Related papers: Transverse limits on the uni-directional pulse pro…
I apply the method of characteristics to both bi-directional and uni-directional pulse propagation in dispersionless media containing nonlinearity of arbitrary order. The differing analytic predictions for the shocking distance quantify the…
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 equations for optical pulses are needed to assist in describing applications in ever more extreme situations -- including those in metamaterials with linear and nonlinear magnetic responses. Here I show how to derive a single…
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…
I construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. The emphasis is on detailed…
Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully…
We investigate the interplay of diffraction and nonlinear effects during propagation of very short light pulses. Adapting the factorization approach to the problem at hand by keeping the transverse-derivative terms apart from the residual…
Propagation of few-cycle laser pulses in optical fiber is investigated beyond the unidirectional approximation. Considered medium parameters include dispersion, Kerr and Raman nonlinearities. High intensities of ~10^10 kW/cm^2 lead to…
We theoretically describe the quasi one-dimensional transverse spreading of a light pulse propagating in a defocusing nonlinear optical material in the presence of a uniform background light intensity. For short propagation distances the…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
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…
I derive directional wave equations useful for pulses propagating in beam, rod, pipe, and disk geometries by using a cylindrical coordinate system; the scheme works equally well for either long multi-cycle or single-cycle ultrashort pulses.…
We construct combined electric and magnetic field variables which independently represent energy flows in the forward and backward directions respectively, and use these to re-formulate Maxwell's equations. These variables enable us to not…
We consider in the unidirectional approximation the propagation of an ultra short electromagnetic pulse in a resonant medium consisting of molecules characterized by a transition operator with both diagonal and non-diagonal matrix elements.…
We present a systematic study on linear propagation of ultrashort laser pulses in media with dispersion, dispersionless media and vacuum. The applied method of amplitude envelopes gives the opportunity to estimate the limits of slowly…
In the spirit of continued study of general plasma wave properties we investigated the boundary problem with the simplest form of electric field pulse at the edge x=0 of half-infinite uniform plasma slab with Maxwellian electron…
In the current work we investigate the propagation of electromagnetic waves in the field of gravitational waves. Starting with simple case of an electromagnetic wave travelling in the field of a plane monochromatic gravitational wave we…
I present an overview of pulse propagation methods used in nonlinear optics, covering both full-field and envelope-and-carrier methods. Both wideband and narrowband cases are discussed. Three basic forms are considered -- those based on (a)…