Stable propagation of pulsed beams in Kerr focusing media with modulated dispersion

Abstract

We propose the modulation of dispersion to prevent collapse of planar pulsed beams which propagate in Kerr-type self-focusing optical media. As a result, we find a new type of two-dimensional spatio-temporal solitons stabilized by dispersion management. We have studied the existence and properties of these solitary waves both analytically and numerically. We show that the adequate choice of the modulation parameters optimizes the stabilization of the pulse.The analysis of the propagation of high power pulsed laser beams is among the most active fields of study in Nonlinear Optics, where the main dynamics phenomenon is the dependence of the refractive index of the materials with the amplitude of light fields. For propagation in materials showing a linear dependence of the refractive index with the laser intensity, the mathematical formulation of the beam dynamics is adequately described by the cubic nonlinear Schrödinger equation (NLSE) [1]. In this case, the excitation of optical solitons is one of the most significant phenomena [2].Despite the success of the concept of soliton, these structures mostly arise in 1+1-dimensional configurations. This is mainly due to the well known collapse property of the cubic NLSE in multi-dimensional scenarios. This implies that a two-dimensional laser beam which propagates in a Kerr-type nonlinear medium, will be strongly self-focused to a singularity if the power exceeds a threshold critical value, whereas for lower powers it will spread as it propagates. Since collapse prevents the stability of multidimensional "soliton bullets" in systems ruled by the cubic NLSE, a great effort has been devoted to search for systems with stable solitary waves in multidimensional configurations [3]. It has been recently shown that a modulation of the nonlinearity along the propagation direction in the optical material can be used to prevent the collapse of two-dimensional laser beams [4]. The concept has been extended to the case of several incoherent optical beams [5] and to the case of matter waves [6].In this paper we use a similar idea to stabilize against collapse pulsed laser beams propagating in planar waveguides. This configuration is of great importance, as it is the common experimental procedure used for exciting spatial optical solitons. Instead of making a modulation of the nonlinearity our idea is to act on the chromatic dispersion term of the NLSE. Thus, our procedure resembles that used to obtain dispersion-managed temporal solitons in optical fibers.We consider the paraxial propagation along z of a pulsed beam of finite size in time t and spatially confined by a waveguide along the y-axis. Thus, diffraction only acts in the x direction and is balanced by the selffocusing nonlinearity given by a refractive index of the form: n = n 0 + n 2 | E| 2 . The dynamics of the slowlyvarying amplitude of the pulse E is described by a 1+2D NLSE of the form:where k 0 , k ′ 0 and k ′′ 0 are respectively the wavenumber in vacuum, the inverse of the group velocity, and the group velocity disp...

A new conserved quantity for non-Kerr law optical solitons

“…The origin of nonlinear response is related to the non-harmonic motion of bound electrons under the influence of an applied field. As a result the Fourier amplitude of the induced polarization from the electric dipoles is not linear in the electric field, but involves higher terms in electric field amplitude [7,16,17,19,20].…”

“…The NLSE, which is the ideal equation in a Kerr nonlinear media. This equation is found to be completely integrable by the method of inverse scattering transform (IST) [1,20] and profound success has been achieved in the development of soliton theory in the framework of the NLSE model. However, communication grade optical fibers or as a matter of fact any optical transmitting medium does posses finite attenuation coefficient, thus optical loss is inevitable and the pulse is often deteriorated by this loss.…”