In this thesis, we investigated the properties of the defect mode in one dimensional phtonic band structure(PBS). We studied the structures $(HL)^nD(LH)^n(HL)^nD(LH)_nL$, $L(HL)^nD(LH)^nL$ where H and L means layers with hign refrative index and low one, respectively.
First we found that the frequency of the defect mode is determined not only by the optical thickness of the defect layer (refractive index × thickness of the defect layer.) but also, by the impedence of the defect layer($\sqrt{\mu/\epsilon}$)
Second the transmittance is determined from the two boundary layers and does not vary as n, the number of periods is increased. Aa n is increased, Just the peak becomes sharper. And when both of two boundary layer are same, that is to say, both are H or L, T is 1 and does not vary as the frequency of the defect mode varies. But When one is H and the other is L, T < 1, and minimum at the center of bandgap and maximum at the edge of the bandgap.
Third we investigate the defect mode of the hetero PBG which consists of PBS's with different photonic bandgap. In this PBG, the defect mode exists only in the common frequency region of each PBG. And the defect peak is maximum at the center of this common PBG and minimum at its edge. Using the hetero PBG with defect, we propose a broad stopband filter which has a transimission peak and a stopband filter which has more than one transmission peaks at whatever frequency we need.
And We developed one dimensional field Calculation method using Trans fer Matrix. And this method may be applied to the two dimensional one.
