Photonic Crystal And Its Application In Numerical Simulation

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 thelight 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.