克尔介质中方位偏振空间暗孤子：麦克斯韦方程组的精确解
Azimuthally polarized spatial dark solitons: exact solutions of Maxwell's equations in a Kerr medium
摘要：
空间Kerr孤子，通常与标准的傍轴非线性薛定谔方程，被证明存在所有的非傍轴订单，作为麦克斯韦方程组的精确解存在的矢量Kerr效应。更精确地说，我们证明了麦克斯韦方程组的方位极化空间暗孤子解的存在性，而精确的线极化（2+1）-D孤子不存在。我们的从头算方法预测暗孤子的存在最大场振幅的上限值，对应于约四分之一的波长的最小孤子宽度。
英文摘要：
Spatial Kerr solitons, typically associated with the standard paraxial nonlinear Schroedinger equation, are shown to exist to all nonparaxial orders, as exact solutions of Maxwell's equations in the presence of vectorial Kerr effect. More precisely, we prove the existence of azimuthally polarized, spatial, dark soliton solutions of Maxwell's equations, while exact linearly polarized (2+1)-D solitons do not exist. Our ab initio approach predicts the existence of dark solitons up to an upper value of the maximum field amplitude, corresponding to a minimum soliton width of about one fourth of the wavelength.
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