Solitons in a linear lattice with defects

Solitons are generated in an anharmonic linear lattice in which neighbouring atoms interact through a Morse potential by giving either a strong initial impulse or a large displacement to an end atom. Studies on the variation of the characteristic properties of the soliton with the strength of the initial pulse show that the velocity and the amplitude of the soliton increase with the strength of the initial impulse, but below a certain critical value for the initial impulse, only an oscillatory tail is generated. It is shown that when a defect is present in the lattice, a localised mode appears at the site of the defect and additional solitons travelling forward or even backwards, are generated. When two solitons collide at a defect region, they reemerge but leave a localised mode at the site of the defect. If an initial velocity is imparted to a particular particle, synchronously with the crossing of the particle by the soliton, a localised mode emerges at the site of the particle and additional solitons are also generated. When a soliton moves from a denser to a rarer medium, a strong localised pulse is created near the region of the density discontinuity and additional solitons appear; and further a weak oscillatory tail is left behind in the denser medium. On the other hand, if a soliton moves from a rarer to a denser medium, it is reflected back and a small localised mode is generated at the site of the density discontinuity. The variation of amplitude of the soliton with the velocity of propagation is also studied.     

Solitons with a localized electronic state in quasi-one-dimensional conductors with a charge-density wave

It is shown that self-trapped soliton states, in which the position of the electronic level in the Peierls gap 2Δ is shifted from the center of the gap by an amount of the order of Δ, can exist in quasi-one-dimensional conductors possessing a charge-density wave. The energy of the level is determined by the local position of the chemical potential and depends on the parameters of the crystal and the temperature. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 1, 49–54 (10 January 1996)     

Solitons in a disordered anisotropic optical medium

The radiation-mediated interaction of solitons in a one-dimensional nonlinear medium (optical fiber) with birefringent disorder is shown to be independent of the separation between solitons. The effect produces a potentially dangerous contribution to the signal lost.     

Solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain

By use of the Hartree approximation and the method of multiple scales, we investigate quantum solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain. It is shown that there exist solitons of two different quantum frequency bands: i.e., magnetic optical solitons and acoustic solitons. At the boundary of the Brillouin zone, these solitons become quantum intrinsic localized modes: their quantum eigenfrequencies are below the bottom of the harmonic optical frequency band and above the top of the harmonic acoustic frequency band.     

Nonlinear localized waves in a periodic medium

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.     

Nonlinear equations for a slow magnetogasdynamic quasi-monochromatic wave in a medium with dispersion and dissipation

Evolutionary equations are obtained in the vicinity of a singularity for a slow wave with allowance for the quadratic nonlinearity, dispersion, and dissipation. It is demonstrated that the propagation of quasi-monochromatic waves in a current-conducting gas—liquid mixture is described by ordinary differential equations for the amplitudes in the aforementioned region.     

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.     

Interaction of solitons in a medium with relaxation of gain and saturable absorption

Results of numerical simulation of soliton interaction in a laser with relaxation of gain and saturable saturation are presented. Interactions of co-and counterpropagating fast and slow solitons are analyzed. Typical scenarios of collisions and new resulting soliton-like structures are found.     

Kink dynamics in the medium with a random force and dissipation in the sine-Gordon model

Within the formalism of the Fokker-Planck equation, the influence of nonstationary external force, random force, and dissipation effects on the kink dynamics is investigated in the sine-Gordon model. The equation of evolution of the kink momentum is obtained in the form of the stochastic differential equation in the Stratonovich sense within the framework of the well-known McLaughlin and Scott energy approach. The corresponding Fokker-Planck equation for the momentum distribution function coincides with the equation describing the Ornstein-Uhlenbek process with a regular nonstationary external force. The influence of the nonlinear stochastic effects on the kink dynamics is considered with the help of the Fokker-Planck nonlinear equation with the shift coefficient dependent on the first moment of the kink momentum distribution function. Expressions are derived for average value and variance of the momentum. Examples are considered which demonstrate the influence of the external regular and random forces on the evolution of the average value and variance of the kink momentum. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 44–51, February, 2008.     

