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Fano Approximation as a Fast and Effective Way for Estimating Resonance Characteristics of Surface Plasmon Structures

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Abstract

Developing efficient methods for evaluating resonance characteristics of resonance structures is of particular importance in sensing, spectroscopy, and optical filtration. In the past, the resonance characteristics were evaluated using exact approaches with time-consuming data post-processing algorithms. In this work, using the Fano approximation of the resonance line shapes appearing in spectra of planar plasmonic structures, we obtain analytical expressions for the surface field enhancement, resonance width and height, and sensitivity as functions of structural optical parameters. Approximate data for three-layer Au-, Ag-, Cu-, and Al-based structures in aqueous environment are compared with exact values to estimate the approximation error in the visible and infrared regions. We obtain overall good fits of the approximated estimations to the exact data over the wavelength regions considered, which ensure the validity of the Fano-based approach. Furthermore, by applying the Fano-based approach to gas sensing, we demonstrate that in the angular spectra of the three-layer structures, the excitation of propagating plasmons in the infrared region leads to narrower resonance line shapes due to the decrease in the plasmonic mode damping, resulting in higher sensitivities to changes in air environment. The Fano-based expressions tangibly increase the speed of calculations, provide an insight into fundamental aspects of resonance physics, and can be used for designing efficient sensing structures and characterizing optical changes in the environment.

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Data Availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Nylander C, Liedberg B, Lind T (1982) Gas detection by means of surface plasmon resonance. Sensors Actuators 3:79–88

    Article  CAS  Google Scholar 

  2. Homola J (2008) Surface plasmon resonance sensors for detection of chemical and biological species. Chem Rev 108:462–493

    Article  CAS  Google Scholar 

  3. Meyer SA, Le Ru EC, Etchegoin PG (2011) Combining surface plasmon resonance (SPR) spectroscopy with surface-enhanced Raman scattering (SERS). Anal Chem 83:2337–2344

    Article  CAS  Google Scholar 

  4. Elhani S, Ishitobi H, Inouye Y, Ono A, Hayashi S, Sekkat Z (2020) Surface enhanced visible absorption of dye molecules in the near-field of gold nanoparticles. Sci Rep 10:3913

    Article  CAS  Google Scholar 

  5. Zhu T, Zhou Y, Lou Y, Ye H, Qiu M, Ruan Z, Fan S (2017) Plasmonic computing of spatial differentiation. Nat Commun 8:1–6

    Article  Google Scholar 

  6. Ashwell G, Roberts M (1996) Highly selective surface plasmon resonance sensor for NO2. Electron Lett 32:2089–2091

    Article  CAS  Google Scholar 

  7. Lang T, Hirsch T, Fenzl C, Brandl F, Wolfbeis OS (2012) Surface plasmon resonance sensor for dissolved and gaseous carbon dioxide. Anal Chem 84:9085–9088

    Article  CAS  Google Scholar 

  8. Manera MG, Montagna G, Ferreiro-Vila E, González-García L, Sánchez-Valencia J, González-Elipe AR, Cebollada A, Garcia-Martin JM, García-Martín A, Armelles G (2011) Enhanced gas sensing performance of TiO2 functionalized magneto-optical SPR sensors. J Mater Chem 21:16049–16056

    Article  CAS  Google Scholar 

  9. Berrier A, Offermans P, Cools R, van Megen B, Knoben W, Vecchi G, Rivas JG, Crego-Calama M, Brongersma SH (2011) Enhancing the gas sensitivity of surface plasmon resonance with a nanoporous silica matrix. Sensors Actuators B Chem 160:181–188

    Article  CAS  Google Scholar 

  10. Maharana PK, Jha R, Padhy P (2015) On the electric field enhancement and performance of SPR gas sensor based on graphene for visible and near infrared. Sensors Actuators B Chem 207:117–122

    Article  CAS  Google Scholar 

  11. Miwa S, Arakawa T (1996) Selective gas detection by means of surface plasmon resonance sensors. Thin Solid Films 281:466–468

    Article  Google Scholar 

  12. Petty M (1995) Gas sensing using thin organic films. Biosens Bioelectron 10:129–134

    Article  CAS  Google Scholar 

  13. Ignac-Nowicka J, Pustelny T, Opilski Z, Maciak E, Jakubik WP, Urbanczyk MW (2003) Examination of thin films of phthalocyanines in plasmon system for application in NO2 sensors. Opt Eng 42:2978–2986

