volume | PIER Journals

Abstract

This paper considers an electromagnetic waveguide composed of two periodic, perfectly conducting, rippled surfaces. This periodic system has a band structure given by a dispersion relation that allows us characterize eigenmodes of the system. We considered the cases of both smooth and rough surfaces, using an integral numerical method to calculate field intensities corresponding to eigenmodes over a wide frequency range. Under certain conditions, the system presents disordered patterns of field intensities with smooth surfaces. We believe that the explanation of disordered patterns is the following: for smooth surfaces, the phenomenon of electromagnetic chaos; and for rough surfaces, the speckle phenomenon. Since it is well known that the surfaces of materials always have a certain degree of roughness, it can be concluded that both chaos and speckle contribute to the presence of disordered field patterns.

1. Shen, J.-T. and S. Fan, "Strongly correlated two-electron transport in a quantum waveguide having a single Anderson impurity," New J. Phys., Vol. 11, 113024, 2009.
doi:10.1088/1367-2630/11/11/113024 Google Scholar

2. Rayleigh, L., "On the resultant of a large number of vibrations of the same pitch and of arbitrary phase," Phil. Mag., Vol. 10, 73-78, 1880. Google Scholar

3. Rigden, J. D. and E. I. Gordon, "The granularity of scattered optical maser light," Proc. IRE, Vol. 50, 2367-2368, 1962. Google Scholar

4. Oliver, B. M., "Sparkling spots and random diffraction," Proc. IEEE, Vol. 5, 220-221, 1963.
doi:10.1109/PROC.1963.1686 Google Scholar

5. Sheng, P., "Scattering and Localization of Classical Waves in Random Media," World Scientific Publishing, Singapore, 1990. Google Scholar

6. Anderson, P. W., "Absence of diffusion in certain random lattices," Phys. Rev. B, Vol. 109, No. 5, 1492-1505, 1958.
doi:10.1103/PhysRev.109.1492 Google Scholar

7. Michel, T. R. and K. A. O'Donnell, "Angular correlation functions of amplitudes scattered from a one-dimensional, perfectly conducting rough surface," J. Opt. Soc. Am. A, Vol. 9, No. 8, 1374-1384, 1992.
doi:10.1364/JOSAA.9.001374 Google Scholar

8. Webb, R. A., S. Washburn, C. P. Umbach, and R. B. Laibowitz, "Observation of h/e Aharonov-Bohm oscillations in normal-metal rings," Phys. Rev. Lett,, Vol. 54, No. 25, 2696-2699, 1985.
doi:10.1103/PhysRevLett.54.2696 Google Scholar

9. Mirlin, A. D., A. MÄuller-Groeling, and M. R. Zirnbauer, "Conductance °uctuations of disordered wires: Fourier analysis on supersymmetric spaces," Ann. Phys., Vol. 236, 325-373, 1994. Google Scholar

10. Chang, A. M., H. U. Baranger, L. N. Pfeiffer, and K. W. West, "Weak localization in chaotic versus nonchaotic cavities: A striking difference in the line shape," Phys. Rev. Lett., Vol. 73, No. 15, 2111-2114, 1994.
doi:10.1103/PhysRevLett.73.2111 Google Scholar

11. Luna-Acosta, G. A., A. A. Krokhin, M. A. Rodriguez, and P. H. Hernandez-Tejeda, "Classical chaos and ballistic transport in a mesoscopic channe," Phys. Rev. B, Vol. 54, No. 16, 11410-11416, 1996.
doi:10.1103/PhysRevB.54.11410 Google Scholar

12. Herrera-Gonzalez, I. F., G. Arroyo-Correa, A. Mendoza-Suarez, and E. S. Tututi, "Study of the resistivity in a channel with dephased ripples," Int. J. Mod. Phys. B, Vol. 25, 683-698, 2011.
doi:10.1142/S0217979211057943 Google Scholar

13. Mendoza-Suarez, A., H. Perez-Aguilar, and F. Villa-Villa, "Optical response of a perfect conductor waveguide that behaves as a photonic crystal," Progress In Electromagnetics Research, Vol. 121, 433-452, 2011.
doi:10.2528/PIER11082405 Google Scholar

14. Zhang, G. G., H. Zhang, Z. L. Yuan, Z. M. 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.
doi:10.1163/156939310791036296 Google Scholar

