Abstract

A simple and efficient numerical method for computing the transmission and reflection spectra of periodic arrays of cylinders is developed. For each unit cell containing a cylinder, only the wave field on the edges of the unit cell is computed. For multilayered structures, a marching scheme based on a pair of operators is developed.

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  1. K. Sakoda, "Numerical analysis of the interference patterns in the optical transmission spectra of a square photonic lattice", J. Opt. Soc. Amer. B, Opt. Phys., vol. 14, no. 8, pp. 1961-1966, Aug. 1997.
  2. G. Bao, Z. M. Chen and H. J. Wu, "Adaptive finite-element method for diffraction gratings", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 22, no. 6, pp. 1106-1114, Jun. 2005.
  3. D. Felbacq, G. Tayeb and D. Maystre, "Scattering by a random set of parallel cylinders", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 11, no. 9, pp. 2526-2538, Sep. 1994.
  4. R. C. McPhedran, L. C. Botten and A. A. Asatryan, et al. "Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 60, no. 6, pp. 7614-7617, Dec. 1999.
  5. L. C. Botten, N. A. Nicorovici and A. A. Asatryan, et al. "Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 17, no. 12, pp. 2165-2176, Dec. 2000.
  6. L. C. Botten, T. P. White and A. A. Asatryan, et al. "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 70, no. 5, Nov. 2004.
  7. K. Yasumoto, H. Toyama and T. Kushta, "Accurate analysis of two-dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique", IEEE Trans. Antennas Propag., vol. 52, no. 10, pp. 2603-2611, Oct. 2004.
  8. K. Yasumoto, H. Jia and H. Toyama, "Analysis of two-dimensional electromagnetic crystals consisting of multilayered periodic arrays of circular cylinders", Electron. Commun. Jpn., Part II-Electron., vol. 88, no. 9, pp. 19-28, 2005.
  9. S. Venakides, M. A. Haider and V. Papanicolaou, "Boundary integral calculations of two-dimensional electromagnetic scattering by photonic crystal Fabry-Pérot structures", SIAM J. Appl. Math., vol. 60, no. 5, pp. 1686-1706, May 2000.
  10. R. C. McPhedran, N. A. Nicorovici and L. C. Botten, "Neumann series and lattice sums", J. Math. Phys., vol. 46, no. 8, Aug. 2005.
  11. G. Bao, D. C. Dobson and J. A. Cox, "Mathematical studies in rigorous grating theory", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 12, no. 5, pp. 1029-1042, May 1995.
  12. J. Chandezon, M. T. Dupuis, G. Cornet and D. Maystre, "Multicoated gratings-A differential formalism applicable in the entire optical-region", J. Opt. Soc. Amer., vol. 72, no. 7, pp. 839-846, 1982.
  13. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings", J. Opt. Soc. Amer., vol. 72, no. 10, pp. 1385-1392, 1982.
  14. N. Chateau and J. P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 11, no. 4, pp. 1321-1331, Apr. 1994.
  15. P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 13, no. 4, pp. 779-784, Apr. 1996.
  16. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 13, no. 5, pp. 1024-1035, May 1996.
  17. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 14, no. 10, pp. 2758-2767, Oct. 1997.
  18. Y. Y. Lu and J. R. McLaughlin, "The Riccati method for the Helmholtz equation", J. Acoust. Soc. Amer., vol. 100, no. 3, pp. 1432-1446, Sep. 1996.
  19. Y. Y. Lu, "One-way large range step methods for Helmholtz waveguides", J. Comput. Phys., vol. 152, no. 1, pp. 231-250, Jun. 1999.
  20. Y. Y. Lu, "A fourth order Magnus scheme for Helmholtz equation", J. Comput. Appl. Math., vol. 173, no. 2, pp. 247-258, Jan. 2005.

Other (20)

K. Sakoda, "Numerical analysis of the interference patterns in the optical transmission spectra of a square photonic lattice", J. Opt. Soc. Amer. B, Opt. Phys., vol. 14, no. 8, pp. 1961-1966, Aug. 1997.

G. Bao, Z. M. Chen and H. J. Wu, "Adaptive finite-element method for diffraction gratings", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 22, no. 6, pp. 1106-1114, Jun. 2005.

D. Felbacq, G. Tayeb and D. Maystre, "Scattering by a random set of parallel cylinders", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 11, no. 9, pp. 2526-2538, Sep. 1994.

R. C. McPhedran, L. C. Botten and A. A. Asatryan, et al. "Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 60, no. 6, pp. 7614-7617, Dec. 1999.

L. C. Botten, N. A. Nicorovici and A. A. Asatryan, et al. "Formulation for electromagnetic scattering and propagation through grating stacks of metallic and dielectric cylinders for photonic crystal calculations. Part I. Method", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 17, no. 12, pp. 2165-2176, Dec. 2000.

L. C. Botten, T. P. White and A. A. Asatryan, et al. "Bloch mode scattering matrix methods for modeling extended photonic crystal structures. I. Theory", Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat. Interdiscip. Top., vol. 70, no. 5, Nov. 2004.

K. Yasumoto, H. Toyama and T. Kushta, "Accurate analysis of two-dimensional electromagnetic scattering from multilayered periodic arrays of circular cylinders using lattice sums technique", IEEE Trans. Antennas Propag., vol. 52, no. 10, pp. 2603-2611, Oct. 2004.

K. Yasumoto, H. Jia and H. Toyama, "Analysis of two-dimensional electromagnetic crystals consisting of multilayered periodic arrays of circular cylinders", Electron. Commun. Jpn., Part II-Electron., vol. 88, no. 9, pp. 19-28, 2005.

S. Venakides, M. A. Haider and V. Papanicolaou, "Boundary integral calculations of two-dimensional electromagnetic scattering by photonic crystal Fabry-Pérot structures", SIAM J. Appl. Math., vol. 60, no. 5, pp. 1686-1706, May 2000.

R. C. McPhedran, N. A. Nicorovici and L. C. Botten, "Neumann series and lattice sums", J. Math. Phys., vol. 46, no. 8, Aug. 2005.

G. Bao, D. C. Dobson and J. A. Cox, "Mathematical studies in rigorous grating theory", J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 12, no. 5, pp. 1029-1042, May 1995.

J. Chandezon, M. T. Dupuis, G. Cornet and D. Maystre, "Multicoated gratings-A differential formalism applicable in the entire optical-region", J. Opt. Soc. Amer., vol. 72, no. 7, pp. 839-846, 1982.

M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings", J. Opt. Soc. Amer., vol. 72, no. 10, pp. 1385-1392, 1982.

N. Chateau and J. P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 11, no. 4, pp. 1321-1331, Apr. 1994.

P. Lalanne and G. M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 13, no. 4, pp. 779-784, Apr. 1996.

L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 13, no. 5, pp. 1024-1035, May 1996.

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings", J. Opt. Soc. Amer. A, Opt., Image Sci., vol. 14, no. 10, pp. 2758-2767, Oct. 1997.

Y. Y. Lu and J. R. McLaughlin, "The Riccati method for the Helmholtz equation", J. Acoust. Soc. Amer., vol. 100, no. 3, pp. 1432-1446, Sep. 1996.

Y. Y. Lu, "One-way large range step methods for Helmholtz waveguides", J. Comput. Phys., vol. 152, no. 1, pp. 231-250, Jun. 1999.

Y. Y. Lu, "A fourth order Magnus scheme for Helmholtz equation", J. Comput. Appl. Math., vol. 173, no. 2, pp. 247-258, Jan. 2005.

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