Abstract

We have analytically studied uniaxial, birefringent, one-dimensional multilayer structures and found that in such structures birefringence leads to an interesting phenomenon of omnidirectional transmission. In particular, we have demonstrated analytically that the bigger the birefringence in the layers is, the better the omnidirectional transmission is. We demonstrated this property for all kinds of multilayers with absorption and dispersion.

© 2005 Optical Society of America

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  1. S. Venkataraman, J. Murakowski, G. J. Schneider, and D. W. Prather, "Fabrication of 3D silicon photonic crystal structures using conventional micromachining technology," in Micromachining Technology for Micro-Optics and Nano-Optics II, E.G.Johnson and G.P.Nordin, eds., Proc. SPIE 5347, 195-204 (2003).
  2. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
    [CrossRef] [PubMed]
  3. J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
    [CrossRef]
  4. D. N. Chigrin, A. V. Lavrienko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
    [CrossRef]
  5. M. Deopura, C. K. Ullal, B. Temelkuran, and Y. Fink, "Dielectric omnidirectional visible reflector," Opt. Lett. 26, 1197-1199 (2001).
    [CrossRef]
  6. B. Gallas, S. Fisson, E. Charron, A. Brunet-Bruneau, G. Vuye, and J. Rivory, "Making an omnidirectional reflector," Appl. Opt. 40, 5056-5063 (2001).
    [CrossRef]
  7. Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
    [CrossRef]
  8. M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
    [CrossRef] [PubMed]
  9. E. Cojocaru, "Omnidirectional reflection from finite periodic and Fibonacci quasi-periodic multilayers of alternating isotropic and birefringent thin films," Appl. Opt. 41, 747-755 (2002).
    [CrossRef] [PubMed]
  10. K. Kaminska and K. Robbie, "Birefringent omnidirectional reflector," Appl. Opt. 43, 1570-1576 (2004)
    [CrossRef] [PubMed]
  11. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ" Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  12. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  13. Negative Refraction and Metamaterials, J.B.Pendry, ed., Opt. Express 11, 639 (2003), and references therein.
  14. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  15. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
    [CrossRef]
  16. C. Luo, S. G. Johnson, and J. D. Joannopoulos, "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
    [CrossRef]
  17. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
    [CrossRef]
  18. Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total negative refraction in real crystals for ballistic electrons and light," Phys. Rev. Lett. 91, 157404 (2003).
    [CrossRef] [PubMed]
  19. Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
    [CrossRef]
  20. A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
    [CrossRef]
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2004 (3)

K. Kaminska and K. Robbie, "Birefringent omnidirectional reflector," Appl. Opt. 43, 1570-1576 (2004)
[CrossRef] [PubMed]

Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
[CrossRef]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

2003 (3)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total negative refraction in real crystals for ballistic electrons and light," Phys. Rev. Lett. 91, 157404 (2003).
[CrossRef] [PubMed]

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

2002 (3)

E. Cojocaru, "Omnidirectional reflection from finite periodic and Fibonacci quasi-periodic multilayers of alternating isotropic and birefringent thin films," Appl. Opt. 41, 747-755 (2002).
[CrossRef] [PubMed]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

2001 (3)

2000 (2)

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1999 (1)

D. N. Chigrin, A. V. Lavrienko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

1998 (2)

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

1990 (1)

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ" Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1948 (1)

Bertolotti, M.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

Brunet-Bruneau, A.

Charron, E.

Chen, C.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Chigrin, D. N.

D. N. Chigrin, A. V. Lavrienko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Cho, C.

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

Chui, S. T.

Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
[CrossRef]

Cojocaru, E.

Crook, A. W.

Deopura, M.

Fan, S.

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Fink, Y.

Fisson, S.

Fluegel, B.

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total negative refraction in real crystals for ballistic electrons and light," Phys. Rev. Lett. 91, 157404 (2003).
[CrossRef] [PubMed]

Gallas, B.

Gaponenko, S. V.

D. N. Chigrin, A. V. Lavrienko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Gilbert, L. R.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[CrossRef] [PubMed]

Haus, J. W.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

Jaggard, D. L.

Jeon, H.

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Kaminska, K.

Lavrienko, A. V.

D. N. Chigrin, A. V. Lavrienko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Lin, Z.

Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
[CrossRef]

Liu, Z.

Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
[CrossRef]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Mandatori, A.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

Mascarenhas, A.

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total negative refraction in real crystals for ballistic electrons and light," Phys. Rev. Lett. 91, 157404 (2003).
[CrossRef] [PubMed]

Michel, J.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Murakowski, J.

S. Venkataraman, J. Murakowski, G. J. Schneider, and D. W. Prather, "Fabrication of 3D silicon photonic crystal structures using conventional micromachining technology," in Micromachining Technology for Micro-Optics and Nano-Optics II, E.G.Johnson and G.P.Nordin, eds., Proc. SPIE 5347, 195-204 (2003).

