4.1.3 Quality factor (Q)

In this part, we calculate the quality factor based on the following formula: Q ¼ � f =Δf, where Δf is the Full Width at Half Maximum (FWHM) of transmis- <sup>c</sup> sion peak and fc is the wavelength of maximum transmission.

Our calculation is summarized in Figure 5 which gives the evolution of quality factor Q versus the frequency center of resonant transmission peak for different superconductor temperatures T. We remark that Q is very sensitive to the position of resonant peaks in 170–171 THz frequency range and it is inversely proportional to superconductor's temperature T. The FWHM are approximately equal for the lower frequencies and it sharply increase for the higher frequencies range. Then, a high pass filter can be obtained for lower T.

In order to show the consequences of the variation of parameter p of GTM sequence, we determine the transmittance T versus the frequency for p = 7.

As it can be seen from Figure 6, the number of defect modes or channels depends on the superconductor's thicknesses and the distribution of layers. Moreover, the transmission spectrum exhibit a stacking of narrow gaps without oscillatory behavior. The bandwidth of each gap decreases regularly for an increase of parameter n and it probably forms a great wide PBG covering all telecommunication frequency range. The number of the transmission peaks increases as p increases. The band gaps are symmetrical about the separated transmission due to the symmetry of layers within the GTM structure.
