Vidal Sébastien, Luce Jacques, Hocquet Steve, Gouédard Claude, Calvet Pierre, Penninckx Denis
CEA, DAM, CESTA, BP No. 2, F-33114 Le Barp, France.
Appl Opt. 2012 Aug 20;51(24):5818-25. doi: 10.1364/AO.51.005818.
It is known that a linear filter may be easily compensated with its inverse transfer function. However, it was shown that this approach could also be valid even for such a complex nonlinear system as frequency conversion. As a matter of fact, it is possible to at least partly precompensate for distortions occurring within, or even downstream from, frequency conversion crystals with a simple linear optical filter set upstream. In this paper, we give the theoretical background and derive the optimum precompensation filter from simple analytical formulas even in the case of saturation. We first show the relevance of our approach for Gaussian pulses: the pulse may be short or not and chirped or not, and the same linear precompensation filter may be used as long as saturation is not reached. We then study the case of phase-modulated pulses, as can be found on high power lasers such as lasers for fusion. We show that previous experimental results are in perfect agreement with these calculations. Finally, justified by our simple analytical formulas, we present a rigorous parametrical study giving the distortion reduction for any second and third harmonic generation system in the case of phase-modulated pulses.
众所周知，线性滤波器可以很容易地用其逆传递函数进行补偿。然而，已经表明，这种方法对于诸如频率转换这样复杂的非线性系统也可能是有效的。事实上，利用设置在频率转换晶体上游的简单线性光学滤波器，至少可以部分地预补偿在频率转换晶体内部甚至下游出现的失真。在本文中，我们给出了理论背景，并从简单的解析公式中推导出了即使在饱和情况下的最佳预补偿滤波器。我们首先展示了我们的方法对于高斯脉冲的相关性：脉冲可以是短脉冲或非短脉冲，可以是啁啾脉冲或非啁啾脉冲，并且只要未达到饱和，就可以使用相同的线性预补偿滤波器。然后我们研究相位调制脉冲的情况，这种情况可以在高功率激光器（如用于核聚变的激光器）上找到。我们表明先前的实验结果与这些计算结果完全一致。最后，基于我们简单的解析公式，我们进行了严格的参数研究，给出了在相位调制脉冲情况下任何二次和三次谐波产生系统的失真降低情况。
