Sakaguchi Hidetsugu, Malomed Boris A
Department of Applied Science for Electronics and Materials, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Kasuga, Fukuoka 816-8580, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026606. doi: 10.1103/PhysRevE.80.026606. Epub 2009 Aug 26.
We introduce a model which integrates the complex Ginzburg-Landau equation in two dimensions (2Ds) with the linear-cubic-quintic combination of loss and gain terms, self-defocusing nonlinearity, and a periodic potential. In this system, stable 2D dissipative gap solitons (DGSs) are constructed, both fundamental and vortical ones. The soliton families belong to the first finite band gap of the system's linear spectrum. The solutions are obtained in a numerical form and also by means of an analytical approximation, which combines the variational description of the shape of the fundamental and vortical solitons and the balance equation for their total power. The analytical results agree with numerical findings. The model may be implemented as a laser medium in a bulk self-defocusing optical waveguide equipped with a transverse 2D grating, the predicted DGSs representing spatial solitons in this setting.
我们引入了一个模型，该模型将二维（2D）复金兹堡 - 朗道方程与损耗和增益项的线性 - 立方 - 五次组合、自散焦非线性以及周期性势相结合。在这个系统中，构建了稳定的二维耗散间隙孤子（DGS），包括基态孤子和涡旋孤子。孤子族属于系统线性谱的第一个有限带隙。通过数值形式以及解析近似获得了解，解析近似结合了基态孤子和涡旋孤子形状的变分描述及其总功率的平衡方程。解析结果与数值结果一致。该模型可作为配备横向二维光栅的块状自散焦光波导中的激光介质来实现，在此设置中预测的DGS代表空间孤子。
