Abstract

A photonic bandgap (PBG) structure for a polaritonic photonic crystal (PPC) containing lithium tantalate (LiTaO3) in the negative refractive index (NRI) region has been theoretically investigated. This region consists of a narrow frequency range of anomalous dispersion and a wide range of normal dispersion. The result shows that such PPC has a multiple-PBG structure with one gap located in the anomalous dispersion region and others in the normal dispersion region. PBG in the anomalous region is invariant with filling factor and scaling. This gap is further proven to be independent of the angle of incidence for both TE and TM nodes, leading to the existence of an omnidirectional gap. BPGs within the normal dispersion region are, however, strongly affected by the above three factors, especially for gaps near the upper limit of the NRI region.

© 2014 Optical Society of America

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  1. E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef]
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    [CrossRef]
  3. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).
  4. S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutger University, 2008), www.ece.rutgers.edu/~orfanidi/ewa .
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    [CrossRef]
  6. C. H. R. Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920–5923 (2000).
    [CrossRef]
  7. C.-J. Wu, C.-L. Liu, and T.-J. Yang, “Investigation of photonic band structure in a one-dimensional superconducting photonic crystal,” J. Opt. Soc. Am. B 26, 2089–2094 (2009).
    [CrossRef]
  8. J. Manzanares-Martinez and F. Ramos-Mendieta, “One-dimensional photonic crystal with semiconducting constituents: the effects of the absorption mechanisms,” Rev. Mex. Fis. S54, 95–100 (2008).
  9. L. E. Gonzalez and N. Porras-Montenegro, “Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal,” Physica E 44, 773–777 (2012).
    [CrossRef]
  10. T.-C. King, C.-C. Wang, W.-K. Kuo, and C.-J. Wu, “Analysis of effective plasma frequency in a magnetized extrinsic photonic crystal,” IEEE Photon. J. 5, 2700706 (2013).
    [CrossRef]
  11. H.-C. Hung, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Magneto-optical effect in wave properties for a semiconductor photonic crystal at near-infrared,” IEEE Photon. J. 4, 903–911 (2012).
    [CrossRef]
  12. H. Tian and J. Zi, “One-dimensional tunable photonic crystals by means of external magnetic fields,” Opt. Commun. 252, 321–328 (2005).
    [CrossRef]
  13. A. S. Sanchez and P. Halevi, “Simulation of tuning of one-dimensional photonic crystals in the presence of free electrons and holes,” J. Appl. Phys. 94, 797–799 (2003).
    [CrossRef]
  14. V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  15. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [CrossRef]
  16. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef]
  17. J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic bandgap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
    [CrossRef]
  18. P. Yeh, Optical Waves in Layered Media (Wiley, 1998).
  19. C. Kittel, Introduction to Solid State Physics (Wiley, 2005).
  20. H. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003).
    [CrossRef]
  21. C. A. A. Araujo, M. S. Vasconcelos, P. W. Mauriz, and E. L. Albuquerque, “Omnidirectional bandgaps in quasi-periodic photonic crystals in the THz region,” Opt. Mater. 35, 18–24 (2012).
    [CrossRef]
  22. V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Math. Phys. 17, 3717–3734 (2005).
  23. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
    [CrossRef]
  24. P. Markos and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-Hand Materials (Princeton University, 2008).

2013

T.-C. King, C.-C. Wang, W.-K. Kuo, and C.-J. Wu, “Analysis of effective plasma frequency in a magnetized extrinsic photonic crystal,” IEEE Photon. J. 5, 2700706 (2013).
[CrossRef]

2012

H.-C. Hung, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Magneto-optical effect in wave properties for a semiconductor photonic crystal at near-infrared,” IEEE Photon. J. 4, 903–911 (2012).
[CrossRef]

C. A. A. Araujo, M. S. Vasconcelos, P. W. Mauriz, and E. L. Albuquerque, “Omnidirectional bandgaps in quasi-periodic photonic crystals in the THz region,” Opt. Mater. 35, 18–24 (2012).
[CrossRef]

L. E. Gonzalez and N. Porras-Montenegro, “Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal,” Physica E 44, 773–777 (2012).
[CrossRef]

2009

2008

J. Manzanares-Martinez and F. Ramos-Mendieta, “One-dimensional photonic crystal with semiconducting constituents: the effects of the absorption mechanisms,” Rev. Mex. Fis. S54, 95–100 (2008).