Nevitt, T. J.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[CrossRef] [PubMed]

Ouderkirk, A. J.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[CrossRef] [PubMed]

Park, Y.

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Prather, D. W.

S. Venkataraman, J. Murakowski, G. J. Schneider, and D. W. Prather, "Fabrication of 3D silicon photonic crystal structures using conventional micromachining technology," in Micromachining Technology for Micro-Optics and Nano-Optics II, E.G.Johnson and G.P.Nordin, eds., Proc. SPIE 5347, 195-204 (2003).

Rivory, J.

Robbie, K.

Roh, Y.

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

Scalora, M.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

Schneider, G. J.

S. Venkataraman, J. Murakowski, G. J. Schneider, and D. W. Prather, "Fabrication of 3D silicon photonic crystal structures using conventional micromachining technology," in Micromachining Technology for Micro-Optics and Nano-Optics II, E.G.Johnson and G.P.Nordin, eds., Proc. SPIE 5347, 195-204 (2003).

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] [PubMed]

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] [PubMed]

Sibilia, C.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

Smith, D. R.

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

Stover, C. A.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[CrossRef] [PubMed]

Sun, X.

Sung, M. G.

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

Temelkuran, B.

Thomas, E. L.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

Ullal, C. K.

Venkataraman, S.

S. Venkataraman, J. Murakowski, G. J. Schneider, and D. W. Prather, "Fabrication of 3D silicon photonic crystal structures using conventional micromachining technology," in Micromachining Technology for Micro-Optics and Nano-Optics II, E.G.Johnson and G.P.Nordin, eds., Proc. SPIE 5347, 195-204 (2003).

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ" Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vuye, G.

Weber, M. F.

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[CrossRef] [PubMed]

Winn, J. N.

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, "Omnidirectional reflection from a one-dimensional photonic crystal," Opt. Lett. 23, 1573-1575 (1998).
[CrossRef]

Woo, J. C.

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

Yarotsky, D. A.

D. N. Chigrin, A. V. Lavrienko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Zhang, Y.

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total negative refraction in real crystals for ballistic electrons and light," Phys. Rev. Lett. 91, 157404 (2003).
[CrossRef] [PubMed]

Zhukovsky, S.

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. A (1)

D. N. Chigrin, A. V. Lavrienko, D. A. Yarotsky, and S. V. Gaponenko, "Observation of total omnidirectional reflection from a one-dimensional dielectric lattice," Appl. Phys. A 68, 25-28 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

Y. Park, Y. Roh, C. Cho, H. Jeon, M. G. Sung, and J. C. Woo, "GaAs-based near infrared omnidirectional reflector," Appl. Phys. Lett. 82, 2770-2772 (2003).
[CrossRef]

C. Luo, S. G. Johnson, and J. D. Joannopoulos, "All-angle negative refraction in a three-dimensionally periodic photonic crystal," Appl. Phys. Lett. 81, 2352-2354 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (3)

Phys. Rev. B (4)

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Subwavelength imaging in photonic crystals," Phys. Rev. B 68, 045115 (2003).
[CrossRef]

Z. Liu, Z. Lin, and S. T. Chui, "Negative refraction and omnidirectional total transmission at a planar interface associated with a uniaxial medium," Phys. Rev. B 69, 115402 (2004).
[CrossRef]

A. Mandatori, C. Sibilia, M. Bertolotti, S. Zhukovsky, J. W. Haus, and M. Scalora, "Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials," Phys. Rev. B 70, 165107 (2004).
[CrossRef]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B 65, 201104 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

Y. Zhang, B. Fluegel, and A. Mascarenhas, "Total negative refraction in real crystals for ballistic electrons and light," Phys. Rev. Lett. 91, 157404 (2003).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Science (3)

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

Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, "A dielectric omnidirectional reflector," Science 282, 1679-1682 (1998).
[CrossRef] [PubMed]

M. F. Weber, C. A. Stover, L. R. Gilbert, T. J. Nevitt, and A. J. Ouderkirk, "Giant birefringent optics in multilayer polymer mirrors," Science 287, 2451-2456 (2000).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and µ" Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other (2)

S. Venkataraman, J. Murakowski, G. J. Schneider, and D. W. Prather, "Fabrication of 3D silicon photonic crystal structures using conventional micromachining technology," in Micromachining Technology for Micro-Optics and Nano-Optics II, E.G.Johnson and G.P.Nordin, eds., Proc. SPIE 5347, 195-204 (2003).

Negative Refraction and Metamaterials, J.B.Pendry, ed., Opt. Express 11, 639 (2003), and references therein.

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Figures (7)

Fig. 1
Fig. 1

Representation of a one-layer anisotropic structure. (a) different rays in input and output of the structure. (b) Ellipsoid of the central anisotropic layer. (c) Section of the ellipsoid inside the central anisotropic layer.

Fig. 2
Fig. 2

Dependence of the phase factor [ α n ( α 2 + tan 2 φ i ) 1 2 ] versus incident angle φ i for α = 1.0 , 1.15, 1.33, 1.5, and 2.0.

