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耦合广义非线性薛定谔方程的相互作用表象龙格库塔算法及其误差分析*
A fourth-order Runge-Kutta in the interaction picture algorithm for simulating coupled generalized nonlinear Schr¨odinger equation and its error analysis*
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摘要: 本文通过表象变换，将耦合广义非线性薛定谔方程(C-GNLSE)变换成相互作用表象中的向量方程，再利用向量形式的4阶龙格-库塔迭代格式，建立了一种在频域内求解 C-GNLSE 的同步更新迭代算法。通过将该向量形式的相互作用表象中的4阶龙格-库塔(V-JH-RK4IP)算法应用于高双折射光子晶体光纤中超连续谱产生的数值模拟，验证了算法的有效性，通过与现有其他典型算法的比较，表明以 V-JH-RK4IP 算法求解 C-GNLSE 具有最高的计算精度和计算效率。
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关键词:
- 耦合广义非线性薛定谔方程 (C-GNLSE) /
- 相互作用表象 /
- 4 阶龙格-库塔算法 /
- 超连续谱产生
Abstract: The numerical simulation method for accurately solving the coupled generalized nonlinear Schr¨odinger equations (C-GNLSE) is essential for describing the dynamic behavior of ultrashort pulse propagating in optical fiber and developing the corresponding nonlin-ear fiber-optic devices. C-GNLSE in the normal picture is first mapped into the interaction picture by the representation transformation, and then, the two coupled nonlinear partial differential equations in the interaction picture are solved in frequency domain, with syn-chronous data updating in each iteration step, by using the vector form of Hult’s fourth-order Runge-Kutta iterative scheme. The proposed vector form algorithm of fourth-order Runge-Kutta in interaction picture (V-JH-RK4IP) is verified by using it in simulating the supercontinuum generation in high birefringence photonic crystal fiber. Moreover, the V-JH-RK4IP algorithm also exhibits the highest accuracy and computational efficiency as compared to other classical algorithms. -
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