Abstract

The transmission properties of a one-dimensional photonic crystal containing uniaxial indefinite metamaterial are investigated using the transfer matrix method. It is shown that the photonic bandgaps of the structure strongly depend on the orientation of the optical axis of the indefinite metamaterial. The results show that it is possible to obtain the Brewster condition for both TE and TM polarizations. This condition noticeably affects the profiles of the electromagnetic field inside the one-dimensional periodic structure.

© 2012 Optical Society of America

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  1. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [CrossRef]
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    [CrossRef]
  3. J. B. Pendry, “Negative refraction makes light run backward in time,” Phys. World 13, 27–29 (2000).
  4. N. Seddon and T. Beapark, “Observation of inverse Doppler effect,” Science 302, 1537–1540 (2003).
    [CrossRef]
  5. I. V. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
    [CrossRef]
  6. D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional refection from a one-dimensional dielectric lattice,” Appl. Phys. A: Mater. Sci. Process. 68, 25–28 (1999).
    [CrossRef]
  7. S. John, “Strong localization of photon in certain disordered dielectric superlattice,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef]
  8. S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
    [CrossRef]
  9. P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgapes and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
    [CrossRef]
  10. S. Y. Lin, E. Chow, and V. Hietala, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
    [CrossRef]
  11. B. Temelkuran and E. Ozbay, “Experimental demonstration of photonic crystal based waveguides,” Appl. Phys. Lett. 74, 486–488 (1999).
    [CrossRef]
  12. J. Li, L. Zhou, C. T. Chan, and P. Sheng, “Photonic band gap from a stack of positive and negative index materials,” Phys. Rev. Lett. 90, 083901 (2003).
    [CrossRef]
  13. H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
    [CrossRef]
  14. H. Jiang, H. Chen, H. Li, and Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
    [CrossRef]
  15. I. V. Shadrivov, A. A. Sukhorukov, and Yuri S. Kivshar, “Beam shaping by a periodic structure with negative refraction,” Appl. Phys. Lett. 82, 3820–3822 (2003).
    [CrossRef]
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  18. H. Luo, Z. Ren, W. Shu, and F. Li, “Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation,” Appl. Phys. A 87, 245–249 (2007).
    [CrossRef]
  19. T. Pan, G.-D. Xu, T.-C. Zang, and L. Gao, “Study of a slab waveguide loaded with dispersive anisotropic metamaterials,” Appl. Phys. A 95, 367–372 (2009).
    [CrossRef]
  20. Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos-Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
    [CrossRef]
  21. M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
    [CrossRef]
  22. N. V. Ilin, A. I. Smirnov, and I. G. Kondratiev, “Features of surface modes in metamaterial layers,” Metamaterials 3, 82–89 (2009).
    [CrossRef]
  23. N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
    [CrossRef]
  24. G. Ren, Z. Lai, C. Wang, Q. Feng, L. Liu, K. Liu, and X. Luo, “Subwavelength focusing of light in the planar anisotropic metamaterials with zone plates,” Opt. Express 18, 18151–18157 (2010).
    [CrossRef]
  25. D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
    [CrossRef]
  26. Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
    [CrossRef]
  27. Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
    [CrossRef]
  28. L. Liu, L. Zhang, and Y. Zhang, “The transmission properties of one-dimensional photonic crystals containing indefinite metamaterials,” in Proceedings of 2008 International Workshop on Metamaterials (IEEE, 2008), pp. 221–224.
  29. T. Pan, G. Xu, T. Zang, and L. Gao, “Goos-Hänchen shift in one-dimensional photonic crystals containing uniaxial indefinite medium,” Phys. Status Solidi B 246, 1088–1093 (2009).
    [CrossRef]
  30. W. Shu, Z. Ren, H. Luo, and F. Li, “Brewster angle for anisotropic materials from the extinction theorem,” Appl. Phys. A 87, 297–303 (2007).
    [CrossRef]
  31. T. Grzegorczyk, Z. Thomas, and J. Kong, “Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials,” Appl. Phys. Lett. 86, 251909 (2005).
    [CrossRef]
  32. A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings,” Phys. Rev. Lett. 106, 123902 (2011).
    [CrossRef]
  33. C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
    [CrossRef]

