4.2.2 The effect of contrast indices on hybrid GF(m, n) system

In this subsection, we show the effect of the contrast indices between two alternating materials on the filtering properties. The contrast indices satisfy the following relation: Δn ¼ ns � nd with ns and nd represent the refractive indices of superconductor and dielectric, respectively. The same conditions are conserved to extract the transmission through the considered GF heterostructure.

Figure 12 gives the transmittance spectrum for different values of contract indices. We mention that the GF form exhibits a large frequency range with zero transmission and shows at limited gap a sharp transition from 0 to 1 at given Δn.

The intermediate point between inhibited and propagated waves indicates the cut-off frequency that allows the signal to propagate again, showing itself as a stop band filer. Moreover, we remark that the positions of the two cut-off frequencies fcL and fcH are very sensitive to the contrast indices. As long as Δn augments, the PBG increases similarly with the high cut-off frequency. Such interesting property may be applied to design a perfect reflector for high refractive index of superconductors. Thus, this type of reflectors exhibits a large bandwidth that contains the optical telecommunication frequency range.

Photonic Quasicrystals for Filtering Application DOI: http://dx.doi.org/10.5772/intechopen.81572

Figure 11.

Transmittance spectrums from 1D hybrid GF structure containing alternating dielectric/superconducting layers at given parameters: n set to be 2, 3 and 4 with m = 2.

## Figure 12.

Schematic representation of transmittance spectrums from 1D GF multilayered stacks at given Δn: n set to be 3,4 and 5 with nd = 1.45.
