Search results for " Nonlinear"
showing 10 items of 1224 documents
Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra
1988
We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the ‘renormalization’ β factor of L(z)
Algebraic quantization on a group and nonabelian constraints
1989
A generalization of a previous group manifold quantization formalism is proposed. In the new version the differential structure is circumvented, so that discrete transformations in the group are allowed, and a nonabelian group replaces the ordinary (central)U(1) subgroup of the Heisenberg-Weyl-like quantum group. As an example of the former we obtain the wave functions associated with the system of two identical particles, and the latter modification is used to account for the Virasoro constraints in string theory.
Influence of pump coherence on the dynamic behavior of a laser
1988
The dynamic behavior of a coherently pumped single-mode unidirectional ring laser with a homogeneously broadened three-level active medium is studied. Our formulation is based on a set often real equations of the plane-wave, mean-field Maxwell–Bloch type. The instability domain in the main control parameters space is determined. Our numerical study of these equations for a parameter range of the type explored in the recent experiments by Weiss Brock [ Phys. Rev. Lett.57, 2804 ( 1986)] reveals some similarities, but striking differences between our theoretical predictions and their experimental observations are also noted.
Dynamic effects in nonlinear magneto-optics of atoms and molecules: review
2004
A brief review is given of topics relating to dynamical processes arising in nonlinear interactions between light and resonant systems (atoms or molecules) in the presence of a magnetic field.
Quantum repulsive Nonlinear Schrödinger models and their ‘Superconductivity’
1995
Abstract The fundamental role played by the quantum repulsive Nonlinear Schrodinger (NLS) equation in the evolution of our understanding of the phenomenon of superconductivity in appropriate metals at very low temperatures is surveyed. The first major work was that in 1947 by N. N. Bogoliubov, who studied the very physical 3-space-dimensions problem and super fluidity; and the survey takes the form of an actual dedication to that outstanding scientist who died four years ago. The 3-space-dimensions NLS equation is not integrable either classically or quantum mechanically. But a number of recently discovered closely related lattices in one space dimension (one space plus one time dimension) …
Parametric self-trapping in the presence of randomized quasi phase matching
2010
We report on experimental evidence of parametric spatial solitons in a quadratic crystal with randomized periodic ferroelectric poling. Two-color self-focusing via quadratic cascading overcomes the diffractive nature of both fundamental and frequency-doubled beams.
Ultraviolet quasi-phase-matched second harmonic generation in surface periodically poled lithium niobate optical waveguides
2007
The compatibility of low concentration (alpha-phase) proton exchange channel waveguides with electric field surface periodic poling of congruent lithium niobate (SPPLN) crystals has been experimentally demonstrated. With such waveguides, we obtained ultraviolet second harmonic generation (SHG) by first order quasi-phase-matching (QPM), a result made possible by the fabrication, on Z-cut LN crystals, of periodic structures with a pitch down to 750 nm. Nonlinear copropagating QPM-SHG measurements have been carried out on such structures. The pump source was a Ti:sapphire laser with a tunability range of 700-980 nm and a 40 GHz linewidth. We have measured UV continuous wave light at 390 nm by …
Growth, percolation, and correlations in disordered fiber networks
1997
This paper studies growth, percolation, and correlations in disordered fiber networks. We start by introducing a 2D continuum deposition model with effective fiber-fiber interactions represented by a parameter $p$ which controls the degree of clustering. For $p=1$, the deposited network is uniformly random, while for $p=0$ only a single connected cluster can grow. For $p=0$, we first derive the growth law for the average size of the cluster as well as a formula for its mass density profile. For $p>0$, we carry out extensive simulations on fibers, and also needles and disks to study the dependence of the percolation threshold on $p$. We also derive a mean-field theory for the threshold ne…
COST 241 intercomparison of nonlinear refractive index measurements in dispersion shifted optical fibres at =1550 nm
1997
COST 241 measurements of the nonlinear refractive index, n/sub 2/, exhibit a large scatter depending on the specific measurement technique. This is largely due to the electrostrictive contribution to the Kerr nonlinearity, as is revealed by the resonant behaviour of n/sub 2/ (with peak values up to 3.9 10/sup -20/ m/sup 2/ W/sup -1/) observed with signal modulation frequencies in the 0.11 GHz range.
AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond
2018
We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …