Spatial resonator solitons

Spatial solitons can exist in various kinds of nonlinear optical resonators with and without amplification. In the past years different types of these localized structures such as vortices, bright, dark solitons, and phase solitons have been experimentally shown to exist. Many links appear to exist to fields different from optics, such as fluids, phase transitions, or particle physics. These spatial resonator solitons are bistable and due to their mobility suggest schemes of information processing not possible with the fixed bistable elements forming the basic ingredient of traditional electronic processing. The recent demonstration of existence and manipulation of spatial solitons in semiconductor microresonators represents a step in the direction of such optical parallel processing applications. We review some proof of principle soliton experiments on slow systems, and describe in more detail the experiments on semiconductor resonator solitons which are aimed at applications.     

Incoherently coupled screening photovoltaic spatial solitons in biased photovoltaic photorefractive crystals

Propagation characteristics and stability properties of two-component composite screening photovoltaic spatial solitons have been analyzed in this paper. Employing paraxial ray approximation, we have identified a very large family of new two-component composite screening photovoltaic solitons in photovoltaic-photorefractive crystals. These composite solitons can exist only when the carrier beams have the same polarization, wavelength and are mutually incoherent. We have identified a wide parameter space involving spatial width and power where these composite solitons can exist as a stationary entity. The identified regions of existence of solitons give a deeper understanding of these solitons and reveal some interesting properties. We have shown that composite solitons with different widths cannot propagate as a stationary entity. A relevant example has been provided where the crystal is LiNbO₃ or BaTiO₃. In addition, we have shown that in the new family of solitons, a degenerate pair with equal peak power possesses bistable property. Both paraxial theory and numerical simulation show that the identified family of composite solitons is stable.     

Nonlinear light propagation in the defect band of one-dimensional defective structures

In this paper we numerically investigate the nonlinear propagation of defect state in one-dimensional structures with defects. We investigate the nonlinear transmission spectra and the bistable response for defective structures with different index gradients. The results show that positive Kerr nonlinearity can suppress the Wannier-Stark localization. And the nonlinear response of defect states band exhibits an optical switch behavior, which may be applied to all-optical devices. And the gap solitons from these defect states are presented.     

Hysteresis of switching waves and dissipative solitons in nonlinear magnetic metamaterials

Localized structures forming in the bistable regimes in a chain of weakly coupled split ring resonators, which are the building blocks of a nonlinear magnetic metamaterial, where electric current is generated by external electromagnetic radiation, have been studied analytically and numerically. The hysteresis of the velocity of switching waves (fronts) has been revealed and discrete dissipative solitons have been found.     

Nonlinear polarization bistability in optical nanowires

Using the full vectorial nonlinear Schr?dinger equations that describe nonlinear processes in isotropic optical nanowires, we show that there exist structural anisotropic nonlinearities that lead to unstable polarization states that exhibit periodic bistable behavior. We analyze and solve the nonlinear equations for continuous waves by means of a Lagrangian formulation and show that the system has bistable states and also kink solitons that are limiting forms of the bistable states.     

非相干多分量空间双稳态孤子

非相干多分量光束在高阶非线性介质中可以形成双稳态孤子.利用相干密度法首次得到了非相干多分量双稳态孤子的解析表达式.介质的高阶非线性决定了双稳态孤子的存在范围和峰值强度.得到了光束的截止波长，最小宽度和介质的非线性条件，并研究了非相干多分量光束中相干分量的传输演化.利用稳定性条件，严格证明了非相干多分量双稳态孤子在介质中可以保持稳定传播. 关键词： 非相干多分量光束 空间孤子 双稳态     

Solitons and vortices in lasers

We give in this article the mathematical background for pattern formation in nonlinear active resonators, elucidating the relation of optics with other fields of physics, and demonstrate experimentally the existence, properties, and dynamics of: (i) vortices in lasers, (ii) bright spatial solitons in lasers with saturable absorber, and (iii) spatial solitons in degenerate parametric mixing. All these structures are by definition bistable so that they are potentially useful for parallel optical information processing. Received: 8 June 1998     

Specific Features of State Switching in Threshold Bistable Systems

A threshold bistable system is investigated near the threshold of state switching. It is shown that in spite of the fact that the equation describing this system has no stable localized structures among its solutions, their wave packets can form solitons of the nonlinear Schrödinger equation. The dynamic critical index related to the cross section of scattering on fluctuation modes is calculated in the vicinity of the same point for the second-order expansion in .     

