First Observation Of Higher Order Planar Soliton Beams

Abstract

Transmission of quasi-monochromatic powerful laser beams through materials exhibiting intensity dependence of their refractive index (optical Kerr nonlinearity) frequently results in chaotic breakdown of the propagated beams. This corresponds to recognized instabilities of the solutions of the three-dimensional propagation equation (cubic nonlinear Schrödinger equation). Two -dimensional stable "soliton" solutions were found theoretically by Zakharov and Shabat in 1972 [1]. These solutions describe,for the fundamental order stable self -trapping of single mode, two -dimensional monochromatic beams through homogeneous nonlinear slab. Higher orders solutions consist in periodical narrowings and spreadings of the guided beam. We experimentally demonstrated the existence of the "first order (fundamental) soliton beam" in 1985 [2]. Now we present the first generation of second and third order soliton beams in a planar nonlinear waveguide illuminated by suitably shaped modelocked YAg /Nd laser pulses and their observation by time resolved imaging through the slit of a picosecond streak camera. -SOLITON BEAMSIntense laser beams propagating in a nonlinear Kerr and of the self induced variation of the refractive index. For in an hyperbolic secante spatial distributicin, the induced index to a self-guided propagation : it's the 1s order soliton beam medium suffer the opposite effects of diffraction a beam carrying the fundamental soliton power Ps gradient gives rise, in a two dimensional feature, (Fig. lb). For comparison we show on figure 1(a) the linear behaviour of the same beam. The second order soliton beam corresponds simply to a power fourtimes higher. In this case, preponderant nonlinear effects make the beam to converge until its size becomes sufficiently small so that diffraction dominates in turn and spreads it to its initial pattern. The propagation length above which the optical field recovers its initial distribution is called the soliton period Z ( fig. 1(c)). After that length a b d an other cycle begins.For a nine times higher power (9 Ps), corresponding to a third order soliton beam, the propagation remains periodic with the same periodicity Z but transient structures are more complex (Fig. 1(d)).Note that the beim spatial shape after a propagation over a half soliton period allows to discriminate the order of the observed soliton. Figure 1 3 -1st, 2ndAND 3rd ORDER SOLITON BEAMS OBSERVATION Soliton beams propagations may appear at precise intensity levels and require then a C.W. light source. Nevertheless, in front of the high intensities that were needed, we were obliged to use pulsed laser. So a pulse shaping stage [3] has been employed to obtain 200 ps rectangular shaped pulses from 30 ps laser pulses ( X = 0,53 microns), in order to make a quasi constant illumination. The following step consisted in the conformation of the spatial distribution of the laser beam to the soliton pattern. As soliton solutions exist only in a two dimensional propagation feature we have chosen for the nonlinear medium a CS...

Multistable dissipative structures pinned to dual hot spots

“…We stress that the shift is a property of the exact analytical solution, as given by Eqs. (4) and (6), and is not a result of the replacement of the ideal δ functions by their regularized counterparts (2). The shift effect is only observed in the parametric regions of B < 0, E > 0, or B = 0, 2 < 0, where the multistability may occur.…”

Families of spatial solitons in a two-channel waveguide with the cubic-quintic nonlinearity

“…Nevertheless, according to analysis reported in Ref. [11], effects of the loss may be neglected in physically relevant settings, as experiments in optical crystals are conducted over sufficiently short propagation distances (a few centimeters) [1,3]. It is also relevant to mention that the CQ nonlinearity was predicted [12] and recently observed [13] in composite optical media (colloids).…”

“…Self-trapping of light beams in the form of spatial solitons in planar waveguides, which was demonstrated experimentally about two decades ago [1], is one of fundamental effects in nonlinear optics . The variety of the spatial solitons may be greatly expanded if the waveguide is equipped with a multi-channel structure [2], that can be created by a permanent transverse modulation of the refractive index, or induced, in a photorefractive crystal, by a pair of laser beams (with the ordinary polarization) illuminating the crystal in transverse directions, while the probe beam, that creates the soliton(s), is launched in the extraordinary polarization [3].…”

Stable and Quasistable Spatio-Temporal Solitons in Cubic Quintic Nonlinear Media

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] It is well established that, the longitudinal pulse broadening in time owing to dispersion can be counterbalanced by nonlinearity-induced self-phase modulation (SPM), giving rise to the generation of temporal soliton. 3 On the other hand, the transverse broadening of the pulse due to self-diffraction can be counterbalanced by the nonlinearity-induced self-focusing, leading to the generation of spatial soliton.…”