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首页> 外文期刊>Optics Letters >Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity
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Stable two-dimensional solitons supported by radially inhomogeneous self-focusing nonlinearity

机译：径向非均匀自聚焦非线性支撑的稳定二维孤子

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摘要

We demonstrate that modulation of the local strength of the cubic self-focusing (SF) nonlinearity in the two-dimensional geometry, in the form of a circle with contrast (DELTA)g of the SF coefficient relative to the ambient medium with a weaker nonlinearity, stabilizes a family of fundamental solitons against the critical collapse. The result is obtained in an analytical form, using the variational approximation and Vakhitov-Kolokolov stability criterion, and corroborated by numerical computations. For the small contrast, the stability interval of the soliton's norm scales as (DELTA)N approx (DELTA)g (the replacement of the circle by an annulus leads to a reduction of the stability region by perturbations breaking the axial symmetry). To further illustrate this mechanism, we demonstrate, in an exact form, the stabilization of one-dimensional solitons against the critical collapse under the action of a locally enhanced quintic SF nonlinearity.
机译：我们证明了二维几何形状中立方自聚焦（SF）非线性局部强度的调制，形式为圆形，SF系数相对于周围介质的对比度为（DELTA）g，非线性较弱，可以稳定一系列基本孤子，以防止严重崩溃。使用变分近似和Vakhitov-Kolokolov稳定性准则以解析形式获得结果，并通过数值计算得到证实。对于小的反差，孤子范数的稳定区间为ΔN约Δg（用圆环代替圆会导致扰动破坏轴向对称性，从而减小稳定区域）。为了进一步说明这种机制，我们以精确的形式证明了在局部增强的五次SF非线性作用下，一维孤子对临界坍塌的稳定作用。

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