基于FlexPDE研究顺电相KTN晶体中大调制度全息光栅的形成

Research on Forming of Holographic Grating in Paraelectric KTN Crystals at Large Modulation Depth Based on FlexPDE

在用带输运模型研究光折变效应时,大多数情况下都限定入射的相干光调制度远小于1,对方程做线性化近似以便于求解,这在求解小调制度问题时可以达到满意的精度。但在很多实际情况下光调制度接近于1,此时线性理论不再适用。基于FlexPDE程序提出了一种新的求解方法,适用于大调制度时的情况。采用有限元算法,严格求解光折变带输运方程,研究了外加电场时顺电相KTN晶体中大调制度全息光栅的形成,给出了晶体中的空间电荷场、光激发电子、离化施主、晶体折射率等的分布情况和时间演化曲线。计算结果表明,采用FlexPDE程序不仅可以大大降低带输运模型的求解难度,而且能够实时动态显示全息光栅的形成过程,具有直观性。

The modulation of incident coherent beams is limited much less than 1 to linearize the equations easily in the study of the photorefractive effect with band transport model. The linearization can get good precision if the light modulation is small. However, in most cases the modulation approximates to 1 and the linear theory is not available any more. A new solution based on FlexPDE is put forward to solve the problem at large modulation depth. The photorefractive equations are rigorously solved based on the algorithm of finite element method. The forming of holographic grating in paraelectric KTN crystals at large modulation depth is researched. The distributions and time evolvement curves of space charge filed, light excitated electrons, ionized donors, and crystal refractive index are shown. Calculation indicates that the FlexPDE can reduce the difficulty of solving the photorefractive equations, and display the forming process with visualization of holographic grating dynamically on real time.