Biomedical subjects
Publications and source records attributed to D V Skryabin.
We report families of discrete optical solitons in frequency space, or spectral-discrete solitons existing in a dispersive Raman medium, where individual sidebands are coupled by coherence. The associated time-domain patterns correspond either to trains of ultrashort pulses or to weakly modulated waves. We describe the physics behind the spectral localization and study soliton bifurcations, stability, and dynamics.
We consider the coupled propagation of the pump and Stokes waves in a Raman active medium accounting for the group velocity walk off and group velocity dispersion. Interplay of the Raman coherence and the dispersion can lead to the formation of a complete band gap in the spectrum of linear waves consisting of the two consecutive subgaps located at different frequencies. Using an approximate analytic technique, we find exponentially localized solitons residing in the complete gap, and find algebraic solitons when the gap is closed. Feasibility of observation of these structures in hollow fibers is discussed.
Using cross-correlation frequency-resolved optical gating, we observe the phase-sensitive resonance in the interaction of a soliton with a continuous wave in a photonic crystal fiber. This interaction strongly depends on the difference in the phase velocities of the orthogonally polarized fiber modes and leads to generation of a new spectral peak. The spectral and temporal structure of this signal is revealed in our measurements, which are supported by analytical theory and numerical simulations.
We derive model equations for the propagation of ultrashort pulses in materials with resonant linear and quadratic nonlinear responses and find approximate soliton solutions describing all-bright and dark-bright polaritons. We report the specific phase matching condition for efficient 2nd harmonic generation, which involves detuning from the resonance. We also demonstrate that the 2nd harmonic emission by the polaritonic pulses can lead to reduction of their group velocity, having zero as a theoretical limit. Our analytical results are supported by numerical simulations.
Using analytical and numerical methods we demonstrate that the pulse propagation equations accounting for the quantum description of the Raman transition and for the optical Kerr nonlinearity have a multiparameter family of nontopological solitary wave solutions. We study properties of these solitons and report the transition from stable to unstable regimes of propagation. We also discuss the feasibility of observation of these structures in gas filled hollow-core photonic crystal fibers.
Scattering of a dispersive wave by optical solitons is studied experimentally in photonic crystal fibers in cases when the soliton and the dispersive wave have either identical or orthogonal polarization states. Observations of new resonant frequencies are reported. The experimental results are compared to numerical simulations and predictions from the recently derived wave vector matching conditions.
We develop a theory of the generation of new spectral components in optical fibers pumped with a solitonic pulse and a weak continuous wave (cw). We derive the wave number matching conditions for the above process and present an analytical method of finding the amplitudes of the generated waves. We discuss related effects of the depletion of the cw pump and spectral recoil on the soliton. We also point out examples of the generation of supercontinuum spectra in fibers, where mixing between solitons and dispersive waves plays an important role.
We derive phase-matching conditions for four-wave mixing between solitons and linear waves in optical fibers with arbitrary dispersion and demonstrate resonant excitation of new spectral components via this process.
We predict a strong effective Kerr nonlinearity in hollow-core photonic crystal fibers filled with a Raman active gas which exceeds the intrinsic Kerr nonlinearity by 2 orders of magnitude. Two-color bright-bright and dark-bright solitons supported by this nonlinearity are found and the feasibility of their experimental observation is demonstrated.
We develop a theory of the soliton self-frequency shift compensation by the resonant radiation recently observed in photonic crystal fibers. Our approach is based on the calculation of the soliton plus radiation solution of the generalized nonlinear Schrödinger (GNLS) equation and on subsequent use of the adiabatic theory leading to a system of equations governing evolution of the soliton parameters in the presence of the Raman effect and radiation. Our theoretical results are found to be in good agreement with direct numerical modeling of the GNLS equation.
We demonstrate that matter-wave solitary pulses formed from Bose condensed atoms moving inside optical lattices continuously radiate dispersive matter waves with prescribed momentum. Our analytical results for the radiation parameters and the soliton decay rate are found to be in excellent agreement with numerical modeling performed for experimentally relevant parameters.