2012

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

2011

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings,” Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

2010

2009

T. Pan, G. Xu, T. Zang, and L. Gao, “Goos-Hänchen shift in one-dimensional photonic crystals containing uniaxial indefinite medium,” Phys. Status Solidi B 246, 1088–1093 (2009).
[CrossRef]

T. Pan, G.-D. Xu, T.-C. Zang, and L. Gao, “Study of a slab waveguide loaded with dispersive anisotropic metamaterials,” Appl. Phys. A 95, 367–372 (2009).
[CrossRef]

N. V. Ilin, A. I. Smirnov, and I. G. Kondratiev, “Features of surface modes in metamaterial layers,” Metamaterials 3, 82–89 (2009).
[CrossRef]

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

2008

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos-Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

2007

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[CrossRef]

W. Shu, Z. Ren, H. Luo, and F. Li, “Brewster angle for anisotropic materials from the extinction theorem,” Appl. Phys. A 87, 297–303 (2007).
[CrossRef]

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

H. Luo, Z. Ren, W. Shu, and F. Li, “Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation,” Appl. Phys. A 87, 245–249 (2007).
[CrossRef]

2006

2005

T. Grzegorczyk, Z. Thomas, and J. Kong, “Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials,” Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

2004

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

2003

H. Jiang, H. Chen, H. Li, and Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

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

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

N. Seddon and T. Beapark, “Observation of inverse Doppler effect,” Science 302, 1537–1540 (2003).
[CrossRef]

I. V. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

2001

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef]

2000

J. B. Pendry, “Negative refraction makes light run backward in time,” Phys. World 13, 27–29 (2000).

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

1999

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional refection from a one-dimensional dielectric lattice,” Appl. Phys. A: Mater. Sci. Process. 68, 25–28 (1999).
[CrossRef]

B. Temelkuran and E. Ozbay, “Experimental demonstration of photonic crystal based waveguides,” Appl. Phys. Lett. 74, 486–488 (1999).
[CrossRef]

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgapes and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

1998

S. Y. Lin, E. Chow, and V. Hietala, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef]

1994

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef]

1987

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

Akozbek, N.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

Alu, A.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings,” Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Argyropoulos, C.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

Beapark, T.

N. Seddon and T. Beapark, “Observation of inverse Doppler effect,” Science 302, 1537–1540 (2003).
[CrossRef]

Bloemer, M. J.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings,” Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Brueck, S. R. J.

Chan, C. T.

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

Chen, H.

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

H. Jiang, H. Chen, H. Li, and Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

Chen, R.

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

Cheng, M.

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional refection from a one-dimensional dielectric lattice,” Appl. Phys. A: Mater. Sci. Process. 68, 25–28 (1999).
[CrossRef]

Chow, E.

S. Y. Lin, E. Chow, and V. Hietala, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef]

D’Aguanno, G.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings,” Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Dai, X.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[CrossRef]

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

Economou, E. N.

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

Fan, D.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[CrossRef]

Feng, Q.

Feng, S.

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

Foteinopoulou, S.

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

Gao, L.

T. Pan, G.-D. Xu, T.-C. Zang, and L. Gao, “Study of a slab waveguide loaded with dispersive anisotropic metamaterials,” Appl. Phys. A 95, 367–372 (2009).
[CrossRef]

T. Pan, G. Xu, T. Zang, and L. Gao, “Goos-Hänchen shift in one-dimensional photonic crystals containing uniaxial indefinite medium,” Phys. Status Solidi B 246, 1088–1093 (2009).
[CrossRef]

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional refection from a one-dimensional dielectric lattice,” Appl. Phys. A: Mater. Sci. Process. 68, 25–28 (1999).
[CrossRef]

Grzegorczyk, T.

