Abstract

Large photonic bandgaps (PBGs) have been obtained by sweeping linearly the parameters of complex sublattices inside the unitary cells of square- and triangular-lattice photonic crystals. An efficient frequency-domain finite-element method with periodical boundary conditions has been used for theoretical analyses. PBGs in silicon/air photonic crystals for both polarization modes have been considered for up to 21 eigenmodes and both low- and high-order PBGs have been obtained by this relatively simple systematic process.

© 2012 IEEE

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
  2. J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton Univ. Press, 1995).
  3. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2004).
  4. M. Notomi, "Manipulating light with strongly modulated photonic crystals," Rep. Prog. Phys. 73, 096501 (2010).
  5. Y. S. Chan, C. T. Chan, Z. Y. Liu, "Photonic band-gaps in two-dimensional photonic quasi-crystals," Phys. Rev. Lett. 80, 956-959 (1998).
  6. M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, M. C. Nett, "Complete photonic band-gaps in 12-fold symmetric quasicrystals," Nature (London) 404, 740-743 (2000).
  7. C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. Z. Zhang, "Two-dimensional dodecagonal and decagonal quasi-periodic photonic crystals in the microwave region," Phys. Rev. B 61, 762-767 (2000).
  8. M. Bayindir, E. Cubukcu, I. Bubu, E. Ozbay, "Photonic bandgap effect, localization, and waveguiding in the two-dimensional Penrose lattice," Phys. Rev. B. 63, 161104 (2001).
  9. M. Marrone, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "A novel numerical approach for the analysis of 2d photonics crystals: The cell method," Opt. Exp. 10, 1299-1304 (2002).
  10. G. N. Malheiros-Silveira, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "Strategy of search and refinement by GA in 2-D photonic crystals with absolute PBG," IEEE J. Quantum Electron. 47, 431-438 (2011).
  11. D. Wang, Z. Yu, Y. Liu, P. Lu, L. Han, H. Feng, X. Guo, H. Ye, "The optimal structure of two dimensional photonic crystals with the large absolute band gap," Opt. Exp. 19, 19346-19353 (2011).
  12. H. Men, N. C. Nguyen, R. M. Freund, P. A. Parrilo, J. Peraire, "Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods," J. Comput. Phys. 229, 3706-3725 (2010).
  13. C. Y. Kao, S. Osher, E. Yablonovitch, "Maximizing band gaps in two-dimensional photonic crystals by using level set methods," Appl. Phys. B 81, 235-244 (2005).
  14. G. N. Malheiros-Silveira, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "Exploring photonic band gaps in sub-lattices in unitary cells in air/silicon," Proc. IEEE Photon. Conf. (2011) pp. 813-814.
  15. F. Quiñónez, J. W. Menezes, L. Cescato, V. F. Rodríguez-Esquerre, H. E. Hernandez-Figueroa, R. D. Mansano, "Band gap of hexagonal 2D photonic crystals with elliptical holes recorded by interference lithography," Opt. Exp. 14, 4873-4879 (2006).
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  18. N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).
  19. S. Zarei, M. Shahabadi, S. Mohajerzadeh, "Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals," J. Mod. Opt. 55, 2971-2980 (2008).
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2011

G. N. Malheiros-Silveira, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "Strategy of search and refinement by GA in 2-D photonic crystals with absolute PBG," IEEE J. Quantum Electron. 47, 431-438 (2011).

D. Wang, Z. Yu, Y. Liu, P. Lu, L. Han, H. Feng, X. Guo, H. Ye, "The optimal structure of two dimensional photonic crystals with the large absolute band gap," Opt. Exp. 19, 19346-19353 (2011).

2010

H. Men, N. C. Nguyen, R. M. Freund, P. A. Parrilo, J. Peraire, "Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods," J. Comput. Phys. 229, 3706-3725 (2010).

M. Notomi, "Manipulating light with strongly modulated photonic crystals," Rep. Prog. Phys. 73, 096501 (2010).

2009

G. Barillaro, L. M. Strambini, V. Annovazzi-Lodi, S. Merlo, "Optical characterization of high-order 1-D silicon photonic crystals," IEEE J. Sel. Topics Quantum Electron. 15, 1359-1367 (2009).

2008

S. Zarei, M. Shahabadi, S. Mohajerzadeh, "Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals," J. Mod. Opt. 55, 2971-2980 (2008).

2006

F. Quiñónez, J. W. Menezes, L. Cescato, V. F. Rodríguez-Esquerre, H. E. Hernandez-Figueroa, R. D. Mansano, "Band gap of hexagonal 2D photonic crystals with elliptical holes recorded by interference lithography," Opt. Exp. 14, 4873-4879 (2006).

2005

C. Y. Kao, S. Osher, E. Yablonovitch, "Maximizing band gaps in two-dimensional photonic crystals by using level set methods," Appl. Phys. B 81, 235-244 (2005).

