Skip to main content
SpringerLink
Log in

Mode solvers for very thin long–range plasmonic waveguides

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

We present two mode solvers applied to a very thin long–range plasmonic waveguide. We compare the guided mode complex effective index obtained either applying a Fourier modal method or calculating density of guided modes using the Green’s dyad technique. We achieve good agreement for both effective indices and mode profiles. We also observe a different behaviour compared to long–range surface plasmon supported by thicker films.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anemogiannis E., Glytsis E., Gaylord T.: Determination of guided and leaky modes in lossless and lossy planar multilayer optical waveguides: Reflection pole method and wavector density method. J. Lightwav. Technol. 17, 929–941 (1999)

    Article  ADS  Google Scholar 

  • Barnes W.L., Dereux A., Ebbesen T.W.: Surface plasmon subwavelength optics. Nature 424, 824–830 (2003)

    Article  ADS  Google Scholar 

  • Berini P.: Plasmon-polariton waves guided by thin lossy metal films of finite width:bound modes of symmetric structures. Phys. Rev. B 61, 10484 (2000)

    Article  ADS  Google Scholar 

  • Berini P.: Long–range surface plasmon polaritons. Adv. Opt. Photonics 1, 484–588 (2009)

    Article  Google Scholar 

  • Berini P., Buckley R.: On the convergence and accuracy of numerical mode computations of surface plasmon waveguides. J. Comput. Theor. Nanosci. 6, 2040–2053 (2003)

    Article  Google Scholar 

  • Bienstman P., Seller S., Rosa L., Uranus H.P., Hopman W.C.L., Costa R., Melloni A., Andreani L.C., Hugonin J.P., Lalanne P., Pinto D., Obaya S.S.A., Dems M., Panajotov K.: Modelling leaky photonic wires: a mode solver comparison. Opt. Quantum Electron. 38, 731–759 (2006)

    Article  Google Scholar 

  • Chiang K.S.: Review of numerical and approximate methods for the modal analysis of general optical dielectric waveguides. Opt. Quantum Electron. 26, S113–S134 (1994)

    Article  Google Scholar 

  • Colas des Francs G., Grandidier J., Massenot S., Bouhelier A., Weeber J.C., Dereux A.: Integrated plasmonic waveguides: a mode solver based on density of states formulation. Phys. Rev. B 80, 115419 (2009)

    Article  ADS  Google Scholar 

  • Colas des Francs G., Girard C., Weeber J.-C., Chicanne C., David T., Dereux A., Peyrade D.: Optical analogy to electronic quantum corrals. Phys. Rev. Lett. 86, 4950–4953 (2001)

    Article  ADS  Google Scholar 

  • Colas des Francs G., Girard C., Dereux A.: Theory of near-field optical imaging with a single molecule as a light source. J. Chem. Phys. 117, 4659–4666 (2002)

    Article  ADS  Google Scholar 

  • Colas des Francs G., Bramant P., Grandidier J., Bouhelier A., Weeber J.-C., Dereux A.: Optical gain, spontaneous and stimulated emission of surface plasmon–polaritons in confined plasmonic waveguide. Opt. Express 18, 16327–16334 (2010)

    Article  ADS  Google Scholar 

  • Ctyroky J.: Improved bidirectional-mode expansion propagation algorithm based on fourier series. J. Lightwav. Technol. 25, 2321–2330 (2007)

    Article  ADS  Google Scholar 

  • Ctyroky J.: Efficient boundary conditions for bidirectional propagation algorithm based on fourier series. J. Lightwav. Technol. 27, 2575–2582 (2009)

    Article  ADS  Google Scholar 

  • Dereux A., Vigneron J.P., Lambin P., Lucas A.: Polaritons in semiconductor multilayered materials. Phys. Rev. B 38, 5438–5452 (1988)

    Article  ADS  Google Scholar 

  • Dereux A., Girard C., Chicanne C., Colas Francs G., David T., Bourillot E., Lacroute Y., Weeber J.C.: Subwavelength mapping of surface photonic states. Nanotechnology 14, 935–938 (2003)