T. Grzegorczyk, Z. Thomas, and J. Kong, “Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials,” Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

Hietala, V.

S. Y. Lin, E. Chow, and V. Hietala, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef]

Ilin, N. V.

N. V. Ilin, A. I. Smirnov, and I. G. Kondratiev, “Features of surface modes in metamaterial layers,” Metamaterials 3, 82–89 (2009).
[CrossRef]

Jiang, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

H. Jiang, H. Chen, H. Li, and Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

John, S.

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef]

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

Kafesaki, M.

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

Kivshar, Y. S.

I. V. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Kivshar, Yuri S.

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

Kondratiev, I. G.

N. V. Ilin, A. I. Smirnov, and I. G. Kondratiev, “Features of surface modes in metamaterial layers,” Metamaterials 3, 82–89 (2009).
[CrossRef]

Kong, J.

T. Grzegorczyk, Z. Thomas, and J. Kong, “Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials,” Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

Koschny, T.

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

Lai, Z.

Lavrinenko, A. V.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional refection from a one-dimensional dielectric lattice,” Appl. Phys. A: Mater. Sci. Process. 68, 25–28 (1999).
[CrossRef]

Li, F.

H. Luo, Z. Ren, W. Shu, and F. Li, “Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation,” Appl. Phys. A 87, 245–249 (2007).
[CrossRef]

W. Shu, Z. Ren, H. Luo, and F. Li, “Brewster angle for anisotropic materials from the extinction theorem,” Appl. Phys. A 87, 297–303 (2007).
[CrossRef]

Li, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

H. Jiang, H. Chen, H. Li, and Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

Li, J.

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

Lin, S. Y.

S. Y. Lin, E. Chow, and V. Hietala, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef]

Liu, K.

Liu, L.

G. Ren, Z. Lai, C. Wang, Q. Feng, L. Liu, K. Liu, and X. Luo, “Subwavelength focusing of light in the planar anisotropic metamaterials with zone plates,” Opt. Express 18, 18151–18157 (2010).
[CrossRef]

L. Liu, L. Zhang, and Y. Zhang, “The transmission properties of one-dimensional photonic crystals containing indefinite metamaterials,” in Proceedings of 2008 International Workshop on Metamaterials (IEEE, 2008), pp. 221–224.

Luo, H.

W. Shu, Z. Ren, H. Luo, and F. Li, “Brewster angle for anisotropic materials from the extinction theorem,” Appl. Phys. A 87, 297–303 (2007).
[CrossRef]

H. Luo, Z. Ren, W. Shu, and F. Li, “Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation,” Appl. Phys. A 87, 245–249 (2007).
[CrossRef]

Luo, X.

Mattiucci, N.

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings,” Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

Nemat-Nasser, S. C.

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

Osgood, R. M.

Ozbay, E.

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

B. Temelkuran and E. Ozbay, “Experimental demonstration of photonic crystal based waveguides,” Appl. Phys. Lett. 74, 486–488 (1999).
[CrossRef]

Padilla, W. J.

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

Pan, T.

T. Pan, G. Xu, T. Zang, and L. Gao, “Goos-Hänchen shift in one-dimensional photonic crystals containing uniaxial indefinite medium,” Phys. Status Solidi B 246, 1088–1093 (2009).
[CrossRef]

T. Pan, G.-D. Xu, T.-C. Zang, and L. Gao, “Study of a slab waveguide loaded with dispersive anisotropic metamaterials,” Appl. Phys. A 95, 367–372 (2009).
[CrossRef]

Panoiu, N. C.

Pendry, J. B.

J. B. Pendry, “Negative refraction makes light run backward in time,” Phys. World 13, 27–29 (2000).

Quang, T.

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef]

Ren, G.

