Abstract

We have derived a modified finite-difference frequency-domain (FDFD) algorithm for two-dimensional (2-D) metallic photonic crystal (MPC) analysis. Using this method, the numerical results for the transverse-electric (TE) and transverse-magnetic (TM) modes in square and triangular lattices are in excellent agreements with those from other method. Then the correspondence of the band gaps between a unit cell and a supercell is demonstrated. Furthermore, by comparing the field distributions of the defect modes in a point defected MPC and a point defected dielectric photonic crystal (DPC), it is found that the defect MPC has a higher degree of localization, which means that MPC is preponderant for resonator and waveguide applications in millimeter wave and sub-millimeter wave bands.

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  1. E. Yablonoviteh, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
  3. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
  4. F. Brechet, J. Marcou, D. Pagnoux, P. Roy, "Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method," Opt. Fiber Technol. 6, 181-191 (2000).
  5. A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, "Design of photonic crystal optical waveguides with singlemodepropagation in the photonic bandgap," J. Lightw. Technol. 18, 1376-1378 (2000).
  6. M. A. Shapiro, W. J. Brown, I. Mastovsky, J. R. Sirigiri, R. J. Temkin, "17 GHz photonic bandgap cavity with improved input coupling," Phys. Rev., Special Topics: Accelerators and Beams 4, 042001(1)-042001(6) (2001).
  7. D. F. Sievenpiper, M. E. Sickmiller, E. Yablonovitch, "3D wire mesh photonic crystals," Phys. Rev. Lett. 76, 2480-2483 (1996).
  8. J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
  9. J. R. Sirigiri, K. E. Kreischer, J. Machuzak, I. Mastovsky, M. A. Shapiro, R. J. Temkin, "Photonic-band-gap resonator gyrotron," Phys. Rev. Lett. 86, 5628-5631 (2001).
  10. V. Kuzimiak, Maradudin, F. Pincemin, "Photonic band structures of two-dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).
  11. M. Qiu, S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. App. Phys. 87, 8268-8275 (2000).
  12. J. B. Pendry, A. Mackinnon, "Calculation of photon dispersion relations," Phys. Rev. Lett. 69, 2772-2775 (1992).
  13. M. Sigalas, C. M. Soukoulis, E. N. Economou, "Photonic band gaps and defects in two dimensions: Studies of the transmission coefficient," Phys. Rev. B 48, 14121-14126 (1993).
  14. Z. Zhu, T. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Opt. Exp. 10, 853-864 (2002).
  15. C. P. Yu, H. C. Chang, "Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals," Opt. Exp. 12, 1397-1408 (2004).
  16. H. C. Chang, C. P. Yu, "Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguide and photonic crystal fibers," Opt. Exp. 12, 6165-6177 (2004).
  17. T. Ando, H. Nakayama, S. Numata, J. Yamauchi, H. Nakano, "Eigenmode analysis of optical waveguides by a yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface," J. Lightw. Technol. 20, 1627-1634 (2002).
  18. S. Guo, F. Wu, S. Albin, "Photonic bandgap analysis using finite-difference frequency-domain method," Opt. Exp. 12, 1741-1746 (2004).
  19. E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, "Simulation of photonic band gaps in metal rod lattices for microwave applications," J. App. Phys. 91, 960-968 (2002).

2004 (3)

C. P. Yu, H. C. Chang, "Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals," Opt. Exp. 12, 1397-1408 (2004).

H. C. Chang, C. P. Yu, "Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguide and photonic crystal fibers," Opt. Exp. 12, 6165-6177 (2004).

S. Guo, F. Wu, S. Albin, "Photonic bandgap analysis using finite-difference frequency-domain method," Opt. Exp. 12, 1741-1746 (2004).

2002 (3)

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, "Simulation of photonic band gaps in metal rod lattices for microwave applications," J. App. Phys. 91, 960-968 (2002).

T. Ando, H. Nakayama, S. Numata, J. Yamauchi, H. Nakano, "Eigenmode analysis of optical waveguides by a yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface," J. Lightw. Technol. 20, 1627-1634 (2002).

Z. Zhu, T. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Opt. Exp. 10, 853-864 (2002).

2001 (2)

M. A. Shapiro, W. J. Brown, I. Mastovsky, J. R. Sirigiri, R. J. Temkin, "17 GHz photonic bandgap cavity with improved input coupling," Phys. Rev., Special Topics: Accelerators and Beams 4, 042001(1)-042001(6) (2001).

