In this work, we consider a waveguide composed of two periodic, perfectly conducting, one-dimensional rough surfaces. This periodic system has a band structure similar in some aspects to a one-dimensional photonic crystal. However, our system has some additional interesting features. We calculate the band structure and the reflectivity of a corresponding finite waveguide. We found that the variation of the roughness amplitude and the relative phases allow to control at a certain degree the band structure of the system. Particularly, wide gaps can be obtained. It is even possible to obtain discrete modes for some frequency range and then the periodic waveguide acts as an unimodal filter. The system considered constitutes itself a photonic crystal whose band structure corresponds in many ways to a conventional photonic crystal but using just a single material. The key properties of this system are that it really constitutes a waveguide whose optical response is similar to that of a one-dimensional photonic crystal.
1. Elliot, R. S., "On the theory of corrugated plane surfaces," IRE Trans. AP, Vol. 2, 71-81, 1954.
2. Jancewicz, B., "Plane electromagnetic wave in PEMC," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 5, 647-659, 2006.
3. Lindell, I. V. and A. H. Sihvola, "The PEMC resonator," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 7, 849-859, 2006.
4. Lindell, I. V. and A. H. Sihvola, "Reflection and transmission of waves at the interface of perfect electromagnetic conductor (PEMC) ," Progress In Electromagnetics Research B, Vol. 5, 169-183, 2008.
5. Imran, A., Q. A. Naqvi, and K. Hongo, "Diffraction of electromagnetic plane wave from a slit in PEMC plane," Progress In Electromagnetic Research M, Vol. 8, 67-77, 2009.
6. Zhang, G., H. Zhang, Z. Yuan, Z. Wang, and D. Wang, "A novel broadband E-plane omni-directional planar antenna," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5-6, 663-670, 2010.
7. Liu, Y. and S.-X. Gong, "Design of a compact broadband double-ridged horn antenna," Journal of Electromagnetic Waves and Applications, Vol. 24, No. 5-6, 765-774, 2010.
8. Hammou, D., E. Moldovan, and S. O. Tatu, "V-band microstrip to standard rectangular waveguide transition using a substrate integrated waveguide (SIW)," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 2-3, 221-230, 2009.
9. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, 77-79, 2001.
10. Pendry, J. B., L. Martín-Moreno, and F. J. García-Vidal, "Mimicking surface plasmons with structured surfaces," Science, Vol. 305, No. 5685, 847-848, 2004.
11. García-Vidal, F. J., L. Martín-Moreno, and J. B. Pendry, "Surfaces with holes in them: New plasmonic metamaterials," J. Opt. A: Pure and Appl. Opt., Vol. 7, S97-S101, 2005.
12. García de Abajo, F. J. and J. J. Sáenz, "Electromagnetic surface states in structured perfect-conductor surfaces," Phys. Rev. Lett., Vol. 95, 233901, 2005.
13. Qiu, M., "Photonic band structures for surface waves on structured metal surfaces," Opt. Express, Vol. 13, No. 19, 7583-7588, 2005.
14. Oh, S. S., S.-G. Lee, J.-E. Kim, and H. Y. Park, "Self-collimation phenomena of surface waves in structured perfect electric conductors and metal surfaces," Opt. Express, Vol. 15, No. 3, 1205-1210, 2007.
15. Inoue, K. and K. Ohkata, Photonic Crystals, Springer, Germany, 2004.
16. Maradudin, A. A. and A. R. McGurn, "Photonic band structure of a truncated, two-dimensional, periodic dielectric medium," J. Opt. Soc. Am. B, Vol. 10, No. 2, 307-313, 1993.
17. Luna-Acosta, G. A., K. Na, L. E. Reichl, and A. Krokhin, "Band structure and quantum Poincaré sections of a classically chaotic quantum rippled channel," Phys. Rev. E, Vol. 53, No. 4, 3271-3283, 1996.
18. Herrera-González, I., G. Arroyo-Correa, A. Mendoza-Suárez, and E. Tútuti-Hernández, "Study of the resistivity in a channel with dephased ripples," Int. J. Mod. Phys. B, Vol. 25, No. 5, 683-698, 2011.
19. Mendoza-Suárez, A., F. Villa-Villa, and J. A. Gaspar-Armenta, "Numerical method based on the solution of integral equations for the calculation of the band structure and reflectance of one- and two-dimensional photonic crystals," J. Opt. Soc. Am. B, Vol. 23, No. 10, 2249-2256, 2006.
20. Pérez, H. I., E. R. Méndez, C. I. Valencia, and J. A. Sánchez-Gil, "On the transmission of diffuse light through thick slits," J. Opt. Soc. Am. A, Vol. 26, No. 4, 909-918, 2009.
21. Mendoza-Surez, A., F. Villa-Villa, and J. A. Gaspar-Armenta, "Band structure of two-dimensional photonic crystals that include dispersive left-handed materials and dielectrics in the unit cell," J. Opt. Soc. Am. B, Vol. 24, No. 12, 3091-3098, 2007.
22. Villa-Villa, F., J. A. Gaspar-Armenta, and A. Mendoza-Suárez, "Surface modes in one dimensional photonic crystals that include left handed materials," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 4, 485-499, 2007.
23. Villa-Villa, F., J. A. Gaspar-Armenta, and F. Ramos-Mendieta, "One-dimensional photonic crystals --- Equivalent systems to single layers with a classical oscillator like dielectric function," Optics Comm., Vol. 216, 361-367, 2003.
24. Joannopoulos, J. D., S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, Princeton University Press, New Jersey, 2008.
25. Méndez, E. R., M. A. Ponce, V. Ruiz-Cortés, and Z. H. Gu, "Photofabrication of one-dimensional rough surfaces for light scattering experiments," Appl. Opt., Vol. 30, No. 28, 4103-4113, 1991.
26. Maradudin, A. A., T. Michel, A. R. McGurn, and E. R. Méndez, "Enhanced backscattering of light from a random grating," Ann. Phys., Vol. 203, No. 2, 255-307, 1990.
27. Mendoza-Suárez, A. and E. R. Méndez, "Light scattering by a reentrant fractal surface," Appl. Opt., Vol. 36, No. 15, 3521-3531, 1997.
28. Valencia, C. I., E. R. Méndez, and B. S. Mendoza, "Second-harmonic generation in the scattering of light by two-dimensional particles," J. Opt. Soc. Am. B, Vol. 20, No. 10, 2150-2161, 2003.