Ren, Z.

W. Shu, Z. Ren, H. Luo, and F. Li, “Brewster angle for anisotropic materials from the extinction theorem,” Appl. Phys. A 87, 297–303 (2007).
[CrossRef]

H. Luo, Z. Ren, W. Shu, and F. Li, “Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation,” Appl. Phys. A 87, 245–249 (2007).
[CrossRef]

Roberts, P. J.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgapes and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Russell, P. St. J.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgapes and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef]

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

Schurig, D.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

Seddon, N.

N. Seddon and T. Beapark, “Observation of inverse Doppler effect,” Science 302, 1537–1540 (2003).
[CrossRef]

Shadrivov, I. V.

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

I. V. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef]

Shen, N.-H.

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

Sheng, P.

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

Shu, W.

W. Shu, Z. Ren, H. Luo, and F. Li, “Brewster angle for anisotropic materials from the extinction theorem,” Appl. Phys. A 87, 297–303 (2007).
[CrossRef]

H. Luo, Z. Ren, W. Shu, and F. Li, “Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation,” Appl. Phys. A 87, 245–249 (2007).
[CrossRef]

Smirnov, A. I.

N. V. Ilin, A. I. Smirnov, and I. G. Kondratiev, “Features of surface modes in metamaterial layers,” Metamaterials 3, 82–89 (2009).
[CrossRef]

Smith, D. R.

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef]

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

Soukoulis, C. M.

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

Sukhorukov, A. A.

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

Temelkuran, B.

B. Temelkuran and E. Ozbay, “Experimental demonstration of photonic crystal based waveguides,” Appl. Phys. Lett. 74, 486–488 (1999).
[CrossRef]

Thomas, Z.

T. Grzegorczyk, Z. Thomas, and J. Kong, “Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials,” Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

Tredwell, S.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgapes and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Vier, D. C.

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

Wang, C.

G. Ren, Z. Lai, C. Wang, Q. Feng, L. Liu, K. Liu, and X. Luo, “Subwavelength focusing of light in the planar anisotropic metamaterials with zone plates,” Opt. Express 18, 18151–18157 (2010).
[CrossRef]

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos-Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Wang, L.-G.

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Wang, Z. P.

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos-Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Wen, S.

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[CrossRef]

Xiang, Y.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[CrossRef]

Y. Xiang, X. Dai, and S. Wen, “Omnidirectional gaps of one-dimensional photonic crystals containing indefinite metamaterials,” J. Opt. Soc. Am. B 24, 2033–2039 (2007).
[CrossRef]

Xu, G.

T. Pan, G. Xu, T. Zang, and L. Gao, “Goos-Hänchen shift in one-dimensional photonic crystals containing uniaxial indefinite medium,” Phys. Status Solidi B 246, 1088–1093 (2009).
[CrossRef]

Xu, G.-D.

T. Pan, G.-D. Xu, T.-C. Zang, and L. Gao, “Study of a slab waveguide loaded with dispersive anisotropic metamaterials,” Appl. Phys. A 95, 367–372 (2009).
[CrossRef]

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional refection from a one-dimensional dielectric lattice,” Appl. Phys. A: Mater. Sci. Process. 68, 25–28 (1999).
[CrossRef]

Zang, T.

T. Pan, G. Xu, T. Zang, and L. Gao, “Goos-Hänchen shift in one-dimensional photonic crystals containing uniaxial indefinite medium,” Phys. Status Solidi B 246, 1088–1093 (2009).
[CrossRef]

Zang, T.-C.

T. Pan, G.-D. Xu, T.-C. Zang, and L. Gao, “Study of a slab waveguide loaded with dispersive anisotropic metamaterials,” Appl. Phys. A 95, 367–372 (2009).
[CrossRef]

Zhang, L.