2005

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Math. Phys. 17, 3717–3734 (2005).

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

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

2003

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic bandgap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

H. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003).
[CrossRef]

A. S. Sanchez and P. Halevi, “Simulation of tuning of one-dimensional photonic crystals in the presence of free electrons and holes,” J. Appl. Phys. 94, 797–799 (2003).
[CrossRef]

2000

C. H. R. Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920–5923 (2000).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

1999

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered lattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

1968

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Albuquerque, E. L.

C. A. A. Araujo, M. S. Vasconcelos, P. W. Mauriz, and E. L. Albuquerque, “Omnidirectional bandgaps in quasi-periodic photonic crystals in the THz region,” Opt. Mater. 35, 18–24 (2012).
[CrossRef]

Alexopoulos, N. G.

Araujo, C. A. A.

C. A. A. Araujo, M. S. Vasconcelos, P. W. Mauriz, and E. L. Albuquerque, “Omnidirectional bandgaps in quasi-periodic photonic crystals in the THz region,” Opt. Mater. 35, 18–24 (2012).
[CrossRef]

Au Yeung, T. C.

C. H. R. Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920–5923 (2000).
[CrossRef]

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic bandgap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Chang, S.-J.

H.-C. Hung, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Magneto-optical effect in wave properties for a semiconductor photonic crystal at near-infrared,” IEEE Photon. J. 4, 903–911 (2012).
[CrossRef]

Contopanagos, H.

Gonzalez, L. E.

L. E. Gonzalez and N. Porras-Montenegro, “Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal,” Physica E 44, 773–777 (2012).
[CrossRef]

Halevi, P.

A. S. Sanchez and P. Halevi, “Simulation of tuning of one-dimensional photonic crystals in the presence of free electrons and holes,” J. Appl. Phys. 94, 797–799 (2003).
[CrossRef]

Hung, H.-C.

H.-C. Hung, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Magneto-optical effect in wave properties for a semiconductor photonic crystal at near-infrared,” IEEE Photon. J. 4, 903–911 (2012).
[CrossRef]

Joannopoulos, J. D.

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

John, S.

S. John, “Strong localization of photons in certain disordered lattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Kam, C. H.

C. H. R. Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920–5923 (2000).
[CrossRef]

King, T.-C.

T.-C. King, C.-C. Wang, W.-K. Kuo, and C.-J. Wu, “Analysis of effective plasma frequency in a magnetized extrinsic photonic crystal,” IEEE Photon. J. 5, 2700706 (2013).
[CrossRef]

Kittel, C.

C. Kittel, Introduction to Solid State Physics (Wiley, 2005).

Kivshar, Y. S.

H. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003).
[CrossRef]

Kuo, W.-K.

T.-C. King, C.-C. Wang, W.-K. Kuo, and C.-J. Wu, “Analysis of effective plasma frequency in a magnetized extrinsic photonic crystal,” IEEE Photon. J. 5, 2700706 (2013).
[CrossRef]

Li, J.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic bandgap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Lim, T. K.

C. H. R. Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920–5923 (2000).
[CrossRef]

Liu, C.-L.

Manzanares-Martinez, J.

J. Manzanares-Martinez and F. Ramos-Mendieta, “One-dimensional photonic crystal with semiconducting constituents: the effects of the absorption mechanisms,” Rev. Mex. Fis. S54, 95–100 (2008).

Markos, P.

P. Markos and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-Hand Materials (Princeton University, 2008).

Mauriz, P. W.

