Abstract

In thisPlease provide the IEEE membership details (membership grades and years in which these obtained), if any, for W.-L. Yeh and N.-Y. Shih. paper, multidomain pseudospectral (MDPS) method is adopted to analyze the diffraction of electromagnetic waves by the metallic lamellar grating. This method is based on applying a spectral accuracy at the Chebyshev collocation points to the spatial derivatives in Helmholtz equation, and then dividing the computational domain into nonoverlapping subdomains. Finally, the physical boundary conditions at the subdomain interfaces enforce the subdomains to a global system. The numerical examples for 1-D binary gratings composed of different highly conducting materials are presented. The validity of results by MDPS is compared with commonly used rigorous coupled wave analysis for TM polarization. The numerical evidence shows that the developed method has better stability and higher efficiency.

© 2009 IEEE

PDF Article

References

  • View by:
  • |
  • |

  1. D. Rosenblatt, A. Sharon, A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33, 2038-2059 (1997).
  2. A. Mandatori, M. Bertolotti, C. Sibilia, "Asymmetric transmission of some two dimensional photonic crystals," J. Opt. Soc. Amer. B, Opt. Phys. 24, 685-690 (2007).
  3. F. Deng, C. Du, X. Luo, "Characteristic analysis of evanescent wave moire fringes," J. Opt. Soc. Amer. B, Opt. Phys. 25, 443-447 (2008).
  4. S. Kameda, Y. Ohta, H. Kikuta, "Refraction and diffraction by a metal-dielectric multilayered structure," J. Opt. Soc. Amer. A, Opt. Image Sci. 25, 903-910 (2008).
  5. S. Banerjee, T. Hoshino, J. B. Cole, "Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference timedomain algorithm," J. Opt. Soc. Amer. A, Opt. Image Sci. 25, 1921-1928 (2008).
  6. S. D. Gedney, R. Mittra, "Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution," IEEE Trans. Antennas Propag. 39, 1605-1614 (1991).
  7. L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).
  8. S. Peng, G. M. Morris, "Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 12, 1087-1096 (1995).
  9. J. P. Boyd, Chebyshev and Fourier Spectral Methods (Springer-Verlag, 2001).
  10. D. Gottlieb, S. A. Orszag, "Numerical analysis of spectral methods: Theory and Applications," CBMS-NSF Regional Conf. Series Appl. Math., SIAM PhiladelphiaPA (1977).
  11. M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Amer. 71, 811-818 (1981).
  12. M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of grating diffraction: E-mode polarization and losses," J. Opt. Soc. Amer. 73, 451-455 (1983).
  13. M. G. Moharam, T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Amer. 73, 1105-1112 (1983).
  14. L. Li, C. W. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 10, 1184-1189 (1993).
  15. P. Lalanne, G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Amer. A, Opt. Image Sci. 13, 779-784 (1996).
  16. E. Popov, M. Neviere, "Differential theory for diffraction gratings: A new formulation for TM polarization with rapid convergence," Opt. Lett. 25, 598-600 (2000).
  17. E. Popov, B. Chernov, M. Neviere, N. Bonod, "Differential theory: Application to highly conducting gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 199-206 (2004).
  18. K. Watanabe, "Study of the differential theory of lamellar gratings made of highly conducting materials," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 69-72 (2006).
  19. N. M. Lyndin, O. Parriaux, A. V. Tishchenko, "Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 24, 3781-3787 (2007).
  20. A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Eletron. 37, 309-330 (2005).
  21. M. Foresti, L. Menez, A. V. Tishchenko, "Modal method in deep metal-dielectric gratings: The decisive role of hidden modes," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 2501-2509 (2006).
  22. Y. Todorov, C. Minot, "Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure," J. Opt. Soc. Amer. A, Opt. Image Sci. 24, 1084-7529 (2007).
  23. Q. H. Liu, "A pseudospectral frequency-domain (PSFD) method for computational electromagnetics," IEEE Antennas Wireless Propag. Lett. 1, 131-134 (2002).
  24. L. N. Trefethen, Spectral Methods in Matlab (SIAM, 2000).
  25. T. J. Rivlin, The Chebyshev Polynomials (Wiley, 1974).
  26. J. Y. Wang, C. C. Yang, Y. W. Kiang, "Numerical study on surface plasmon polariton behaviors in periodic metal-dieletric structures using a plane-wave-assisted boundary integral-equation method," Opt. Exp. 15, 9048-9062 (2007).
  27. Y.-P. Chiou, Y.-C. Chiang, C.-H. Lai, C.-H. Du, H.-C. Chang, "Finite-difference modeling of dielectric waveguides with sharp corners and slanted facets," IEEE/OSA J. Lightw. Technol. 27, 2077-2086 (2009).

