at the interface are investigated analytically by means of the variational approximation (VA) and in a numerical form. The VA predicts that two asymmetric and two antisymmetric branches exist in the entire parameter space, while four asymmetric modes and the symmetric one can be found below some critical value of the inter-lattice coupling parameter—actually, past the symmetry-breaking bifurcation. At this bifurcation point, the symmetric branch is destabilized and two new asymmetric soliton branches appear, one stable and the other unstable. In this area, the antisymmetric branch changes its character, getting stabilized against oscillatory perturbations. In direct simulations, unstable symmetric modes radiate a part of their power, staying trapped around the interface. Highly unstable asymmetric modes transform into localized breathers traveling from the interface region across the lattice without significant power loss.     

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.     

Nonlinear modes of a macroscopic quantum oscillator

We consider the Bose–Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes — a nonlinear generalisation of the (symmetric and antisymmetric) Hermite–Gauss eigenmodes of a harmonic quantum oscillator.     

Asymmetric vortex solitons in nonlinear periodic lattices

We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice and also describe novel coherent states where the populations of clockwise and anticlockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in different nonlinear lattice systems, including optically induced photonic lattices, nonlinear photonic crystals, and Bose-Einstein condensates in optical lattices.     

Optical solitons in PT periodic potentials

We investigate the effect of nonlinearity on beam dynamics in parity-time (PT) symmetric potentials. We show that a novel class of one- and two-dimensional nonlinear self-trapped modes can exist in optical PT synthetic lattices. These solitons are shown to be stable over a wide range of potential parameters. The transverse power flow within these complex solitons is also examined.     

Effects of saturation on optical bistability with coupled surface plasmons

We present exact numerical results for a symmetric layered medium (prism/Ag film/nonlinear dielectric/Ag film/prism) where the middle dielectric slab is assumed to have a saturation-type nonlinearity. We show bistable behaviour in the power dependence of the reflectivity ofp-polarized light under the condition when coupled surface modes are excited in the structure. Moreover, we study the effect of saturation on the bistable behaviour to show that multivalued character is inhibited by saturation effects. The field distributions corresponding to the minimum reflectivity states of the nonlinear structure are also presented.     

Fundamental modes in waveguide pipe twisted by saturated double-well potential

We study fundamental modes trapped in a rotating ring with a saturated nonlinear double-well potential. This model, which is based on the nonlinear Schrödinger equation, can be constructed in a twisted waveguide pipe in terms of light propagation, or in a Bose–Einstein condensate (BEC) loaded into a toroidal trap under a combination of a rotating π-out-of-phase linear potential and nonlinear pseudopotential induced by means of a rotating optical field and the Feshbach resonance. Three types of fundamental modes are identified in this model, one symmetric and the other two asymmetric. The shape and stability of the modes and the transitions between different modes are investigated in the first rotational Brillouin zone. A similar model used a Kerr medium to build its nonlinear potential, but we replace it with a saturated nonlinear medium. The model exhibits not only symmetry breaking, but also symmetry recovery. A specific type of unstable asymmetric mode is also found, and the evolution of the unstable asymmetric mode features Josephson oscillation between two linear wells. By considering the model as a configuration of a BEC system, the ground state mode is identified among these three types, which characterize a specific distribution of the BEC atoms around the trap.     

Comparative study of asymmetric versus symmetric planar slab dielectric optical waveguides

In this paper we have studied the asymmetric versus symmetric planar waveguide in terms of their usefulness in optical fiber communication systems. We have explored the thin waveguide versus thick waveguide first. Later on usefulness of asymmetric versus symmetric waveguide is carried out to target for WDM optical network application. All kinds of optical network components are fabricated on Si substrate with the point of view of their application. Here asymmetric planar structure may be more useful compared to symmetric waveguide in terms of their non-uniform power confinement properties. However, the symmetric waveguide structure may be more useful for their high power confinement properties. It is well known that the thin symmetric waveguide supports at least one mode. However the thick waveguide may support many even as well as odd modes. We study the power confinement properties for symmetric as well as asymmetric waveguide structure. We conclude that higher order modes show the nonlinear power variations. Mode field profile for various cases is discussed as well. Comparative study between asymmetric versus symmetric waveguide has a lot of significance in optical network area. It has been shown through analysis that in asymmetric waveguide, the power flows more through film region in the case of fundamental mode. Power confinement properties for asymmetric waveguide versus symmetric waveguide have been studied.     

克尔型非线性薄膜波导的TE模

对于芯区为克尔型非线性介质，覆盖层和衬底为线性介质的平板波导，用Ｋｒｙｌｏｖ－Ｂｏｇｏｌｉｕｂｏｖ－Ｍｉｔｒｏｐｏｌｓｋｙ的渐近法导出了色散方程及场分布的二阶近似数学表达式，计算量大为减少且结果精确。给出了对称和非对称情况的典型实例。     

Dispersive medium’s normal coupled modes and low threshold optical bistability in a symmetric one-dimensional photonic crystal

We present a detailed study of the dispersive medium’s normal coupled modes in a symmetric one-dimensional photonic crystals (1D PCs). The splitting, homogeneous broadening effect, and the detuning effect of the normal coupled modes can be well controlled by adjusting the parameters of the dispersive medium. The bistable behavior of the PCs with Kerr medium is also investigated and it is found that the threshold intensity of nonlinear optical bistability (OB) of 1D PCs with dispersive medium is much lower than that of structure without dispersive medium. The threshold intensity is strikingly sensitive to the coupling strength of the dispersive medium.     

The dispersion relations for surface plasmon in a nonlinear-metal-nonlinear dielectric structure

In the asymmetric and symmetric nonlinear-metal-nonlinear dielectric structures, this paper studies the analytic dispersion relation for surface plasmon in a system consisting of a thin metallic film covered on two sides media of intensity-dependent refractive indexes by applying a generalised first integral approach. Especially in the symmetric waveguide structure, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the squared magnitude of the electric field at the interface appears and alters the dispersion relations. Numerical results are compared to those from a certain approximate treatment.     

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.     

Nonlinear Spin and Pseudo-Spin Symmetric Dirac Equations

Nonlinear Dirac equations are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1 space-time, we show that these requirements result in the “conventional” quartic form of the nonlinear interaction and present the general equation for various coupling modes. These include, but not limited to, the Thirring and Gross-Neveu models. We consider the spin and pseudo-spin symmetric models and obtain a numerical solution. We also propose a two-component “minimal” pseudo-scalar coupling model.     

对称平板漏波导中的非线性导波

本文从平面波理论出发,研究了薄膜为非线性介质的对称平板漏波导的TE_0模传输特性.计算结果表明,膜厚大于一临界值时,不存在稳定的TE_0模,膜厚小于临界值时,最多能存在两种峰值场强的TE_0模.膜厚越小,两种峰值场强相差越大.