DOI QR코드

DOI QR Code

Modal Analysis of Point and Discretized Continuous Spectra for Metal-Insulator-Metal Waveguides in the Terahertz Region

  • Hur, Jun (School of Electronic and Electrical Engineering, Hongik University) ;
  • Choo, Hosung (School of Electronic and Electrical Engineering, Hongik University) ;
  • Park, Jong-Eon (Metamaterial Electronic Device Research Center, Hongik University)
  • Received : 2017.12.04
  • Accepted : 2018.02.06
  • Published : 2018.07.01

Abstract

Eigenvalue distributions for a periodic metal-insulator-metal waveguide, classified into the point spectrum and the discretized continuous spectrum (DCS), are investigated as functions of frequencies, gap widths, and periods. Muller's method is suggested for solving exact eigenvalues, and we propose the scheme for finding proper initial values in the Muller's method by considering only ${\Re}e({\varepsilon}_r)$ in the dispersion equation. We then find that anti-crossing behavior, repulsive effect between the point spectrum and the DCS, becomes stronger when the real parts of the roots in the point spectrum have smaller values. Finally, we examine the transmittances of a single subwavelength slit for real metals using the mode matching technique. The transmittances in real metals similarly follow those of the perfect electric conductor (PEC) at low frequencies, while the patterns at higher frequencies begin to differ from the PEC.

