Abstract

In this paper, we theoretically investigate the effect of an external magnetic field on the properties of photonic band structures in two-dimensional n-doped semiconductor photonic crystals. We used the frequency-dependent plane wave expansion method. The numerical results reveal that the external magnetic field has a significant effect on the permittivity of the semiconductor materials. Therefore, the photonic band structures can be strongly tuned and controlled. The proposed structure is a good candidate for many applications, including filters, switches, and modulators in optoelectronics and microwave devices.

© 2015 Optical Society of America

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References

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    [Crossref]
  3. A. A. Krokhin, E. Reyes, and L. Gumen, “Low-frequency index of refraction for a two-dimensional metallodielectric photonic crystal,” Phys. Rev. B 75(4), 045131 (2007).
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  4. C. Cheng and C. Xu, “Photonic bands in two-dimensional metallodielectric photonic crystals composed of metal coated cylinders,” J. Appl. Phys. 106(3), 033101 (2009).
    [Crossref]
  5. A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96(6), 063903 (2006).
    [Crossref] [PubMed]
  6. S. A. El-Naggar, “Dependency of the photonic band gaps in two-dimensional metallic photonic crystals on the shapes and orientations of rods,” Opt. Eng. 51(6), 068001 (2012).
    [Crossref]
  7. H. Hojo and A. Mase, “Electromagnetic wave transmittance characteristics in one-dimensional plasma photonic crystals,” J. Plasma Fusion Res. Series 8, 477–479 (2009).
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  10. L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
    [Crossref]
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    [Crossref]
  12. J. Barvestani, E. Rezaei, and A. S. Vala, “Tunability of waveguide modes in two-dimensional photonic crystals based on superconducting materials,” Opt. Commun. 297(15), 74–78 (2013).
    [Crossref]
  13. R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
    [Crossref]
  14. C. J. Wu, J. J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” J. Electromagnet. Wave. 24(4), 531–542 (2010).
  15. Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
    [Crossref]
  16. H. A. Elsayed, S. A. El-Naggar, and A. H. Aly, “Thermal properties and two-dimensional photonic band gaps,” J. Mod. Opt. 61(5), 385–389 (2014).
    [Crossref]
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    [Crossref]
  18. C. A. Duque, N. P. Montenegro, S. B. Cavalcanti, and L. E. Oliveira, “Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field,” J. Appl. Phys. 105(3), 034303 (2009).
    [Crossref]
  19. C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
    [Crossref]
  20. S. V. Chernovtsev, D. P. Belozorov, and S. I. Tarapov, “Magnetically controllable 1D magnetophotonic crystal in millimetre wavelength band,” J. Phys. D Appl. Phys. 40(2), 295–299 (2007).
    [Crossref]
  21. W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
    [Crossref]
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    [Crossref]
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  24. V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
    [Crossref]
  25. P. Halevi, A. S. Sanchez, and E. G. Linares, “Tuning and switching of the spontaneous emission in one-dimensional photonic crystals,” Opt. Commun. 269(2), 351–355 (2007).
    [Crossref]
  26. A. Hatef and M. R. Singh, “Effect of a magnetic field on a two-dimensional metallic photonic crystal,” Phys. Rev. A 86(4), 043839 (2012).
    [Crossref]
  27. H. Tian and J. Zi, “One-dimensional tunable photonic crystals by means of external magnetic fields,” Opt. Commun. 252(4–6), 321–328 (2005).
    [Crossref]
  28. P. Halevi and F. Ramos-Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85(9), 1875–1878 (2000).
    [Crossref] [PubMed]

2014 (2)

S. A. El-Naggar, H. A. Elsayed, and A. H. Aly, “Maximization of photonic bandgaps in two-dimensional superconductor photonic crystals,” J. Supercond. Nov. Magn. 27(7), 1615–1621 (2014).
[Crossref]