C. A. A. Araujo, M. S. Vasconcelos, P. W. Mauriz, and E. L. Albuquerque, “Omnidirectional bandgaps in quasi-periodic photonic crystals in the THz region,” Opt. Mater. 35, 18–24 (2012).
[CrossRef]

Meade, R. D.

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

Moroz, A.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Math. Phys. 17, 3717–3734 (2005).

Nemat-nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Ooi, C. H. R.

C. H. R. Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920–5923 (2000).
[CrossRef]

Orfanidis, S. J.

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutger University, 2008), www.ece.rutgers.edu/~orfanidi/ewa .

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

Porras-Montenegro, N.

L. E. Gonzalez and N. Porras-Montenegro, “Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal,” Physica E 44, 773–777 (2012).
[CrossRef]

Ramos-Mendieta, F.

J. Manzanares-Martinez and F. Ramos-Mendieta, “One-dimensional photonic crystal with semiconducting constituents: the effects of the absorption mechanisms,” Rev. Mex. Fis. S54, 95–100 (2008).

Sanchez, A. S.

A. S. Sanchez and P. Halevi, “Simulation of tuning of one-dimensional photonic crystals in the presence of free electrons and holes,” J. Appl. Phys. 94, 797–799 (2003).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Shadrivov, H. V.

H. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003).
[CrossRef]

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic bandgap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Soukoulis, C. M.

P. Markos and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-Hand Materials (Princeton University, 2008).

Sukhorukov, A. A.

H. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003).
[CrossRef]

Tian, H.

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

Vasconcelos, M. S.

C. A. A. Araujo, M. S. Vasconcelos, P. W. Mauriz, and E. L. Albuquerque, “Omnidirectional bandgaps in quasi-periodic photonic crystals in the THz region,” Opt. Mater. 35, 18–24 (2012).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Wang, C.-C.

T.-C. King, C.-C. Wang, W.-K. Kuo, and C.-J. Wu, “Analysis of effective plasma frequency in a magnetized extrinsic photonic crystal,” IEEE Photon. J. 5, 2700706 (2013).
[CrossRef]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

Winn, J. N.

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

Wu, C.-J.

T.-C. King, C.-C. Wang, W.-K. Kuo, and C.-J. Wu, “Analysis of effective plasma frequency in a magnetized extrinsic photonic crystal,” IEEE Photon. J. 5, 2700706 (2013).
[CrossRef]

H.-C. Hung, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Magneto-optical effect in wave properties for a semiconductor photonic crystal at near-infrared,” IEEE Photon. J. 4, 903–911 (2012).
[CrossRef]

C.-J. Wu, C.-L. Liu, and T.-J. Yang, “Investigation of photonic band structure in a one-dimensional superconducting photonic crystal,” J. Opt. Soc. Am. B 26, 2089–2094 (2009).
[CrossRef]

Yablonovitch, E.

Yang, T.-J.

H.-C. Hung, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Magneto-optical effect in wave properties for a semiconductor photonic crystal at near-infrared,” IEEE Photon. J. 4, 903–911 (2012).
[CrossRef]

C.-J. Wu, C.-L. Liu, and T.-J. Yang, “Investigation of photonic band structure in a one-dimensional superconducting photonic crystal,” J. Opt. Soc. Am. B 26, 2089–2094 (2009).
[CrossRef]

Yannopapas, V.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Math. Phys. 17, 3717–3734 (2005).

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, 1998).

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic bandgap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Zi, J.

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

Appl. Phys. Lett.

H. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003).
[CrossRef]

IEEE Photon. J.

