Nonlinear nanophotonic and nanoplasmonic directional couplers: comparison of modelling methods

Abstract

Two different in-house software tools for numerical modelling of structures with a very high refractive index contrast and a strong χ (3) nonlinearity are briefly presented. Results of their application for modelling nonlinear nanophotonic and nanoplasmonic directional couplers based on slot waveguide geometry are successfully mutually compared and assessed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. Čtyroký, J.: Efficient boundary conditions for bidirectional propagation algorithm based on Fourier series. J. Lightwave Technol. 27, 2575–2582 (2009)

    Article  ADS  Google Scholar 

  2. Čtyroký, J.: 3-D Bidirectional propagation algorithm based on Fourier series. J. Lightwave Technol. 30, 3699–3708 (2012)

    Article  ADS  Google Scholar 

  3. Čtyroký, J., Kwiecien, P., Richter, I.: Fourier series-based bidirectional propagation algorithm with adaptive spatial resolution. J. Lightwave Technol. 28, 2969–2976 (2010)

    Article  ADS  Google Scholar 

  4. Čtyroký, J., Kwiecien, P., Richter, I.: Analysis of hybrid dielectric-plasmonic slot waveguide structures with 3D Fourier modal methods. J. Eur. Opt. Soc. 8, 13024-1–13024-6 (2013)

    Google Scholar 

  5. Davoyan, A.R., Shadrivov, I.V., Kivshar, Y.S.: Nonlinear plasmonic slot waveguides. Opt. Express 16, 21209–21214 (2008)

    Article  ADS  Google Scholar 

  6. Davoyan, A.R., Shadrivov, I.V., Kivshar, Y.S.: Nonlinear plasmonic slot waveguides: erratum. Opt. Express 17, 4833 (2009)

  7. Deng, H., Yevick, D.: The nonunitarity of finite-element beam propagation algorithms. IEEE Photonics Technol. Lett. 17, 1429–1431 (2005)

    Article  ADS  Google Scholar 

  8. Fujii, M., Leuthold, J., Freude, W.: Dispersion relation and loss of subwavelength confined mode of metal-dielectric-gap optical waveguides. IEEE Photonics Technol. Lett. 21, 362–364 (2009)

    Article  ADS  Google Scholar 

  9. Fujisawa, T., Koshiba, M.: Full-vector finite-element beam propagation method for three-dimensional nonlinear optical waveguides. J. Lightwave Technol. 20, 1876–1884 (2002)

    Article  ADS  Google Scholar 

  10. Fujisawa, T., Koshiba, M.: Guided modes of nonlinear slot waveguides. IEEE Photonics Technol. Lett. 18, 1530–1532 (2006)

    Article  ADS  Google Scholar 

  11. Granet, G.: Reformulation of the lamellar grating problem through the concept of adaptive spatial resolution. J. Opt. Soc. Am. A 16, 2510–2516 (1999)

    MathSciNet  Article  ADS  Google Scholar 

  12. He, T., Cheng, Y., Du, Y., Mo, Y.: Z-scan determination of third-order nonlinear optical nonlinearity of three azobenzenes doped polymer films. Opt. Commun. 275, 240–244 (2007)

    Article  ADS  Google Scholar 

  13. Huang, W.-P., Mu, J.: Complex coupled-mode theory for optical waveguides. Opt. Express 17, 19134–19152 (2009)

    Article  ADS  Google Scholar 

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

    MathSciNet  Article  ADS  Google Scholar 

  15. Jensen, S.M.: The non-linear coherent coupler. IEEE J. Quantum Electron. 18, 1580–1583 (1982)

    Article  ADS  Google Scholar 

  16. Komatsu, M-a, Saitoh, K., Koshiba, M.: Design of highly-nonlinear horizontal slot waveguide with low and flat dispersion. Opt. Commun. 298, 180–184 (2013a)

    Article  ADS  Google Scholar 

  17. Komatsu, M., Saitoh, K., Koshiba, M.: Design of highly-nonlinear horizontal slot waveguide with low and flat dispersion. Opt. Commun. 298–299, 180–184 (2013b)

    Article  Google Scholar 

  18. Koshiba, M., Tsuji, Y.: Curvilinear hybrid edge/nodal elements with triangular shape for guided-wave problems. J. Lightwave Technol. 18, 737–743 (2000)

    Article  ADS  Google Scholar 

  19. Li, L.: New formulation of the Fourier modal method for crossed surface-relief gratings. J. Opt. Soc. Am. A 14, 2758–2767 (1997)