L. Liu, L. Zhang, and Y. Zhang, “The transmission properties of one-dimensional photonic crystals containing indefinite metamaterials,” in Proceedings of 2008 International Workshop on Metamaterials (IEEE, 2008), pp. 221–224.

Zhang, S.

Zhang, Y.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

H. Jiang, H. Chen, H. Li, and Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

L. Liu, L. Zhang, and Y. Zhang, “The transmission properties of one-dimensional photonic crystals containing indefinite metamaterials,” in Proceedings of 2008 International Workshop on Metamaterials (IEEE, 2008), pp. 221–224.

Zhang, Z. H.

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos-Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Zharov, A.

I. V. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

Zhou, L.

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

Zhu, S.-Y.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

Zi, J.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Appl. Phys. A

H. Luo, Z. Ren, W. Shu, and F. Li, “Wave propagation in an anisotropic metamaterial with single-sheeted hyperboloid dispersion relation,” Appl. Phys. A 87, 245–249 (2007).
[CrossRef]

T. Pan, G.-D. Xu, T.-C. Zang, and L. Gao, “Study of a slab waveguide loaded with dispersive anisotropic metamaterials,” Appl. Phys. A 95, 367–372 (2009).
[CrossRef]

W. Shu, Z. Ren, H. Luo, and F. Li, “Brewster angle for anisotropic materials from the extinction theorem,” Appl. Phys. A 87, 297–303 (2007).
[CrossRef]

Appl. Phys. A: Mater. Sci. Process.

D. N. Chigrin, A. V. Lavrinenko, D. A. Yarotsky, and S. V. Gaponenko, “Observation of total omnidirectional refection from a one-dimensional dielectric lattice,” Appl. Phys. A: Mater. Sci. Process. 68, 25–28 (1999).
[CrossRef]

Appl. Phys. Lett.

I. V. Shadrivov, A. Zharov, and Y. S. Kivshar, “Giant Goos-Hanchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
[CrossRef]

H. Jiang, H. Chen, H. Li, and Y. Zhang, “Omnidirectional gap and defect mode of one-dimensional photonic crystals containing negative-index materials,” Appl. Phys. Lett. 83, 5386–5388 (2003).
[CrossRef]

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

B. Temelkuran and E. Ozbay, “Experimental demonstration of photonic crystal based waveguides,” Appl. Phys. Lett. 74, 486–488 (1999).
[CrossRef]

T. Grzegorczyk, Z. Thomas, and J. Kong, “Inversion of critical angle and Brewster angle in anisotropic left-handed metamaterials,” Appl. Phys. Lett. 86, 251909 (2005).
[CrossRef]

Eur. Phys. J. D

M. Cheng, R. Chen, and S. Feng, “Lateral shifts of an optical beam in an anisotropic metamaterial slab,” Eur. Phys. J. D 50, 81–85 (2008).
[CrossRef]

J. Appl. Phys.

Y. Xiang, X. Dai, S. Wen, and D. Fan, “Properties of omnidirectional gap and defect mode of one-dimensional photonic crystal containing indefinite metamaterials with a hyperbolic dispersion,” J. Appl. Phys. 102, 093107 (2007).
[CrossRef]

J. Opt. Soc. Am. B

Metamaterials

N. V. Ilin, A. I. Smirnov, and I. G. Kondratiev, “Features of surface modes in metamaterial layers,” Metamaterials 3, 82–89 (2009).
[CrossRef]

Opt. Commun.

