Abstract

A novel scheme based on a 2-D finite element method (2-D-FEM) for the frequency domain, in cylindrical coordinates in conjunction with the perfectly matched layers (PML), is proposed and validated here. This scheme permits the analysis and simulation of photonic devices, including discontinuities along the propagation direction. Also, the present approach takes into account the dispersive nature of metals at optical wavelengths.

© 2009 IEEE

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  1. C. E. Rubio-Mercedes, H. E. Hernández-Figueroa, "Padé boundary conditions for the finite-element solution of arbitrary planar junctions," J. Lightw. Technol. 22, 669-676 (2004).
  2. Y. Tsuji, M. Koshiba, "Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems," J. Lightw. Technol. 20, 463-470 (2002).
  3. M. Koshiba, Optical Waveguide Theory by the Finite Element Method (Kluwer, 1992).
  4. J. Jin, The Finite Element Method in Electromagnetics (Wiley, 2002).
  5. G. R. Cowper, "Gaussian quadrature formulas for triangles," Int. J. Numer. Meth. Eng. 7, 405-408 (1973).
  6. J. Shibayama, T. Takahashi, J. Yamauehi, H. Nakano, "Efficient time-domain finite-difference beam propagation methods for the analysis of slab and circularly symmetric waveguides," J. Lightw. Technol. 18, 437-442 (2000).
  7. T. Okoshi, Optical Fibers (Academic, 1982).
  8. A. W. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983).
  9. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).
  10. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Exp. 13, 6815-6820 (2005).
  11. N. Engheta, A. Salandrino, A. Alu, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
  12. R. Merlin, "Radiationless electromagnetic interference: Diffractive evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).
  13. A. Grbic, R. Merlin, "Near-field focusing plates and their design," IEEE Trans. Antennas Propagat. 56, 3159-3165 (2007).

2007

R. Merlin, "Radiationless electromagnetic interference: Diffractive evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).

A. Grbic, R. Merlin, "Near-field focusing plates and their design," IEEE Trans. Antennas Propagat. 56, 3159-3165 (2007).

2005

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Exp. 13, 6815-6820 (2005).

N. Engheta, A. Salandrino, A. Alu, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).

2004

C. E. Rubio-Mercedes, H. E. Hernández-Figueroa, "Padé boundary conditions for the finite-element solution of arbitrary planar junctions," J. Lightw. Technol. 22, 669-676 (2004).

2002

Y. Tsuji, M. Koshiba, "Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems," J. Lightw. Technol. 20, 463-470 (2002).

2000

J. Shibayama, T. Takahashi, J. Yamauehi, H. Nakano, "Efficient time-domain finite-difference beam propagation methods for the analysis of slab and circularly symmetric waveguides," J. Lightw. Technol. 18, 437-442 (2000).

1973

G. R. Cowper, "Gaussian quadrature formulas for triangles," Int. J. Numer. Meth. Eng. 7, 405-408 (1973).

IEEE Trans. Antennas Propagat.

A. Grbic, R. Merlin, "Near-field focusing plates and their design," IEEE Trans. Antennas Propagat. 56, 3159-3165 (2007).

Int. J. Numer. Meth. Eng.

G. R. Cowper, "Gaussian quadrature formulas for triangles," Int. J. Numer. Meth. Eng. 7, 405-408 (1973).

J. Lightw. Technol.

J. Shibayama, T. Takahashi, J. Yamauehi, H. Nakano, "Efficient time-domain finite-difference beam propagation methods for the analysis of slab and circularly symmetric waveguides," J. Lightw. Technol. 18, 437-442 (2000).

C. E. Rubio-Mercedes, H. E. Hernández-Figueroa, "Padé boundary conditions for the finite-element solution of arbitrary planar junctions," J. Lightw. Technol. 22, 669-676 (2004).

Y. Tsuji, M. Koshiba, "Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems," J. Lightw. Technol. 20, 463-470 (2002).

Opt. Exp.

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Exp. 13, 6815-6820 (2005).

Phys. Rev. Lett.

N. Engheta, A. Salandrino, A. Alu, "Circuit elements at optical frequencies: Nanoinductors, nanocapacitors, and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).

Science

R. Merlin, "Radiationless electromagnetic interference: Diffractive evanescent-field lenses and perfect focusing," Science 317, 927-929 (2007).

Other

M. Koshiba, Optical Waveguide Theory by the Finite Element Method (Kluwer, 1992).

J. Jin, The Finite Element Method in Electromagnetics (Wiley, 2002).

T. Okoshi, Optical Fibers (Academic, 1982).

A. W. Snyder, J. Love, Optical Waveguide Theory (Springer, 1983).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1991).

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