„2+1...-dimensional stable spatial Raman solitons

نویسنده

  • M. Y. Shverdin
چکیده

The generation of stable spatial optical solitons is of great interest due to the variety of the solitons’ interactions, their particlelike characteristics, and their potential technological applications [1]. Spatial soliton formation requires a balance between the beam’s tendencies to self-focus and diffract. In bulk [three-dimensional (3D)] media, such propagation is unstable, unless the focusing nonlinearity saturates with the intensity [2,3]. Experimentally, spatial s2+1d-dimensional solitons have been demonstrated in a variety of physical systems, including photorefractive media [4,5], quadratic media [6,7], and saturable Kerr media [8,9]. While the equations governing the various types of self-trapped waves differ, the fundamental propagation and interaction properties remain the same [10]. We have recently proposed a method for generating spatial Raman solitons [11]. We adiabatically prepare a Raman transition in a single eigenstate near maximum molecular coherence by driving the medium with two opposite circularly polarized laser fields whose frequency difference is slightly detuned from the Raman resonance (Fig. 1). Depending on the sign of the detuning Dv, the adiabatically established molecular coherence is either in phase or out of phase with the strong two-photon drive. Angular-momentum conservation rules prevent Stokes and anti-Stokes sideband generation [12]. Instead the molecular coherence modifies the refractive indices of the driving lasers [13–15] and leads to either focusing or defocusing, depending on the sign on the detuning [16]. An appropriate choice of the input intensities and the two-photon detuning from the Raman resonance leads to bright sDv.0d or dark sDv,0d soliton formation. In this paper, we extend the analysis of bright Raman solitons to three spatial dimensions. We numerically and theoretically demonstrate that these solitary waves are stable to perturbations and survive soliton-soliton collisions. Stability is achieved by operating near maximum molecular coherence, urabu<1/2, and thereby saturating the Raman nonlinearity with the laser intensity. Adiabatic preparation of near maximum coherence is essential and ties this work to broadband Raman generation [17] and electromagnetically induced transparency [18]. Following Ref. [19], we consider a model Raman system excited with opposite circularly polarized pump, Ep, and Stokes, Es, lasers, oscillating at frequencies vp and vs. The analysis applies to beams propagating along the z axis with the electric field oscillating in two transverse dimensions (x and y). We assume no time variation in the propagating beam profiles. Experimentally, this can be realized using flat-top pulses. The slowly varying envelope propagation equations for the pump and the Stokes beams at steady state are

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تاریخ انتشار 2004