P. St. J. Russell, S. Tredwell, and P. J. Roberts, “Full photonic bandgapes and spontaneous emission control in 1D multilayer dielectric structures,” Opt. Commun. 160, 66–71 (1999).
[CrossRef]

Z. P. Wang, C. Wang, and Z. H. Zhang, “Goos-Hänchen shift of the uniaxially anisotropic left-handed material film with an arbitrary angle between the optical axis and the interface,” Opt. Commun. 281, 3019–3024 (2008).
[CrossRef]

Opt. Express

Phys. Rev. A

S. John and T. Quang, “Spontaneous emission near the edge of a photonic band gap,” Phys. Rev. A 50, 1764–1769 (1994).
[CrossRef]

Phys. Rev. B

L.-G. Wang, H. Chen, and S.-Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

C. Argyropoulos, G. D’Aguanno, N. Mattiucci, N. Akozbek, M. J. Bloemer, and A. Alu, “Matching and funneling light at the plasmonic Brewster angle,” Phys. Rev. B 85, 024304 (2012).
[CrossRef]

N.-H. Shen, S. Foteinopoulou, M. Kafesaki, T. Koschny, E. Ozbay, E. N. Economou, and C. M. Soukoulis, “Compact planar far-field superlens based on anisotropic left-handed metamaterials,” Phys. Rev. B 80, 115123 (2009).
[CrossRef]

Phys. Rev. E

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S.-Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
[CrossRef]

Phys. Rev. Lett.

A. Alu, G. D’Aguanno, N. Mattiucci, and M. J. Bloemer, “Plasmonic Brewster angle: broadband extraordinary transmission through optical gratings,” Phys. Rev. Lett. 106, 123902 (2011).
[CrossRef]

D. R. Smith and D. Schurig, “Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors,” Phys. Rev. Lett. 90, 077405 (2003).
[CrossRef]

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

S. John, “Strong localization of photon in certain disordered dielectric superlattice,” 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 simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[CrossRef]

Phys. Status Solidi B

T. Pan, G. Xu, T. Zang, and L. Gao, “Goos-Hänchen shift in one-dimensional photonic crystals containing uniaxial indefinite medium,” Phys. Status Solidi B 246, 1088–1093 (2009).
[CrossRef]

Phys. World

J. B. Pendry, “Negative refraction makes light run backward in time,” Phys. World 13, 27–29 (2000).

Science

N. Seddon and T. Beapark, “Observation of inverse Doppler effect,” Science 302, 1537–1540 (2003).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
[CrossRef]

S. Y. Lin, E. Chow, and V. Hietala, “Experimental demonstration of guiding and bending of electromagnetic waves in a photonic crystal,” Science 282, 274–276 (1998).
[CrossRef]

Other

L. Liu, L. Zhang, and Y. Zhang, “The transmission properties of one-dimensional photonic crystals containing indefinite metamaterials,” in Proceedings of 2008 International Workshop on Metamaterials (IEEE, 2008), pp. 221–224.

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Figures (8)

Fig. 1.
Fig. 1.

Structure of the 1D PC consisting of alternate layers of isotropic material (A) and uniaxial indefinite metamaterial (B).

Fig. 2.
Fig. 2.

Diagonal and nondiagonal elements of ε B and μ B as a function of ω (in units of 10 9 rad / s ) and φ (in degrees).

Fig. 3.
Fig. 3.

Transmission spectrum of the 1D PC for the cases of (a)  φ = 0 ° , (b)  φ = 15 ° , (c)  φ = 30 ° , (d)  φ = 45 ° , (e)  φ = 60 ° , and (f)  φ = 90 ° . Here we show only the TE wave spectrum for the normal incidence of light.

Fig. 4.
Fig. 4.

Transmission of the 1D PC as a function of φ and ω for the normal incidence of the waves. The gaps are denoted by the dark areas, while the bright areas show the allowed bands for the TE and TM polarizations.

Fig. 5.
Fig. 5.

Transmission of the 1D PC as a function of θ and ω for the cases of (a)  φ = 0 ° and (b)  φ = 30 ° .

Fig. 6.
Fig. 6.

Photonic bandgaps as a function of incidence angle θ for an infinite 1D PC for the cases of (a)  φ = 0 and (b)  φ = 30 ° . The gaps are denoted by the shaded areas, while the unshaded areas show the allowed bands.

Fig. 7.
Fig. 7.

