s u

is that the interaction of parametric waves in s2d focus is proportional to Im in a Kerr x medium and 1/2 s2dx media can lead to the formation of higher-dimensional solitons (or, more properly, solitonlike waves). More recently, the problem has been re-visited by Hayata and Koshiba,6 who analyzed mul-tidimensional confinement, using an approximate solitary-wave solution in a phase-matched configu-ration. Our goal here is to identify the conditions required for the actual excitation of (2 1 1) soli-tons and to show that indeed these solitons form under a variety of currently accessible experimental conditions, in the presence of finite mismatch and linear walk-off between the fundamental and second-harmonic waves. We consider cw light beams traveling in a x s2d ac-tive bulk crystal. We write the electric field of each of the waves in the form Esr, td Asrdexpsikz 2 ivtd, to Im in a x medium, with Im being the maxi-mum light intensity; in both cases, the rate at which a beam tends to diffract is proportional to h22. Be-cause energy is conserved, Imh2 may be assumed to be roughly constant when a beam with radial symme-try collapses; hence, under this assumption, the rate at which a beam diffracts is proportional to Im. In a x s3d medium the rate of diffraction matches the rate of self-focusing. In contrast, in a x s2d medium the diffraction rate will always become greater than the rate at which the beam focuses, so that Eqs. (1) will not exhibit collapse. An important point that war-rants emphasis is that the x s2d nonlinearity acts like the x s3d nonlinearity only when the coherence length is short compared with the diffractive scale length, so that the wave evolution in x s2d media can be ap-Two-dimensional solitons wi