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General Conditions of Confinement of the Electromagnetic Wave at the Metal-Dielectric Interface

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Abstract

The confinement of electromagnetic waves in a metal-dielectric interface involves a series of applications of practical interest, including optical absorption at interfaces, solar cells, and sensors. The condition used to obtain confinement appears to be insufficient to guarantee the observation of phenomena. In this work, an analytical study of confinement conditions was done without assumed approximations for permittivity. Thus, it has been possible to separate the real and imaginary parts of the wave vector and find the general conditions for confinement, which shows that in several metal-dielectric interfaces, you cannot have a confined wave. This obtained result shows that the wave in interface can cease to exist even with a small change in dielectric constant. Based on these new conditions, we reviewed a wide range of materials that can be used as adjacent to traditional metals (Ag and Au) and calculated their solar cell’s efficiency and the length of propagation.

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References

  1. W.L. Barnes, A. Dereux, T.W. Ebbesen, Nature 424, 824 (2003)

    Article  ADS  Google Scholar 

  2. U. Fano, JOSA 31, 213 (1941)

    ADS  Google Scholar 

  3. R.H. Ritchie, Phy. Rev. 106, 874 (1957)

    ADS  Google Scholar 

  4. A. Otto, Zeitschrift für Physik A: Hadrons and Nuclei 219, 227 (1969)

    Google Scholar 

  5. A. Otto, Zeitschrift für Physik A: Hadrons and Nuclei 216, 398 (1968)

    Google Scholar 

  6. E.N. Economou, Phy. Rev. 182, 539 (1969)

    ADS  Google Scholar 

  7. E. Kretschmann, Zeitschrift für Physik A: Hadrons and Nuclei 241, 313 (1971)

    Google Scholar 

  8. B. Dastmalchi, P. Tassin, T. Koschny, C.M. Soukoulis, Adv. Opt. Mater. 1, 177 (2016)

    Google Scholar 

  9. A. Kolomenski, A. Kolomenskii, J. Noel, S. Peng, Hans Schuessler. Appl. Opt. 48, 5683 (2009)

    ADS  Google Scholar 

  10. A. V. Andrade-neto, A. Ribeiro Neto, Aroldo, A. Jorio, Rev. Bras. Ensino. Fís. 39, 3 (2017)

  11. C.D. Bohn, A. Agrawal, Y. Lee, C.J. Choi, M.S. Davis, P.M. Haney, H.J. Lezeca, V.A. Szalai, Phys. Chem. Chem. Phys. 16, 6084 (2014)

    Google Scholar 

  12. L. Li, Int J Microw Wirel T. 11, 792 (2019)

  13. C.P. McPolin, J.S. Bouillard, S. Vilain, A.V. Krasavin, W. Dickson, D. O’Connor, G.A. Wurtz, J. Justice, B. Corbett, A.V. Zayats, Nat. Commun. 7, 1 (2016)

    Google Scholar 

  14. C. Vernoux, Y. Chen, L. Markey, C. Spârchez, J. Arocas, T. Felder, M. Neitz, L. Brusberg, J. Weeber, S. Bozhevolnyi, A. Dereux, Opt. Mater. Express 8, 469 (2018)

    ADS  Google Scholar 

  15. Q. Wang, X. Wang, S. Hang, W. Zhao, J. Jing, Opt Laser Technol. 124, 106002 (2020)

    Google Scholar 

  16. P.M. Bolger, W. Dickson, A.V. Krasavin, L. Liebscher, S.G. Hickey, D.V. Skryabin, A.V. Zayats, Opt. Lett. 35, 1197 (2010)

    ADS  Google Scholar 

  17. M.A. Noginov, V.A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J.A. Adegoke, B.A. Ritzo, K. Reynolds, International Society for Optics and Photonics 6642, 664218 (2017)

    Google Scholar 

  18. M.H. Chu, M. Trinh, IEEE Photonics J. 11, 1 (2019)

    Google Scholar 

  19. I. De Leon, P. Berini, Nat. Photon. 4, 382 (2010)

    ADS  Google Scholar 

  20. S. Kéna-Cohen, P.N. Stavrinou, D.D.C. Bradley, S.A. Maier, Nano Lett. 13, 1323 (2013)

    ADS  Google Scholar 

  21. C. Liu, F. Hu, W. Yang, J. Xu, Y. Chen, Trac-Trend. Anal Chem. 97, 354 (2017)

    Google Scholar 

  22. I. Suárez, A. Ferrando, J. Marques-Hueso, A. Díez, R. Abargues, P.J. Rodríguez-Cantó, Juan P. Martínez-Pastor, Nanophotonics 6, 1109 (2017)

