Propagation of exremely short pulses in non-resonant media: the total Maxwell-Duffing model

I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the competing spatially propagated models. The exact coupled bi-directional equations that this approach generates can be efficiently approximated down to a uni-directional form in cases where an optical pulse changes little over one optical cycle. They also permit a direct term-to-term comp...

A simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phenomena in cubicly nonlinear optical media. The model has a simple Poisson bracket structure with the Hamiltonian encoding all of the nonlinear coupling of the fields. The field-independence of the Poisson bracket facilitates a straightforward Hamiltonian structure-preserving discretization using fini...

A system of equations, describing the evolution of electromagnetic fields, is introduced and discussed. The model is strictly related to Maxwell's equations. As a matter of fact, the Lagrangian is the same, but the variations are subjected to a suitable constraint. This allows to enlarge the space of solutions, including for example solitary waves with compact support. In this way, without altering the physics, one is able to deal with vector waves as they were massless parti...

I derive unidirectional wave equations for fields propagating in materials with both electric and magnetic dispersion and nonlinearity. The derivation imposes no conditions on the pulse profile except that the material modulates the propagation slowly, that is, that loss, dispersion, and nonlinearity have only a small effect over the scale of a wavelength. It also allows a direct term-to-term comparison of the exact bidirectional theory with its approximate unidirectional cou...

We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced electric field.

Matrix representations of the Maxwell equations are well-known. However, all these representations lack an exactness or/and are given in terms of a {\em pair} of matrix equations. We present a matrix representation of the Maxwell equation in presence of sources in a medium with varying permittivity and permeability. It is shown that such a representation necessarily requires $8 \times 8$ matrices and an explicit representation for them is presented.

A time-domain approach is proposed for the propagation of ultrashort electro- magnetic wave packets beyond the paraxial and the slowly-varying-envelope approximations. An analytical method based on perturbation theory is used to solve the wave equation in free space without resorting to Fourier trans- forms. An exact solution is obtained in terms of successive temporal and spatial derivatives of a monochromatic paraxial beam. The special case of a radially polarized transvers...

The distinctive features of passing the two-component extremely short pulses through the nonlinear media are discussed. The equations considered describe the propagation in the two-level anisotropic medium of the electromagnetic pulses consisting of ordinary and extraordinary components and an evolution of the transverse-longitudinal acoustic pulses in a crystal containing the paramagnetic impurities with effective spin S=1/2. The solutions decreasing exponentially and algebr...

We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R}, $$ satisfying Maxwell's equations in a nonlinear and cylindrically symmetric medium. We obtain a sequence of solutions with diverging energy that is different from that obtained by McLeod, Stuart, and Troy. In addition, we consider a more general nonlinearity, controlled by an \textit{N}-function.

This work deals with exact solutions to the wave equations. We start by introducing the Non-Diffracting Waves (NDW), and by a definition of NDWs. Afterwards we recall -besides ordinary waves (gaussian beams, gaussian pulses)- the simplest non diffracting waves (Bessel beams, X-shaped pulses,...). In Sec.2 we show how to eliminate any backward-traveling components, first in the case of ideal NDW pulses, and then, in Sec.3, for realistic finite-energy NDW pulses. In particular,...