Terahertz transmission properties of a stage 3 triadic-Cantor-set photonic crystal (S3 TCS PC) containing a semiconductor of n-InSb are theoretically investigated. With the resonant frequency in the permittivity function of n-InSb, transmission responses can be classified as three regions. In the two regions with frequencies well above and below the resonant frequency, the permittivity functions are nearly a positive constant and n-InSb is dielectric-like. For these two regions, transmittance response of S3 TCS PC at a given number of periods Np reveals that, within a photonic band gap, there are two groups of defect modes with numbers of Np and Np-1, respectively. Defect modes are shown to be blue-shifted as the angle of incidence increases for both TE and TM waves. Additionally, adjusting the layer thickness enables us to control mode positions for the group of (Np-1)-mode, but the one with Np-mode is not able to be controlled. In a region of 5.1-6.2 THz, where the loss is large, there also are many transmission modes.
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