Fig. 3
Fig. 3

Dependence of transmission power ( t i a 2 ) for TM polarization for (a) n i = 1.33 , Δ n = n y n z = 0.2 , and n y = 1.33 , 1.5, 1.7, 2.0, 2.5; (b) n i = 1.33 , n a n i = 1.5 , and Δ n = n y n z = 0.0 , 0.1, 0.2, 0.3.

Fig. 4
Fig. 4

Dependence of transmitted power t i a 2 on the incident angle φ i and on the wavelength λ for an interface of dispersive media having a Lorentz dispersion curve [Eq. (11)]. The off-resonance refraction index contrast n 0 ( a ) n 0 ( i ) equals 1.25, and the absorption-peak frequencies are according to the condition (12).

Fig. 5
Fig. 5

Transmission-spectrum function of wavelength and incident angle for a different level of anisotropy for an eight-layer periodic structure (ABABABAB) for dispersive media (Example 1): (a) all materials are isotropic; (b) all materials have Δ ϵ = ϵ zz ϵ yy = 1 ; (c) all materials have Δ ϵ = ϵ zz ϵ yy = 4 . The red areas denote high transmission, while the blue areas denote low transmission.

Fig. 6
Fig. 6

Transmission-spectrum function of wavelength and incident angle for a different level of anisotropy for an eight-layer periodic structure (ABABABAB) for dispersive and absorptive media (Example 2): (a) all materials are isotropic; (b) all materials have Δ ϵ = ϵ zz ϵ yy = 4 .

Fig. 7
Fig. 7

Transmission-spectrum function of wavelength and incident angle for a different level of anisotropy for an eight-layer periodic structure (ABABABAB). The anisotropy is introduced in every other layer rather than in each layer (Example 3): (a) all A layers have Δ ϵ = ϵ zz ϵ yy = 1 . (b) all A layers have Δ ϵ = ϵ zz ϵ yy = 4 .

Equations (24)

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n i sin φ i = n a sin φ a = n o sin φ o .
n a = n z n y ( n y 2 cos 2 φ a + n z 2 sin 2 φ a ) 1 2 .
n a = ( n z 2 + n i 2 sin 2 φ i n y 2 n z 2 n y 2 ) 1 2 ,
sin φ a = n i sin φ i ( n z 2 + n i 2 sin 2 φ i n y 2 n z 2 n y 2 ) 1 2 .
t i a o = E t E i = t i a t a o Δ a 1 r a i r a o Δ a 2 ,
Δ a = exp ( i k a z ) l = z ,
Δ a = exp ( i k a z ) = exp ( 2 π i λ n a l cos φ a ) .
n a = n z cos φ a .
Δ a = exp ( i k a z ) = exp ( 2 π i λ n z cos φ a l cos φ a ) = exp ( 2 π i λ n z l )
Δ a = exp [ 2 π i λ α n z ( α 2 + tan 2 φ a ) 1 2 ] ,
T s = 2 sin φ a cos φ i sin ( φ i + φ a ) ,
T p = sin φ a cos φ i sin ( φ i + φ a ) cos ( φ i φ a ) ,
n ( λ ) = n 0 + g λ 0 2 ( 1 λ 2 1 λ 0 2 ) i Δ λ λ 3 .
λ 0 ( a ) λ 0 ( i ) + 0.8 Δ λ ( i ) ,
t i a b o = t i a [ b o ] = t i a t a b o Δ a 1 r a i r a b o Δ a 2 = t i a t a b t b o Δ a Δ b 1 r a i r a b Δ a 2 r b a r b o Δ b 2 r a i r b o Δ a 2 Δ b 2 .
t i a b c o = t i a t a b t b c t c o Δ a Δ b Δ c ( 1 r a i r a b Δ a 2 r b a r b c Δ b 2 r c b r c o Δ c 2 r a i r b c Δ a 2 Δ b 2 r b a r c o Δ b 2 Δ c 2 r a i r c o Δ a 2 Δ b 2 Δ c 2 ) .
t i ( a 1 ... a N ) o = t i a 1 t a 1 a 2 t a N 1 a N t a N o Δ a 1 Δ a 2 Δ a N 1 j = 1 N k = j N r a j a j 1 r a k a k + 1 m = j k Δ a m 2 .
n ( λ ) = a + b λ + c λ 2 + d λ 3 ,
ϵ a x x = n A 2 , ϵ a y y = n A 2 , ϵ a z z = n A 2 + 1 ;
ϵ b x x = n B 2 , ϵ b y y = n B 2 , ϵ b z z = n B 2 + 1 .
ϵ a x x = n A 2 , ϵ a y y = n A 2 , ϵ a z z = n A 2 + 4 ;
ϵ b x x = n B 2 , ϵ b y y = n B 2 , ϵ b z z = n B 2 + 4 .
n B = a λ 2 + b λ + c + d λ ,
k B = a + b λ + c λ 2 + d λ 3 ,

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