Defect modes properties in self-similar fractal multilayer structures containing lossless single negative metamaterials

Transfer matrix method is used to investigate the electromagnetic transmission spectra of a one-dimensional photonic fractal multilayer structure composed of single-negative metamaterial when common positive dielectric defect layers of are introduced. It is found that the frequency of the resonance defect modes can be tuned independently by varying the defect layer thicknesses. It is also found that by increasing the value of refractive index of defect layers and the number of periods, the full width half maximum of defect modes will be narrowed and shifted to lower frequencies. Also, our investigations show that for both TE and TM polarizations moving away from normal incidence to oblique incidence shows that the defect modes shift to upper frequencies. In other words, the defect modes inside the band gap depend on the incident angle and polarization. More interesting, for angles of incidence greater than 55° the defect modes for TE polarization (unlike to TM polarization) are eliminated. Moreover, the electromagnetic fields in the defect layers are strongly localized, and they can be excite independently. We believe that the proposed fractal structures can be useful in designing tunable independently high-Q filters with specific channels by adjusting their structural parameters.