H. A. Elsayed, S. A. El-Naggar, and A. H. Aly, “Thermal properties and two-dimensional photonic band gaps,” J. Mod. Opt. 61(5), 385–389 (2014).
[Crossref]

2013 (1)

J. Barvestani, E. Rezaei, and A. S. Vala, “Tunability of waveguide modes in two-dimensional photonic crystals based on superconducting materials,” Opt. Commun. 297(15), 74–78 (2013).
[Crossref]

2012 (2)

S. A. El-Naggar, “Dependency of the photonic band gaps in two-dimensional metallic photonic crystals on the shapes and orientations of rods,” Opt. Eng. 51(6), 068001 (2012).
[Crossref]

A. Hatef and M. R. Singh, “Effect of a magnetic field on a two-dimensional metallic photonic crystal,” Phys. Rev. A 86(4), 043839 (2012).
[Crossref]

2011 (1)

2010 (2)

C. J. Wu, J. J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” J. Electromagnet. Wave. 24(4), 531–542 (2010).

N. P. Montenegro and C. A. Duque, “Temperature and hydrostatic pressure effects on the photonic band structure of a 2D honeycomb lattice,” Physica E 42(6), 1865–1869 (2010).
[Crossref]

2009 (3)

C. A. Duque, N. P. Montenegro, S. B. Cavalcanti, and L. E. Oliveira, “Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field,” J. Appl. Phys. 105(3), 034303 (2009).
[Crossref]

H. Hojo and A. Mase, “Electromagnetic wave transmittance characteristics in one-dimensional plasma photonic crystals,” J. Plasma Fusion Res. Series 8, 477–479 (2009).

C. Cheng and C. Xu, “Photonic bands in two-dimensional metallodielectric photonic crystals composed of metal coated cylinders,” J. Appl. Phys. 106(3), 033101 (2009).
[Crossref]

2008 (1)

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

2007 (3)

A. A. Krokhin, E. Reyes, and L. Gumen, “Low-frequency index of refraction for a two-dimensional metallodielectric photonic crystal,” Phys. Rev. B 75(4), 045131 (2007).
[Crossref]

P. Halevi, A. S. Sanchez, and E. G. Linares, “Tuning and switching of the spontaneous emission in one-dimensional photonic crystals,” Opt. Commun. 269(2), 351–355 (2007).
[Crossref]

S. V. Chernovtsev, D. P. Belozorov, and S. I. Tarapov, “Magnetically controllable 1D magnetophotonic crystal in millimetre wavelength band,” J. Phys. D Appl. Phys. 40(2), 295–299 (2007).
[Crossref]

2006 (1)

A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96(6), 063903 (2006).
[Crossref] [PubMed]

2005 (2)

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

H. Tian and J. Zi, “One-dimensional tunable photonic crystals by means of external magnetic fields,” Opt. Commun. 252(4–6), 321–328 (2005).
[Crossref]

2003 (3)

W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
[Crossref]

H. Takeda and K. Yoshino, “Tunable photonic band schemes in two-dimensional photonic crystals composed of copper oxide high-temperature superconductors,” Phys. Rev. B 67(24), 245109 (2003).
[Crossref]

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

2001 (2)

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

2000 (1)

P. Halevi and F. Ramos-Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85(9), 1875–1878 (2000).
[Crossref] [PubMed]

1997 (1)

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[Crossref]

1967 (1)

P. S. Pershan, “Magneto-optical effect,” J. Appl. Phys. 38(3), 1482–1490 (1967).
[Crossref]

Aly, A. H.

S. A. El-Naggar, H. A. Elsayed, and A. H. Aly, “Maximization of photonic bandgaps in two-dimensional superconductor photonic crystals,” J. Supercond. Nov. Magn. 27(7), 1615–1621 (2014).
[Crossref]

H. A. Elsayed, S. A. El-Naggar, and A. H. Aly, “Thermal properties and two-dimensional photonic band gaps,” J. Mod. Opt. 61(5), 385–389 (2014).
[Crossref]

Barvestani, J.