    Google Scholar 

  23. N. Zhanga, T. Fuc, H. Xu, W. Wang, Nano Energy 68, 104322 (2020)

    Google Scholar 

  24. J. Zhu et al., Results in Phys. 7, 895 (2017)

    ADS  Google Scholar 

  25. A.P. Amalathas, M.M. Alkaisi, Micromachines 10, 619 (2019)

    Google Scholar 

  26. X. Sheng, J. Hu, J. Michel, L.C. Kimerling, Opt. Express 20, 496 (2012)

    ADS  Google Scholar 

  27. I. Abdulhalim, M. Zourob, A. Lakhtakia, Electromagnetics 28, 214 (2008)

    Google Scholar 

  28. S. Deng, P. Wang, X. Yu, Sensors 17, 2819 (2017)

    Google Scholar 

  29. J. Homola, S.S. Yee, G. Gauglitz, Sensor Actuat B-Chem. 54, 3 (1999)

    Google Scholar 

  30. J. Homola, Chem. Rev. 108, 462 (2008)

    Google Scholar 

  31. P. Arora, A. Krishnan, J. Phys. Comm. 2, 085012 (2018)

    ADS  Google Scholar 

  32. A.L. Gerardo, E.M. Carmen, M. Soler, L.M. Lechuga, Nanophotonics 6, 123 (2017)

    Google Scholar 

  33. W. Chen, S. Zhang, Q. Deng, H. Xu, Nat. Commun. 9, 1 (2018)

    ADS  Google Scholar 

  34. P. Kvasnička, K. Chadt, M. Vala, M. Bocková, J. Homola, Optics Lett. 37, 163 (2012)

    ADS  Google Scholar 

  35. A.D. Mcfarland, R.P. Van Duyne, Nano Lett. 3, 1057 (2003)

    ADS  Google Scholar 

  36. J.B. Khurgin, Nat. Nanotechnol. 10, 2 (2015)

    ADS  Google Scholar 

  37. N.N. Lal, H. Zhou, M. Hawkeye, J.K. Sinha, N.P. Bartlett, G.A.J. Amaratunga, J.J. Baumberg, Phys. Rev. B 85, 1 (2012)

    Google Scholar 

  38. K. Johansen, H. Arwin, I. Lundström, B. Liedberg, Rev Sci Instrum 71, 3530 (2000)

    ADS  Google Scholar 

  39. W. Lukosz, Biosens. Bioelectron. 6, 215 (1991)

    Google Scholar 

  40. A. Shalabney, I. Abdulhalim, Laser Photonics Rev 5, 571 (2011)

    ADS  Google Scholar 

  41. S. A. Maier, Plasmonics: Fundamentals and Applications, Springer (2007)

  42. H. Raether, Surface Plasmons on Smooth Surfaces, Springer (1988)

  43. I. Avrutsky, Phys. Rev. B 15, 155416 (2004)

    ADS  Google Scholar 

  44. N.M. Lawandy, Appl Phys Lett 85, 5040 (2004)

    ADS  Google Scholar 

  45. M.P. Nezhad, K. Tetz, Y. Fainman, Opt. Express 12, 4072 (2004)

    ADS  Google Scholar 

  46. M.A. Noginov, V.A. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J.A. Adegoke, B.A. Ritzo, K. Reynolds, Opt. Express 16, 1385 (2008)

    ADS  Google Scholar 

  47. L. Liu, Z. Li, B. Xu, C. Gu, X. Chen, H. Sun, Y. Zhou, Q. Qing, P. Shum, Y. Luo, IEEE Trans. Microw. Theory Tech. 65, 2008 (2017)

