694 research outputs found
Nonlinear Propagation of Light in One Dimensional Periodic Structures
We consider the nonlinear propagation of light in an optical fiber waveguide
as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is
assumed to have an index of refraction which varies periodically along its
length. The wavelength of light is selected to be in resonance with the
periodic structure (Bragg resonance). The AMLE system considered incorporates
the effects non-instantaneous response of the medium to the electromagnetic
field (chromatic or material dispersion), the periodic structure (photonic band
dispersion) and nonlinearity. We present a detailed discussion of the role of
these effects individually and in concert. We derive the nonlinear coupled mode
equations (NLCME) which govern the envelope of the coupled backward and forward
components of the electromagnetic field. We prove the validity of the NLCME
description and give explicit estimates for the deviation of the approximation
given by NLCME from the {\it exact} dynamics, governed by AMLE. NLCME is known
to have gap soliton states. A consequence of our results is the existence of
very long-lived {\it gap soliton} states of AMLE. We present numerical
simulations which validate as well as illustrate the limits of the theory.
Finally, we verify that the assumptions of our model apply to the parameter
regimes explored in recent physical experiments in which gap solitons were
observed.Comment: To appear in The Journal of Nonlinear Science; 55 pages, 13 figure
Fundamentals and applications of spatial dissipative solitons in photonic devices : [Chapter 6]
We review the properties of optical spatial dissipative solitons (SDS). These are stable, self‐localized optical excitations sitting on a uniform, or quasi‐uniform, background in a dissipative environment like a nonlinear optical cavity. Indeed, in optics they are often termed “cavity solitons.” We discuss their dynamics and interactions in both ideal and imperfect systems, making comparison with experiments. SDS in lasers offer important advantages for applications. We review candidate schemes and the tremendous recent progress in semiconductor‐based cavity soliton lasers. We examine SDS in periodic structures, and we show how SDS can be quantitatively related to the locking of fronts. We conclude with an assessment of potential applications of SDS in photonics, arguing that best use of their particular features is made by exploiting their mobility, for example in all‐optical delay lines
Shock Dynamics in Layered Periodic Media
Solutions of constant-coefficient nonlinear hyperbolic PDEs generically
develop shocks, even if the initial data is smooth. Solutions of hyperbolic
PDEs with variable coefficients can behave very differently. We investigate
formation and stability of shock waves in a one-dimensional periodic layered
medium by computational study of time-reversibility and entropy evolution. We
find that periodic layered media tend to inhibit shock formation. For small
initial conditions and large impedance variation, no shock formation is
detected even after times much greater than the time of shock formation in a
homogeneous medium. Furthermore, weak shocks are observed to be dynamically
unstable in the sense that they do not lead to significant long-term entropy
decay. We propose a characteristic condition for admissibility of shocks in
heterogeneous media that generalizes the classical Lax entropy condition and
accurately predicts the formation or absence of shocks in these media
Turbulence-driven ion beams in space plasmas
The description of the local turbulent energy transfer and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at subion scales. When the small-scale energy transfer is dominated by Alfv´enic, correlated velocity, and magnetic field fluctuations, beams of accelerated particles are more likely observed. Both space observations and numerical simulations suggest the nonlinear wave-particle interaction as one possible mechanism for the energy dissipation in space plasmas
ASHEE: a compressible, equilibrium-Eulerian model for volcanic ash plumes
A new fluid-dynamic model is developed to numerically simulate the
non-equilibrium dynamics of polydisperse gas-particle mixtures forming volcanic
plumes. Starting from the three-dimensional N-phase Eulerian transport
equations for a mixture of gases and solid particles, we adopt an asymptotic
expansion strategy to derive a compressible version of the first-order
non-equilibrium model, valid for low concentration regimes and small particles
Stokes . When the model reduces to the dusty-gas one. The
new model is significantly faster than the Eulerian model while retaining the
capability to describe gas-particle non-equilibrium. Direct numerical
simulation accurately reproduce the dynamics of isotropic turbulence in
subsonic regime. For gas-particle mixtures, it describes the main features of
density fluctuations and the preferential concentration of particles by
turbulence, verifying the model reliability and suitability for the simulation
of high-Reynolds number and high-temperature regimes. On the other hand,
Large-Eddy Numerical Simulations of forced plumes are able to reproduce their
observed averaged and instantaneous properties. The self-similar radial profile
and the development of large-scale structures are reproduced, including the
rate of entrainment of atmospheric air. Application to the Large-Eddy
Simulation of the injection of the eruptive mixture in a stratified atmosphere
describes some of important features of turbulent volcanic plumes, including
air entrainment, buoyancy reversal, and maximum plume height. Coarse particles
partially decouple from the gas within eddies, modifying the turbulent
structure, and preferentially concentrate at the eddy periphery, eventually
being lost from the plume margins due to the gravity. By these mechanisms,
gas-particle non-equilibrium is able to influence the large-scale behavior of
volcanic plumes.Comment: 29 pages, 22 figure
The ultra-wideband pulse
Since the birth of mode-locking the temporal duration of optical pulses has radically
diminished. In parallel to this, bandwidths have grown so large that almost entire
frequency octaves are present in today’s few-cycle pulses.
This thesis investigates the character of ultra-wideband pulses in nonlinear environments.
Because of the growth in optical bandwidths, traditional definitions and propagation
models break down, requiring newer more accurate numerical techniques. A
novel approach capturing the uni-directionality of pulses is presented in the form of Gvariables
by combining the electric and magnetic field descriptions. These G-variables
have the advantage of both an accurate spectral representation and a reduced computational
overhead, making them significantly more efficient than existing direct Maxwell
solvers. Such approaches are particularly important where large propagation distances
and/or transverse dimensions are concerned.
Pseudo-spectral techniques play a key role in the success of these wideband models
enabling sub-cycle dynamics to be studied. One such phenomenon is Carrier Wave
Shocking (CWS), where the optical carrier undergoes self-steepening in the presence of
third-order nonlinearity. This process is carefully studied, focussing on the effect of dispersion
and the feasibility of its physical realisation. The process is then generalised to
arbitrary nonlinear order, where the quadratic form finds potential applications in High
Harmonic Generation (HHG). Shock detection schemes are also developed, and agree
with analytical solutions in the dispersionless regime.
To fully characterise few-cycle pulses, the absolute Carrier Envelope Phase (CEP)
must be known. A novel 0 − f self-referencing scheme relying on wideband interference
is investigated. By applying robust frequency domain definitions a proposal is made to
convert this scheme into one that determines absolute CEP. The scheme maps the level
of spectral interference to absolute CEP using numerical simulations
Uniformly Valid Asymptotics for Carrier’s Mathematical Model of String Oscillations
In the paper, an asymptotic analysis of G.F. Carrier’s mathematical model of string oscillation is presented. The model consists of a system of two nonlinear second order partial differential equations and periodic initial conditions. The longitudinal and transversal string oscillations are analyzed together when at the initial moment of time the system’s solutions have amplitudes proportional to a small parameter. The problem is reduced to a system of two weakly nonlinear wave equations. The resonant interaction of periodic waves is analyzed. An uniformly valid asymptotic approximation in the long time interval, which is inversely proportional to the small parameter, is constructed. This asymptotic approximation is a solution of averaged along characteristics integro-differential system. Conditions of appearance of combinatoric resonances in the system have been established. The results of numerical experiments are presented
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