Crasovan L C, Malomed B, Mihalache D, Lederer F
Institute of Solid State Theory and Theoretical Optics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D-07743 Jena, Germany.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Jun;59(6):7173-7. doi: 10.1103/physreve.59.7173.
A family of exact temporal solitary-wave solutions (dissipative solitons) to the equations governing second-harmonic generation in quadratically nonlinear optical waveguides, in the presence of linear bandwidth-limited gain at the fundamental harmonic and linear loss at the second harmonic, is found, and the existence domain for the solutions is delineated. Direct numerical simulations of the solitons demonstrate that, as well as the classical pulse solutions to the cubic Ginzburg-Landau equation, the dissipative solitons can propagate robustly over a considerable distance before the model's intrinsic instability leads to onset of "turbulence." Two-soliton bound states are also predicted and then found in the direct simulations. We estimate real values of the physical parameters necessary for the existence of the solitons predicted, and conclude that they can be observed experimentally. A promising application for the solitons is their use in closed-loop cavities.
在二次非线性光波导中，研究了在基波存在线性带宽受限增益且二次谐波存在线性损耗的情况下， governing二次谐波产生方程的一族精确时间孤立波解（耗散孤子），并划定了解的存在域。对孤子的直接数值模拟表明，与三次金兹堡 - 朗道方程的经典脉冲解一样，耗散孤子在模型的固有不稳定性导致“湍流”开始之前，可以在相当长的距离内稳健传播。还预测了双孤子束缚态，随后在直接模拟中发现。我们估计了所预测孤子存在所需物理参数的实际值，并得出结论，它们可以通过实验观察到。孤子的一个有前景的应用是在闭环腔中的使用。