2002

M. Marrone, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "A novel numerical approach for the analysis of 2d photonics crystals: The cell method," Opt. Exp. 10, 1299-1304 (2002).

N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).

2001

M. Bayindir, E. Cubukcu, I. Bubu, E. Ozbay, "Photonic bandgap effect, localization, and waveguiding in the two-dimensional Penrose lattice," Phys. Rev. B. 63, 161104 (2001).

2000

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, M. C. Nett, "Complete photonic band-gaps in 12-fold symmetric quasicrystals," Nature (London) 404, 740-743 (2000).

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. Z. Zhang, "Two-dimensional dodecagonal and decagonal quasi-periodic photonic crystals in the microwave region," Phys. Rev. B 61, 762-767 (2000).

1998

Y. S. Chan, C. T. Chan, Z. Y. Liu, "Photonic band-gaps in two-dimensional photonic quasi-crystals," Phys. Rev. Lett. 80, 956-959 (1998).

1987

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

Appl. Phys. B

C. Y. Kao, S. Osher, E. Yablonovitch, "Maximizing band gaps in two-dimensional photonic crystals by using level set methods," Appl. Phys. B 81, 235-244 (2005).

IEEE J. Quantum Electron.

G. N. Malheiros-Silveira, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "Strategy of search and refinement by GA in 2-D photonic crystals with absolute PBG," IEEE J. Quantum Electron. 47, 431-438 (2011).

IEEE J. Sel. Topics Quantum Electron.

G. Barillaro, L. M. Strambini, V. Annovazzi-Lodi, S. Merlo, "Optical characterization of high-order 1-D silicon photonic crystals," IEEE J. Sel. Topics Quantum Electron. 15, 1359-1367 (2009).

J. Appl. Phys.

N. Susa, "Large absolute and polarization-independent photonic band gaps for various lattice structures and rod shapes," J. Appl. Phys. 91, 3501-3510 (2002).

J. Comput. Phys.

H. Men, N. C. Nguyen, R. M. Freund, P. A. Parrilo, J. Peraire, "Bandgap optimization of two-dimensional photonic crystals using semidefinite programming and subspace methods," J. Comput. Phys. 229, 3706-3725 (2010).

J. Mod. Opt.

S. Zarei, M. Shahabadi, S. Mohajerzadeh, "Symmetry reduction for maximization of higher-order stop-bands in two-dimensional photonic crystals," J. Mod. Opt. 55, 2971-2980 (2008).

Nature (London)

M. E. Zoorob, M. D. B. Charlton, G. J. Parker, J. J. Baumberg, M. C. Nett, "Complete photonic band-gaps in 12-fold symmetric quasicrystals," Nature (London) 404, 740-743 (2000).

Opt. Exp.

M. Marrone, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "A novel numerical approach for the analysis of 2d photonics crystals: The cell method," Opt. Exp. 10, 1299-1304 (2002).

D. Wang, Z. Yu, Y. Liu, P. Lu, L. Han, H. Feng, X. Guo, H. Ye, "The optimal structure of two dimensional photonic crystals with the large absolute band gap," Opt. Exp. 19, 19346-19353 (2011).

F. Quiñónez, J. W. Menezes, L. Cescato, V. F. Rodríguez-Esquerre, H. E. Hernandez-Figueroa, R. D. Mansano, "Band gap of hexagonal 2D photonic crystals with elliptical holes recorded by interference lithography," Opt. Exp. 14, 4873-4879 (2006).

Phys. Rev. B.

M. Bayindir, E. Cubukcu, I. Bubu, E. Ozbay, "Photonic bandgap effect, localization, and waveguiding in the two-dimensional Penrose lattice," Phys. Rev. B. 63, 161104 (2001).

Phys. Rev. Lett.

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

Phys. Rev. B

C. J. Jin, B. Y. Cheng, B. Y. Man, Z. L. Li, D. Z. Zhang, "Two-dimensional dodecagonal and decagonal quasi-periodic photonic crystals in the microwave region," Phys. Rev. B 61, 762-767 (2000).

Phys. Rev. Lett.

Y. S. Chan, C. T. Chan, Z. Y. Liu, "Photonic band-gaps in two-dimensional photonic quasi-crystals," Phys. Rev. Lett. 80, 956-959 (1998).

Rep. Prog. Phys.

M. Notomi, "Manipulating light with strongly modulated photonic crystals," Rep. Prog. Phys. 73, 096501 (2010).

Other

J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals, Molding the Flow of Light (Princeton Univ. Press, 1995).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, 2004).

G. N. Malheiros-Silveira, V. F. Rodríguez-Esquerre, H. E. Hernández-Figueroa, "Exploring photonic band gaps in sub-lattices in unitary cells in air/silicon," Proc. IEEE Photon. Conf. (2011) pp. 813-814.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

GiD http://gid.cimne.upc.es/.

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