Ablowitz Mark J, Julien Keith, Musslimani Ziad H, Weinstein Michael I
Department of Applied Mathematics, University of Colorado, Campus Box 526, Boulder, Colorado 80309-0526, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 2):055602. doi: 10.1103/PhysRevE.71.055602. Epub 2005 May 11.
A model describing wave propagation in optically modulated waveguide arrays is proposed. In the weakly guided regime, a two-dimensional semidiscrete nonlinear Schrödinger equation with the addition of a bulk diffraction term and an external "optical trap" is derived from first principles, i.e., Maxwell equations. When the nonlinearity is of the defocusing type, a family of unstaggered localized modes are numerically constructed. It is shown that the equation with an induced potential is well-posed and gives rise to localized dynamically stable nonlinear modes. The derived model is of the Gross-Pitaevskii type, a nonlinear Schrödinger equation with a linear optical potential, which also models Bose-Einstein condensates in a magnetic trap.
提出了一种描述光调制波导阵列中波传播的模型。在弱导 regime 下，从第一原理即麦克斯韦方程组推导出一个二维半离散非线性薛定谔方程，该方程添加了体衍射项和外部“光阱”。当非线性为散焦型时，通过数值方法构造了一族非交错局域模。结果表明，带有感应势的方程是适定的，并产生局域动态稳定的非线性模。所推导的模型属于格罗斯 - 皮塔耶夫斯基类型，即一个带有线性光学势的非线性薛定谔方程，它也可用于模拟磁阱中的玻色 - 爱因斯坦凝聚体。
