DOI QR코드

DOI QR Code

Investigation of the Convergence Behavior with Fluctuation Features in the Fourier Modal Analysis of a Metallic Grating

  • Kim, Hwi (Department of Electronics and Information Engineering, College of Science and Technology, Korea University, Sejong Campus) ;
  • Park, Gwanwoo (Department of Electronics and Information Engineering, College of Science and Technology, Korea University, Sejong Campus) ;
  • Kim, Changsoon (Graduate School of Convergence Science and Technology, Seoul National University)
  • Received : 2012.08.27
  • Accepted : 2012.09.05
  • Published : 2012.09.25

Abstract

We observe that the transmission and reflection efficiencies of a one-dimensional metallic grating under transverse-magnetic illumination calculated using the Fourier modal method (FMM) with the Fourier factorization rules have peculiar fluctuations, albeit small in magnitude, as the number of field harmonics increases. It is shown that when the number of Fourier terms for the electromagnetic field is increased from that in the conventional FMM, the fluctuations due to non-convergent highly evanescent eigenmodes can be eliminated. Our examination reveals that the fluctuations originate from the Gibbs phenomenon inherent in the Fourier-series representation of a permittivity function with discontinuities, and from non-convergence of highly evanescent internal Bloch eigenmodes.

Keywords

References

  1. H. Kim, J. Park, and B. Lee, Fourier Modal Method and Its Applications in Computational Nanophotonics (CRC Press, Boca Raton, FL, USA, 2012).
  2. P. Lalanne and E. Silberstein, "Fourier-modal methods applied to waveguide computational problems," Opt. Lett. 25, 1092-1094 (2000). https://doi.org/10.1364/OL.25.001092
  3. Q. Cao, P. Lalanne, and J. Hugonin, "Stable and efficient Bloch-mode computational method for one-dimensional grating waveguides," J. Opt. Soc. Am. A 19, 335-338 (2002). https://doi.org/10.1364/JOSAA.19.000335
  4. H. Kim, I.-M. Lee, and B. Lee, "Extended scattering-matrix method for efficient full parallel implementation of rigorous coupled-wave analysis," J. Opt. Soc. Am. A 24, 2313-2327 (2007). https://doi.org/10.1364/JOSAA.24.002313
  5. H. Kim and B. Lee, "Mathematical modeling of crossed nanophotonic structures with generalized scattering- matrix method and local Fourier modal analysis," J. Opt. Soc. Am. B 25, 518-544 (2008). https://doi.org/10.1364/JOSAB.25.000518
  6. C.-H. Sun, P. Jiang, and B. Jiang, "Broadband moth-eye antireflection coatings on silicon," Appl. Phys. Lett. 92, 061112 (2008). https://doi.org/10.1063/1.2870080
  7. C. Mateus, M. Huang, Y. Deng, A. Neureuther, and C. Chang- Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004). https://doi.org/10.1109/LPT.2003.821258
  8. Y. Ding and R. Magnusson, "Resonant leaky-mode spectralband engineering and device applications," Opt. Express 12, 5661-5674 (2004). https://doi.org/10.1364/OPEX.12.005661
  9. S. B. Mallick, N. P. Sergeant, M. Agrawal, J.-Y. Lee, and P. Peumans, "Coherent light trapping in thin-film photovoltaics," MRS Bull. 36, 453-460 (2011). https://doi.org/10.1557/mrs.2011.113
  10. E. Silberstein, P. Lalanne, J. Hugonin, and Q. Cao, "Use of grating theories in integrated optics," J. Opt. Soc. Am. A 18, 2865-2875 (2001). https://doi.org/10.1364/JOSAA.18.002865
  11. D. Carr, J. Sullivan, and T. Friedmann, "Laterally deformable nanomechanical zeroth-order gratings: anomalous diffraction studied by rigorous coupled-wave analysis," Opt. Lett. 28, 1636-1638 (2003). https://doi.org/10.1364/OL.28.001636
  12. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). https://doi.org/10.1364/JOSAA.13.001870
  13. P. Lalanne and G. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996).
  14. G. Granet and B. Guizal, "Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996). https://doi.org/10.1364/JOSAA.13.001019
  15. H. Liu and P. Lalanne, "Microscopic theory of the extraordinary optical transmission," Nature 452, 728-731 (2008). https://doi.org/10.1038/nature06762
  16. K. Koerkamp, S. Enoch, F. Segerink, N. van Hulst, and L. Kuipers, "Strong influence of hole shape on extraordinary transmission through periodic arrays of subwavelength holes," Phys. Rev. Lett. 92, 183901 (2004). https://doi.org/10.1103/PhysRevLett.92.183901
  17. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, NY, USA, 1997).
  18. G. P. Tolstov, Fourier Series (Dover Publications, Mineola, NY, USA, 1976).
  19. M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, "Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit," Nat. Photonics 3, 152-156 (2009). https://doi.org/10.1038/nphoton.2009.22

Cited by

  1. Polarization-dependent transmission through a bull's eye with an elliptical aperture vol.316, 2014, https://doi.org/10.1016/j.optcom.2013.10.081
  2. Through-focus scanning optical microscopy with the Fourier modal method vol.26, pp.9, 2018, https://doi.org/10.1364/OE.26.011649
  3. Metrological sensitivity improvement of through-focus scanning optical microscopy by controlling illumination coherence vol.27, pp.3, 2019, https://doi.org/10.1364/OE.27.001981