    Article  CAS  Google Scholar 

  14. Yang D, Lu HH, Chen B, Lin CW (2010) Surface plasmon resonance of SnO2/Au Bi-layer films for gas sensing applications. Sensors Actuators B Chem 145:832–838

    Article  CAS  Google Scholar 

  15. Herminjard S, Sirigu L, Herzig HP, Studemann E, Crottini A, Pellaux JP, Gresch T, Fischer M, Faist J (2009) Surface plasmon resonance sensor showing enhanced sensitivity for CO2 detection in the mid-infrared range. Opt Express 17:293–303

    Article  CAS  Google Scholar 

  16. Herminjard S, Crottini A, Vaccaro L, Herzig H, Studemann E, Nicolle G (2006) Surface plasmon waveguide resonance spectroscopy applied on food dyes solutions under anomalous dispersion. Proc. EOS Topical Meeting on Molecular Plasmonic Devices, 1, 13, Engelberg, Switzerland, pp 3–4

  17. Shin W, Matsumiya M, Qiu F, Izu N, Murayama N (2004) Thermoelectric gas sensor for detection of high hydrogen concentration. Sensors Actuators B Chem 97:344–347

    Article  CAS  Google Scholar 

  18. Takeuchi K, Tanaka T, Ikeda M, Shibata K, Sakauchi Y, Yamada Y, Nakano S (1993) Highly accurate CO2 gas sensor using a modulation-type pyroelectric infrared detector. Jpn J Appl Phys 32:221

    Article  CAS  Google Scholar 

  19. Nesterenko DV, Pavelkin RA, Hayashi S, Soifer VA (2019) Analysis of the resonance characteristics of surface plasmon polariton modes at air-metal interfaces in the ultraviolet, visible and infrared regions. J Phys Conf Ser 1368:022062

    Article  CAS  Google Scholar 

  20. Nesterenko DV, Hayashi S, Sekkat Z (2016) Extremely narrow resonances, giant sensitivity and field enhancement in low-loss waveguide sensors. J Opt 18:065004

    Article  Google Scholar 

  21. Hayashi S, Fujiwara Y, Kang B, Fujii M, Nesterenko DV, Sekkat Z (2017) Line shape engineering of sharp Fano resonance in Al-based metal-dielectric multilayer structure. J Appl Phys 122:163103

    Article  Google Scholar 

  22. Shalabney A, Abdulhalim I (2011) Sensitivity-enhancement methods for surface plasmon sensors. Laser Photonics Rev 5:571–606

    Article  CAS  Google Scholar 

  23. Homola J, Koudela I, Yee SS (1999) Surface plasmon resonance sensors based on diffraction gratings and prism couplers: sensitivity comparison. Sensors Actuators B Chem 54:16–24

    Article  CAS  Google Scholar 

  24. Johansen K, Stålberg R, Lundström I, Liedberg B (2000) Surface plasmon resonance: instrumental resolution using photo diode arrays. Meas Sci Technol 11:1630–1638

    Article  CAS  Google Scholar 

  25. Raether H (1988) Surface plasmons on smooth and rough surfaces and on gratings. Springer-Verlag, Berlin Heidelberg, Berlin

    Book  Google Scholar 

  26. Ruan Z, Wu H, Qiu M, Fan S (2014) Spatial control of surface plasmon polariton excitation at planar metal surface. Opt Lett 39:3587

    Article  Google Scholar 

  27. Kurihara K, Nakamura K, Suzuki K (2002) Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle. Sensors Actuators B Chem 86:49–57

    Article  CAS  Google Scholar 

  28. Knobloch H, Brunner H, Leitner A, Aussenegg F, Knoll W (1993) Probing the evanescent field of propagating plasmon surface polaritons by fluorescence and Raman spectroscopies. J Chem Phys 98:10093–10095

    Article  CAS  Google Scholar 

  29. Knobloch H, Knoll W (1991) Raman-imaging and -spectroscopy with surface plasmon light. J Chem Phys 94:835–842

    Article  CAS  Google Scholar 

  30. Nesterenko DV, Sekkat Z (2013) Resolution estimation of the Au, Ag, Cu, and Al single- and double-layer surface plasmon sensors in the ultraviolet, visible, and infrared regions. Plasmonics 8:1585–1595. https://doi.org/10.1007/s11468-013-9575-1

    Article  CAS  Google Scholar 

  31. Nesterenko DV, Hayashi S, Sekkat Z (2018a) Asymmetric surface plasmon resonances revisited as Fano resonances. Phys Rev B 97:235437. https://doi.org/10.1103/PhysRevB.97.235437

