**4.1.1 Case 1: A is a dielectric material**

Figure 4 presents the optical transmission of the three types of the studied photonic crystals versus of the frequency of the light beam so that we can observe easily the band-gaps.

One easily observes that the (AB)16 type photonic crystals have two band gaps, the (ABBA)8 type crystals have three band-gaps and the (ABBABAAB)4 type crystals have four bandgaps. The values are given in table 1.


Table 1. The photonic band-gaps for (AB)16, (ABBA)8 and (ABBABAAB)4 one-dimensional photonic crystal

The Optical Transmission of One-Dimensional

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

(ABBABAAB)4 type structure.

localized states.

Photonic Crystals Containing Double-Negative Materials 47

It is also observed that the (AB)16 type crystals have wider band-gaps. The (ABBA)8 type crystals have the smallest band-gaps. The maximum band-gap is obtained for a

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

a)

b)

c) 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

Fig. 4. 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

a)

b)

c) Fig. 4. 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

It is also observed that the (AB)16 type crystals have wider band-gaps. The (ABBA)8 type crystals have the smallest band-gaps. The maximum band-gap is obtained for a (ABBABAAB)4 type structure.
