Multiple-wavelength-transmission filters based on Si-SiO_2 one-dimensional photonic crystals

摘要

The Si/SiO_2 one-dimensional photonic crystals of heterostructural multilayers with two periods, Λ_A and Λ_B, have great potential for multiple-wavelength-transmission filters. These structures were prepared by inserting N pairs of Λ_B (as the defect region) in the middle of two sets of two pairs of Λ_A, so that the structure becomes air→ [(2· Λ_A)→ (N· Λ_B)→ (2· Λ_A )]→ substrate. N means the number of Λ_B pairs in the defect region. The complex refractive indices of Si and SiO_2 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 divided into a uniform frequency interval. In particular, we claim that the transmission-defect branches can be precisely tuned by controlling the incident angles without external applied bias.