Heat dissipative solitons in optical fibers

We propose a one-dimensional model governing the propagation of heat waves in an optical fiber (the “fiber fuse”). The model has solutions in the form of high temperature localized waves moving towards the input end of the fiber, fueled by the laser power. These waves can be ignited by local heating at any point along the fiber. The effect of such a wave is irreversible damage to the fiber core. The phenomenon was observed earlier by Hand and Russell, when locally heating a fiber through which CW light of modest intensity was propagating. This induced self-destruction of the optical fiber core.     

Waves that appear from nowhere and disappear without a trace

The title (WANDT) can be applied to two objects: rogue waves in the ocean and rational solutions of the nonlinear Schrödinger equation (NLSE). There is a hierarchy of rational solutions of ‘focussing’ NLSE with increasing order and with progressively increasing amplitude. As the equation can be applied to waves in the deep ocean, the solutions can describe “rogue waves” with virtually infinite amplitude. They can appear from smooth initial conditions that are only slightly perturbed in a special way, and are given by our exact solutions. Thus, a slight perturbation on the ocean surface can dramatically increase the amplitude of the singular wave event that appears as a result.     

Are rogue waves robust against perturbations?

We study the effect of various perturbations on the fundamental rational solution of the nonlinear Schrödinger equation (NLSE). This solution describes generic nonlinear wave phenomena in the deep ocean, including the notorious rogue waves. It also describes light pulses in optical fibres. We find that the solution can survive at least three types of perturbations that are often used in the physics of nonlinear waves. We show that the rational solution remains rational and localized in each direction, thus representing a modified rogue wave.     

Order parameter equation and model equation for high Prandtl number. Rayleigh-Bénard convection in a rotating large aspect ratio system

We derive the order parameter equation which describes the evolution of spatio-temporal patterns close to the Bénard instability in a rotating large aspect ratio system for high Prandtl number fluids. Since this order parameter equation contains rather complicated nonlinear terms we present a model equation which can be obtained from the order parameter equation by suitable simplification of the nonlinearity. For this model equation we calculate the family of roll solutions and investigate their stability with respect to long scale instabilities and examine the onset of the Küppers-Lortz instability. Then we present spatiotemporal patterns which are obtained from a numerical evaluation of the model equation.     

Derivation of the amplitude equation for a hydromagnetic convective problem

The amplitude equation for a convective system under a vertical magnetic field is derived. The coefficients in these equations have been numerically calculated for infinite Prandtl number fluids and for boundary conditions both free and rigid top and bottom. The results confirm that, for realistic parameter values only stationary convection can be present and the pattern is made by convective rolls.     

Far-field distribution of third-harmonic generation by two crossed beams

The far-field intensity distribution of the third harmonic generated in a thin silica plate by two laser beams crossed at a small angle comprises four peaks approximately symmetric with respect to the bisector. The measurement of the intensity ratio of the inner to the outer peaks yielded values scattered from 10 to 20, surprisingly larger than the combinatorial value 9. The phase-matching factor, as determined by the full three-dimensional calculations required by the absence of axial symmetry, accounts for the observed ratio and its fluctuations. Received: 14 November 2002 / Published online: 22 May 2003 RID="*" ID="*"Corresponding author. Fax: +7-95/1941-994, E-mail: fomichev@imp.kiae.ru     

Stimulated Raman Scattering in a Weakly Polar Ⅲ-Ⅴ Semiconductor： Effect of dc Magnetic Field and Free Carrier Concentration

Using the hydrodynamic model of semiconductor plasmas, we perform an analytical investigation of stimulated Raman scattering （SITS） of an electromagnetic pump wave in a transversely magnetized weakly polar semicon- ductor arising from electron-density perturbations and molecular vibrations of the medium both produced at the longitudinal optical phonon frequency. Assuming that the origin of SItS lies in the third-order susceptibility of the medium, we investigate the growth rate of Stokes mode. The dependence of stimulated Raman gain on the external dc magnetic field strength and free carrier concentration is reported. The possibility of the occurrence of optical phase conjugation via SItS is also studied. The steady-state Raman gain is found to be greatly enhanced by the presence of the strong external dc magnetic field.     

Incoherently coupled vector dipole soliton pairs in nonlocal media

We investigate the incoherently and strongly coupled Manakov vector dipole soliton pairs in nonlocal nonlinear media. We use variational approach, to describe analytical properties of these solutions in a strongly nonlocal regime. We show that the presence of fundamental component improve stability of the dipole nonlocal soliton. In the limit of highly nonlocal nonlinearity, the evolution behaviors of the vector solitons is determined by their total power.     

Stability of non-degenerate parametric soliton in quadratic media

The non-degenerate solitons due to three-wave mixing in a quadratic medium are analyzed. A new stability criterion for these solitons is found and verified numerically. The influence of the non-paraxial terms on the instability threshold is also discussed.     

