Abstract

We study the electromagnetic beam reflection from layered structures that include the so-called ε-negative and the μ-negative materials, also called single negative materials. We predict that such structures can demonstrate a giant lateral Goos–Hänchen shift of the resonant excitation of surface waves at the interface between the conventional and single negative materials, as well as due to the excitation of leaky modes in the layered structures. Then we replace the conventional layer with a left-handed layer (a material with both ε<0 and μ<0). We show that the Goos-Hänchen shift can be positive and negative depending on the type of this layer (conventional or LH material), which can support TE or TM surface waves.

© 2012 Optical Society of America

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  1. F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436, 333–346 (1947).
    [CrossRef]
  2. L. G. Wang, H. Chen, and S. Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30, 2936–2938 (2005).
    [CrossRef]
  3. X. Chen, M. Sheng, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” Appl. Phys. 104, 123101 (2008).
    [CrossRef]
  4. L. G. Wang and S. Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31, 101–103 (2006).
    [CrossRef]
  5. X. B. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
    [CrossRef]
  6. Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
    [CrossRef]
  7. C. W. Chen, W. C. Lin, L. S. Liao, Z. H. Lin, H. P. Chiang, P. T. Leung, E. Sijercic, and W. S. Tse, “Optical temperature sensing based on the Goos-Hänchen effect,” Appl. Opt. 46, 5347–5351 (2007).
    [CrossRef]
  8. T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
    [CrossRef]
  9. V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen effect at the reflection from left-handed metamaterials,” Appl. Phys. Lett. 83, 2713–2715 (2003).
    [CrossRef]
  10. P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
    [CrossRef]
  11. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  12. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
    [CrossRef]
  13. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef]
  14. R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61–64 (2000).
    [CrossRef]
  15. I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
    [CrossRef]
  16. H. T. Jiang, H. Chen, H. Q. Li, Y. W. Zhang, J. Zi, and S. Y. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69, 066607 (2004).
    [CrossRef]
  17. H. Daninthe, S. Foteinopoulou, and C. M. Soukoulis, “Omnireflectance and enhanced resonant tunneling from multilayers containing left-handed materials,” Photon. Nanostr. Fundam. Appl. 4, 123–131 (2006).
    [CrossRef]
  18. 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]
  19. L. G. Wang, H. Chen, and S. Y. Zhu, “Omnidirectional gap and defect mode of one-dimensional photonic crystals with singlenegative materials,” Phys. Rev. B 70, 245102 (2004).
    [CrossRef]
  20. R. Srivastava, S. Pati, and S. P. Ojha, “Enhancement of nomnidirectional reflection in photonic crystal hetrostructures,” Prog. Electromagnet. Res. B 1, 197–208 (2008).
  21. S. K. Srivastava and S. P. Ojha, “Enhancement of omnidirectional reflection bands in one-dimentional photonic crystals with left-handed materials,” Prog. Electromagn. Res. 68, 91–111 (2007).
    [CrossRef]
  22. D. R. Fredkin and A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett. 81, 1753–1755 (2002).
    [CrossRef]
  23. G. V. Morozov, D. W. L. Sprung, and J. Martorell, “Semiclassical coupled-wave theory and its application to TE waves in onedimensional photonic crystals,” Phys. Rev. E 69, 016612 (2004).
    [CrossRef]
  24. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).
  25. J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A: Pure Appl. Opt. 8, 630–638 (2006).
    [CrossRef]
  26. M. Miri, A. Naqavi, A. Khavasi, K. Mehrany, S. Khorasani, and B. Rashidian, “Geometrical approach in physical understanding of the Goos-Hänchen shift in one- and two-dimensional periodic structures,” Opt. Lett. 33, 2940–2942 (2008).
    [CrossRef]

2008 (4)

X. Chen, M. Sheng, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” Appl. Phys. 104, 123101 (2008).
[CrossRef]

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
[CrossRef]

R. Srivastava, S. Pati, and S. P. Ojha, “Enhancement of nomnidirectional reflection in photonic crystal hetrostructures,” Prog. Electromagnet. Res. B 1, 197–208 (2008).

M. Miri, A. Naqavi, A. Khavasi, K. Mehrany, S. Khorasani, and B. Rashidian, “Geometrical approach in physical understanding of the Goos-Hänchen shift in one- and two-dimensional periodic structures,” Opt. Lett. 33, 2940–2942 (2008).
[CrossRef]

2007 (2)

C. W. Chen, W. C. Lin, L. S. Liao, Z. H. Lin, H. P. Chiang, P. T. Leung, E. Sijercic, and W. S. Tse, “Optical temperature sensing based on the Goos-Hänchen effect,” Appl. Opt. 46, 5347–5351 (2007).
[CrossRef]

S. K. Srivastava and S. P. Ojha, “Enhancement of omnidirectional reflection bands in one-dimentional photonic crystals with left-handed materials,” Prog. Electromagn. Res. 68, 91–111 (2007).
[CrossRef]

2006 (4)

H. Daninthe, S. Foteinopoulou, and C. M. Soukoulis, “Omnireflectance and enhanced resonant tunneling from multilayers containing left-handed materials,” Photon. Nanostr. Fundam. Appl. 4, 123–131 (2006).
[CrossRef]

X. B. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

L. G. Wang and S. Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31, 101–103 (2006).
[CrossRef]

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A: Pure Appl. Opt. 8, 630–638 (2006).
[CrossRef]

2005 (1)

2004 (4)

G. V. Morozov, D. W. L. Sprung, and J. Martorell, “Semiclassical coupled-wave theory and its application to TE waves in onedimensional photonic crystals,” Phys. Rev. E 69, 016612 (2004).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
[CrossRef]

H. T. Jiang, H. Chen, H. Q. Li, Y. W. 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 singlenegative materials,” Phys. Rev. B 70, 245102 (2004).
[CrossRef]

2003 (2)

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]

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

2002 (1)

D. R. Fredkin and A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

2001 (1)

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

2000 (2)

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61–64 (2000).
[CrossRef]

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

1977 (1)

1947 (1)

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

Boardman, A. D.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
[CrossRef]

Cao, Z.

