Modal analysis and coupling in metal-insulator-metal waveguides

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 3, 2009, Pages

  Kocabaş, Şükrü Ekin ^a   Veronis, Georgios ^b   Miller, David A B ^a   Fan, Shanhui ^a  

^a STANFORD UNIVERSITY   (United States)

^b LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 60449119421     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.035120     Document Type: Article

References (108)

1. E. Özbay, Science 311, 189 (2006). 10.1126/science.1114849
2. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Thomson Learning, Philadelphia, 1976).
3. Here, we are assuming that the fields are time harmonic with exp (+iωt) time dependence. For exp (-iωt) time dependence, we get a positive imaginary value for the permittivity.
4. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
5. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic Press, San Diego, CA, 1991).
6. C. Davis and T. Tamir, Int. J. Electron. 19, 323 (1965). 10.1080/00207216508937824
7. C. Davis and T. Tamir, J. Appl. Phys. 37, 461 (1966). 10.1063/1.1707885
8. E. N. Economou, Phys. Rev. 182, 539 (1969). 10.1103/PhysRev.182.539
9. T. Takano and J. Hamasaki, IEEE J. Quantum Electron. 8, 206 (1972). 10.1109/JQE.1972.1076923
10. I. P. Kaminow, W. L. Mammel, and H. P. Weber, Appl. Opt. 13, 396 (1974). 10.1364/AO.13.000396
11. B. Prade, J. Y. Vinet, and A. Mysyrowicz, Phys. Rev. B 44, 13556 (1991). 10.1103/PhysRevB.44.13556
12. F. Villa, T. Lopez-Rios, and L. E. Regalado, Phys. Rev. B 63, 165103 (2001). 10.1103/PhysRevB.63.165103
13. D.-K. Qing and G. Chen, Phys. Rev. B 71, 153107 (2005). 10.1103/PhysRevB.71.153107
14. J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, Phys. Rev. B 73, 035407 (2006). 10.1103/PhysRevB.73.035407
15. P. Ginzburg, D. Arbel, and M. Orenstein, Opt. Lett. 31, 3288 (2006). 10.1364/OL.31.003288
16. K. Y. Kim, Y. K. Cho, H.-S. Tae, and J.-H. Lee, Opt. Express 14, 320 (2006). 10.1364/OPEX.14.000320
17. R. Gordon, Phys. Rev. B 73, 153405 (2006). 10.1103/PhysRevB.73.153405
18. E. Feigenbaum and M. Orenstein, J. Lightwave Technol. 25, 2547 (2007). 10.1109/JLT.2007.903558
19. Y. Kurokawa and H. T. Miyazaki, Phys. Rev. B 75, 035411 (2007). 10.1103/PhysRevB.75.035411
20. X. Wang and K. Kempa, Phys. Rev. B 75, 245426 (2007). 10.1103/PhysRevB.75.245426
21. Z. J. Sun and D. Y. Zeng, J. Opt. Soc. Am. B 24, 2883 (2007). 10.1364/JOSAB.24.002883
22. A. R. Zakharian, J. V. Moloney, and M. Mansuripur, Opt. Express 15, 183 (2007). 10.1364/OE.15.000183
23. B. Sturman, E. Podivilov, and M. Gorkunov, Phys. Rev. B 76, 125104 (2007). 10.1103/PhysRevB.76.125104
24. T. Tamir and A. A. Oliner, Proc. IEEE 51, 317 (1963). 10.1109/PROC.1963.1758
25. C. R. Paiva and A. M. Barbosa, IEEE Trans. Microwave Theory Tech. 39, 330 (1991). 10.1109/22.102978
26. T. F. Jablonski, J. Opt. Soc. Am. A 11, 1272 (1994). 10.1364/JOSAA.11. 001272
27. W. Shu and J. M. Song, PIER 65, 103 (2006). 10.2528/PIER06081601
28. K. Y. Kim, Y. K. Cho, H. S. Tae, and J. H. Lee, J. Korean Phys. Soc. 49, 577 (2006).
29. For a more detailed coverage on vector spaces and operators, we refer the reader to Refs.. We will use italic letters for scalar variables, bold letters for vector variables, sans-serif letters for operators, and script style for linear spaces.
30. G. W. Hanson and A. B. Yakovlev, Operator Theory for Electromagnetics (Springer-Verlag, New York, 2002).
31. E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, New York, 1978).
32. B. Friedman, Principles and Techniques of Applied Mathematics (Dover, New York, 1990).
33. J. Locker, Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators (American Mathematical Society, Providence, 2000).
34. R. V. Churchill, Fourier Series and Boundary Value Problems (McGraw-Hill, New York, 1941).
