**4.1.2 Case 2: A is an epsilon negative material**

Figure 5 presents the optical transmission of the three types of the studied photonic crystals versus the frequency of the light beam so that to observe easily the band-gaps and the localized states.

Fig. 5. the optical transmission function of the frequency of the incident radiation for 1D PC of different types: a) (AB)16; b) (ABBA)8; c) (ABBABAAB)4

The Optical Transmission of One-Dimensional

Photonic Crystals Containing Double-Negative Materials 49

c)

a)

b)

c)

Fig. 7. The optical transmission function of the frequency for 1D PC of (ABBA)8 type:

a) without defect; b) with A type defect; c) with B type defect.

Fig. 6. The optical transmission function of the frequency for 1D PC of (AB)16 type:

a) without defect; b) with A type defect; c) with B type defect.

From the graphics above it is observed that for the (AB)16 type photonic crystal it is obtained a localized state with an optical transmission of 96% at the frequency of 0.99 GHz and a group of localized states with high optical transmission between the frequencies of 2.5 GHz and 3.5 GHz. One of these localized states has an optical transmission of 100%. This localized state is obtained at 3.07 GHz. For the (ABBA)8 type structure it is obtained a localized state at 4.2 GHz with an optical transmission of 100%. The results obtained for the (ABBABAAB)4 type crystal are not important because the optical transmissions of the localized states are very small (under 15%).
