Multiple-wavelength-transmission filters based on Si-SiO2 one-dimensional photonic crystals

The Si/SiO2 one-dimensional photonic crystals of heterostructural multilayers with two periods, ΛA and ΛB, have great potential for multiple-wavelength-transmission filters. These structures were prepared by inserting N pairs of ΛB (as the defect region) in the middle of two sets of two pairs of ΛA, so that the structure becomes air→[(2∙ΛA)→(N∙ΛB)→(2∙ΛA)]→substrate. N means the number of ΛB pairs in the defect region. The complex refractive indices of Si and SiO2 are assumed to be 3.7+i0 and 1.5+i0 in the transfer matrix calculation. The number of transmission channels or defect branches m is given by 2N, that is, m=2N. For large N(>10), the photonic band gap exists in a normalized frequency range ω of 0.0846–0.3838, which corresponds to the wavelength range of 0.84–6.67 μm. The defect branches are placed on a branch band between two symmetric flat bands. For a filling factor η=0.406, a matching condition of optical length in two alternating layers, the branches at the center of the branch band are divide...