Efficient Adaptive Step Size Method for the Simulation of Supercontinuum Generation in Optical Fibers
Efficient Adaptive Step Size Method for the Simulation of Supercontinuum Generation in Optical Fibers
复制标题
DOI：
10.1109/jlt.2009.2021538
复制
发表时间：
2009-09-15
影响因子：
4.7
通讯作者：
Heidt, Alexander M.
中科院分区：
文献类型：
--
作者：
Heidt, Alexander M.
使用自适应步长选择可显着减少广义非线性薛定谔方程 (GNLSE) 数值求解的计算量。最常用的自适应步长方法是基于通过应用步长加倍和局部外推来估计局部误差。虽然该方法与全局二阶分步傅里叶（SSF）积分方案结合使用效果良好，但当使用最近引入非线性光学领域的交互图（RK4IP）方法中的高精度四阶龙格-库塔积分时，可以显着改善该方法。结果表明，可以使用守恒量误差（CQE）来估计局部误差，而无需步长加倍。详细解释了求解 GNLSE 的 CQE 方法，此外，该概念被转移到普通非线性薛定谔方程中，并扩展到包括线性损耗。事实证明，RK4IP-CQE 组合是光纤中超短脉冲传播建模最有效的算法，相对于局部误差方法，计算量减少了近 50%。
The use of an adaptive step size selection significantly reduces the computational effort for the numerical solution of the generalized nonlinear Schrodinger equation (GNLSE). The most commonly employed adaptive step size method is based on the estimation of the local error by applying step size doubling and local extrapolation. While this method works well in combination with the globally second-order split-step Fourier (SSF) integration scheme, it can be significantly improved when the highly accurate fourth-order Runge-Kutta in the Interaction Picture (RK4IP) method is used for integration, which was recently introduced into the nonlinear optics field. It is demonstrated that the local error can then be estimated using a conservation quantity error (CQE) without the necessity of step size doubling. The CQE method for solving the GNLSE is explained in detail, and in addition the concept is transferred to the normal nonlinear Schrodinger equation and extended to include linear loss. The RK4IP-CQE combination proves to be the most efficient algorithm for the modeling of ultrashort pulse propagation in optical fiber, reducing the computational effort by up to similar to 50% relative to the local error method.