volume | PIER Journals

Abstract

In this paper, the surface states (or so called Tamm states) of a nonlinear self-focusing slab sandwiched between a uniform medium and a one-dimensional photonic crystal has been investigated based on the first integral of nonlinear Helmholtz wave equation. The consider slabs can be a left-handed metamaterial or a conventional material. It is shown that the structure can support the Tamm states with two different transverse electric structure. In one kind, the surface waves has a hump at the surface of photonic crystal, and the other one has two humps. We reveal that in the case of self-focusing left-handed metamaterial slab, there is possibility for change of total flow's direction of surface waves by adjusting of the intensity of exciting electromagnetic field.

1. John, S., "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett., Vol. 58, 2486, 1987.
doi:10.1103/PhysRevLett.58.2486 Google Scholar

2. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton, Princeton University Press, NJ, 1995.

3. Rahimi, H., A. Namdar, S. Roshan Entezar, and H. Tajali, "Photonic transmission spectra in one-dimensional fibonacci multilayer structures containing single-negative metamaterials," Progress In Electromagnetics Research, Vol. 102, 15, 2010.
doi:10.2528/PIER09122303 Google Scholar

4. Nozhat, N. and N. Granpayeh, "Specialty fibers designed by photonic crystals," Progress In Electromagnetics Research, Vol. 99, 225, 2009.
doi:10.2528/PIER09092309 Google Scholar

5. Robertson, W. M., G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett., Vol. 18, 528, 1993.
doi:10.1364/OL.18.000528 Google Scholar

6. Meade, R. D., K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B, Vol. 44, 10961, 1991.
doi:10.1103/PhysRevB.44.10961 Google Scholar

7. Rahimi, H., "Backward tamm states in 1D single-negative metamaterial photonic crystals," Progress In Electromagnetics Research Letters, Vol. 13, 149, 2010.
doi:10.2528/PIERL09121305 Google Scholar

8. Martorell, J., D. W. L. Sprung, and G. Morozov, "Surface TE waves on 1D photonic crystals," J. Opt. A: Pure Appl. Opt., Vol. 8, 630, 2006.
doi:10.1088/1464-4258/8/8/003 Google Scholar

9. Namdar, A., I. V. Shadrivov, and Y. S. Kinshar, "Backward Tamm states in left-handed metamaterials," Apll. Phys. Lett., Vol. 89, 114104, 2006.
doi:10.1063/1.2352794 Google Scholar

10. Boardman, A. D. and P. Egan, "Novel nonlinear surface and guided TE waves in asymmetric LHM waveguides," J. Opt. A: Pure Appl. Opt., Vol. 11, 114302, 2009. Google Scholar

11. Glushko, E. Y., "Analytical solution for the field in photonic structures containing cubic nonlinearity," Opt. Commun., Vol. 259, 342, 2006.
doi:10.1016/j.optcom.2005.08.065 Google Scholar

12. Schürmann, H. W., V. S. Serov, and Y. V. Shestopalov, "TE-polarized waves guided by a lossless nonlinear three-layer structures," Phys. Rev. E, Vol. 58, 1040, 1998.
doi:10.1103/PhysRevE.58.1040 Google Scholar

13. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77, 2001.
doi:10.1126/science.1058847 Google Scholar

14. Chigrin, D. N., A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A: Mater. Sci. Process., Vol. 68, 25, 1999.
doi:10.1007/s003390050849 Google Scholar

15. Chettiar, U. K., A. V., Kildishev, H. K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, "Dual-band negative index metamaterial: Double negative at 813nm and single negative at 772 nm," Opt. Lett. , Vol. 32, 1671, 2007.
doi:10.1364/OL.32.001671 Google Scholar

16. Boltasseva, A. and V. M. Shalaev, "Fabrication of optical negative-index metamaterials: Recent advances and outlook," Metamaterials, Vol. 2, 1, 2008.
doi:10.1016/j.metmat.2008.03.004 Google Scholar

17. Zharov, A. A., I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett., Vol. 91, 37401, 2003.
doi:10.1103/PhysRevLett.91.037401 Google Scholar

18. Namdar, A., I. V. Shadrivov, and Y. S. Kinshar, "Excitation of backward Tamm states at an interface between a periodic photonic crystal and a left-handed metamaterials," Phys. Rev. A, Vol. 75, 053812, 2007.
doi:10.1103/PhysRevA.75.053812 Google Scholar

19. Yariv, A., P. Yeh, and , Optical Waves in Layered Media, Wiley, New York, 1988.

20. Abramowitz, M. and A. S. Stegun, Handbook of Mahematical Function, Dover, New York, 1972.

21. Shadrivov, I. V., A. A. Sukhorukov, and Y. S. Kivshar, "Nonlinear surface waves in left-handed materials," Phys. Rev. E, Vol. 69, 016617, 2004.
doi:10.1103/PhysRevE.69.016617 Google Scholar

Dr. Zahra Eyni

Dr. Samad Roshan Entezar

Dr. Abdolrahman Namdar

Dr. Habib Tajalli