Keywords

References

  1. B. Sturman, E. Podivilov, and M. Gorkunov, "Eigenmodes for metal-dielectric light-transmitting nanostructures," Physical Review B, vol. 76, no. 12, pp. 125104(11), Sept. 2007. https://doi.org/10.1103/PhysRevB.76.125104
  2. B. Sturman, E. Podivilov, and M. Gorkunov, "Eigenmodes for the problem of extraordinary light transmission through subwavelength holes," EPL, vol. 80, no. 2, pp. 24002(5), Oct. 2007. https://doi.org/10.1209/0295-5075/80/24002
  3. B. Sturman, E. Podivilov, and M. Gorkunov, "Theory of extraordinary light transmission through arrays of subwavelength slits," Physical Review B, vol. 77, no. 7, pp. 075106(12), Feb. 2008. https://doi.org/10.1103/PhysRevB.77.075106
  4. S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, "Modal analysis and coupling in metal-insulator- metal waveguides," Physical Review B, vol. 79, no. 3, pp. 035120(17), Jan. 2009. https://doi.org/10.1103/PhysRevB.79.035120
  5. M. Gorkunov, E. Podivilov, and B. Sturman, "Transmission and scattering properties of subwavelength slits in metals," Physical Review B, vol. 83, no. 3, pp. 035414(11), Jan. 2011. https://doi.org/10.1103/PhysRevB.83.035414
  6. B. Sturman, E. Podivilov, and M. Gorkunov, "Elementary processes of light transformation for slit structures in real and perfect metals," Photonics and Nanostructures - Fundamentals and Applications, vol. 10, no. 4, pp. 409-415, Oct. 2012. https://doi.org/10.1016/j.photonics.2012.06.004
  7. J.-E. Park, F. L. Teixeira, and B.-H. V. Borges, "Analysis of deep-subwavelength Au and Ag slit transmittances at terahertz frequencies," Journal of the Optical Society of America B, vol. 33, no. 7, pp. 1355-1364, Jul. 2016. https://doi.org/10.1364/JOSAB.33.001355
  8. C. F. Bohren and D. R. Huffman, "Absorption and scattering of light by small particles," Wiley, New York, 1983.
  9. J. Won, S. Jeon, and S. Nam, "Identifying the appropriate position on the ground plane for MIMO antennas using characteristic mode analysis," J Electromagn Eng Sci, vol. 16, no. 2, pp. 119-125, Apr. 2016. https://doi.org/10.5515/JKIEES.2016.16.2.119
  10. N. Zhang and W. Nah, "Mode analysis of cascaded four-conductor lines using extended mixed-mode S- Parameters," J Electromagn Eng Sci, vol. 16, no. 1, pp. 57-65, Jan. 2016. https://doi.org/10.5515/JKIEES.2016.16.1.57
  11. E. Kreyszig, "Introductory functional analysis with applications," Wiley, New York, 1978.
  12. J. Locker, "Spectral theory of non-self-adjoint two-point differential operators," American Mathematical Society, Providence, 2000.
  13. K. E. Atkinson, "An introduction to numerical analysis," Wiley, 1989.
  14. G. Veronis, Z. Yu, S. E. Kocabas, D. A. B. Miller, M. L. Brongersma, and S. Fan, "Metal-dielectric-metal plasmonic waveguide devices for manipulating light at the nanoscale," Chinese Optics Letters, vol. 7, no. 4, pp. 302-308, Apr. 2009. https://doi.org/10.3788/COL20090704.0302
  15. G. Wang, H. Lu, X. Liu, D. Mao, and L. Duan, "Tunable multi-channel wavelength demultiplexer based on MIM plasmonic nanodisk resonators at telecommunications regime," Optics Express, vol. 19, no. 4, pp. 3513-3518, Feb. 2011. https://doi.org/10.1364/OE.19.003513
  16. P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations," Physical Review B, vol. 26, no. 6, pp. 2907-2916, Sept. 1982. https://doi.org/10.1103/PhysRevB.26.2907
  17. E. Feigenbaum and M. Orenstein, "Modeling of complementary (void) plasmon waveguiding", Journal of Lightwave Technology, vol. 25, no. 9, pp. 2547- 2562, Sept. 2007. https://doi.org/10.1109/JLT.2007.903558
  18. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, "Optical properties of metallic films for vertical-cavity optoelectronic devices," Applied Optics, vol. 37, no. 22, pp. 5271-5283, Aug. 1998. https://doi.org/10.1364/AO.37.005271
  19. E. Anemogiannis and E. N. Glytsis, "Multilayer waveguide: Efficient numerical analysis of general structures," Journal of Lightwave Technology, vol. 10, no. 10, pp. 1344-1351, Oct. 1992. https://doi.org/10.1109/50.166774
  20. R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, "Mode determination for planar waveguides using the four-sheeted dispersion relation," IEEE Journal of Quantum Electronics, vol. 28, no. 6, pp. 1520-1526, Jun. 1992. https://doi.org/10.1109/3.135305
  21. Min-Suk Kwon and Sang-Yung Shin, "Simple and fast numerical analysis of multilayer waveguide modes," Optics Communications, vol. 233, no. 1, pp. 119-126, Mar. 2004. https://doi.org/10.1016/j.optcom.2004.01.037
  22. R. Rodriguez-Berral, F. Mesa, and F. Medina, "Appropriate formulation of the characteristic equation for open nonreciprocal layered waveguides with different upper and lower half-spaces," IEEE Transactions on microwave theory and techniques, vol. 53, no. 5, pp. 1613-1623, May 2005. https://doi.org/10.1109/TMTT.2005.847051
  23. R. F. Harrington and D. T. Auckland, "Electro-magnetic transmission through narrow slots in thick conducting screens," IEEE Transactions on Antennas and Propagation, vol. 28, no. 5, pp. 616-622, Sept. 1980. https://doi.org/10.1109/TAP.1980.1142382
  24. A. Wexler, "Solution of waveguide discontinuities by modal analysis," IEEE Transactions on Microwave Theory and Techniques, vol. 15, no. 9, pp. 508-517, Sept. 1967. https://doi.org/10.1109/TMTT.1967.1126521
  25. W. C. Chew, "Waves and Fields in Inhomogeneous Media," Wiley-IEEE, 1999.
  26. Y. Takakura, "Optical resonance in a narrow slit in a thick metallic screen," Physical Review Letters, vol. 86, no. 24, pp. 5601-5603, Jun. 2001. https://doi.org/10.1103/PhysRevLett.86.5601
  27. F. Yang and J. R. Sambles, "Resonant transmission of microwaves through a narrow metallic slit," Physical Review Letters, vol. 89, no. 6, pp. 063901(3), Jul. 2002. https://doi.org/10.1103/PhysRevLett.89.063901
  28. J. Bravo-Abad, L. Martin-Moreno, and F. J. Garcia-Vidal, "Transmission properties of a single metallic slit: From the subwavelength regime to the geometrical-optics limit," Physical Review E, vol. 69, no. 2, pp. 026601(6), Feb. 2004. https://doi.org/10.1103/PhysRevE.69.026601
  29. F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, "Transmission of light through a single rectangular hole," Physical Review Letters, vol. 95, no. 10, pp. 103901(4), Aug. 2005. https://doi.org/10.1103/PhysRevLett.95.103901
  30. J. -E. Park, K. Y. Kim, and J. -W. Song, "Comparison of mutual coupling phenomena in subwavelength ridged circular apertures and half-wavelength dipole antenna arrays," International journal of antennas and propagation, vol. 2012, pp. 129469(8), Dec. 2012.