4.1.5 Enhancement of PBGs by applying a particular deformation

In order to improve the characteristics of filtering channels, we apply a particular deformation <sup>h</sup> satisfying the following low <sup>y</sup> <sup>¼</sup> <sup>x</sup>hþ1, where, <sup>x</sup> and <sup>y</sup> represent the coordinates of the main and the deformed GTM heterostructures, respectively.

We recall that in the main structure, two forms of layer, H and L are organized in a GTM sequence, where H and L are the superconductor and dielectric materials, respectively.

Then, the optical phase becomes: φ<sup>j</sup>�<sup>1</sup> ¼ 2π=λx<sup>0</sup> <sup>0</sup> cos θ<sup>j</sup>�1. Here, the optical thickness ˜ ° j th � th after deformation noted <sup>x</sup><sup>0</sup> <sup>0</sup> satisfied the following form: x<sup>0</sup> <sup>0</sup> ¼ λ0=4 ðj � 1Þ . In this case, j and λ<sup>0</sup> indicate the optical thickness of jth layer which depends on deformation value h and the reference wavelength. According to this notion, Figure 8 illustrates the distributed of H and L with low and high refractive indices of the main and deformed multilayered stack. We take h = 0.1 and m = n = 2.

Figure 9 shows the reflectance spectrum for a corresponding deformed GTM heterostructure. For the optimum value of deformation, similar peaks of transmission appear inside all PBGs. This selective channel of transmission is sensitive to parameter n of GTM. The reflection bands form a typical output multichannel. Also, the number of channels and transmission peaks within PBGs increase when n augments. The channel of each PBG becomes narrow as n increases. In this case, m was maintained fix at 2. As a result, the characteristics of PBG are improved by applying the deformation h. Consequently, it is possible to improve the filtering properties by varying the suitable configuration of GTM parameters and the deformation h.

In order to improve the characteristics of filtering channels, we apply a deformation to the whole thicknesses of the main GTM structure. Figure 10 shows the distributed of transmission versus frequency for varying deformation h.
