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

Fig. 20. The variation of the position of the defect :a) (AB)4B(AB)12; b) (AB)5B(AB)11; c) (AB)6B(AB)10; d) (AB)7B(AB)9

The Optical Transmission of One-Dimensional

configurations are the following three:

Press, Cambridge, England,1999

**5. Conclusions** 

filters.

**6. References** 

2008

No. 2, 2008

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Photonic Crystals Containing Double-Negative Materials 63

From the graphics above it is observed that the thickness of the defect layer influences the

The insertion of a double negative material defect layer in the structure of the onedimensional photonic crystal structure generates localized states. The optical transmission in these localized states and the value of the frequency at which the localized states are obtained depend on the thickness and position in which we have inserted the defect layer. Analyzing the simulations results it is reached the conclusion that the best photonic crystal

From the results obtained it can be said that the studied structures can be used as optical

Allouche, J. P. & Shallit, J. (2003). *Automatic Sequences: Theory, Applications, Generalizations*, pp. 152-153, Cambridge University Press, Cambridge, England, 2003 Born M. & Wolf, E. (1999). *Principles of Optics*, 7th ed., Sect. 1.6, pp. 54–74, Cambridge U.

Eleftheriades G. V.; Iyer A. K. & Kremer P. C. (2002). *Planar negative refractive index media* 

Deng X. & Liu N. (2008). *Resonant tunneling properties of photonic crystals consisting of* 

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Pendry J. B. (2000). *Negative refraction makes a perfect lens*. Physics Review Letters, Vol. 85, No.

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*negative refractive index structural defects, Progress in Electromagnetics Research*, PIER

*and μ*. Soviet Physics Uspekhi, Vol.10, No. 4, pp. 509-514, 1968

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*using periodically L-C loaded transmission lines*. IEEE Transactions on Microwave

*single-negative materials*. Chinese Science Bulletin, Vol. 53, No. 4, pp. 529-533, Feb.

*containing double-negative and single-negative materials*, Chinese Optics Letters, Vol. 6,

value of the frequency at which we obtain the localized states (figure 21 d).

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)

In figure 20 it is showed the influence of the position of the defect layer upon the transmission of the 1D PC. If the defect layer is inserted after an even number of (AB) groups the transmission in the localized states is near 100%. If the defect layer is inserted after an ode number of (AB) groups the transmission is low (under 30%).

Fig. 21. The variation of the thickness of the B type layer a) dB=3 mm; b) dB=6 mm; c) dB=9 mm; d) the frequency of the localized state vs. the position of the defect

Now it is analyzed the influence of the thickness of the B type defect layer upon the optical transmission of the 1D PC. The defect layer is inserted after 8 (AB) groups. The variation of the thickness of the defect layer doesn't influence the optical transmission of the crystal but if it is varied the thickness of all B type layers in the crystal structure are obtained some interesting results as it can be seen in the following graphics.

From the graphics above it is observed that the thickness of the defect layer influences the value of the frequency at which we obtain the localized states (figure 21 d).