J. Barvestani, E. Rezaei, and A. S. Vala, “Tunability of waveguide modes in two-dimensional photonic crystals based on superconducting materials,” Opt. Commun. 297(15), 74–78 (2013).
[Crossref]

Belozorov, D. P.

S. V. Chernovtsev, D. P. Belozorov, and S. I. Tarapov, “Magnetically controllable 1D magnetophotonic crystal in millimetre wavelength band,” J. Phys. D Appl. Phys. 40(2), 295–299 (2007).
[Crossref]

Cavalcanti, S. B.

C. A. Duque, N. P. Montenegro, S. B. Cavalcanti, and L. E. Oliveira, “Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field,” J. Appl. Phys. 105(3), 034303 (2009).
[Crossref]

Chang, T. W.

C. J. Wu, J. J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” J. Electromagnet. Wave. 24(4), 531–542 (2010).

Chen, X.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Chen, Y. B.

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Chen, Y. F.

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Cheng, C.

C. Cheng and C. Xu, “Photonic bands in two-dimensional metallodielectric photonic crystals composed of metal coated cylinders,” J. Appl. Phys. 106(3), 033101 (2009).
[Crossref]

Chernovtsev, S. V.

S. V. Chernovtsev, D. P. Belozorov, and S. I. Tarapov, “Magnetically controllable 1D magnetophotonic crystal in millimetre wavelength band,” J. Phys. D Appl. Phys. 40(2), 295–299 (2007).
[Crossref]

Chutinan, A.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

Duque, C. A.

N. P. Montenegro and C. A. Duque, “Temperature and hydrostatic pressure effects on the photonic band structure of a 2D honeycomb lattice,” Physica E 42(6), 1865–1869 (2010).
[Crossref]

C. A. Duque, N. P. Montenegro, S. B. Cavalcanti, and L. E. Oliveira, “Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field,” J. Appl. Phys. 105(3), 034303 (2009).
[Crossref]

El-Naggar, S. A.

H. A. Elsayed, S. A. El-Naggar, and A. H. Aly, “Thermal properties and two-dimensional photonic band gaps,” J. Mod. Opt. 61(5), 385–389 (2014).
[Crossref]

S. A. El-Naggar, H. A. Elsayed, and A. H. Aly, “Maximization of photonic bandgaps in two-dimensional superconductor photonic crystals,” J. Supercond. Nov. Magn. 27(7), 1615–1621 (2014).
[Crossref]

S. A. El-Naggar, “Dependency of the photonic band gaps in two-dimensional metallic photonic crystals on the shapes and orientations of rods,” Opt. Eng. 51(6), 068001 (2012).
[Crossref]

Elsayed, H. A.

S. A. El-Naggar, H. A. Elsayed, and A. H. Aly, “Maximization of photonic bandgaps in two-dimensional superconductor photonic crystals,” J. Supercond. Nov. Magn. 27(7), 1615–1621 (2014).
[Crossref]

H. A. Elsayed, S. A. El-Naggar, and A. H. Aly, “Thermal properties and two-dimensional photonic band gaps,” J. Mod. Opt. 61(5), 385–389 (2014).
[Crossref]

Feng, L.

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Fu, C. H.

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

Fu, R.

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

Fujishima, A.

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

Gao, Y.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Gu, Z. Z.

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

Gumen, L.

A. A. Krokhin, E. Reyes, and L. Gumen, “Low-frequency index of refraction for a two-dimensional metallodielectric photonic crystal,” Phys. Rev. B 75(4), 045131 (2007).
[Crossref]

Halevi, P.

P. Halevi, A. S. Sanchez, and E. G. Linares, “Tuning and switching of the spontaneous emission in one-dimensional photonic crystals,” Opt. Commun. 269(2), 351–355 (2007).
[Crossref]

P. Halevi and F. Ramos-Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85(9), 1875–1878 (2000).
[Crossref] [PubMed]

Hatef, A.