    Article  Google Scholar 

  32. Nesterenko D, Pavelkin R, Hayashi S, Soifer V (2020) Analysis of resonance characteristics of surface plasmon-polariton modes at water-metal interfaces by Fano approximation. J Phys: Conf Ser 1461:012115

    CAS  Google Scholar 

  33. Nesterenko DV, Pavelkin RA, Hayashi S (2019) Estimation of resonance characteristics of single-layer surface-plasmon sensors in liquid solutions using Fanos approximation in the visible and infrared regions. Comput Opt 43:596–604

    Article  Google Scholar 

  34. Kretschmann E, Raether H (1968) Notizen: radiative decay of non radiative surface plasmons excited by light. Z Naturforsch A 23:235437

    Google Scholar 

  35. Novotny L, Hecht B (2006) Principles of nano-optics. Cambridge University Press, New York

    Book  Google Scholar 

  36. Nesterenko DV, Hayashi S, Sekkat Z (2018b) Coupled-mode theory of field transfer processes in surface plasmon resonance structures. J Phys Conf Ser 1092:012097

    Article  Google Scholar 

  37. Piliarik M, Homola J (2009) Surface plasmon resonance (SPR) sensors: approaching their limits? Opt Express 17:16505–16517

    Article  CAS  Google Scholar 

  38. SCHOTT Zemax catalog 2017–01–20b. http://www.schott.com/advanced_optics/english/download/. Accessed 10 Jan 2020

  39. Palik ED (1998) Handbook of optical constants of solids. Academic press, Boston

    Google Scholar 

  40. Rakic AD (1995) Algorithm for the determination of intrinsic optical-constants of metal-films—application to aluminum. Appl Opt 34:4755–4767

    Article  CAS  Google Scholar 

  41. Johnson PB, Christy R-W (1972) Optical constants of the noble metals. Phys Rev B 6:4370

    Article  CAS  Google Scholar 

  42. Segelstein DJ (1981) The complex refractive index of water. MS thesis (University of Missouri)

  43. Katsidis CC, Siapkas DI (2002) General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference. Appl Opt 41:3978–3987

    Article  Google Scholar 

  44. Querry MR (1987) Optical constants of minerals and other materials from the millimeter to the ultraviolet. Chemical Research, Development & Engineering Center, US Army Armament Munitions Chemical Command, Kansas City

Download references

Funding

This research was funded by Ministry of Science and Higher Education of Russian Federation (State assignment to FSRC “Crystallography and Photonics” RAS) and by Russian Foundation for Basic Research (project numbers 18-29-20006 and 18-07-00613).

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Authors and Affiliations

  1. Faculty of Information Technology, Samara National Research University, Samara, 443086, Russia

    Dmitry V. Nesterenko & Victor Soifer

  2. Diffractive Optics Laboratory, IPSI RAS - Branch of the FSRC “Crystallography and Photonics” RAS, Samara, 443086, Russia

    Dmitry V. Nesterenko & Victor Soifer

  3. Faculty of Electronics and Instrument Engineering, Samara National Research University, Samara, 443086, Russia

    Roman Pavelkin

  4. Department of Electrical and Electronic Engineering, Graduate School of Engineering, Kobe University, Kobe, 657-8501, Japan

    Shinji Hayashi

  5. Optics and Photonics Center, Moroccan Foundation for Science, Innovation and Research (MAScIR), Rabat, 10100, Morocco

    Shinji Hayashi & Zouheir Sekkat

  6. Graduate School of Engineering, Osaka University, Suita, 565-0871, Japan

    Zouheir Sekkat

  7. Faculty of Sciences, Mohammed V University in Rabat, Rabat, 10010, Morocco

    Zouheir Sekkat

Authors
  1. Dmitry V. Nesterenko
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  2. Roman Pavelkin
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  3. Shinji Hayashi
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  4. Zouheir Sekkat
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  5. Victor Soifer
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Contributions

Conceptualization, data curation, and methodology, D.N.; investigation, formal analysis, software, visualization, writing—original draft preparation, writing—review and editing, R.P. and D.N.; supervision and revision of the manuscript, validation, S.H., Z.S., and V.S. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Dmitry V. Nesterenko.

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Nesterenko, D., Pavelkin, R., Hayashi, S. et al. Fano Approximation as a Fast and Effective Way for Estimating Resonance Characteristics of Surface Plasmon Structures. Plasmonics 16, 1001–1011 (2021). https://doi.org/10.1007/s11468-020-01364-8

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