Incoherent optical switching of semiconductor resonator solitons

We demonstrate experimentally the bistable nature of the bright resonator solitons in a semiconductor microresonator with mixed absorptive/defocusing nonlinearity and show that they can be written and erased by incoherent local optical injection. Received: 22 February 2001 / Published online: 27 April 2001     

Switching spatial dissipative solitons in a VCSEL with frequency selective feedback

The process of switching on bistable spatial dissipative solitons in a VCSEL with frequency selective feedback is analyzed experimentally and theoretically. Two regimes of successful writing of spatial solitons with an external pulse are identified: for short durations of the writing beam pulse, the input amplitude has to increase, while for longer durations, the input amplitude can remain constant. Switch on spectrograms of the frequency spectrum show a transient dynamics over many modes of the external cavity with a drift of the central frequency from higher to lower frequency. Such a multi-mode regime is almost independent of the frequency of the writing beam. It is interpreted to be due to the existence of multiple unstable solitons with different frequencies which channel the transient dynamics. Good agreement between experimental results and numerical simulations in both the time and frequency domains is found.     

Bistable soliton states and switching in doubly inhomogeneously doped fiber couplers

Switching between the bistable soliton states in a doubly and inhomogeneously doped fiber system is studied numerically. Both the cases of lossless as well as lossy couplers are considered. It is shown that both up-switching (from the low state to the high state) and down-switching (from the high state to the low state) of solitons between bistable states are realizable, if the amplification of the input soliton for up-switching and the extraction of energy from it for down-switching are suitably adjusted.     

Bright screening solitons in a photorefractive waveguide

Characteristics of propagation of bright screening solitons are studied in a photorefractive waveguide. The investigation is performed under paraxial wave approximation and Wentzel–Kramers–Brillouin–Jefferys approximation. A Gaussian ansatz for the soliton shape is used instead of the numerical solutions. The planar waveguide structure intensifies the self-focussing while decreasing the minimum or threshold power required for self trapping. The waveguide structure embedded in the crystal can self trap a soliton of power lower than the threshold power. As the waveguide parameter increases, minimum required power to self trap the beam decreases. The existence of bistable states is also predicted. Four regimes of power are identified in which the solitons behaviour is studied. Propagation of screening solitons in a photorefractive waveguide is studied in the absence of the photovoltaic and pyroelectric effect for the first time.     

Dynamical toroidal Hopfions in a ferromagnet with easy-axis anisotropy

Three-dimensional toroidal precession solitons with a nonzero Hopf index, which uniformly move along the anisotropy axis in a uniaxial ferromagnet, have been found. The structure and existence region of the solitons have been numerically determined by solving the Landau-Lifshitz equation.     

Symmetric and antisymmetric vector solitons for the fractional quadric-cubic coupled nonlinear Schrödinger equation

The fractional quadric-cubic coupled nonlinear Schrödinger equation is concerned, and vector symmetric and antisymmetric soliton solutions are obtained by the square operator method. The relationship between the Lévy index and the amplitudes of vector symmetric and antisymmetric solitons is investigated. Two components of vector symmetric and antisymmetric solitons show a positive and negative trend with the Lévy index, respectively. The stability intervals of these solitons and the propagation constants corresponding to the maximum and minimum instability growth rates are studied. Results indicate that vector symmetric solitons are more stable and have better interference resistance than vector antisymmetric solitons.     

