Electromagnetic transmission through Cantor multilayers with defects

Transfer matrix method is used to investigate the electromagnetic transmission spectrum of a triadic Cantor multilayer when one or two dielectric defects are introduced. Unlike the periodic multilayer, the defects only cause frequency shift and distortion of the transmission spectrum. When the defect with a positive refractive index, we obtain a negative frequency shift. On the contrary, when the defect has negative refractive index, it causes a positive frequency shift. If we insert these two kinds of defects into the Cantor multilayer simultaneously, both frequency shifts exist, moreover, the frequency shift is a non-monotonic function of the thickness of the defects. This is different from the result of the triadic Cantor multilayer with only one defect.