光子晶体及其应用的数值模拟研究
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摘要
光子晶体是一种存在带隙的周期结构的人造材料。其特点是光子晶体能够完全反射频率处于带隙内的电磁波或完全抑制频率处于带隙内的自发辐射。由于光子晶体能带理论是一种精确的理论，因此，在光子晶体的研究中，理论工作就有着特别重要的意义。
本文首先详细讨论了用于光子晶体能带计算的Order-N算法和直角坐标系下用于发光二极管光输出效率计算的电磁场的时域有限差分算法。
其次，我们利用一般坐标系下的Order-N算法计算了Sierpinski地毯结构光子晶体的能带。计算结果表明，这种准分形结构光子晶体的能带具有一定的自相似性。其带隙具有多频带隙的特性且带隙的中心频率会随着分形结构单元几何形状的改变而改变。当这种准分形结构光子晶体中含有理想导体时，其能带不但具有大的绝对带隙，多频带隙的特性，而且，随着分形级数的增大，能带会迅速趋向于能级结构．
再次，利用上述能带的特性，我们讨论了这种准分形结构光子晶体在波分复用滤波器上的应用。计算结果表明，通过改变分形结构单元的几何形状，我们可以较方便地调谐波分复用滤波器的滤波频率。
最后，利用直角坐标系下的时域有限差分算法，我们详细讨论了光子晶体在提高GaN发光二极管光输出效率中的作用。计算结果表明，对于GaN材料，选择石墨点阵柱状光子晶体在制备上较有利，同时，只有含中心柱结构的这种光子晶体可以提高GaN发光二极管的光输出效率。另外，在塔状光子晶体柱角度合适的情况下，塔状光子晶体柱能有效地提高GaN发光二极管的光输出效率。而光子晶体柱半径和柱心位置的随机变化会随机地改变GaN发光二极管的光输出效率。根据上述结果，我们给出了GaN光子晶体发光二极管的一般设计原则。
Photonic crystal is a kind of artificial periodic structure with photonic band gaps, which can eliminate electromagnetic wave in photonic band gaps. Because photonic band theory is accurate, the theoretical method is very important in studying photonic crystal.In this thesis, firstly, we have studied systematically the Order-N method in general coordinate, which is used in calculating the photonic band and the finite-difference time-domain method in right angle coordinate, which is used in calculating light extraction efficiency of the GaN light emitting diode.Secondly, the photonic band of Sierpinski carpet structure has been calculated by the Order-N method. The numerical results show that there are self-similarity in photonic bands and multifrequency photonic band gaps for the fractal photonic crystal, the center frequencies of the photonic band gaps are influenced by the shape of the fractal structure unit. Moreover, the photonic band of a set of fractal photonic crystal including idealized metal has been calculated by this method. The numerical results show that not only there are several and big absolute photonic band gaps, but also the photonic bands trend to energy levels rapidly with increasing the fractal orders.Thirdly, a kind of fractal photonic crystal wavelength division multiplexed filter has been studied theoretically. The numerical results show that we can tune the frequency of the filter conveniently by changing the shape of the fractal structure unit.Finally, we have systematically studied the effect of the photonic crystal on improving the light extraction efficiency of the GaN light emitting diode. The numerical results show that the graphite lattice photonic crystal with rods should be a good choice for GaN material and only this kind of photonic crystal with thick central pillar can enhance the extraction efficiency for the light emitting diode. Moreover, the results show that the tower -type photonic crystal pillars benefit the output efficiency of the light emitting diode when its angle is optimal. The results also show that the
light extraction efficiency varies randomly with the change of photonic crystal pillars in size and site in some extents randomly, but does not change very much. With the results discussing above, we have given some design rules for the photonic crystal used in the light emitting diodes.
本文首先详细讨论了用于光子晶体能带计算的Order-N算法和直角坐标系下用于发光二极管光输出效率计算的电磁场的时域有限差分算法。
其次，我们利用一般坐标系下的Order-N算法计算了Sierpinski地毯结构光子晶体的能带。计算结果表明，这种准分形结构光子晶体的能带具有一定的自相似性。其带隙具有多频带隙的特性且带隙的中心频率会随着分形结构单元几何形状的改变而改变。当这种准分形结构光子晶体中含有理想导体时，其能带不但具有大的绝对带隙，多频带隙的特性，而且，随着分形级数的增大，能带会迅速趋向于能级结构．
再次，利用上述能带的特性，我们讨论了这种准分形结构光子晶体在波分复用滤波器上的应用。计算结果表明，通过改变分形结构单元的几何形状，我们可以较方便地调谐波分复用滤波器的滤波频率。
最后，利用直角坐标系下的时域有限差分算法，我们详细讨论了光子晶体在提高GaN发光二极管光输出效率中的作用。计算结果表明，对于GaN材料，选择石墨点阵柱状光子晶体在制备上较有利，同时，只有含中心柱结构的这种光子晶体可以提高GaN发光二极管的光输出效率。另外，在塔状光子晶体柱角度合适的情况下，塔状光子晶体柱能有效地提高GaN发光二极管的光输出效率。而光子晶体柱半径和柱心位置的随机变化会随机地改变GaN发光二极管的光输出效率。根据上述结果，我们给出了GaN光子晶体发光二极管的一般设计原则。
Photonic crystal is a kind of artificial periodic structure with photonic band gaps, which can eliminate electromagnetic wave in photonic band gaps. Because photonic band theory is accurate, the theoretical method is very important in studying photonic crystal.In this thesis, firstly, we have studied systematically the Order-N method in general coordinate, which is used in calculating the photonic band and the finite-difference time-domain method in right angle coordinate, which is used in calculating light extraction efficiency of the GaN light emitting diode.Secondly, the photonic band of Sierpinski carpet structure has been calculated by the Order-N method. The numerical results show that there are self-similarity in photonic bands and multifrequency photonic band gaps for the fractal photonic crystal, the center frequencies of the photonic band gaps are influenced by the shape of the fractal structure unit. Moreover, the photonic band of a set of fractal photonic crystal including idealized metal has been calculated by this method. The numerical results show that not only there are several and big absolute photonic band gaps, but also the photonic bands trend to energy levels rapidly with increasing the fractal orders.Thirdly, a kind of fractal photonic crystal wavelength division multiplexed filter has been studied theoretically. The numerical results show that we can tune the frequency of the filter conveniently by changing the shape of the fractal structure unit.Finally, we have systematically studied the effect of the photonic crystal on improving the light extraction efficiency of the GaN light emitting diode. The numerical results show that the graphite lattice photonic crystal with rods should be a good choice for GaN material and only this kind of photonic crystal with thick central pillar can enhance the extraction efficiency for the light emitting diode. Moreover, the results show that the tower -type photonic crystal pillars benefit the output efficiency of the light emitting diode when its angle is optimal. The results also show that the
light extraction efficiency varies randomly with the change of photonic crystal pillars in size and site in some extents randomly, but does not change very much. With the results discussing above, we have given some design rules for the photonic crystal used in the light emitting diodes.
引文
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