35. A. Zettl, Sturm-Liouville Theory (American Mathematical Society, Providence, 2005).
36. R. Richardson, Am. J. Math. 40, 283 (1918). 10.2307/2370485
37. Examples on how to calculate operator adjoints can be found in Ref., pp. 150-154.
38. A. Mostafazadeh, J. Math. Phys. 43, 3944 (2002). 10.1063/1.1489072
39. A. Mostafazadeh and F. Loran, EPL 81, 10007 (2008). 10.1209/0295-5075/81/ 10007
40. M. Mrozowski, Guided Electromagnetic Waves (Research Studies Press, Somerset, England, 1997).
41. E. B. Davies, Bull. London Math. Soc. 34, 513 (2002). 10.1112/S0024609302001248
42. V. V. Shevchenko, Continuous Transitions in Open Waveguides (Golem, Boulder, CO, 1971).
43. T. Rozzi and M. Mongiardo, Open Electromagnetic Waveguides (The Institution of Electrical Engineers, London, 1997).
44. D. A. B. Miller, Quantum Mechanics for Scientists and Engineers (Cambridge University Press, Cambridge, 2008).
45. W. C. Chew, Waves and Fields in Inhomogenous Media (Van Nostrand Reinhold, New York, 1990).
46. R. E. Collin, Field Theory of Guided Waves, 2nd ed. (Wiley-Interscience, New York, 1991).
47. A. Kostenbauder, Y. Sun, and A. Siegman, J. Opt. Soc. Am. A Opt. Image Sci. Vis 14, 1780 (1997). 10.1364/JOSAA.14.001780
48. C. R. MacCluer and Y. Chait, SIAM Rev. 33, 467 (1991). 10.1137/1033102
49. V. V. Shevchenko, Phys. Usp. 50, 287 (2007). 10.1070/ PU2007v050n03ABEH006243
50. H. J. Hagemann, W. Gudat, and C. Kunz, J. Opt. Soc. Am. 65, 742 (1975). 10.1364/JOSA.65.000742
51. Handbook of Optical Constants of Solids, edited by, E. D. Palik, (Academic, New York, 1985).
52. P. J. B. Clarricoats and K. R. Slinn, Proc. Inst. Electr. Eng. 114, 878 (1967).
53. P. Bienstman, Ph.D. thesis, Ghent University, 2001.
54. I. Breukelaar and P. Berini, J. Opt. Soc. Am. A Opt. Image Sci. Vis 23, 1971 (2006). 10.1364/JOSAA.23.001971
55. I. Breukelaar, R. Charbonneau, and P. Berini, J. Appl. Phys. 100, 043104 (2006). 10.1063/1.2244479
56. R. F. Oulton, D. F. P. Pile, Y. Liu, and X. Zhang, Phys. Rev. B 76, 035408 (2007). 10.1103/PhysRevB.76.035408
57. Here, we borrow the terminology from Ref. for our détournement.
58. L. P. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (IEEE, New York, 1994).
59. K. A. Zaki, C. Seng-Woon, and C. Chunming, IEEE Trans. Microwave Theory Tech. 36, 1804 (1988). 10.1109/22.17416
60. A. S. Omar and K. Schunemann, IEEE Trans. Microwave Theory Tech. 35, 268 (1987). 10.1109/TMTT.1987.1133638
61. A. S. Omar and K. Schunemann, IEEE Trans. Microwave Theory Tech. 33, 1313 (1985). 10.1109/TMTT.1985.1133219
62. A. S. Omar and K. F. Schunemann, IEEE Trans. Microwave Theory Tech. 34, 1508 (1986). 10.1109/TMTT.1986.1133570
63. B. Sturman, E. Podivilov, and M. Gorkunov, Europhys. Lett. 80, 24002 (2007). 10.1209/0295-5075/80/24002
64. B. Sturman, E. Podivilov, and M. Gorkunov, Phys. Rev. B 77, 075106 (2008). 10.1103/PhysRevB.77.075106
65. G. V. Eleftheriades, A. S. Omar, L. P. B. Katehi, and G. M. Rebeiz, IEEE Trans. Microwave Theory Tech. 42, 1896 (1994). 10.1109/22.320771
66. G. Veronis and S. H. Fan, Appl. Phys. Lett. 87, 131102 (2005). 10.1063/1.2056594
67. Ş. E. Kocabaş, G. Veronis, D. A. B. Miller, and S. Fan, IEEE J. Sel. Top. Quantum Electron. 14, 1462 (2008). 10.1109/JSTQE.2008.924431
68. A. K. Bhattacharyya, IEEE Trans. Antennas Propag. 51, 1599 (2003). 10.1109/TAP.2003.813614
69. S. W. Lee, W. R. Jones, and J. J. Campbell, IEEE Trans. Microwave Theory Tech. 19, 528 (1971). 10.1109/TMTT.1971.1127569
70. M. Leroy, IEEE Trans. Antennas Propag. 31, 655 (1983). 10.1109/TAP.1983.1143095
71. R. Mittra, T. Itoh, and T. shu Li, IEEE Trans. Microwave Theory Tech. 20, 96 (1972). 10.1109/TMTT.1972.1127691
72. Here, we are assuming that we are operating at a frequency well above the plasma frequency, ωp, where ∈m = |∈m| <1 so that the MIM geometry describes a conventional dielectric slab waveguide as illustrated in the introduction section.
73. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, Science 302, 419 (2003). 10.1126/science.1089171
74. I. Kay and H. Moses, J. Appl. Phys. 27, 1503 (1956). 10.1063/1.1722296
75. J. Lekner, Theory of Reflection (Kluwer, Hingham, MA, 1987).
76. C. Siewert, J. Math. Phys. 19, 434 (1978). 10.1063/1.523662
77. P. Paul and D. Nkemzi, J. Math. Phys. 41, 4551 (2000). 10.1063/1.533361
78. R. Blümel, J. Phys. A 38, L673 (2005). 10.1088/0305-4470/38/42/L02
79. Z. Ahmed, J. Phys. A 33, 3161 (2000). 10.1088/0305-4470/33/16/308
80. C. M. Bender, Rep. Prog. Phys. 70, 947 (2007). 10.1088/0034-4885/70/6/R03
81. H. B. Geyer, W. D. Heiss, and F. G. Scholtz, arXiv:0710.5593 (unpublished).
82. David Krejcirik and M. Tater, J. Phys. A: Math. Theor. 41, 244013 (2008). 10.1088/1751-8113/41/24/244013
83. S. Albeverio, U. Guenther, and S. Kuzhel, arXiv:0811.0365 (unpublished).
84. S. Kuzhel, arXiv:0802.4269 (unpublished).
85. D. Williams, B. Alpert, U. Arz, D. Walker, and H. Grabinski, IEEE Trans. Adv. Packag. 26, 165 (2003). 10.1109/TADVP.2003.817339
86. M. Haakestad and J. Skaar, Opt. Express 13, 9922 (2005). 10.1364/OPEX.13.009922
87. F. Lopez-Tejeira, Nat. Phys. 3, 324 (2007). 10.1038/nphys584
88. E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, Nano Lett. 8, 2925 (2008). 10.1021/nl801781g
89. J. A. Dionne, E. Verhagen, A. Polman, and H. A. Atwater, Opt. Express 16, 19001 (2008). 10.1364/OE.16.019001
90. V. V. Klimov and M. Ducloy, Phys. Rev. A 69, 013812 (2004). 10.1103/PhysRevA.69.013812
91. D. E. Chang, A. S. Sorensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006). 10.1103/PhysRevLett.97.053002
92. D. Chang, A. Sørensen, E. Demler, and M. Lukin, Nat. Phys. 3, 807 (2007). 10.1038/nphys708
93. Y. C. Jun, R. D. Kekapture, J. S. White, and M. L. Brongersma, Phys. Rev. B 78, 153111 (2008). 10.1103/PhysRevB.78.153111
94. F. Intravaia and A. Lambrecht, Phys. Rev. Lett. 94, 110404 (2005). 10.1103/PhysRevLett.94.110404
95. F. Capasso, J. Munday, D. Iannuzzi, and H. Chan, IEEE J. Sel. Top. Quantum Electron. 13, 400 (2007). 10.1109/JSTQE.2007.893082
96. S. Collin, F. Pardo, and J. L. Pelouard, Opt. Express 15, 4310 (2007). 10.1364/OE.15.004310
97. F. M. Kong, K. Li, B. I. Wu, H. Huang, H. S. Chen, and J. A. Kong, PIER 76, 449 (2007). 10.2528/PIER07070203
98. F. M. Kong, B. I. Wu, H. S. Chen, and J. A. Kong, Opt. Express 15, 12331 (2007). 10.1364/OE.15.012331
99. M. W. Vogel and D. K. Gramotnev, Phys. Lett. A 363, 507 (2007). 10.1016/j.physleta.2006.11.041
100. E. Anemogiannis and E. N. Glytsis, J. Lightwave Technol. 10, 1344 (1992). 10.1109/50.166774
101. A. Bakhtazad, H. Abiri, and R. Ghayour, J. Lightwave Technol. 15, 383 (1997). 10.1109/50.554392
102. M. S. Kwon and S. Y. Shin, Opt. Commun. 233, 119 (2004). 10.1016/j.optcom.2004.01.037
103. R. Rodriguez-Berral, F. Mesa, and F. Medina, IEEE Trans. Microwave Theory Tech. 53, 1613 (2005). 10.1109/TMTT.2005.847051
104. R. Rodriguez-Berral, F. Mesa, and F. Medina, Int. J. RF Microwave Comput.-Aided Eng. 14, 73 (2004). 10.1002/mmce.10120
105. R. E. Smith, S. N. Houde-Walter, and G. W. Forbes, IEEE J. Quantum Electron. 28, 1520 (1992). 10.1109/3.135305
106. The variable z in this appendix denotes an arbitrary complex number in the complex plane. It is not the space coordinate used in the rest of the paper.
107. The concept of Riemann surface is another way to look at the branch points of complex functions. For instance, the square-root function has a two-sheeted Riemann surface due to the two possible ways of choosing the sign of the result. Reference visualizes and talks about Riemann surfaces.
108. R. Bousso and J. Polchinski, J. High Energy Phys. 2000, 006 (2000). 10.1088/1126-6708/2000/06/006