Vol. 48
Latest Volume
All Volumes
PIERB 105 [2024] PIERB 104 [2024] PIERB 103 [2023] PIERB 102 [2023] PIERB 101 [2023] PIERB 100 [2023] PIERB 99 [2023] PIERB 98 [2023] PIERB 97 [2022] PIERB 96 [2022] PIERB 95 [2022] PIERB 94 [2021] PIERB 93 [2021] PIERB 92 [2021] PIERB 91 [2021] PIERB 90 [2021] PIERB 89 [2020] PIERB 88 [2020] PIERB 87 [2020] PIERB 86 [2020] PIERB 85 [2019] PIERB 84 [2019] PIERB 83 [2019] PIERB 82 [2018] PIERB 81 [2018] PIERB 80 [2018] PIERB 79 [2017] PIERB 78 [2017] PIERB 77 [2017] PIERB 76 [2017] PIERB 75 [2017] PIERB 74 [2017] PIERB 73 [2017] PIERB 72 [2017] PIERB 71 [2016] PIERB 70 [2016] PIERB 69 [2016] PIERB 68 [2016] PIERB 67 [2016] PIERB 66 [2016] PIERB 65 [2016] PIERB 64 [2015] PIERB 63 [2015] PIERB 62 [2015] PIERB 61 [2014] PIERB 60 [2014] PIERB 59 [2014] PIERB 58 [2014] PIERB 57 [2014] PIERB 56 [2013] PIERB 55 [2013] PIERB 54 [2013] PIERB 53 [2013] PIERB 52 [2013] PIERB 51 [2013] PIERB 50 [2013] PIERB 49 [2013] PIERB 48 [2013] PIERB 47 [2013] PIERB 46 [2013] PIERB 45 [2012] PIERB 44 [2012] PIERB 43 [2012] PIERB 42 [2012] PIERB 41 [2012] PIERB 40 [2012] PIERB 39 [2012] PIERB 38 [2012] PIERB 37 [2012] PIERB 36 [2012] PIERB 35 [2011] PIERB 34 [2011] PIERB 33 [2011] PIERB 32 [2011] PIERB 31 [2011] PIERB 30 [2011] PIERB 29 [2011] PIERB 28 [2011] PIERB 27 [2011] PIERB 26 [2010] PIERB 25 [2010] PIERB 24 [2010] PIERB 23 [2010] PIERB 22 [2010] PIERB 21 [2010] PIERB 20 [2010] PIERB 19 [2010] PIERB 18 [2009] PIERB 17 [2009] PIERB 16 [2009] PIERB 15 [2009] PIERB 14 [2009] PIERB 13 [2009] PIERB 12 [2009] PIERB 11 [2009] PIERB 10 [2008] PIERB 9 [2008] PIERB 8 [2008] PIERB 7 [2008] PIERB 6 [2008] PIERB 5 [2008] PIERB 4 [2008] PIERB 3 [2008] PIERB 2 [2008] PIERB 1 [2008]
2013-01-30
Disordered Field Patterns in a Waveguide with Periodic Surfaces
By
Progress In Electromagnetics Research B, Vol. 48, 329-346, 2013
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.
Citation
Hector Perez-Aguilar, Alberto Mendoza-Suarez, Eduardo S. Tututi, and Ivan F. Herrera-Gonzalez, "Disordered Field Patterns in a Waveguide with Periodic Surfaces," Progress In Electromagnetics Research B, Vol. 48, 329-346, 2013.
doi:10.2528/PIERB12120509
References

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

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.

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

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

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

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

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

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

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.

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

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

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

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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.

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