A. Hatef and M. R. Singh, “Effect of a magnetic field on a two-dimensional metallic photonic crystal,” Phys. Rev. A 86(4), 043839 (2012).
[Crossref]

Hayami, S.

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

Hirao, K.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

Hojo, H.

H. Hojo and A. Mase, “Electromagnetic wave transmittance characteristics in one-dimensional plasma photonic crystals,” J. Plasma Fusion Res. Series 8, 477–479 (2009).

Hu, X.

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
[Crossref]

Ito, T.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

Jia, W.

W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
[Crossref]

Jiang, P.

W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
[Crossref]

Kawai, N.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

Kong, X.

Krokhin, A. A.

A. A. Krokhin, E. Reyes, and L. Gumen, “Low-frequency index of refraction for a two-dimensional metallodielectric photonic crystal,” Phys. Rev. B 75(4), 045131 (2007).
[Crossref]

Kuzmiak, V.

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[Crossref]

Li, C.

Li, H.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Li, Y.

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

Liao, J. J.

C. J. Wu, J. J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” J. Electromagnet. Wave. 24(4), 531–542 (2010).

Linares, E. G.

P. Halevi, A. S. Sanchez, and E. G. Linares, “Tuning and switching of the spontaneous emission in one-dimensional photonic crystals,” Opt. Commun. 269(2), 351–355 (2007).
[Crossref]

Liu, S.

Liu, X.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
[Crossref]

Liu, X. P.

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Loidl, A.

A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96(6), 063903 (2006).
[Crossref] [PubMed]

Lu, W.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Maradudin, A. A.

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[Crossref]

Mase, A.

H. Hojo and A. Mase, “Electromagnetic wave transmittance characteristics in one-dimensional plasma photonic crystals,” J. Plasma Fusion Res. Series 8, 477–479 (2009).

Meng, Q. B.

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

Mitsuyu, T.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

Montenegro, N. P.

N. P. Montenegro and C. A. Duque, “Temperature and hydrostatic pressure effects on the photonic band structure of a 2D honeycomb lattice,” Physica E 42(6), 1865–1869 (2010).
[Crossref]

C. A. Duque, N. P. Montenegro, S. B. Cavalcanti, and L. E. Oliveira, “Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field,” J. Appl. Phys. 105(3), 034303 (2009).
[Crossref]

Noda, S.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

Oliveira, L. E.

C. A. Duque, N. P. Montenegro, S. B. Cavalcanti, and L. E. Oliveira, “Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field,” J. Appl. Phys. 105(3), 034303 (2009).
[Crossref]

Pershan, P. S.

P. S. Pershan, “Magneto-optical effect,” J. Appl. Phys. 38(3), 1482–1490 (1967).
[Crossref]

Pimenov, A.

A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96(6), 063903 (2006).
[Crossref] [PubMed]

Qiao, F.

W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
[Crossref]

Ramos-Mendieta, F.

P. Halevi and F. Ramos-Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85(9), 1875–1878 (2000).
[Crossref] [PubMed]

Ren, J.

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Reyes, E.

A. A. Krokhin, E. Reyes, and L. Gumen, “Low-frequency index of refraction for a two-dimensional metallodielectric photonic crystal,” Phys. Rev. B 75(4), 045131 (2007).
[Crossref]

Rezaei, E.

J. Barvestani, E. Rezaei, and A. S. Vala, “Tunability of waveguide modes in two-dimensional photonic crystals based on superconducting materials,” Opt. Commun. 297(15), 74–78 (2013).
[Crossref]

Sakoda, K.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

Sanchez, A. S.

P. Halevi, A. S. Sanchez, and E. G. Linares, “Tuning and switching of the spontaneous emission in one-dimensional photonic crystals,” Opt. Commun. 269(2), 351–355 (2007).
[Crossref]

Sato, O.

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

Singh, M. R.

