Photonic crystals are new manual microstructure materials with periodic refractive indices distribution. The photonic crystals have photonic band gaps analogous to the electronic band gaps in semiconductors. If the frequencies of electromagnetic waves are within the photonic band gaps

they cannot propagate in the photonic crystals. We introduce the new structure in the research of photonic crystal microcavities. Two-dimension square photonic crystal microcavities composed of Al

2

O

3

are studied by plane wave expansion method. The physical mechanism and numerical simulation are detailed. We can obtain the band gap and the frequency of defect mode. The range of defect mode is 470～476nm. The spectral curve of defect mode is given by calculating the quality factor of photonic crystal microcavities. In spectral curve

there are many peak values when transmission wavelength is increased. The highest quality factor achieved at 475 nm. And more study on the effective index of cladding was performed by fully vectorial effective index method. We study the stability of photonic crystal microcavities by effective index method

and obtain the variational curve of effective index. There is a steady field when transmission wavelength is about 475nm. These methods are valuable in the design of optical devices based on photonic crystal cavities. Photonic crystal semiconductor laser and photonic crystal diode can be designed under this guidance.