    Article  ADS  Google Scholar 

  • De Leon I., Berini P.: Theory of surface plasmon-polariton amplification in planar structures incorporating dipolar gain media. Phys. Rev. B 78, 161401 (2008)

    Article  ADS  Google Scholar 

  • De Leon I., Berini P.: Amplification of long-range surface plasmons by a dipolar gain medium. Nat. Photonics 4, 382–387 (2010)

    Article  ADS  Google Scholar 

  • Ebbesen T.W., Genet C., Bozhevolnyi S.I.: Surface plasmon circuitry. Phys. Today 61, 44–50 (2008)

    Article  ADS  Google Scholar 

  • Gao G., Torres-Verdín C., Habashy T.M.: Analytical techniques to evaluate the integrals of 3d and 2d spatial dyadic green’s functions. Prog. Electromagnet. Res. 52, 47–80 (2005)

    Article  Google Scholar 

  • Hugonin J.P., Lalanne P., del Villar I., Matias I.R.: Fourier modal methods for modeling optical dielectric waveguides. Opt. Quantum Electron. 37, 107–119 (2005)

    Article  Google Scholar 

  • Hugonin J.P., Lalanne P.: Perfectly-matched-layers as nonlinear coordinate transforms: a generalized formalization. J. Opt. Soc. Am. A. 22, 1844–1849 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  • Gather M.C., Meerholz K., Danz N., Leosson K.: Net optical gain in a plasmonic waveguide embedded in a fluorescent polymer. Nat. Photonics 4, 457–461 (2010)

    Article  ADS  Google Scholar 

  • Girard C., Dereux A., Quidant R., Colas Francs G., Weeber J.-C.: Subwavelength optical devices for nanometer scale applications. Int. J. Nanosci. 1, 63–78 (2002)

    Article  Google Scholar 

  • Gramotnev D.K., Bozhevolnyi S.I.: Plasmonics beyond the diffraction limit. Nat. Photonics 4, 83–91 (2010)

    Article  ADS  Google Scholar 

  • Grandidier J., Massenot S., Colas Francs G., Bouhelier A., Weeber J.-C., Markey L., Dereux A., Renger J., González M.U., Quidant R.: Dielectric-loaded surface plasmon polariton waveguides: figures of merit and mode characterization by image and fourier plane leakage microscopy. Phys. Rev. B 78, 245419 (2008)

    Article  ADS  Google Scholar 

  • Grandidier J., Colas Francs G., Massenot S., Bouhelier A., Markey L., Weeber J.-C., Finot C., Dereux A.: Gain assisted propagation in a plasmonic waveguide at telecom wavelength. Nano Lett. 9, 2935–2939 (2009)

    Article  ADS  Google Scholar 

  • Grandidier J., Colas Francs G., Markey L., Bouhelier A., Massenot S., Weeber J.-C., Dereux A.: Dielectric-loaded surface plasmon polariton waveguides on a finite-width metal strip. Appl. Phys. Lett. 96, 063105 (2010)

    Article  ADS  Google Scholar 

  • Kim J.T., Ju J.J., Park S., Su Kim M., Park S.K., Lee M.-H.: Chip-to-chip optical interconnect using gold long-range surface plasmon polariton waveguides. Opt. Express 16, 13133–13138 (2008)

    Article  ADS  Google Scholar 

  • Ladouceur F.: Boundaryless beam propagation. Opt. Lett. 21, 4–5 (1996)

    Article  ADS  Google Scholar 

  • Lagendijk A., Tiggelen B.: Resonant multiple scattering of light. Phys. Rep. 270, 143–215 (1996)

    Article  ADS  Google Scholar 

  • Lalanne P., Jurek M.P.: Computation of the near-field pattern with the coupled-wave method for tm polarization. J. Mod. Opt. 45, 1357–1374 (1998)

    Article  ADS  Google Scholar 

  • Lévêque G., Colas Francs G., Girard C., Weeber J.-C., Meier C., Robilliard C., Mathevet R., Weiner J.: Polarization state of the optical near-field. Phys. Rev. E 65, 36701 (2002)

    Article  Google Scholar 

  • Lévêque G., Mathevet R., Weiner J., Colas Francs G., Girard C., Quidant R., Weeber J.-C., Dereux A.: Modelling resonant coupling between microring resonators addressed by optical evanescent waves. Nanotechnology 15, 1200–1210 (2004)