A. Hatef and M. R. Singh, “Effect of a magnetic field on a two-dimensional metallic photonic crystal,” Phys. Rev. A 86(4), 043839 (2012).
[Crossref]

Takeda, H.

H. Takeda and K. Yoshino, “Tunable photonic band schemes in two-dimensional photonic crystals composed of copper oxide high-temperature superconductors,” Phys. Rev. B 67(24), 245109 (2003).
[Crossref]

Tang, Y. F.

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Tarapov, S. I.

S. V. Chernovtsev, D. P. Belozorov, and S. I. Tarapov, “Magnetically controllable 1D magnetophotonic crystal in millimetre wavelength band,” J. Phys. D Appl. Phys. 40(2), 295–299 (2007).
[Crossref]

Tian, H.

H. Tian and J. Zi, “One-dimensional tunable photonic crystals by means of external magnetic fields,” Opt. Commun. 252(4–6), 321–328 (2005).
[Crossref]

Vala, A. S.

J. Barvestani, E. Rezaei, and A. S. Vala, “Tunability of waveguide modes in two-dimensional photonic crystals based on superconducting materials,” Opt. Commun. 297(15), 74–78 (2013).
[Crossref]

Wang, X.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Wu, C. J.

C. J. Wu, J. J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” J. Electromagnet. Wave. 24(4), 531–542 (2010).

Wu, L.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Xu, C.

C. Cheng and C. Xu, “Photonic bands in two-dimensional metallodielectric photonic crystals composed of metal coated cylinders,” J. Appl. Phys. 106(3), 033101 (2009).
[Crossref]

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

Yoshino, K.

H. Takeda and K. Yoshino, “Tunable photonic band schemes in two-dimensional photonic crystals composed of copper oxide high-temperature superconductors,” Phys. Rev. B 67(24), 245109 (2003).
[Crossref]

Zhang, H.

Zhou, B.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Zhou, L.

Zhou, R.

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Zhu, Y. Y.

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Zi, J.

H. Tian and J. Zi, “One-dimensional tunable photonic crystals by means of external magnetic fields,” Opt. Commun. 252(4–6), 321–328 (2005).
[Crossref]

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

J. Appl. Phys. (5)

L. Feng, X. P. Liu, J. Ren, Y. F. Tang, Y. B. Chen, Y. F. Chen, and Y. Y. Zhu, “Tunable negative refractions in two-dimensional photonic crystals with superconductor constituents,” J. Appl. Phys. 97(7), 073104 (2005).
[Crossref]

Q. B. Meng, C. H. Fu, S. Hayami, Z. Z. Gu, O. Sato, and A. Fujishima, “Effects of external electric field upon the photonic band structure in synthetic opal infiltrated with liquid crystal,” J. Appl. Phys. 89(10), 5794–5796 (2001).
[Crossref]

C. A. Duque, N. P. Montenegro, S. B. Cavalcanti, and L. E. Oliveira, “Photonic band structure evolution of a honeycomb lattice in the presence of an external magnetic field,” J. Appl. Phys. 105(3), 034303 (2009).
[Crossref]

P. S. Pershan, “Magneto-optical effect,” J. Appl. Phys. 38(3), 1482–1490 (1967).
[Crossref]

C. Cheng and C. Xu, “Photonic bands in two-dimensional metallodielectric photonic crystals composed of metal coated cylinders,” J. Appl. Phys. 106(3), 033101 (2009).
[Crossref]

J. Electromagnet. Wave. (1)

C. J. Wu, J. J. Liao, and T. W. Chang, “Tunable multilayer Fabry-Perot resonator using electro-optical defect layer,” J. Electromagnet. Wave. 24(4), 531–542 (2010).

