Ultra-short pulses in linear and nonlinear media
Ultra-short pulses in linear and nonlinear media
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DOI：
10.1088/0951-7715/18/3/021
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发表时间：
2004-08
期刊：
影响因子：
1.7
通讯作者：
Y. Chung;C K R T Jones;T. Schäfer;C E Wayne
中科院分区：
文献类型：
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作者：
Y. Chung;C K R T Jones;T. Schäfer;C E Wayne
我们考虑了超短光脉冲在线性和非线性介质中的演化。对于线性情况，我们首先证明了麦克斯韦方程组的初边值问题，其中脉冲在静止介质的左端点注入可以用线性波动方程近似，然后可以进一步简化为线性短脉冲方程（SPE）。从多尺度推导的结果可以看出，在一定的时间尺度上，SPE的解与原波动方程的解保持接近。对于非线性情况，我们比较了传统非线性Schrödinger方程（NLSE）近似与SPE近似的预测结果。我们证明了这两个方程都可以用重整化群方法从麦克斯韦方程组中推导出来，从而得出了对比尺度。两方程与麦克斯韦方程的数值比较清楚地表明，随着脉冲长度的缩短，NLSE近似的精度逐渐降低，而SPE提供了越来越好的近似。
We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium at the left endpoint can be approximated by a linear wave equation which can then be further reduced to the linear short-pulse equation (SPE). A rigorous proof is given that the solution of the SPE stays close to the solutions of the original wave equation over the time scales expected from the multiple scales derivation of the SPE. For the nonlinear case we compare the predictions of the traditional nonlinear Schrödinger equation (NLSE) approximation with those of the SPE. We show that both equations can be derived from Maxwell's equations using the renormalization group method, thus bringing out the contrasting scales. The numerical comparison of both equations with Maxwell's equations shows clearly that as the pulse length shortens, the NLSE approximation becomes steadily less accurate, while the SPE provides a better and better approximation.