Few-Optical-Cycle Solitons and Pulse Self-Compression in a Kerr Medium

Abstract

In a transparent medium with instantaneous Kerr nonlinearity we find a new class of few-optical-cycle solitons and prove them to be the fundamental structures in pulse propagation dynamics. We demonstrate numerically that in the asymptotic stage of pulse propagation the input pulse splits into isolated few-cycle solitons where the quantity and their parameters are determined by the initial pulse. We generalize the concept of the high-order Schrödinger solitons to the few-cycle regime and show how it can be used for efficient pulse compression down to the single cycle duration.

To the problem of numerical simulation of gas optical breakdown on GPU

“…As a way out of this situation one can neglect reflected waves and switch to a reduced equation for laser field. In [1] and some other articles [2,3] an equation with mutual partial derivative is used to investigate evolution of paraxial laser pulses in nonlinear media. The reduced wave equation for the main component of laser field E with axial symmetry in 3D is written in the form…”

“…As a conclusion it must be pointed out that currently there are no libraries for GPU accounting for all specific features of the problem (1,2). In this paper we present an effective implementation of the double-sweep algorithm [7] developed for single GPU platforms.…”

“…Usually [1][2][3] the proposed set of equations is solved with the split-step Fourier [6] method which is based on separating the linear part from the nonlinear one and performing one evolution step along z in Fourier space with respect to time for both parts sequentially. The first linear part in Fourier space takes the following form: …”

Ultrashort pulses and short-pulse equations in 2+1 dimensions

“…In particular, considering general Kramers-Kronig or Sellmeier formulas (see, e.g., Ref. [22]), we assume that the frequency dependence ofˆ ≡ˆ (ω) andμ ≡μ(ω) can be approximated by the relationŝ…”

“…In particular, starting from Maxwell's equations, and assuming general Kramers-Kronig or Sellmeier formulas for the permittivity and permeability (see, e.g., Ref. [22]), we use a multiscale expansion method to obtain the SPE-I and SPE-II models. Then, we study the general properties of each model, present the Hamiltonian, Lagrangian, and momenta, and also obtain zero-mass constraints that are used in the simulations (and, specifically, in the preparation of the initial data).…”