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

H. A. Elsayed, S. A. El-Naggar, and A. H. Aly, “Thermal properties and two-dimensional photonic band gaps,” J. Mod. Opt. 61(5), 385–389 (2014).
[Crossref]

J. Phys. D Appl. Phys. (1)

S. V. Chernovtsev, D. P. Belozorov, and S. I. Tarapov, “Magnetically controllable 1D magnetophotonic crystal in millimetre wavelength band,” J. Phys. D Appl. Phys. 40(2), 295–299 (2007).
[Crossref]

J. Plasma Fusion Res. Series (1)

H. Hojo and A. Mase, “Electromagnetic wave transmittance characteristics in one-dimensional plasma photonic crystals,” J. Plasma Fusion Res. Series 8, 477–479 (2009).

J. Supercond. Nov. Magn. (1)

S. A. El-Naggar, H. A. Elsayed, and A. H. Aly, “Maximization of photonic bandgaps in two-dimensional superconductor photonic crystals,” J. Supercond. Nov. Magn. 27(7), 1615–1621 (2014).
[Crossref]

J. Zi, J. Phys. Condens. Matter (1)

W. Jia, F. Qiao, X. Hu, X. Liu, and P. Jiang, “Tunability of photonic crystals based on the Faraday effect,” J. Zi, J. Phys. Condens. Matter 15(40), 6731–6737 (2003).
[Crossref]

Opt. Commun. (3)

P. Halevi, A. S. Sanchez, and E. G. Linares, “Tuning and switching of the spontaneous emission in one-dimensional photonic crystals,” Opt. Commun. 269(2), 351–355 (2007).
[Crossref]

J. Barvestani, E. Rezaei, and A. S. Vala, “Tunability of waveguide modes in two-dimensional photonic crystals based on superconducting materials,” Opt. Commun. 297(15), 74–78 (2013).
[Crossref]

H. Tian and J. Zi, “One-dimensional tunable photonic crystals by means of external magnetic fields,” Opt. Commun. 252(4–6), 321–328 (2005).
[Crossref]

Opt. Eng. (1)

S. A. El-Naggar, “Dependency of the photonic band gaps in two-dimensional metallic photonic crystals on the shapes and orientations of rods,” Opt. Eng. 51(6), 068001 (2012).
[Crossref]

Phys. Lett. A (1)

R. Zhou, X. Wang, B. Zhou, Y. Gao, X. Liu, L. Wu, H. Li, X. Chen, and W. Lu, “Extrinsic photonic band structure calculations of a doped semiconductor under an external magnetic field,” Phys. Lett. A 372(31), 5224–5228 (2008).
[Crossref]

Phys. Rev. A (1)

A. Hatef and M. R. Singh, “Effect of a magnetic field on a two-dimensional metallic photonic crystal,” Phys. Rev. A 86(4), 043839 (2012).
[Crossref]

Phys. Rev. B (5)

C. Xu, X. Hu, Y. Li, X. Liu, R. Fu, and J. Zi, “Semiconductor-based tunable photonic crystals by means of an external magnetic field,” Phys. Rev. B 68(19), 193201 (2003).
[Crossref]

H. Takeda and K. Yoshino, “Tunable photonic band schemes in two-dimensional photonic crystals composed of copper oxide high-temperature superconductors,” Phys. Rev. B 67(24), 245109 (2003).
[Crossref]

V. Kuzmiak and A. A. Maradudin, “Photonic band structures of one- and two-dimensional periodic systems with metallic components in the presence of dissipation,” Phys. Rev. B 55(12), 7427–7444 (1997).
[Crossref]

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. principle of calculation and accuracy,” Phys. Rev. B 64(4), 045116 (2001).
[Crossref]

A. A. Krokhin, E. Reyes, and L. Gumen, “Low-frequency index of refraction for a two-dimensional metallodielectric photonic crystal,” Phys. Rev. B 75(4), 045131 (2007).
[Crossref]

Phys. Rev. Lett. (2)

P. Halevi and F. Ramos-Mendieta, “Tunable photonic crystals with semiconducting constituents,” Phys. Rev. Lett. 85(9), 1875–1878 (2000).
[Crossref] [PubMed]

