Skip to main content
Log in

Modelling of hundreds of wavelength long, highly resonant, 3D subwavelength patterned scattering structures

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

Abstract

In this paper, we study the performances of the Dipole Discrete Approximation method for modelling the reflectivity of a highly resonant, 3D subwavelength patterned structure extending over tens of thousands wavelength square. The computation time of the whole reflectivity spectrum (80 wavelengths) was about 3 h on a computer and requires about 1.5 GB in memory. These performances make the DDA an unique numerical tool for modelling the scattering by large 3D structures supporting long-range interactions.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Belkebir, K., Chaumet, P.C., Sentenac, A.: Superresolution in total internal reflection tomography. J. Opt. Soc. Am. A 22, 1889–1897 (2005)

    Article  ADS  Google Scholar 

  • Buet, X., Guelmani, A., Monmayrant, A., Calvez, A., Tourte, C., Lozes-Dupuy, F., Gauthier-Lafaye, O.: Wavelength-stabilised external-cavity laser diode using cavity resonator integrated guided mode filter. Electron. Lett. 48, 1619–1621 (2012a)

    Article  Google Scholar 

  • Buet, X., Daran, E., Belharet, D., Lozes-Dupuy, F., Monmayrant, A., Gauthier-Lafaye, O.: High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter. Opt. Express 20, 9322–9327 (2012b)

    Article  ADS  Google Scholar 

  • Chaumet, P.C., Rahmani, A.: Efficient iterative solution of the discrete dipole approximation for magnetodielectric scatterers. Opt. Lett. 34, 917–919 (2009)

    Article  ADS  Google Scholar 

  • Chaumet, P.C., Sentenac, A.: Simulation of light scattering by multilayer cross-gratings with the coupled dipole method. J. Quant. Spect. Rad. Transf. 110, 409–414 (2009)

    Article  ADS  Google Scholar 

  • Chaumet, P.C., Rahmani, A., Bryant, G.W.: Generalization of the coupled dipole method to periodic structures. Phys. Rev. B 67, 165404–165405 (2003)

    Article  ADS  Google Scholar 

  • Chaumet, P.C., Belkebir, K., Rahmani, A.: Coupled-dipole method in time domain. Opt. Express 16, 20157–20165 (2008)

    Article  ADS  Google Scholar 

  • Chaumet, P.C., Zhang, T., Sentenac, A.: Fast far-field calculation in the discrete dipole approximation. J. Quant. Spectrosc. Radiat. Transf. 165, 88–92 (2015). ISSN 0022-4073

  • Chaumet, P.C., Demésy, G., Gauthier-Lafaye, O., Sentenac, A., Popov, E., Fehrembach, A.-L.: Electromagnetic modeling of large subwavelength-patterned highly resonant structures. Opt. Lett. 41, 2358–2361 (2016)

    Article  ADS  Google Scholar 

  • Draine, B.T.: The discrete-dipole approximation and its application to interstellar graphite grains. Astrophys. J. 333, 848–872 (1988)

    Article  ADS  Google Scholar 

  • Flatau, P.J., Stephens, G.L., Draine, B.T.: Light scattering by rectangular solids in the discrete-dipole approximation: a new algorithm exploiting the Block-Toeplitz structure. J. Opt. Soc. Am. A 7, 593–600 (1990)

    Article  ADS  Google Scholar 

  • Golubenko, G., Svakhin, A., Sychugov, V., Tischenko, A.: Total reflection of light from a corrugated surface of a dielectric waveguide. Sov. J. Quantum. Electron. 15, 886–887 (1985)

    Article  ADS  Google Scholar 

  • Golubenko, G., Svakhin, A., Sychugov, V., Tischenko, A., Popov, E., Mashev, L.: Diffraction characteristics of planar corrugated waveguides. Opt. Quantum. Electron. 18, 123–128 (1986)

    Article  Google Scholar 

  • Kintaka, K., Majima, T., Inoue, J., Hatanaka, K., Junji, N., Ura, S.: Cavity-resonator-integrated guided-mode resonance filter for aperture miniaturization. Opt. Express 20, 1444–1449 (2012)

    Article  ADS  Google Scholar 

  • Laberdesque, R., Gauthier-Lafaye, O., Camon, H., Monmayrant, A., Petit, M., Demichel, O., Cluzel, B.: High-order modes in cavity-resonator-integrated guided-mode resonance filters (CRIGFs). J. Opt. Soc. Am. A 32, 1973–1981 (2015)

    Article  ADS  Google Scholar 

  • Mashev, L., Popov, E.: Zero order anomaly of dielectric coated gratings. Opt. Commun. 55, 377–380 (1985)

    Article  ADS  Google Scholar 

  • Patterson, T.N.L.: The optimum addition of points to quadrature formulae. Math. Comput. 22, 847–856 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  • Paulus, M., Gay-Balmaz, P., Martin, O.J.F.: Accurate and efficient computation of the Green’s tensor for stratified media. Phys. Rev. E 62, 5797–807 (2000)

    Article  ADS  Google Scholar 

  • Press, W.H., Flannery, B.P., Teukolski, S.A., Vetterling, W.T.: Numerical Recipes. The Art of Scientific Computing. Cambridge University Press, Cambridge (1986)

    MATH  Google Scholar 

  • Purcell, E.M., Pennypacker, C.R.: Scattering and absorption of light by nonspherical dielectric grains. Astrophys. J. 186, 705–714 (1973)

    Article  ADS  Google Scholar 

  • Rahmani, A., Chaumet, P.C., de Fornel, F., Girard, C.: Field propagator of a dressed junction: fluorescence lifetime calculations in a confined geometry. Phys. Rev. A 56, 3245–3254 (1997)

    Article  ADS  Google Scholar 

  • Rassem, N., Fehrembach, A.-L., Popov, E.: Waveguide mode in the box with an extraordinary flat dispersion curve. J. Opt. Soc. Am. A 32, 420–430 (2015)

    Article  ADS  Google Scholar 

  • Tang, J., Shen, Y., Zheng, Y., Qiu, D.: An efficient and flexible computational model for solving the mild slope equation. Coast. Eng. 51, 143–154 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

This work benefited from the financial support from Agence Nationale de la Recherche and Direction Générale de l’Armement, Astrid program (CALITREC project).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Anne-Laure Fehrembach.

Additional information

This article is part of the Topical Collection on Optical Wave and Waveguide Theory and Numerical Modelling 2016.

Guest edited by Krzysztof Anders, Xuesong Meng, Gregory Morozov, Sendy Phang, and Mariusz Zdanowicz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chaumet, P.C., Sentenac, A. & Fehrembach, AL. Modelling of hundreds of wavelength long, highly resonant, 3D subwavelength patterned scattering structures. Opt Quant Electron 49, 71 (2017). https://doi.org/10.1007/s11082-017-0901-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-017-0901-2

Keywords

Navigation