Control of ultrashort pulses in nonlinear dispersive media

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Hamiltonian structure of propagation equations for ultrashort optical pulses

A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation is first simplified using an unidirectional approximation. All non-resonant nonlinear terms are then rigorously eliminated using a suitable change of variables in the spirit of the canonical perturbation theory. The derived propagation equation operates with a properly defined complexification of the real electric field. It accounts for arbitrary dispersion, four-wave mixing processes, weak absorption, and arbitrary pulse duration. Thereafter the so called normal variables, i.e., classical fields corresponding to the quantum creation and annihilation operators, are introduced. Neglecting absorption we finally derive the Hamiltonian formulation. The latter yields the most essential integrals of motion for the pulse propagation. These integrals reflect the time-averaged fluxes of energy, momentum, and classical photon number transferred by the pulse. The conservation laws are further used to control the numerical solutions when calculating supercontinuum generation by an ultrashort optical pulse

Hamiltonian structure of propagation equations for ultrashort optical pulses

A Hamiltonian framework is developed for a sequence of ultrashort optical pulses propagating in a nonlinear dispersive medium. To this end a second-order nonlinear wave equation is first simplified using an unidirectional approximation. All non-resonant nonlinear terms are then rigorously eliminated using a suitable change of variables in the spirit of the canonical perturbation theory. The derived propagation equation operates with a properly defined complexification of the real electric field. It accounts for arbitrary dispersion, four-wave mixing processes, weak absorption, and arbitrary pulse duration. Thereafter the so called normal variables, i.e., classical fields corresponding to the quantum creation and annihilation operators, are introduced. Neglecting absorption we finally derive the Hamiltonian formulation. The latter yields the most essential integrals of motion for the pulse propagation. These integrals reflect the time-averaged fluxes of energy, momentum, and classical photon number transferred by the pulse. The conservation laws are further used to control the numerical solutions when calculating supercontinuum generation by an ultrashort optical pulse

GNLStools.py: A generalized nonlinear Schrödinger Python module implementing different models of input pulse quantum noise

We provide Python tools enabling numerical simulation and analysis of the propagation dynamics of ultrashort laser pulses in nonlinear waveguides. The modeling approach is based on the widely used generalized nonlinear Schrödinger equation for the pulse envelope. The presented software implements the effects of linear dispersion, pulse self-steepening, and the Raman effect. The focus lies on the implementation of input pulse shot noise, i.e. classical background fields that mimic quantum noise, which are often not thoroughly presented in the scientific literature. We discuss and implement commonly adopted quantum noise models based on pure spectral phase noise, as well as Gaussian noise. Coherence properties of the resulting spectra can be calculated. We demonstrate the functionality of the software by reproducing results for a supercontinuum generation process in a photonic crystal fiber, documented in the scientific literature. The presented Python tools are open-source and released under the MIT license in a publicly available software repository

Supercontinuum generation by the modelation instability

We report on a numerical study of supercontinuum generation in a single-mode optical fiber by the modulation instability. An ultrabroadband octave-spanning continuum is generated for femtosecond pulses with subkilowatt peak power. In particular, we investigate the influence of higher-order effects such as third- and fourth-order dispersion, self-steepening and intrapulse Raman scattering on the supercontinuum generation

Limit for pulse compression by pulse splitting

We have detected a fundamental pulse-compression limit for high-nonlinear fibers in the normal dispersion regime near the zero-dispersion wavelength. The desired generation of a broadband continuum by self-phase modulation is limited by already small amounts of third-order dispersion, which results in pulse splitting above a critical pulse power. We investigate the critical fiber length in dependence on pulse- and fiber parameters

Dynamo action in cellular convection

The dynamo properties of square patterns in Boussinesq Rayleigh-Benard convection in a plane horizontal layer are studied numerically. Cases without rotation and with weak rotation about a vertical axis are considered, particular attention being paid to the relation between dynamo action and the kinetic helicity of the flow. While the fluid layer is symmetric with respect to up-down reflections, the square-pattern solutions may or may not possess this vertical symmetry. Vertically symmetric solutions, appearing in the form of checkerboard patterns, do not possess a net kinetic helicity and we find them to be incapable of dynamo action at least up to magnetic Reynolds numbers of ≈ 12000. Vertically asymmetric squares, a secondary convection pattern appearing via the skewed varicose instability of rolls and being characterized by rising (descending) motion in the centers and descending (rising) motion near the boundaries, can in turn be devided into such that possess full horizontal square symmetry and others lacking also this symmetry. The flows lacking both the vertical and horizontal symmetries are particularly interesting in that they possess kinetic helicity and show kinematic dynamo action even without rotation. The generated magnetic fields are concentrated in vertically oriented filamentary structures near cell boundaries. The dynamos found in the nonrotating case are, however, always only kinematic, never nonlinear dynamos. Nonlinearly the back-reaction of the magnetic field then forces the flow into the basin of attraction of a roll-pattern solution incapable of dynamo action. But with rotation added parameter regions are found where a subtle balance between the Coriolis and Lorentz forces enables nonlinear dynamo action of stationary asymmetric squares. In some parameter regions this balance leads to nonlinear dynamos with flows in the form of oscillating squares or stationary modulated rolls

Analysis of the interplay between soliton fission and modulation instability in supercontinuum generation

We investigate the generation mechanisms for ultrawide spectra in nonlinear optical fibers. Soliton fission and modulation instability represent fundamental mechanisms for the generation process. The primary origin of the spectral broadening changes with the pump-pulse duration. Soliton fission dominates for low input power and short pulses. Its efficiency for supercontinuum generation and especially the extend to the blue side can be increased by proper design of the dispersion profile. The modulation instability has a strong impact for high input powers and greatly enhances the generation process, but leads to a degradation of the coherence properties. Also for short pulses with durations of 60 fs the modulation instability is present and can hardly be suppressed. The interplay between these two effects leads to various characteristics of the resulting spectra, which are modified by to the relative impact of the modulation instability