Raman lasing with a cold atom gain medium in a high-finesse optical cavity

We demonstrate a Raman laser using cold (87)Rb atoms as the gain medium in a high-finesse optical cavity. We observe robust continuous wave lasing in the atypical regime where single atoms can considerably affect the cavity field. Consequently, we discover unusual lasing threshold behavior in the system causing jumps in lasing power, and propose a model to explain the effect. We also measure the intermode laser linewidth, and observe values as low as 80 Hz. The tunable gain properties of this laser suggest multiple directions for future research.     

Dynamics of solitons in a three-level medium with linear birefringence

The dynamics of ultrashort pulses in a three-level or degenerate two-level medium is studied in the framework of integrable systems of the Maxwell-Bloch equations for pulses with a duration much longer than or comparable with the inverse transition frequency, with allowance made for linear birefringence. Using soliton-type solutions, we study the effect of birefringence on soliton conversion for different initial populations of the levels.     

有源耦合腔激光器锁模特性研究

本文在理论上首次发现有源耦合腔激光器的自启动锁模和时域调制特性,并对其进行了全面的分析和计算.对有源耦合腔激光器的自启动锁模机制和时域调制特性给予详尽的数值计算结果和清晰的物理图象解释,提出在有源耦合腔锁模激光器中可用连续泵浦源代替锁模泵浦源,而且有产生更短的光脉冲可能性.     

Plasmon-polariton transport in metal-nanoparticle chains embedded in a gain medium

Plasmon-polariton transport on chains of noncontacting noble-metal nanoparticles suffers from severe attenuation. A possible way of countering the attenuation by embedding the nanoparticle chain in an optical-gain medium is considered. It is found that short-wavelength surface polaritons can acquire exponential growth that can counter nonradiative loss. This is most pronounced for modes polarized transverse to the chain axis immediately outside the light line; this growth factor is likely to be sufficient to counterbalance losses and so lead to low-attenuation propagation of plasmon polaritons in nanoparticle chains.     

Light scattering from a magnetically tunable dense random medium with dissipation: ferrofluid

We present a semi-phenomenological treatment of light transmission through and its reflection from a ferrofluid which we regard as a magnetically tunable system of dense random dielectric scatterers with dissipation. Partial spatial ordering is introduced by the application of a transverse magnetic field that superimposes a periodic modulation on the dielectric randomness. This causes Bragg scattering that effectively enhances the scattering due to the disorder alone, and thus reduces the elastic mean free path towards Anderson localization. A theoretical treatment, based on invariant imbedding, gives a simultaneous decrease of the transmission and the reflection without change of incident linear polarisation as the spatial order is tuned magnetically to the Bragg condition, namely the light wave vector being equal to half the Bragg vector (Q). Our experimental observations are in qualitative agreement with these results. We have also given expressions for the transit (sojourn) time of the light, and for the light energy stored in the random medium under a steady illumination. The ferrofluid thus provides an interesting physical realization of effectively a “Lossy Anderson-Bragg” (LAB) cavity with which to study the effect of interplay of the spatial disorder, partial order and the dissipation on light transport. Given current interests in the light propagation, optical limiting and the storage of light in ferrofluids, the present work seems topical.     

Solitons in a molecular chain with impurities

The propagation of Davydov's soliton in the molecular chain with an impurity has been investigated. The numerical analysis demonstrates that the presence of the impurity leads to the decreasing of the soliton velocity, as well as to the localization (pinning) of the excitation in a region of space close to the impurity or even to the reflection or destruction of the soliton. The analytical results which demonstrate that the influence of the impurity is equivalent to the existence of some localized external inhomogeneous field or friction force have been obtained also.     

Diffusion in a disordered porous medium with localized phase transitions on the pore walls

We derive expressions for the mean ionic components densities of a solution diffusing in a disordered, porous medium. These expressions take into account interphase processes at the pore walls, such as crystallization of salts of the diffusing ionic component. Russian Friends of the Peoples University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 24–31, January, 1997.     

Superradiant decay of localized excitations in a linear atomic chain

The superradiant decay of localized excitations in a linear chain of two-level atoms has been investigated. It is shown that the excitation energy is not completely emitted in the cooperative stage of the process. The residual excitation forms waves propagating from the regions of initial localization to the chain edges.