Anti-Stokes Line in an Index-Guiding Photonic Crystal Fibre with Two Zero-Dispersion Wavelengths

An index-guiding photonic crystal fibre with a small hole in the core is fabricated. The simulated results show that the first higher order mode possesses two zero-dispersion wavelengths, and the phase-matching is possible in the anomalous dispersion regime between the two zero-dispersion wavelengths. Using 200 fs Ti： sapphire laser of 820, 830 and 840nm, the anti-Stokes line around 530nm can be generated efficiently. The maximum ratio of the anti-Stokes signal energy to the pump component in the output spectrum is estimated to be 1.03 and the conversion efficiency is above 50%.     

Method for measurements of second-order nonlinear optical coefficient based on Z-scan

The method for measuring second-order nonlinear optical coefficients based on well-known Z-scan is presented. The influence of linear absorption coefficients on normalized transmittance is discussed. Using this method, we obtained the second-order nonlinear coefficient d₃₁(5%MgO:LiNbO₃) = 4.5 × 10⁻¹² m/v at 1064 nm, which agrees well with theoretical calculations and previous well-known values.     

Incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media

We theoretically investigate the propagation of incoherently coupled Hermite-Gaussian breather and soliton pairs in strongly nonlocal nonlinear media. It is found that multipole-mode soliton pairs with arbitrary different orders of Hermite-Gaussian shape can exist when the total power of two beams equals the critical power and the ratio of the beam widths for the Gaussian part is inversely proportional to the square root of the ratio of the wave numbers. When the total power does not equal the critical power, the Hermite-Gaussian breather pair exists and their beam widths evolve analogously. For general cases where the ratio of the beam widths is arbitrary, soliton-breather pairs or breather-breather pairs can be formed and their beam widths evolve synchronously in-phase or out-of-phase. Numerical simulations directly based on the nonlocal nonlinear Schrödinger equation are conducted for comparison with our theoretical predictions. The numerical stability analysis shows the higher-order Hermite-Gaussian solitons can not be stable for small nonlocality or for some media like liquid crystals.     

Intermediate Self-similar Solutions of the Nonlinear Schrödinger Equation with an Arbitrary Longitudinal Gain Profile

We study pulse propagation in a normal-dispersion optical fibre amplifier with an arbitrary longitudinal gain profile by self-similarity techniques. We show the functional form of the development of low-amplitude wings on the parabolic pulse, which are associated with the evolution of an arbitrary input pulse to the asymptotic parabolic pulse solution. It is found that for the increasing gain the amplifier output corresponding to the input Gaussian pulse converges to the asymptotic parabolic pulse solution more quickly than the output obtained with the input hyperbolic secant pulse, whereas for the decreasing gain the input pulse profiles have nearly no effect on the speed of convergence to the parabolic pulse solution. These theoretical results are confirmed by numerical simulations.     

Homodyne detection of second-harmonic generation as a probe of electric fields

Received: 16 December 1998     

Raman diagnostics of CVD systems: Determination of local temperatures

The suitability of local temperature measurements by cw Raman spectroscopy for the CH₄/H₂ CVD system has been established. The temperature profiles in a model reactor were derived from H₂ pure rotational lines and from hot bands of thev ₁ vibrational band of CH₄. Experimental results are presented for substrate temperatures of 773 K and of 1473 K. High accuracy of measurement and excellent agreement with theoretical solutions for the temperature field within the reactor were found.     

DC-electric-field-modified second-harmonic generation at the Si(100) surface

1 resonances for clean and H covered surfaces shift as a function of the dc field in agreement with experiment. This suggests the presence of built-in electric fields whose strength depends on the H coverage, and which are strongly localized in the subsurface region. Received: 20 September 1998     

Reconstruction of spatio-temporal signals of complex systems

We propose a novel method to analyze spatiotemporal signals emerging from synergetic systems. By this approach we are able to reconstruct the spatial modes, as well as their dynamic interaction close to instabilities. Our method is an extension of the principal component analysis to the case of nonlinear self-organizing systems. We demonstrate our method by an example of a codimension one instability, apply the algorithm to a simulated Bénard instability and present a generalization to bifurcations with several order parameters.     

Effects of Pumping Sizes on THz Radiation Based on Ultrashort Light Pulse Optical Rectification for High Spatial Resolution T-Ray Imaging

We present our experimental studies on the effects of the pumping sizes on THz radiation based on ultrashort light pulse optical rectification for high spatial resolution T-Ray imaging. Our experiments show that high spatial resolution T-ray imaging requires both thin THz emitter and sample, and rigorous tolerance of the gap between the sample and the emitter, as well as small pumping size which usually much smaller compared with THz wavelength. Such a small pumping size results in dramatic decrease of the THz wave power, which originates from strong diffraction of THz wave, the depolarization of the focused tightly pumping beam, the spatial filtering of the emitter exit-surface, and the strong phase-mismatching between the pumping and the high spatial Fourier components of the THz signal, rather than two-photon absorption.     

Operator algebras related to quantum optical systems and integrations

We show that some quantum optical systems generate quantum algebras being the natural generalization of the Heisenberg-Weyl algebra. The importance of these algebras for the integration of the systems under consideration is discussed. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002. This work is supported in part by KBN grant 2 PO3 A 012 19.