Optical solitons in fiber Bragg gratings having Kerr law of refractive index with extended Kudryashov’s method and new extended auxiliary equation approach

This paper reveals optical solitons and other solutions to fiber Bragg gratings with dispersive reflectivity having Kerr law of nonlinear refractive index. Bragg gratings are indeed a technological marvel that supplements chromatic dispersion when its count runs low. The extended Kudryashov’s method and new extended auxiliary equation method have been implemented. Chirped and chirp–free bright, dark and singular solitons, with dispersive reflectivity, are presented.     

Solitons in thermal media with periodic modulation of linear refractive index

We address the existence and properties of solitons in thermal media with periodic modulation of linear refractive index. Many kinds of solitons in such optical lattices, including symmetric and antisymmetric lattices, are found under different conditions. We study the influence of the refractive index difference between two different layers on solitons. It is also found that there do not exist cutoff value of propagation constant and soliton power for shifted lattice solitons. In addition, the solitons launched away from their stationary position may propagate without oscillation when the confinement from lattices is strong.     

Two-dimensional optical lattice solitons

We study various families of two-dimensional discrete or lattice solitons, and show that they are possible only when their power level exceeds a critical threshold. In addition, we show that gap-lattice solitons exist only when the lattice possesses a complete 2D band gap. Our results suggest that these conditions are universally valid, irrespective of the nature of the nonlinearity or the specific structure of the index lattice. The analysis explains fundamental aspects of behavior of two-dimensional discrete solitons that have been very recently observed in photosensitive optical crystals.     

Gap Solitons in Fractional Dimensions With a Quasi‐Periodic Lattice

The existence and stability of gap solitons in the nonlinear fractional Schrödinger equation are investigated with a quasi‐periodic lattice. In the absence of nonlinearity, the exact band‐gap spectrum of the proposed system is obtained, and it is found that the spectrum gap size can be adjusted by the sublattice depth and the Lévy index. Under self‐defocusing nonlinearity, both in‐phase and out‐of‐phase gap solitons have been searched in the first four gaps. It is revealed that in‐phase gap solitons are generally stable in wide regions of their existence, whereas stable out‐of‐phase gap solitons can only exist in the fourth spectrum gap. Linear stability analysis of gap solitons is in good agreement with their corresponding nonlinear evolutions in fractional dimensions. The presented numerical findings may lead to interesting applications, such as transporting of light beams through the optical medium, and other areas connected with the Kerr effect and fractional effect.     

Oscillatory behavior of spatial soliton in a gradient refractive index waveguide with nonlocal nonlinearity

Oscillatory behavior of spatial solitons in a transverse parabolic gradient refractive index distribution (GRIN) waveguide with both local and nonlocal nonlinearity is investigated. Dynamics of such solitons are analyzed by the effective-particle approach method. For weak nonlocal nonlinearity, solitons oscillate in transverse direction periodically during propagation. The normalized width and maximum of refractive index variation of the waveguide play a key role in determining the oscillating period while the position of soliton oscillatory center is slightly influenced by the nonlocal nonlinearity. Stronger nonlocal nonlinearity leads to instability of the oscillatory solitons. Furthermore, the dynamics of the solitons are simulated numerically and good agreements are obtained between the analysis and numerical results. This behavior may be used in all-optical routers, switches etc. PACS 42.65.Tg; 42.65.Jx; 42.65.Wi     

有偏压中心对称光折变晶体中的屏蔽孤子

给出了中心对称光折变晶体中屏蔽孤子的高阶空间电荷场.当高阶项可以忽略时,这个电荷场就变为早前在中心对称光折变晶体中研究的屏蔽孤子的空间电荷场.研究了中心对称光折变晶体中屏蔽孤子的高阶非线性波动方程.在适当的条件下,这个非线性波动方程能够展示明暗空间光孤子.这类晶体不同于非中心对称晶体,其非线性折射率的改变来源于二次电光效应,而不是一般的线性电光效应.应用光束传播的方法,对这些孤子的稳定性进行了讨论.表明在小的微扰下这类孤子是稳定的,不会发生分裂.