2009 (1)

Y.-P. Chiou, Y.-C. Chiang, C.-H. Lai, C.-H. Du, H.-C. Chang, "Finite-difference modeling of dielectric waveguides with sharp corners and slanted facets," IEEE/OSA J. Lightw. Technol. 27, 2077-2086 (2009).

2008 (3)

F. Deng, C. Du, X. Luo, "Characteristic analysis of evanescent wave moire fringes," J. Opt. Soc. Amer. B, Opt. Phys. 25, 443-447 (2008).

S. Kameda, Y. Ohta, H. Kikuta, "Refraction and diffraction by a metal-dielectric multilayered structure," J. Opt. Soc. Amer. A, Opt. Image Sci. 25, 903-910 (2008).

S. Banerjee, T. Hoshino, J. B. Cole, "Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference timedomain algorithm," J. Opt. Soc. Amer. A, Opt. Image Sci. 25, 1921-1928 (2008).

2007 (4)

A. Mandatori, M. Bertolotti, C. Sibilia, "Asymmetric transmission of some two dimensional photonic crystals," J. Opt. Soc. Amer. B, Opt. Phys. 24, 685-690 (2007).

N. M. Lyndin, O. Parriaux, A. V. Tishchenko, "Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 24, 3781-3787 (2007).

J. Y. Wang, C. C. Yang, Y. W. Kiang, "Numerical study on surface plasmon polariton behaviors in periodic metal-dieletric structures using a plane-wave-assisted boundary integral-equation method," Opt. Exp. 15, 9048-9062 (2007).

Y. Todorov, C. Minot, "Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure," J. Opt. Soc. Amer. A, Opt. Image Sci. 24, 1084-7529 (2007).

2006 (2)

K. Watanabe, "Study of the differential theory of lamellar gratings made of highly conducting materials," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 69-72 (2006).

M. Foresti, L. Menez, A. V. Tishchenko, "Modal method in deep metal-dielectric gratings: The decisive role of hidden modes," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 2501-2509 (2006).

2005 (1)

A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Eletron. 37, 309-330 (2005).

2004 (1)

E. Popov, B. Chernov, M. Neviere, N. Bonod, "Differential theory: Application to highly conducting gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 199-206 (2004).

2002 (1)

Q. H. Liu, "A pseudospectral frequency-domain (PSFD) method for computational electromagnetics," IEEE Antennas Wireless Propag. Lett. 1, 131-134 (2002).

2000 (1)

1997 (1)

D. Rosenblatt, A. Sharon, A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33, 2038-2059 (1997).

1996 (1)

P. Lalanne, G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Amer. A, Opt. Image Sci. 13, 779-784 (1996).

1995 (1)

S. Peng, G. M. Morris, "Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 12, 1087-1096 (1995).

1993 (1)

L. Li, C. W. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 10, 1184-1189 (1993).

1991 (1)

S. D. Gedney, R. Mittra, "Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution," IEEE Trans. Antennas Propag. 39, 1605-1614 (1991).

1983 (2)

M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of grating diffraction: E-mode polarization and losses," J. Opt. Soc. Amer. 73, 451-455 (1983).

M. G. Moharam, T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Amer. 73, 1105-1112 (1983).

1981 (2)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).

M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Amer. 71, 811-818 (1981).

IEEE Antennas Wireless Propag. Lett. (1)

Q. H. Liu, "A pseudospectral frequency-domain (PSFD) method for computational electromagnetics," IEEE Antennas Wireless Propag. Lett. 1, 131-134 (2002).

IEEE J. Quantum Electron. (1)

D. Rosenblatt, A. Sharon, A. A. Friesem, "Resonant grating waveguide structures," IEEE J. Quantum Electron. 33, 2038-2059 (1997).

IEEE Trans. Antennas Propag. (1)

S. D. Gedney, R. Mittra, "Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution," IEEE Trans. Antennas Propag. 39, 1605-1614 (1991).

