Search results for "Linear system"

Adaptive Kerr-Assisted Transverse Mode Selection in Multimode Fibers

2019

Multimode optical fibers (MMFs) have recently regained interest because of the degrees of freedom associated with their different eigenmodes. In the nonlinear propagation regime in particular, new phenomena have been unveiled in graded-index (GRIN) MMFs such as geometric parametric instabilities and Kerr beam self-cleaning [1, 2]. The speckled pattern observed at the output of the MMF at low powers, is transformed at high powers into a bell-shaped beam close to the fundamental mode. Recent work has also demonstrated that Kerr beam self-cleaning can lead to a low-order spatial mode, different from a bell-shape, by adjusting the laser beam in-coupling conditions [3]. An attractive way to syst…

Inverse dispersion engineering in silicon waveguides

2014

We present a numerical tool that searches an optimal cross section geometry of silicon-on-insulator waveguides given a target dispersion profile. The approach is a gradient-based multidimensional method whose efficiency resides on the simultaneous calculation of the propagation constant derivatives with respect to all geometrical parameters of the structure by using the waveguide mode distribution. The algorithm is compatible with regular mode solvers. As an illustrative example, using a silicon slot hybrid waveguide with 4 independent degrees of freedom, our approach finds ultra-flattened (either normal or anomalous) dispersion over 350 nm bandwidth in less than 10 iterations.

Non-Linear Relativistic Evolution of Cosmological Perturbations in Irrotational Dust

2008

Longterm damped dynamics of the extensible suspension bridge

2010

This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the ends are pinned, long-term dynamics is scrutinized for arbitrary values of axial load p and stiffness k^2. For a general external source f, we prove the existence of bounded absorbing sets.When f is timeindependent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity and its characterization is given in terms of the steady states of the problem.

A Nonlinear Nonviscous Hydrodynamical Model for Change Transport Derived from Kinetic Theory

2002

In the paper, methods of Extended Thermodynamics are used to derive nonlinear closure relations for hydrodynamical models for charge transport in metals or in semiconductors, neglecting viscous phenomena. For the sake of simplicity only the case of single parabolic band approximation is studied. In this work the velocity v i is not considered as a small parameter; therefore, the models obtained can be useful when one wishes to study phenomena in a neighborhood of a stationary non-equilibrium process.

Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation

2004

In this paper we, to our knowledge, for the first time obtain the rate equations for Zeeman coherences in the broad line approximation and steady-state balance equations directly from optical Bloch equations without the use of the perturbation theory. The broad line approximation allows us to use the adiabatic elimination procedure in order to eliminate the optical coherences from the optical Bloch equations, but the steady-state condition allows us to derive the balance equations straightforward. We compare our approach with the perturbation theory approach as given previously and show that our approach is more flexible in analyzing various experiments. Meanwhile we also show the validity …

Interface states in polariton topological insulators

2019

We address linear and nonlinear topological interface states in polariton condensates excited at the interface of the honeycomb and Lieb arrays of microcavity pillars in the presence of spin-orbit coupling and Zeeman splitting in the external magnetic field. Such interface states appear only in total energy gaps of the composite structure when parameters of the honeycomb and Lieb arrays are selected such that some topological gaps in the spectrum of one of the arrays overlap with topological or nontopological gaps in the spectrum of the other array. This is in contrast to conventional edge states at the interface of periodic topological and uniform trivial insulators, whose behavior is dete…

Contour detection based on nonlinear discrete diffusion in a cellular nonlinear network

2001

International audience; A contour detection based on a diffusive cellular nonlinear network is proposed. It is shown that there exists a particular nonlinear function for which, numerically, the obtained contour is satisfactory. Furthermore, this nonlinear function can be achieved using analog components.

Diffusion effects in a nonlinear electrical lattice

1998

International audience; We consider a nonlinear electrical network modeling the generalized Nagumo equation. Focusing on the particular case where the initial load of the lattice consists in the superimposition of a coherent information weakly varying in space and a perturbation of small amplitude, we show that the perturbation can be eliminated quickly, almost without disturbing the information.

Remarks on quadratic Hamiltonians in spaceflight mechanics

2006

A particular family of Hamiltonian functions is considered. Such functions are quadratic in the moment variables and arise in spaceflight mechanics when the averaged system of energy minimizing trajectories of the Kepler equation is computed. An important issue of perturbation theory and averaging is to provide integrable approximations of nonlinear systems. It turns out that such integrability properties hold here.