ASYMMETRIC SOLITONS IN COUPLED SECOND-HARMONIC-GENERATING WAVEGUIDES
ASYMMETRIC SOLITONS IN COUPLED SECOND-HARMONIC-GENERATING WAVEGUIDES
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DOI：
10.1103/physreve.57.1092
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发表时间：
1998
影响因子：
2.4
通讯作者：
W. Mak;B. Malomed;P. Chu
中科院分区：
文献类型：
--
作者：
W. Mak;B. Malomed;P. Chu
本文报道了两个线性耦合二次谐波波导系统中孤子的解析和数值计算结果。我们考虑了具有任意基次谐波和次谐波耦合常数的系统，以及每个波导内部任意（但相等）失配的系统（在以前的工作中，仅考虑了相等耦合常数的极限情况和单个失配值）。确定了非平凡非对称孤子态存在的两个区域，以及它们从明显对称孤子分叉的分岔线。解析方法是基于变分近似，然后直接数值解平稳常微分方程。除了在一个非常狭窄的参数区域，孤子的二次谐波分量正在改变其符号，具有非单调形状外，分析结果和数值结果是相当一致的。我们进一步建立了非对称孤子的稳定性，模拟了相应的偏微分方程，同时证明了共存的对称孤子是不稳定的。然后，我们详细分析了两个核心之间的行走（空间错位）的影响。我们证明了非对称孤子在偏离较小的情况下保持稳定。当渐行渐远时，孤子发生强烈的畸变，渐行渐远时孤子最终发生破坏。
We report results of analytical and numerical consideration of solitons in a system of two linearly coupled second-harmonic-generating waveguides. We consider the system with arbitrary coupling constants for the fundamental and second harmonics, and with an arbitrary (but equal) mismatch inside each waveguide (in a previous work, only the limit case of equal coupling constants, and a single value of the mismatch, were considered). Two regions of existence of nontrivial asymmetric soliton states, along with bifurcation lines at which they bifurcate from obvious symmetric solitons, are identified. The analytical approach is based on the variational approximation, which is followed by direct numerical solution of the stationary ordinary differential equations. The analytical and numerical results are found to be in fairly good agreement, except for a very narrow parametric region, where the second-harmonic component of the soliton is changing its sign, having a nonmonotonous shape. We further establish the stability of the asymmetric solitons, simulating the corresponding partial differential equations, and simultaneously show that the coexisting symmetric solitons are unstable. We then analyze in detail the effects of a walkoff (spatial misalignment) between the two cores. We demonstrate that the asymmetric solitons remain stable if walkoff is small. When the walkoff becomes larger, the solitons get strongly distorted, and finally destruct when walkoff gets too large.