IEEE/OSA J. Lightw. Technol. (1)

Y.-P. Chiou, Y.-C. Chiang, C.-H. Lai, C.-H. Du, H.-C. Chang, "Finite-difference modeling of dielectric waveguides with sharp corners and slanted facets," IEEE/OSA J. Lightw. Technol. 27, 2077-2086 (2009).

J. Opt. Soc. Amer. (3)

M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Amer. 71, 811-818 (1981).

M. G. Moharam, T. K. Gaylord, "Rigorous coupled-wave analysis of grating diffraction: E-mode polarization and losses," J. Opt. Soc. Amer. 73, 451-455 (1983).

M. G. Moharam, T. K. Gaylord, "Three-dimensional vector coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Amer. 73, 1105-1112 (1983).

J. Opt. Soc. Amer. A, Opt. Image Sci. (10)

L. Li, C. W. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 10, 1184-1189 (1993).

P. Lalanne, G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Amer. A, Opt. Image Sci. 13, 779-784 (1996).

E. Popov, B. Chernov, M. Neviere, N. Bonod, "Differential theory: Application to highly conducting gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 21, 199-206 (2004).

K. Watanabe, "Study of the differential theory of lamellar gratings made of highly conducting materials," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 69-72 (2006).

N. M. Lyndin, O. Parriaux, A. V. Tishchenko, "Modal analysis and suppression of the Fourier modal method instabilities in highly conductive gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 24, 3781-3787 (2007).

S. Peng, G. M. Morris, "Efficient implementation of rigorous coupled-wave analysis for surface-relief gratings," J. Opt. Soc. Amer. A, Opt. Image Sci. 12, 1087-1096 (1995).

S. Kameda, Y. Ohta, H. Kikuta, "Refraction and diffraction by a metal-dielectric multilayered structure," J. Opt. Soc. Amer. A, Opt. Image Sci. 25, 903-910 (2008).

S. Banerjee, T. Hoshino, J. B. Cole, "Simulation of subwavelength metallic gratings using a new implementation of the recursive convolution finite-difference timedomain algorithm," J. Opt. Soc. Amer. A, Opt. Image Sci. 25, 1921-1928 (2008).

M. Foresti, L. Menez, A. V. Tishchenko, "Modal method in deep metal-dielectric gratings: The decisive role of hidden modes," J. Opt. Soc. Amer. A, Opt. Image Sci. 23, 2501-2509 (2006).

Y. Todorov, C. Minot, "Modal method for conical diffraction on a rectangular slit metallic grating in a multilayer structure," J. Opt. Soc. Amer. A, Opt. Image Sci. 24, 1084-7529 (2007).

J. Opt. Soc. Amer. B, Opt. Phys. (2)

A. Mandatori, M. Bertolotti, C. Sibilia, "Asymmetric transmission of some two dimensional photonic crystals," J. Opt. Soc. Amer. B, Opt. Phys. 24, 685-690 (2007).

F. Deng, C. Du, X. Luo, "Characteristic analysis of evanescent wave moire fringes," J. Opt. Soc. Amer. B, Opt. Phys. 25, 443-447 (2008).

Opt. Acta (1)

L. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, "The dielectric lamellar diffraction grating," Opt. Acta 28, 413-428 (1981).

Opt. Exp. (1)

J. Y. Wang, C. C. Yang, Y. W. Kiang, "Numerical study on surface plasmon polariton behaviors in periodic metal-dieletric structures using a plane-wave-assisted boundary integral-equation method," Opt. Exp. 15, 9048-9062 (2007).

Opt. Lett. (1)

Opt. Quantum Eletron. (1)

A. V. Tishchenko, "Phenomenological representation of deep and high contrast lamellar gratings by means of the modal method," Opt. Quantum Eletron. 37, 309-330 (2005).

Other (4)

J. P. Boyd, Chebyshev and Fourier Spectral Methods (Springer-Verlag, 2001).

D. Gottlieb, S. A. Orszag, "Numerical analysis of spectral methods: Theory and Applications," CBMS-NSF Regional Conf. Series Appl. Math., SIAM PhiladelphiaPA (1977).

L. N. Trefethen, Spectral Methods in Matlab (SIAM, 2000).

T. J. Rivlin, The Chebyshev Polynomials (Wiley, 1974).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.