Abstract: In order to design a new type of photonic crystal microcavity with a high quality factor and to study the relationship between the resonant mode wavelength and the lattice constant of a single-defect photonic crystal microcavity,the finite difference time-domain method and the Padé approximation together with Baker’s algorithm are employed to calculate the resonant mode wavelength and quality factor of air hole photonic crystal microcavities made of semiconductor material.The quality factor of this photonic crystal microcavity is 246510,and it has a linear relationship such that a change of three nanometers in the resonant mode wavelength results in a change of only one nanometer in the lattice constant of the single defect photonic crystal microcavity for a fixed hole radius.These results provide theoretical instruction for fabricating photonic crystal microcavity lasers.

Key words: photonic crystal, microcavities, semiconductor lasers, difference time-domain method, quality factor