A. Pimenov and A. Loidl, “Conductivity and permittivity of two-dimensional metallic photonic crystals,” Phys. Rev. Lett. 96(6), 063903 (2006).
[Crossref] [PubMed]

Physica E (1)

N. P. Montenegro and C. A. Duque, “Temperature and hydrostatic pressure effects on the photonic band structure of a 2D honeycomb lattice,” Physica E 42(6), 1865–1869 (2010).
[Crossref]

Other (2)

C. R. Pidgeon, Handbook on Semiconductors (North-Holland Amsterdam, 1980).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding The Flow Of Light (Princeton University, 2008).

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Figures (6)

Fig. 1
Fig. 1 Transverse cross section of the 2D n-doped semiconductor PCs composed of cylindrical rods of Si with a dielectric constant ε(ω) that have been arranged into a square lattice of dielectric material with a dielectric constant εb. The first Brillouin zone of the square lattice is shown in (b).
Fig. 2
Fig. 2 The real portion of the Si permittivity vs frequency for various values of the cyclotron frequency for a) LCP and b) RCP.
Fig. 3
Fig. 3 (a) The variation in Δω/ωg vs. f.f at different values of ωc for LCP. (b, c and d) The photonic band structures of the circular rods of n-doped Si in a square lattice of air at ωc = 0, 0.25ωpe, and 0.5ωpe, respectively.
Fig. 4
Fig. 4 (a) The variation of Δω/ωg vs. f.f at different values of ωc for RCP. (b, c and d) The photonic band structures of the circular rods of n-doped Si in a square lattice of air at ωc = 0, 0.25 ωpe, and 0.5 ωpe, respectively.
Fig. 5
Fig. 5 The variation in the lower and upper frequencies of the 1st PBG with ωc: (a) LCP and (b) RCP.
Fig. 6
Fig. 6 The response of the dispersionless bands with the cyclotron frequency for RCP: (a) ωc = 0.25 ωpe and (b) 0.5ωpe.

Equations (14)

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ε ± ( ω ) = ε ( 1 ω p e 2 ω ( ω ω c i γ e ) ω p h 2 ω ( ω ω c i γ h ) ) ,
ω c = e m e B ,
E z ( r , t ) = E z ( r ) exp ( i ω t ) ,
( 2 x 2 + 2 y 2 ) E z ( r ) + ω 2 c 2 ε ( r ) E z ( r ) = 0 ,
ε ( r ) = G ε ( G ) exp ( i G .r ) ,
E z ( r ) = G E z ( G ) exp ( i ( k + G ) .r ) ,
( k + G ) 2 E z ( G ) = ( ω c ) 2 G ε ( G G ) E z ( G ) ,
( ω c ) 3 A E z ( G ) = ( ( ω c ) 2 B + ( ω c ) 2 C + D ) E z ( G ) ,
A = { 2 f . f [ ε ε b ] J 1 ( ( G G ) r ) ( G G ) r G G ε b ( 1 f . f ) + ε f . f G = G ,
B = { 2 f . f ( ω c c ) [ ε b ε ] J 1 ( ( G G ) r ) ( G G ) r G G ( ω c c ) [ ε b ( f . f 1 ) ε f . f ] G = G ,
C = { 0 G G ( k + G ) 2 + f . f ( ε ) ( ω p e + ω p h c ) 2 G = G ,
D = { 0 G G ( ω c c ) ( k + G ) 2 G = G .
( 0 I 0 0 0 I A 1 D A 1 C ω c c I ) ( E z ( G ) μ E z ( G ) μ 2 E z ( G ) ) = μ ( E z ( G ) μ E z ( G ) μ 2 E z ( G ) )
Im ( ε ( ω ) ) Re ( ε ( ω ) ) ω p 2 γ ω ( ω 2 ω p 2 + γ 2 ) .

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