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Nonlinear nanophotonic and nanoplasmonic directional couplers: comparison of modelling methods

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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.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • 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 

  • 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 

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

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  • 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 

  • 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 

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

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  • 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 

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

    Article  ADS  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 

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

    Article  ADS  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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 

  • 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)

  • 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)

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • 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 

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

  • 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 

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

    Article  ADS  Google Scholar 

  • 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 

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

    Article  Google Scholar 

  • 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 

  • 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 

  • 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 

  • 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)

  • 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 

  • 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 

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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.

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Correspondence to Jiří Čtyroký.

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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

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  • DOI: https://doi.org/10.1007/s11082-015-0203-5

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