T.-C. King, C.-C. Wang, W.-K. Kuo, and C.-J. Wu, “Analysis of effective plasma frequency in a magnetized extrinsic photonic crystal,” IEEE Photon. J. 5, 2700706 (2013).
[CrossRef]

H.-C. Hung, C.-J. Wu, T.-J. Yang, and S.-J. Chang, “Magneto-optical effect in wave properties for a semiconductor photonic crystal at near-infrared,” IEEE Photon. J. 4, 903–911 (2012).
[CrossRef]

J. Appl. Phys.

A. S. Sanchez and P. Halevi, “Simulation of tuning of one-dimensional photonic crystals in the presence of free electrons and holes,” J. Appl. Phys. 94, 797–799 (2003).
[CrossRef]

J. Math. Phys.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Math. Phys. 17, 3717–3734 (2005).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

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

Opt. Mater.

C. A. A. Araujo, M. S. Vasconcelos, P. W. Mauriz, and E. L. Albuquerque, “Omnidirectional bandgaps in quasi-periodic photonic crystals in the THz region,” Opt. Mater. 35, 18–24 (2012).
[CrossRef]

Phys. Rev. B

C. H. R. Ooi, T. C. Au Yeung, C. H. Kam, and T. K. Lim, “Photonic band gap in a superconductor-dielectric superlattice,” Phys. Rev. B 61, 5920–5923 (2000).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, “Inhibited spontaneous emission in solid state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered lattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-nasser, and S. Schultz, “Composite medium with simultaneous negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef]

J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic bandgap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Physica E

L. E. Gonzalez and N. Porras-Montenegro, “Pressure, temperature and plasma frequency effects on the band structure of a 1D semiconductor photonic crystal,” Physica E 44, 773–777 (2012).
[CrossRef]

Rev. Mex. Fis.

J. Manzanares-Martinez and F. Ramos-Mendieta, “One-dimensional photonic crystal with semiconducting constituents: the effects of the absorption mechanisms,” Rev. Mex. Fis. S54, 95–100 (2008).

Science

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004).
[CrossRef]

Sov. Phys. Usp.

V. G. Veselago, “The electrodynamics of substance with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
[CrossRef]

Other

P. Yeh, Optical Waves in Layered Media (Wiley, 1998).

C. Kittel, Introduction to Solid State Physics (Wiley, 2005).

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

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutger University, 2008), www.ece.rutgers.edu/~orfanidi/ewa .

P. Markos and C. M. Soukoulis, Wave Propagation: From Electrons to Photonic Crystals and Left-Hand Materials (Princeton University, 2008).

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Figures (5)

Fig. 1.
Fig. 1.

Calculated frequency-dependent real and imaginary parts of the refractive index for LiTaO3. The negative Re(n2) occurs in the frequency range of ωc,L=161.78ωc,H=270.90THz.

Fig. 2.
Fig. 2.

Reflectance spectra for PC with Λ=4.5μm for different filling factor, f=1/5,1/10,1/20, and 1/30, respectively. An apparent shifting feature in PBG 1–4 can be seen.

Fig. 3.
Fig. 3.

Reflectance spectra for PC with a fixed f=1/10 for Λ=2.25 and 9 μm, respectively.

Fig. 4.
Fig. 4.

TE-mode reflectance spectra for PC at different angles of incidence, θ0=10°, 20°, 30°, 35°, 40°, 60°, 80°, and 89°, respectively. Here, Λ=4.5μm and f=1/10.

Fig. 5.
Fig. 5.

TM-mode reflectance spectra for PC at different angles of incidence, θ0=10°, 20°, 30°, 35°, 40°, 60°, 80°, and 89°, respectively. Here, Λ=4.5μm and f=1/10.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

ε2(ω)=ε(1+ωLO2ωTO2ωTO2ω2+jωγ),
μ2(ω)=1Fω2ω2ω02jωΓ.
n2=μ2ε2=Re(n2)jIm(n2).
M=[M11M12M21M22]=D01(D1P1D11D2P2D21)ND0,
Pi=[ejϕi00ejϕi],
ϕi=kidi=ωcnidicosθi,
Dq=[11nqμqcosθqnqμqcosθq](TE mode),
Dq=[cosθqcosθqnqμqnqμq](TM mode),
R=|M21M11|2.

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