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

The propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of a model where the material medium is represented by anharmonic oscillators with cubic nonlinearities (Duffing model) and waves can propagate only in the right direction. The system of reduced Maxwell-Duffing equations admits two families of exact analytical solutions in the form of solitary waves. These are bright spikes propagating on a zero backgroun...

Propagation of extremely short electromagnetic pulses in a homogeneous doubly-resonant medium is considered in the framework of the total Maxwell-Duffing-Lorentz model, where the Duffing oscillators (anharmonic oscillators with cubic nonlinearities) represent the dielectric response of the medium, and the Lorentz harmonic oscillators represent the magnetic response. The wave propagation is governed by the one-dimensional Maxwell equations. It is shown that the model possess...

Propagation of extremely short unipolar pulses of electromagnetic field ("videopulses") is considered in the framework of a model in which the material medium is represented by anharmonic oscillators (approximating bound electrons) with quadratic and cubic nonlinearities. Two families of exact analytical solutions (with positive or negative polarity) are found for the moving solitary pulses. Direct simulations demonstrate that the pulses are very robust against perturbations....

The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of t...

We study the propagation of ultra-short pulses in a cubic nonlinear medium. Using multiple-scale technique, we derive a new wave equation that preserves the nonlocal dispersion present in Maxwell's equations. As a result, we are able to understand how ultra-short nonlinear shocks are stabilized by dispersive terms. A delicate balance between dispersion and nonlinearity leads to a new type of solitary waves. Their stability is confirmed by numerical simulations of full Maxwell...

In this article we consider one dimensional model of an ultra short pulse propagation in isotropic dispersionless media taking into account a nonlinearity of the third order. We introduce a method for Maxwell's equations transformation based on a complete set of projecting operators. The operators generally correspond wave dispersion branches. As a simplest result of the method application we derive a system of equations describing dynamics of ultrashort pulses of opposite di...

The short pulse (SP) equation is a novel model equation describing the propagation of ultra-short optical pulses in nonlinear media. This article reviews some recent results about the SP equation. In particular, we focus our attention on its exact solutions. By using a newly developed method of solution, we derive multisoliton solutions as well as 1-and 2-phase periodic solutions and investigate their properties.

Propagation of the extremely short electromagnetic pulse in non-linear dielectric media without the slowly varying envelope approximation is discussed. The models under consideration take into account both resonant and not-resonant excitations of non-linear medium, and polarisation states of electromagnetic wave. Steady state solutions of the relevant equations are presented for certain of these models.

Sinusoidal wave solutions are obtained for reduced Maxwell-Duffing equations describing the wave propagation in a non-resonant atomic medium. These continuous wave excitations exist when the medium is initially polarized by an electric field. Other obtained solutions include both mono-frequency and cnoidal waves.

In electrodynamics courses and textbooks, the properties of plane electromagnetic waves in both conducting and non-conducting media are typically studied from the point of view of the prototype case of a monochromatic plane wave. In this note an approach is suggested that starts from more general considerations and better exploits the independence of the Maxwell equations.