**4.2.1 Case 1: A a dielectric material**

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

In this case it was introduced, in the structure of the one-dimensional photonic crystal, first an A type defect layer and then a B type defect layer. As before it is considered first that A is a dielectric material and then A is an epsilon negative material. B remains a double negative

In these experiments the thicknesses of the layers were kept constant - *dA* =24mm and

a)

b)

localized states are very small (under 15%).

material in both cases.

**4.2 The optical transmission of 1D PC with defects** 

*dB* =6mm - and the frequency was varied ω∈(0,9)*GHz*.

**4.2.1 Case 1: A a dielectric material** 

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.

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.

The Optical Transmission of One-Dimensional

**4.2.2 Case 2: A an epsilon negative material** 

Photonic Crystals Containing Double-Negative Materials 51

a)

b)

c)

Fig. 9. 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.

Fig. 8. The optical transmission function of the frequency for 1D PC of (ABBABAAB)4 type: a) without defect; b) with A type defect; c) with B type defect.

From the figures above it can be seen that only for the (AB)16 type photonic crystal significant results were obtained.

#### **4.2.2 Case 2: A an epsilon negative material**

50 Photonic Crystals – Innovative Systems, Lasers and Waveguides

a)

b)

c)

Fig. 8. The optical transmission function of the frequency for 1D PC of (ABBABAAB)4 type:

From the figures above it can be seen that only for the (AB)16 type photonic crystal

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

significant results were obtained.

Fig. 9. 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.

The Optical Transmission of One-Dimensional

Photonic Crystals Containing Double-Negative Materials 53

From the figure above it is observed that like in the case of a (AB)16 type crystal in the case of a (ABBA)8 type crystal the insertion of a A type defect layer lowers the optical transmission (from 100 % to 4%) in the localized state obtained at 4.2 GHz while the insertion of a B type

a)

b)

c)

Fig. 11. The optical transmission function of the frequency for 1D PC of (ABBABAAB)4 type:

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

defect layer has little influence upon the optical transmission of the photonic crystal.

Inserting a A type defect layer lowers the optical transmission in the localized state obtained at 0.99 GHz while the insertion of a B type defect layer doesn't have a big influence on the optical transmission of the (AB)16 type photonic crystal.

Fig. 10. 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.

Inserting a A type defect layer lowers the optical transmission in the localized state obtained at 0.99 GHz while the insertion of a B type defect layer doesn't have a big influence on the

a)

b)

c)

Fig. 10. 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.

optical transmission of the (AB)16 type photonic crystal.

From the figure above it is observed that like in the case of a (AB)16 type crystal in the case of a (ABBA)8 type crystal the insertion of a A type defect layer lowers the optical transmission (from 100 % to 4%) in the localized state obtained at 4.2 GHz while the insertion of a B type defect layer has little influence upon the optical transmission of the photonic crystal.

Fig. 11. The optical transmission function of the frequency for 1D PC of (ABBABAAB)4 type: a) without defect; b) with A type defect; c) with B type defect.

The Optical Transmission of One-Dimensional

obtained at a frequency of 6.65 GHz.

Photonic Crystals Containing Double-Negative Materials 55

From the simulations it is observed that the best results are reached if the defect layer is inserted after 8 (AB) groups. A localized state with high optical transmission (95%)is

Keeping the defect layer on position 8 (after 8 (AB) groups) we will now vary its thickness to

a) b)

c) d)

e) f)

b) dA=22 mm; c) dA=24 mm; d) dA=26 mm; e) dA=28 mm; f) the frequency of the localized

Fig. 13. The variation of the thickness of the A type defect layer a) dA=20 mm;

state vs. the thickness of the defect layer

see its influence upon the optical transmission or the frequency of the localized state.

Analyzing the graphics above it was observed that by inserting a defect layer of A type or B type the optical transmission of the (ABBABAAB)4 type photonic crystal in the localized state becomes even smaller (under 0.001 %).

Considering the results obtained till now the following types of photonic crystals will be studied farther more:

