**4.3.1 The (AB)16 type crystal with a A type defect layer (A is a dielectric material)**

Fig. 12. The variation of the position of the defect layer: a) (AB)8A(AB)8; b) (AB)9A(AB)7; c) (AB)10A(AB)6; d) (AB)11A(AB)5

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

Considering the results obtained till now the following types of photonic crystals will be

The influence of the thickness and the position in which is inserted the defect layer in the structure of the photonic crystal will be analyzed. Only the three cases enumerated above

a) b)

c) d)

Fig. 12. The variation of the position of the defect layer: a) (AB)8A(AB)8; b) (AB)9A(AB)7;

**4.3.1 The (AB)16 type crystal with a A type defect layer (A is a dielectric material)** 

a. The (AB)16 type crystal with a A type defect layer (A a dielectric material) b. The (AB)16 type crystal with a B type defect layer (A a dielectric material) c. The (AB)16 type crystal with a B type defect layer (A a epsilon negative material)

**4.3 The optical transmission of 1D PC of (AB)16 type with a defect layer** 

state becomes even smaller (under 0.001 %).

studied farther more:

will be considered.

c) (AB)10A(AB)6; d) (AB)11A(AB)5

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 obtained at a frequency of 6.65 GHz.

Keeping the defect layer on position 8 (after 8 (AB) groups) we will now vary its thickness to see its influence upon the optical transmission or the frequency of the localized state.

Fig. 13. The variation of the thickness of the A type defect layer a) dA=20 mm; b) dA=22 mm; c) dA=24 mm; d) dA=26 mm; e) dA=28 mm; f) the frequency of the localized state vs. the thickness of the defect layer

The Optical Transmission of One-Dimensional

Photonic Crystals Containing Double-Negative Materials 57

g) h)

It is observed that by varying the thickness of all A type layers we influence both the optical transmission and the frequency of the localized state that was initially obtained at 6.65 GHz. By increasing the thickness of the layers the optical transmission of the localized state decreases and the localized state moves to left – the localized state is obtained at smaller

a) b) Fig. 15. a) the optical transmission of the localized state vs. the thickness of the A type layers in the structure of the (AB)8A(AB)8 type photonic crystal; b) the frequency at which is obtained the localized state vs. the thickness of the A type layers in the structure of the

**4.3.2 The (AB)16 type crystal with a B type defect layer (A is a dielectric material)** 

In figure 16 are presented some of the results obtained by changing the position of the defect layer. It is observed that the best position to insert the B type defect layer is after 8 (AB)

Fig. 14. The variation of the thickness of the A type layer: a) dA=20 mm; b) dA=22 mm; c) dA=23 mm; d) dA=24 mm; e) dA=25 mm; f) dA=26 mm; g) dA=27 mm; h) dA=28 mm

values of the frequency (as it can be seen in figure 15 a) and b)).

(AB)8A(AB)8 type photonic crystal.

groups.

Analyzing the graphics above it is reached the conclusion that by increasing the thickness of the defect layer the localized state moves to right and by decreasing the thickness of the defect layer the localized state moves to left. The optical transmission of the localized state is not significantly influenced.

Father on the thickness of all the A type layers in the structure of the crystal is varied to see its influence upon the optical transmission of the photonic crystal.

Analyzing the graphics above it is reached the conclusion that by increasing the thickness of the defect layer the localized state moves to right and by decreasing the thickness of the defect layer the localized state moves to left. The optical transmission of the localized state is

Father on the thickness of all the A type layers in the structure of the crystal is varied to see

a) b)

c) d)

e) f)

its influence upon the optical transmission of the photonic crystal.

not significantly influenced.

Fig. 14. The variation of the thickness of the A type layer: a) dA=20 mm; b) dA=22 mm; c) dA=23 mm; d) dA=24 mm; e) dA=25 mm; f) dA=26 mm; g) dA=27 mm; h) dA=28 mm

It is observed that by varying the thickness of all A type layers we influence both the optical transmission and the frequency of the localized state that was initially obtained at 6.65 GHz. By increasing the thickness of the layers the optical transmission of the localized state decreases and the localized state moves to left – the localized state is obtained at smaller values of the frequency (as it can be seen in figure 15 a) and b)).

Fig. 15. a) the optical transmission of the localized state vs. the thickness of the A type layers in the structure of the (AB)8A(AB)8 type photonic crystal; b) the frequency at which is obtained the localized state vs. the thickness of the A type layers in the structure of the (AB)8A(AB)8 type photonic crystal.

### **4.3.2 The (AB)16 type crystal with a B type defect layer (A is a dielectric material)**

In figure 16 are presented some of the results obtained by changing the position of the defect layer. It is observed that the best position to insert the B type defect layer is after 8 (AB) groups.