    Article  ADS  Google Scholar 

  • Martin O.J.F., Dereux A., Girard Ch.: An iterative scheme to compute exactly the total field propagating in dielectric structures of arbitrary shapes. J. Opt. Soc. A. A 11, 1073–1080 (1994)

    Article  ADS  Google Scholar 

  • Massenot S., Grandidier J., Bouhelier A., Colas Francs G., Weeber J.-C., Markey L., Dereux A., Renger J., Gonzalez M.U., Quidant R.: Polymer-metal waveguides characterization by fourier plane leakage radiation microscopy. Appl. Phys. Lett. 91, 243101 (2007)

    Article  ADS  Google Scholar 

  • Massenot S., Weeber J.-C., Bouhelier A., Colas Francs G., Grandidier J., Markey L., Dereux A.: Differential method for modelling dielectric-loaded surface plasmon polariton waveguides. Opt. Express 16, 17599–17608 (2008)

    Article  ADS  Google Scholar 

  • Moharam M.G., Grann E.B., Pommet D.A., Gaylord T.K.: J. Opt. Soc. Am. A 12, 1068 (1995)

    Article  ADS  Google Scholar 

  • Oulton R., Sorger V., Zentgraf T., Ma R.M., Gladden C., Dai L., Bartal G., Zhang X.: Plasmon lasers at deep subwavelength scale. Nature 461, 629–632 (2009)

    Article  ADS  Google Scholar 

  • Palik E.: Handbook of Optical Constants of Solids. Academic Press - Elsevier, London, Amsterdam (1998)

    Google Scholar 

  • Paulus M., Gay-Balmaz P., Martin O.J.F.: Green’s tensor technique for scattering in two-dimensional stratified media. Phys. Rev. E 63, 66615 (2001)

    Article  ADS  Google Scholar 

  • Quidant R., Weeber J.-C., Dereux A., Peyrade D., Colas Francs G., Girard C., Chen Y.: Addressing and imaging high optical index dielectric ridges in the optical near field. Phys. Rev. E 64, 66607 (2001)

    Article  ADS  Google Scholar 

  • Raether H.: Excitation of Plasmons and Interband Transitions by Electrons. Springer, Berlin (1980)

    Google Scholar 

  • Snyder A.W., Love J.D.: Optical Waveguide Theory. Chapman and Hall, London (1996)

    Google Scholar 

  • Thylen L., He S., Wosynki L.L., Dai D.: The moore’s law for photonic integrated circuits. J. Zhejiang Univ. Sci. A 7, 1961–1967 (2006)

    Article  MATH  Google Scholar 

  • Weeber J.C., Dereux Y., Lacroute A.: Optical near-field distributions of surface plasmon waveguide modes. Phys. Rev. B 68, 115401 (2003)

    Article  ADS  Google Scholar 

  • Yaghjian A.D.: Electric dyadic green’s functions in the source region. Proc. IEEE 68, 248–263 (1980)

    Article  Google Scholar 

  • Zayats A.V., Smolyaninov I.I., Maradudin A.A.: Nano–optics of surface plasmon polaritons. Phys. Rep. 408, 131–314 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR5209 CNRS-Université de Bourgogne, 9, av. Savary, BP 47870, 21078, Dijon, France

    Gérard Colas des Francs

  2. Laboratoire Charles Fabry de l’Institut d’Optique, CNRS-Université Paris Sud Campus Polytechnique, RD 128, 91127, Palaiseau cedex, France

    Jean-Paul Hugonin

  3. Institute of Photonics and Electronics, AS CR v.v.i, Prague, Czech Republic

    Jiřǐ Čtyroký

Authors
  1. Gérard Colas des Francs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jean-Paul Hugonin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiřǐ Čtyroký
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gérard Colas des Francs.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Colas des Francs, G., Hugonin, JP. & Čtyroký, J. Mode solvers for very thin long–range plasmonic waveguides. Opt Quant Electron 42, 557–570 (2011). https://doi.org/10.1007/s11082-010-9428-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11082-010-9428-5

Keywords

Search

Navigation