    Article  ADS  Google Scholar 

  20. Li, Z.Y., Ho, K.M.: Application of structural symmetries in the plane-wave-based transfer-matrix method for three-dimensional photonic crystal waveguides. Phys. Rev. B 68, 245117 (2003)

  21. Lin, Q., Zhang, J., Piredda, G., Boyd, R.W., Fauchet, P.M., Agrawal, G.P.: Dispersion of silicon nonlinearities in the near infrared region. Appl. Phys. Lett. 91, 21111 (2007)

  22. Muellner, P., Wellenzohn, M., Hainberger, R.: Nonlinearity of optimized silicon photonic slot waveguides. Opt. Express 17, 9282–9287 (2009)

    Article  ADS  Google Scholar 

  23. Petracek, J.: Nonlinear directional coupling between plasmonic slot waveguides. Appl. Phys. B Lasers Optics 112, 593–598 (2013)

    Article  ADS  Google Scholar 

  24. Pitilakis, A., Kriezis, E.E.: Highly nonlinear hybrid silicon-plasmonic waveguides: analysis and optimization. J. Opt. Soc. Am. B: Opt. Phys. 30, 1954–1965 (2013)

    Article  ADS  Google Scholar 

  25. Salgueiro, J.R., Kivshar, Y.S.: Complex modes in plasmonic nonlinear slot waveguides. J. Opt. 16, 114007 (2014)

  26. Schulz, D., Glingener, C., Bludszuweit, M., Voges, E.: Mixed finite element beam propagation method. J. Lightwave Technol. 16, 1336–1341 (1998)

    Article  ADS  Google Scholar 

  27. Silberberg, A., Stegeman, G.I.: Nonlinear coupling of waveguide modes. Appl. Phys. Lett. 50, 801–803 (1987)

    Article  ADS  Google Scholar 

  28. Silberstein, E., Lalanne, P., Hugonin, J.P., Cao, Q.: Use of grating theories in integrated optics. J. Opt. Soc. Am. A 18, 2865–2875 (2001)

    Article  ADS  Google Scholar 

  29. Swillam, M.A., Tawfik, S.A.: Plasmonic slot waveguides with core nonlinearity. Plasmonics 9, 409–413 (2014)

    Article  Google Scholar 

  30. Tsilipakos, O., Pitilakis, A., Tasolamprou, A.C., Yioultsis, T.V., Kriezis, E.E.: Computational techniques for the analysis and design of dielectric-loaded plasmonic circuitry. Opt. Quantum Electron. 42, 541–555 (2011)

    Article  Google Scholar 

  31. Tsuji, Y., Koshiba, M.: Adaptive mesh generation for full-vectorial guided-mode and beam-propagation solutions. J. Sel. Top. Quantum Electron. 6, 163–169 (2000)

    Article  Google Scholar 

  32. Vallaitis, T., Bogatscher, S., Alloatti, L., Dumon, P., Baets, R., Scimeca, M.L., Biaggio, I., Diederich, F., Koos, C., Freude, W., Leuthold, J.: Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries. Opt. Express 17, 17357–17368 (2009)

    Article  ADS  Google Scholar 

  33. Walasik, W., Renversez, G., Kartashov, Y.V.: Stationary plasmon-soliton waves in metal-dielectric nonlinear planar structures: modeling and properties. Phys. Rev. A 89, 23816 (2014)

  34. Zhang, L., Yue, Y., Xiao-Li, Y., Wang, J., Beausoleil, R.G., Willner, A.E.: Flat and low dispersion in highly nonlinear slot waveguides. Opt. Express 18, 13187–13193 (2010)

    Article  ADS  Google Scholar 

  35. Zhang, W., Serna, S., Dubreuil, N., Cassan, E.: Nonlinear optimization of slot Si waveguides: TPA minimization with FOMTPA up to 4.25. Opt. Lett. 40, 1212–1215 (2015)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

J.P. acknowledges support of the Ministry of Education, Youth, and Sports of the Czech Republic (Project LD14008) and CEITEC–Central European Institute of Technology (Project CZ.1.05/1.1.00/02.0068), in the framework of European Regional Development Fund.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jiří Čtyroký.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Koška, P., Petráček, J., Kwiecien, P. et al. Nonlinear nanophotonic and nanoplasmonic directional couplers: comparison of modelling methods. Opt Quant Electron 47, 3201–3212 (2015). https://doi.org/10.1007/s11082-015-0203-5

Download citation

Keywords

  • Nonlinear optics
  • Integrated optics
  • Nanophotonics
  • Plasmonics
  • All-optical switching
  • Numerical modelling
  • Optical waveguides
  • Coupled-mode theory
  • Kerr-nonlinearity
  • Beam propagation method
  • Slot waveguides