The Optical Transmission of One-Dimensional

Photonic Crystals Containing Double-Negative Materials 59

c) d)

e) f) Fig. 17. The variation of the thickness of the B type defect layer: a) dB=3 mm; b) dB=6 mm;

a) b) Fig. 18. a) the optical transmission of the localized state vs. the thickness of the B type defect layer in the structure of the (AB)8A(AB)8 type photonic crystal; b) the frequency at which is obtained the localized state vs. the thickness of the B type defect layer in the structure of the

Father on the thickness of all the B type layers in the structure of the crystal is varied to see

By increasing the thickness of all the B type layers in the structure of the (AB)8A(AB)8 type photonic crystal there are no longer obtained localized states but a series of band-gaps.

its influence upon the optical transmission of the photonic crystal.

c)dB=9 mm; d) dB=12 mm; e) dB=14 mm; f) dB=16 mm;

(AB)8A(AB)8 type photonic crystal.

Fig. 16. The variation of the position of the defect layer: a) (AB)5B(AB)11; b) (AB)6B(AB)10; c) (AB)7B(AB)9; d) (AB)8B(AB)8

Keeping the defect layer on position 8 (after 8 (AB) groups) its thickness will be varied to see its influence upon the optical transmission of the (AB)8B(AB)8 type photonic crystal.

It is observed that by increasing the thickness of the B type defect layer a localized state is obtained. The optical transmission and the frequency at which is obtained this state depend on the thickness of the defect layer as it can be seen in the graphics bellow. By increasing the thickness of the defect layer the localized state moves to right – the state is obtained at higher values of the frequency (figure 18 b)). The values of the localized state's optical transmission have mainly an ascending trajectory (figure 18 a)).

a) b)

c) d)

Keeping the defect layer on position 8 (after 8 (AB) groups) its thickness will be varied to see

It is observed that by increasing the thickness of the B type defect layer a localized state is obtained. The optical transmission and the frequency at which is obtained this state depend on the thickness of the defect layer as it can be seen in the graphics bellow. By increasing the thickness of the defect layer the localized state moves to right – the state is obtained at higher values of the frequency (figure 18 b)). The values of the localized state's optical

a) b)

Fig. 16. The variation of the position of the defect layer: a) (AB)5B(AB)11; b) (AB)6B(AB)10;

its influence upon the optical transmission of the (AB)8B(AB)8 type photonic crystal.

transmission have mainly an ascending trajectory (figure 18 a)).

c) (AB)7B(AB)9; d) (AB)8B(AB)8

Fig. 17. The variation of the thickness of the B type defect layer: a) dB=3 mm; b) dB=6 mm; c)dB=9 mm; d) dB=12 mm; e) dB=14 mm; f) dB=16 mm;

Fig. 18. a) the optical transmission of the localized state vs. the thickness of the B type defect layer in the structure of the (AB)8A(AB)8 type photonic crystal; b) the frequency at which is obtained the localized state vs. the thickness of the B type defect layer in the structure of the (AB)8A(AB)8 type photonic crystal.

Father on the thickness of all the B type layers in the structure of the crystal is varied to see its influence upon the optical transmission of the photonic crystal.

By increasing the thickness of all the B type layers in the structure of the (AB)8A(AB)8 type photonic crystal there are no longer obtained localized states but a series of band-gaps.

The Optical Transmission of One-Dimensional

15

21

24

c) (AB)6B(AB)10; d) (AB)7B(AB)9

Table 2.

6 (1.2, 2.7)

<sup>9</sup> (0.85, 0.93)

Photonic Crystals Containing Double-Negative Materials 61

**4.3.3 The (AB)16 type crystal with a B type defect layer (A an epsilon negative material)** 

a) b)

c) d)

Fig. 20. The variation of the position of the defect :a) (AB)4B(AB)12; b) (AB)5B(AB)11;

1.5 2.1

0.08 5.7

0.02 0.06 0.35 5.2

0.02 0.04 0.15 0.65 4

0.01 0.03 0.05 0.2 0.8 3.5

Layer thickness (mm) Band-gaps (GHz) The width of the band-gaps (GHz)

(5.5, 7.6)

(1.8, 7.5)

 (0.7, 0.72) (0.935, 0.995) (1.41, 1.76) (2.9, 8.1)

 (0.78, 0.8) (0.98, 1.02) (1.3, 1.45) (1.95, 2.6) (4,8)

 (0.745, 0.755) (0.89, 0.92) (1.15, 1.2) (1.5, 1.7) (2.2, 3) (4.5, 8)

Fig. 19. The variation of the thickness of the B type layer: a) dB=3 mm; b) dB=6 mm; c) dB=9 mm; d) dB=15 mm; e) dB=21 mm; f) dB=24 mm;


Table 2.

60 Photonic Crystals – Innovative Systems, Lasers and Waveguides

a) b)

c) d)

e) f)

Fig. 19. The variation of the thickness of the B type layer: a) dB=3 mm; b) dB=6 mm;

c) dB=9 mm; d) dB=15 mm; e) dB=21 mm; f) dB=24 mm;
