Solutions to the Optical Cascading Equations

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtainedComment: 21 page

Chaotic pulsations in variable stars with harmonic mode coupling

Some variable stars show multi-periodic behaviour with, among others, peaks in their power spectra at harmonically spaced frequencies with ratios 1:2:4. Such modes are nonlinearly coupled by two second-harmonic interactions and their amplitude equations are shown by a Painlevé analysis to be nonintegrable in a hamiltonian sense. Chaotic phenomena are thus expected, especially when other modes and dissipation are included. An example of stars to which this might apply is G191–16 among the variable white dwarfs

Theory of Pump Depletion and Spike Formation in Stimulated Raman Scattering

By using the inverse spectral transform, the SRS equations are solved and the explicit output data is given for arbitrary laser pump and Stokes seed profiles injected on a vacuum of optical phonons. For long duration laser pulses, this solution is modified such as to take into account the damping rate of the optical phonon wave. This model is used to interprete the experiments of Druhl, Wenzel and Carlsten (Phys. Rev. Lett., (1983) vol. 51, p. 1171), in particular the creation of a spike of (anomalous) pump radiation. The related nonlinear Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike is not a soliton.Comment: LaTex file, includes two figures in LaTex format, 9 page

INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING

Zakharov-Shabat--Ablowitz-Kaup-Newel-Segur representation for Stokes-anti-Stokes stimulated Raman scattering is proposed. Periodical waves, solitons and self-similarity solutions are derived. Transient and bright threshold solitons are discussed.Comment: 16 pages, LaTeX, no figure

Suppression and Enhancement of Soliton Switching During Interaction in Periodically Twisted Birefringent Fiber

Soliton interaction in periodically twisted birefringent optical fibers has been analysed analytically with refernce to soliton switching. For this purpose we construct the exact general two-soliton solution of the associated coupled system and investigate its asymptotic behaviour. Using the results of our analytical approach we point out that the interaction can be used as a switch to suppress or to enhance soliton switching dynamics, if one injects multi-soliton as an input pulse in the periodically twisted birefringent fiber.Comment: 10 pages, 4 figures, Latex, submitted to Phys. Rev.

Quadratic solitons as nonlocal solitons

We show that quadratic solitons are equivalent to solitons of a nonlocal Kerr medium. This provides new physical insight into the properties of quadratic solitons, often believed to be equivalent to solitons of an effective saturable Kerr medium. The nonlocal analogy also allows for novel analytical solutions and the prediction of novel bound states of quadratic solitons.Comment: 4 pages, 3 figure

Modulational instability in periodic quadratic nonlinear materials

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity can drastically alter the gain spectrum but never completely removes the instability. The low-frequency part of the gain spectrum is accurately predicted by an averaged theory and disappears for certain gratings. The high-frequency part is related to the inherent gain of the homogeneous non-phase-matched material and is a consistent spectral feature.Comment: 4 pages, 7 figures corrected minor misprint

Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in appearance of stability (instability) bands in focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolor periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns.Comment: 29 pages, 10 figure

Magnetic correlations and quantum criticality in the insulating antiferromagnetic, insulating spin liquid, renormalized Fermi liquid, and metallic antiferromagnetic phases of the Mott system V_2O_3

Magnetic correlations in all four phases of pure and doped vanadium sesquioxide V_2O_3 have been examined by magnetic thermal neutron scattering. While the antiferromagnetic insulator can be accounted for by a Heisenberg localized spin model, the long range order in the antiferromagnetic metal is an incommensurate spin-density-wave, resulting from a Fermi surface nesting instability. Spin dynamics in the strongly correlated metal are dominated by spin fluctuations in the Stoner electron-hole continuum. Furthermore, our results in metallic V_2O_3 represent an unprecedentedly complete characterization of the spin fluctuations near a metallic quantum critical point, and provide quantitative support for the SCR theory for itinerant antiferromagnets in the small moment limit. Dynamic magnetic correlations for energy smaller than k_BT in the paramagnetic insulator carry substantial magnetic spectral weight. However, the correlation length extends only to the nearest neighbor distance. The phase transition to the antiferromagnetic insulator introduces a sudden switching of magnetic correlations to a different spatial periodicity which indicates a sudden change in the underlying spin Hamiltonian. To describe this phase transition and also the unusual short range order in the paramagnetic state, it seems necessary to take into account the orbital degrees of freedom associated with the degenerate d-orbitals at the Fermi level in V_2O_3.Comment: Postscript file, 24 pages, 26 figures, 2 tables, accepted by Phys. Rev.

Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media

We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the collapse of finite-size beams, and the formation and interaction of spatial solitons.Comment: Review article, will be published in Journal of Optics B, special issue on Optical Solitons, 6 figure