15. Ye, H., H. Wang, S. P. Yeo, and C. Qiu, "Finite-boundary bowtie aperture antenna for trapping nanoparticles," Progress In Electromagnetics Research, Vol. 136, 17-27, 2013. Google Scholar

16. Sanchez-Escuderos, D., M. Ferrando-Bataller, J. I. Herranz, and M. Baquero-Escudero, "Optimization of the E-plane loaded rectangular waveguide for low-loss propagation," Progress In Electromagnetics Research, Vol. 135, 411-433, 2013. Google Scholar

17. Inoue, K. and K. Ohkata, Photonic Crystals, Springer, Germany, 2004.

18. Luna-Acosta, G. A., K. Na, L. E. Reichl, and A. Krokhin, "Band structure and quantum Poincare sections of a classically chaotic quantum rippled channel," Phys. Rev. E, Vol. 53, No. 4, 3271-3283, 1996.
doi:10.1103/PhysRevE.53.3271 Google Scholar

19. Herrera-Gonzalez, I. F., H. I. Perez-Aguilar, A. Mendoza-Suarez, and E. S. Tututi, "Heat conduction in systems with Kolmogorov-Arnold-Moser phase space structure," Phys. Rev. E, Vol. 86, No. 3, 031138-1-031138-9, 2012.
doi:10.1103/PhysRevE.86.031138 Google Scholar

20. Doya, V., O. Legrand, and F. Mortessagne, "Light scarring in an optical fiber," Phys. Rev. Lett., Vol. 88, No. 1, 014102-014105, 2002.
doi:10.1103/PhysRevLett.88.014102 Google Scholar

21. Wilkinson, P. B., T. M. Fromhold, R. P. Taylor, and A. P. Micolich, "Electromagnetic wave chaos in gradient refractive index optical cavities," Phys. Rev. Lett., Vol. 86, No. 24, 5466-5469, 2001.
doi:10.1103/PhysRevLett.86.5466 Google Scholar

22. Awrejcewicz, J. and M. L. Calvisi, "Mechanical models of Chua's circuit," Int. J. Bif. and Chaos, Vol. 12, No. 4, 671-686, 2002.
doi:10.1142/S0218127402004668 Google Scholar

23. Yang, T., C. W. Wu, and L. O. Chua, "Impulsive stabilization for control and synchronization of chaotic systems: Theory and application to secure communication," IEEE Trans. Circuits Syst. 0 --- I, Vol. 44, No. 10, 976-988, 1997.
doi:10.1109/81.633887 Google Scholar

24. Williams, B. and J. Williams, Trading chaos: Maximize Profits with Proven Technical Techniques, Wiley, New York, 2004.

25. Asakura, T., H. Fuji, and K. Murata, "Measurement of spatial coherence using speckle patterns," Opt. Acta, Vol. 19, 273, 1972.
doi:10.1080/713818561 Google Scholar

26. Crane, R. B., "Use of a laser-produced speckle pattern to determine surface roughness," J. Opt. Soc. Am., Vol. 60, No. 12, 1658-1663, 1970.
doi:10.1364/JOSA.60.001658 Google Scholar

27. Tiziani, H. J., "Analysis of mechanical oscillations by speckling," Appl. Opt., Vol. 11, No. 12, 2911-2917, 1972.
doi:10.1364/AO.11.002911 Google Scholar

28. Mendoza-Suarez, 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.
doi:10.1364/JOSAB.23.002249 Google Scholar

29. Mendoza-Suarez, 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.
doi:10.1364/JOSAB.24.003091 Google Scholar

30. Villa-Villa, F., J. A. Gaspar-Armenta, and A. Mendoza-Suarez, "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.
doi:10.1163/156939307779367323 Google Scholar

31. Goodman, J. W., Speckle Phenomena in Optics: Theory and Applications, Roberts & Co., USA, 2007.

32. Leskova, T. A. and A. A. Maradudin, "Multiple-scattering effects in angular intensity correlation functions," Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin (ed.), Springer-Verlag, New York, 2007. Google Scholar

33. Perez, H. I., E. R. Mendez, C. I. Valencia, and J. A. Sanchez-Gil, "On the transmission of diffuse light through thick slits," J. Opt. Soc. Am. A,, Vol. 26, No. 4, 909-918, 2009.
doi:10.1364/JOSAA.26.000909 Google Scholar

Dr. Hector Perez-Aguilar

Dr. Alberto Mendoza-Suarez

Dr. Eduardo S. Tututi

Dr. Ivan F. Herrera-Gonzalez