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. 2008 May;77(5 Pt 2):056606. doi: 10.1103/PhysRevE.77.056606. Epub 2008 May 19.
We introduce a model combining basic elements of conservative systems which give rise to gap solitons, i.e., a periodic potential and self-defocusing cubic nonlinearity, and dissipative terms corresponding to the complex Ginzburg-Landau (CGL) equation of the cubic-quintic type. The model may be realized in optical cavities with a periodic transverse modulation of the refractive index, self-defocusing nonlinearity, linear gain, and saturable absorption. By means of systematic simulations and analytical approximations, we find three species of stable dissipative gap solitons (DGSs), and also dark solitons. They are located in the first finite band gap, very close to the border of the Bloch band separating the finite and the semi-infinite gaps. Two species represent loosely and tightly bound solitons, in cases when the underlying Bloch band is, respectively, relatively broad or very narrow. These two families of stationary solitons are separated by a region of breathers. The loosely bound DGSs are accurately described by means of two approximations, which rely on the product of a carrier Bloch function and a slowly varying envelope, or reduce the model to CGL-Bragg equations. The former approximation also applies to dark solitons. Another method, based on the variational approximation, accurately describes tightly bound solitons. The loosely bound DGSs, as well as dark solitons, are mobile, and their collisions are quasielastic.
我们引入了一个模型，该模型结合了保守系统的基本元素，这些元素会产生带隙孤子，即周期性势和自散焦三次非线性，以及与三次 - 五次型复金兹堡 - 朗道（CGL）方程相对应的耗散项。该模型可以在具有周期性横向调制折射率、自散焦非线性、线性增益和饱和吸收的光学腔中实现。通过系统的模拟和解析近似，我们发现了三种稳定的耗散带隙孤子（DGSs）以及暗孤子。它们位于第一个有限带隙中，非常接近分隔有限隙和半无限隙的布洛赫带的边界。两种类型分别表示松散束缚孤子和紧密束缚孤子，分别对应于基础布洛赫带相对较宽或非常窄的情况。这两类静止孤子被一个呼吸子区域隔开。松散束缚的DGSs可以通过两种近似精确描述，一种近似依赖于载波布洛赫函数与缓慢变化包络的乘积，另一种近似将模型简化为CGL - 布拉格方程。前一种近似也适用于暗孤子。另一种基于变分近似的方法可以精确描述紧密束缚孤子。松散束缚的DGSs以及暗孤子是可移动的，并且它们的碰撞是准弹性的。