J. R. Sirigiri, K. E. Kreischer, J. Machuzak, I. Mastovsky, M. A. Shapiro, R. J. Temkin, "Photonic-band-gap resonator gyrotron," Phys. Rev. Lett. 86, 5628-5631 (2001).

2000 (3)

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, "Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method," Opt. Fiber Technol. 6, 181-191 (2000).

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, "Design of photonic crystal optical waveguides with singlemodepropagation in the photonic bandgap," J. Lightw. Technol. 18, 1376-1378 (2000).

M. Qiu, S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. App. Phys. 87, 8268-8275 (2000).

1996 (3)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

D. F. Sievenpiper, M. E. Sickmiller, E. Yablonovitch, "3D wire mesh photonic crystals," Phys. Rev. Lett. 76, 2480-2483 (1996).

J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).

1994 (1)

V. Kuzimiak, Maradudin, F. Pincemin, "Photonic band structures of two-dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).

1993 (1)

M. Sigalas, C. M. Soukoulis, E. N. Economou, "Photonic band gaps and defects in two dimensions: Studies of the transmission coefficient," Phys. Rev. B 48, 14121-14126 (1993).

1992 (1)

J. B. Pendry, A. Mackinnon, "Calculation of photon dispersion relations," Phys. Rev. Lett. 69, 2772-2775 (1992).

1987 (2)

E. Yablonoviteh, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).

J. App. Phys. (2)

M. Qiu, S. He, "A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions," J. App. Phys. 87, 8268-8275 (2000).

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, R. J. Temkin, "Simulation of photonic band gaps in metal rod lattices for microwave applications," J. App. Phys. 91, 960-968 (2002).

J. Lightw. Technol. (2)

T. Ando, H. Nakayama, S. Numata, J. Yamauchi, H. Nakano, "Eigenmode analysis of optical waveguides by a yee-mesh-based imaginary-distance propagation method for an arbitrary dielectric interface," J. Lightw. Technol. 20, 1627-1634 (2002).

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, A. Scherer, "Design of photonic crystal optical waveguides with singlemodepropagation in the photonic bandgap," J. Lightw. Technol. 18, 1376-1378 (2000).

Opt. Exp. (4)

S. Guo, F. Wu, S. Albin, "Photonic bandgap analysis using finite-difference frequency-domain method," Opt. Exp. 12, 1741-1746 (2004).

Z. Zhu, T. Brown, "Full-vectorial finite-difference analysis of microstructured optical fibers," Opt. Exp. 10, 853-864 (2002).

C. P. Yu, H. C. Chang, "Compact finite-difference frequency-domain method for the analysis of two-dimensional photonic crystals," Opt. Exp. 12, 1397-1408 (2004).

H. C. Chang, C. P. Yu, "Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguide and photonic crystal fibers," Opt. Exp. 12, 6165-6177 (2004).

Opt. Fiber Technol. (1)

F. Brechet, J. Marcou, D. Pagnoux, P. Roy, "Complete analysis of the characteristics of propagation into photonic crystal fibers, by the finite element method," Opt. Fiber Technol. 6, 181-191 (2000).

Phys. Rev. B (2)

V. Kuzimiak, Maradudin, F. Pincemin, "Photonic band structures of two-dimensional systems containing metallic components," Phys. Rev. B 50, 16835-16844 (1994).

M. Sigalas, C. M. Soukoulis, E. N. Economou, "Photonic band gaps and defects in two dimensions: Studies of the transmission coefficient," Phys. Rev. B 48, 14121-14126 (1993).

Phys. Rev. Lett. (7)

J. B. Pendry, A. Mackinnon, "Calculation of photon dispersion relations," Phys. Rev. Lett. 69, 2772-2775 (1992).

D. F. Sievenpiper, M. E. Sickmiller, E. Yablonovitch, "3D wire mesh photonic crystals," Phys. Rev. Lett. 76, 2480-2483 (1996).

J. B. Pendry, A. J. Holden, W. J. Stewart, I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).

J. R. Sirigiri, K. E. Kreischer, J. Machuzak, I. Mastovsky, M. A. Shapiro, R. J. Temkin, "Photonic-band-gap resonator gyrotron," Phys. Rev. Lett. 86, 5628-5631 (2001).

E. Yablonoviteh, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).

Phys. Rev., Special Topics: Accelerators and Beams (1)

M. A. Shapiro, W. J. Brown, I. Mastovsky, J. R. Sirigiri, R. J. Temkin, "17 GHz photonic bandgap cavity with improved input coupling," Phys. Rev., Special Topics: Accelerators and Beams 4, 042001(1)-042001(6) (2001).

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