Four-wave mixing instabilities are theoretically studied for continuous wave propagation in ultrasmall core photonic-crystal and tapered fibers. The waveguide, or geometrical, contribution to the overall dispersion of these structures is much stronger than in conventional fibers. This leads to the appearance of unstable frequency bands that are qualitatively and quantitatively different from those seen in conventional fibers. The four-wave mixing theory developed here is based on the full wave equation, which allows rigorous study of the unstable bands even when the detunings are of the order of the pump frequency itself. Solutions obtained using the generalized nonlinear Schrödinger equation, which is an approximate version of the full wave equation, reveal that it suffers from several deficiencies when used to describe four-wave mixing processes.
We report the cancellation of the soliton self-frequency shift in a silica-core photonic crystal fiber with a negative dispersion slope. Numerical and experimental results show that stabilization of the soliton wavelength is accompanied by exponential amplification of the red-shifted Cherenkov radiation emitted by the soliton. The spectral recoil from the radiation acts on the soliton to compensate for the Raman frequency shift. This phenomenon may find applications in the development of a family of optical parametric amplifiers.
Photonic crystal fibres (PCFs) offer greatly enhanced design freedom compared to standard optical fibres. For example, they allow precise control of the chromatic dispersion (CD) profile--the frequency dependence of propagation speed--over a broad wavelength range. This permits studies of nonlinear pulse propagation in previously inaccessible parameter regimes. Here we report on spectral broadening of 100-fs pulses in PCFs with anomalously flat CD profiles. Maps of the spectral and spatio-temporal behaviour as a function of power show that dramatic conversion (to both longer and shorter wavelengths) can occur in remarkably short lengths of fibre, depending on the magnitude and shape of the CD profile. Because the PCFs used are single-mode at all wavelengths, the light always emerges in a fundamental guided mode. Excellent agreement is obtained between the experimental results and numerical solutions of the nonlinear wave equation, indicating that the underlying processes can be reliably modelled. These results show how, through appropriate choice of CD, nonlinearities can be efficiently harnessed to generate laser light at new wavelengths.
We demonstrate that in the parametrically driven Ginzburg-Landau equation arbitrarily small nongradient corrections lead to qualitative differences in the dynamical properties of domain walls in the vicinity of the transition from rest to motion. These differences originate from singular rotation of the eigenvector governing the transition. We present analytical results on the stability of Ising walls, deriving explicit expressions for the critical eigenvalue responsible for the transition from rest to motion. We then develop a weakly nonlinear theory to characterize the singular character of the transition and analyze the dynamical effects of spatial inhomogeneities.
Nonlinear theory describing the dynamics of solitons in the vicinity of oscillatory instability threshold with a low frequency offset is developed. The theory is tested on the example of parametric degenerate four-wave mixing. All major predictions of our theory are in agreement with the results of direct numerical modeling. This includes the position of oscillatory instability threshold, instability rates, and various instability development scenarios.
Considering a class of Hamiltonian systems, it is demonstrated that energy of the internal modes with real frequencies supported by nonlinear waves and appearing due to perturbations breaking a continuous symmetry has its sign determined by the symmetry itself, independently of the nature of the perturbations. In particular, it is shown that negative energy modes emerge as a result of the breaking of the phase symmetry in the perturbed nonlinear-Schrödinger equation. An expression for energy of the Vakhitov-Kolokolov internal modes is also derived. Comparative analysis of the energy signs of the internal modes in these two cases explains the ubiquity of instabilities with complex frequencies of solitary and continuous waves in systems with broken phase symmetry.
We study the dynamics of cavity solitons under the influence of spatial inhomogeneities and derive generalized equations of motions. For perturbations large compared to the soliton size we find the modulus of the soliton velocity to be proportional to the gradient of the respective perturbation and that the proportionality coefficient changes sign when the soliton peak power drives the cavity beyond the resonance. For short scale perturbations solitons may be trapped at the extrema of the inhomogeneities. Shape and stability of these trapped solitons can be quasianalytically described by means of a perturbation theory. If both types of perturbations act solitons are either trapped or move depending on the strength of the respective perturbation. In the framework of a quasiparticle approach this dynamics is governed by a differential equation that holds for particle motion in a strongly viscous fluid under the action of a constant and harmonically varying force. We also show that in addition to acquiring a velocity the very existence conditions of the solitons (hysteresis curve) are affected by both kinds of perturbations. We find good quantitative agreement between our analytical results and numerical findings, which were obtained for a two wave interaction in a cavity filled with a quadratically nonlinear material.