    ADS  Google Scholar 

  48. A. Paul, Y. Zhen, Y. Wang, W. Chang, Y. Xia, P. Nordlander, S. Link, Nano lett. 14, 3628 (2014)

    ADS  Google Scholar 

  49. A.N. Sudarkin, P.A. Demkovich, Sov. Phys. Tech. Phys. 34, 764 (1989)

    Google Scholar 

  50. X. Guo, M. Qiu, J. Bao, B.J. Wiley, Q. Yang, X. Zhang, Y. Ma, H. Yu, L. Tong, Nano Lett. 9, 4515 (2009)

    ADS  Google Scholar 

  51. Y.J. Li, Y.L. Yan, C. Zhang, Y.S. Zhao, J.N. Yao, Adv. Mater. 25, 2784 (2013)

    Google Scholar 

  52. W. Wang, W. Zhou, T. Fu, F. Wu, Z. Zhang, Q. Li, Z. Xu, W. Liu, Nano Energy 48, 197 (2018)

    Google Scholar 

  53. Y. Yan, C. Zhang, J.Y. Zheng, J. Yao, Y. Zhao, Adv. Mater. 24, 5681 (2012)

    Google Scholar 

  54. D. Zhang, Y. Xiang, J. Chen, J. Cheng, L. Zhu, R. Wang, G. Zou, P. Wang, H. Ming, M. Rosenfeld, R. Badugu, J.R. Lakowicz, Nano Lett. 18, 1152 (2018)

    ADS  Google Scholar 

  55. S. Zhang, H. Xu, ACS Nano 6, 8128 (2012)

    Google Scholar 

  56. N.N. Lal, H. Zhou, M. Hawkeye, J.K. Sinha, P.N. Bartlett, G.A.J. Amaratunga, J.J. Baumberg, Phys. Rev. B 85, 245318 (2012)

    ADS  Google Scholar 

  57. Z. Li, K. Bao, Y. Fang, Z. Guan, N.J. Halas, P. Nordlander, H. Xu, Phys. Rev. B 82, 241402 (2010)

    ADS  Google Scholar 

  58. S. Zhang, K. Bao, N.J. Halas, H. Xu, P. Nordlander, Nano Lett. 11, 1657 (2011)

    ADS  Google Scholar 

  59. B. Liedberg, C. Nylander, I. Lunström, Sensors and actuators 4, 299 (1983)

    Google Scholar 

  60. C. Nylander, B. Liedberg, T. Lind, Sensors and Actuators 3, 79 (1982)

    Google Scholar 

  61. B.A. Prabowo, A. Purwidyantri, K. Liu, Biosensors 8, 80 (2018)

    Google Scholar 

  62. J. Seidel, S. Grafström, L. Eng, Phys. Rev. Lett. 94, 177401 (2005)

    ADS  Google Scholar 

  63. G. Zhu, M. Mayy, V.A. Podolskiy, V.I. Gavrilenko, M.A. Noginov, Opt. Express 16, 15576 (2008)

    ADS  Google Scholar 

  64. I. Yaremchuk, H. Petrovska, V. Fitio, Y. Bobitski, Optik 158, 535 (2018)

    ADS  Google Scholar 

  65. M.A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C.E. Small, B.A. Ritzo, V.P. Drachev, V.M. Shalaev, Optics Lett. 31, 3022 (2006)

    ADS  Google Scholar 

  66. Y. Ye, R. Liu, Z. Song, Z. Liu, T.P. Chen, Opt. Express 27, 9189 (2019)

    ADS  Google Scholar 

  67. Z. Qi, C. Tan, G. Huang, Scientific Reports 6, 1 (2019)

    Google Scholar 

  68. A. Boltasseva, H.A. Atwater, Science 331, 290 (2011)

    ADS  Google Scholar 

  69. Y. Chen, P. Fischer, F.W. Wise, Phys. Rev. Lett. 95, 067402 (2005)

    ADS  Google Scholar 

  70. S. Wuestner, O. Hess, Prog. Opt. 59, 1 (2014)

    ADS  Google Scholar 

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Authors and Affiliations

  1. Multidisciplinary Center of Bom Jesus da Lapa, Federal University of Western Bahia, Bom Jesus da Lapa, BA, 47600-000, Brazil

    Adelmo S. Souza, Vinicius Coelho & Jorge Luís O. Santos

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  1. Adelmo S. Souza
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  2. Vinicius Coelho
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Souza, A.S., Coelho, V. & Santos, J.L.O. General Conditions of Confinement of the Electromagnetic Wave at the Metal-Dielectric Interface. Braz J Phys 51, 449–460 (2021). https://doi.org/10.1007/s13538-021-00868-w

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