Reflection of the 1D PC as function of θ : (a) TE waves for the case of φ = 0 and ω = 5.775 ( 10 9 rad / s ), (b) TE waves for the case of φ = 30 ° and ω = 7.080 ( 10 9 rad / s ), and (c) TM waves for the case of φ = 30 ° and ω = 7.350 ( 10 9 rad / s ). Solid, dotted, and dashed curves show the reflection for the cases of ( γ e = 0 , γ m = 0 ), ( γ e = 0.001 ω p , γ m = 0.001 ω m ), and ( γ e = 0.01 ω p , γ m = 0.01 ω m ), respectively.

Fig. 8.
Fig. 8.

Electric field profile (TE waves) inside the 1D PC for the cases of (a–c) φ = 0 and (d–f) φ = 30 ° for different values of ( θ , ω ): (a) 48.5°, 5.775 ( 10 9 rad / s ), the Brewster condition, (b) 48.5°, 6.050 ( 10 9 rad / s ), (c) 48.5°, 5.550 ( 10 9 rad / s ), (d) 62°, 7.080 ( 10 9 rad / s ), the Brewster condition, (e) 62°, 7.480 ( 10 9 rad / s ), and (f) 62°, 6.750 ( 10 9 rad / s ); the magnetic field profile (TM waves) inside the 1D PC for the case of φ = 30 ° and different values of ( θ , ω ): (g) 33.3°, 7.350 ( 10 9 rad / s ), the Brewster condition, (h) 33.3°, 7.450 ( 10 9 rad / s ), and (i) 33.3°, 7.150 ( 10 9 rad / s ).

Equations (13)

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

ε ¯ B = ( p 0 f 0 ε B 0 f 0 w ) , μ ¯ B = ( u 0 g 0 μ B 0 g 0 v ) ,
p = ε B cos 2 φ + ε B sin 2 φ , u = μ B cos 2 φ + μ B sin 2 φ , w = ε B sin 2 φ + ε B cos 2 φ , v = μ B sin 2 φ + μ B cos 2 φ , f = ( ε B ε B ) sin φ cos φ , g = ( μ B μ B ) sin φ cos φ .
d 2 E y d z 2 + 2 i g v k x d E y d z + ( ω 2 c 2 ε B μ B μ B v u v k x 2 ) E y = 0 ,
ψ ( z ) = ( E y ω μ 0 H x ) ,
ψ ( z ) = M B ( Δ z , ω ) ψ ( z + Δ z ) .
M B ( Δ z , ω ) = e i α 1 Δ z ( cos ( α 2 Δ z ) i q B sin ( α 2 Δ z ) i q B sin ( α 2 Δ z ) cos ( α 2 Δ z ) ) ,
M A ( Δ z , ω ) = ( cos ( k z A Δ z ) i q A sin ( k z A Δ z ) i q A sin ( k z A Δ z ) cos ( k z A Δ z ) ) ,
t ( ω ) = 2 q 0 q 0 x 11 ( ω ) + q s x 22 ( ω ) + q s q 0 x 12 ( ω ) + x 21 ( ω ) ,
d 2 H y d z 2 + 2 i f w k x d H y d z + ( ω 2 c 2 ε B μ B ε B w p w k x 2 ) H y = 0 ,
( a p b p ) = ( M 11 M 12 M 21 M 22 ) ( a p + 1 b p + 1 ) = e i K Λ ( a p + 1 b p + 1 ) ,
e i K Λ = 1 2 ( M 11 + M 22 ) ± { [ 1 2 ( M 11 + M 22 ) ] 2 1 } 1 / 2 .
θ B TE = sin 1 1 μ A ε B μ B ε A 1 μ A μ A μ B μ B , θ B T M = sin 1 1 ε A μ B ε B μ A 1 ε A ε A ε B ε B .
ε B = 1 ω p 2 ω 2 + i γ e ω p , μ B = 1 ω m 2 ω 2 + i γ m ω m ,

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