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
[CrossRef]

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, C. W.

Chen, H.

L. G. Wang, H. Chen, and S. Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30, 2936–2938 (2005).
[CrossRef]

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

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

Chen, X.

X. Chen, M. Sheng, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” Appl. Phys. 104, 123101 (2008).
[CrossRef]

Chiang, H. P.

Daninthe, H.

H. Daninthe, S. Foteinopoulou, and C. M. Soukoulis, “Omnireflectance and enhanced resonant tunneling from multilayers containing left-handed materials,” Photon. Nanostr. Fundam. Appl. 4, 123–131 (2006).
[CrossRef]

Egan, P.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
[CrossRef]

Foteinopoulou, S.

H. Daninthe, S. Foteinopoulou, and C. M. Soukoulis, “Omnireflectance and enhanced resonant tunneling from multilayers containing left-handed materials,” Photon. Nanostr. Fundam. Appl. 4, 123–131 (2006).
[CrossRef]

Fredkin, D. R.

D. R. Fredkin and A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

Goos, F.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

Hänchen, H.

F. Goos and H. Hänchen, “Ein neuer und fundamentaler versuch zur totalreflexion,” Ann. Phys. 436, 333–346 (1947).
[CrossRef]

He, Y.

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
[CrossRef]

Hesselink, L.

X. B. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Hong, C. S.

Jiang, H. T.

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

Khavasi, A.

Khorasani, S.

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
[CrossRef]

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

Leung, P. T.

Li, C. F.

X. Chen, M. Sheng, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” Appl. Phys. 104, 123101 (2008).
[CrossRef]

Li, H.

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
[CrossRef]

Li, H. Q.

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

Liao, L. S.

Lin, W. C.

Lin, Z. H.

Martorell, J.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A: Pure Appl. Opt. 8, 630–638 (2006).
[CrossRef]

G. V. Morozov, D. W. L. Sprung, and J. Martorell, “Semiclassical coupled-wave theory and its application to TE waves in onedimensional photonic crystals,” Phys. Rev. E 69, 016612 (2004).
[CrossRef]

Mehrany, K.

Miri, M.

Morozov, G. V.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A: Pure Appl. Opt. 8, 630–638 (2006).
[CrossRef]

G. V. Morozov, D. W. L. Sprung, and J. Martorell, “Semiclassical coupled-wave theory and its application to TE waves in onedimensional photonic crystals,” Phys. Rev. E 69, 016612 (2004).
[CrossRef]

Naqavi, A.

Ojha, S. P.

R. Srivastava, S. Pati, and S. P. Ojha, “Enhancement of nomnidirectional reflection in photonic crystal hetrostructures,” Prog. Electromagnet. Res. B 1, 197–208 (2008).

S. K. Srivastava and S. P. Ojha, “Enhancement of omnidirectional reflection bands in one-dimentional photonic crystals with left-handed materials,” Prog. Electromagn. Res. 68, 91–111 (2007).
[CrossRef]

Pati, S.

R. Srivastava, S. Pati, and S. P. Ojha, “Enhancement of nomnidirectional reflection in photonic crystal hetrostructures,” Prog. Electromagnet. Res. B 1, 197–208 (2008).

Pendry, J. B.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Rashidian, B.

Ron, A.

D. R. Fredkin and A. Ron, “Effectively left-handed (negative index) composite material,” Appl. Phys. Lett. 81, 1753–1755 (2002).
[CrossRef]

Ruppin, R.

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61–64 (2000).
[CrossRef]

Sakata, T.

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[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]

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
[CrossRef]

Shadrivov, V.

V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen 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, Q.

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
[CrossRef]

Sheng, M.

X. Chen, M. Sheng, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” Appl. Phys. 104, 123101 (2008).
[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]

Shimokawa, F.

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[CrossRef]

Sijercic, E.

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]

Soukoulis, C. M.

H. Daninthe, S. Foteinopoulou, and C. M. Soukoulis, “Omnireflectance and enhanced resonant tunneling from multilayers containing left-handed materials,” Photon. Nanostr. Fundam. Appl. 4, 123–131 (2006).
[CrossRef]

Sprung, D. W. L.

J. Martorell, D. W. L. Sprung, and G. V. Morozov, “Surface TE waves on 1D photonic crystals,” J. Opt. A: Pure Appl. Opt. 8, 630–638 (2006).
[CrossRef]

G. V. Morozov, D. W. L. Sprung, and J. Martorell, “Semiclassical coupled-wave theory and its application to TE waves in onedimensional photonic crystals,” Phys. Rev. E 69, 016612 (2004).
[CrossRef]

Srivastava, R.

R. Srivastava, S. Pati, and S. P. Ojha, “Enhancement of nomnidirectional reflection in photonic crystal hetrostructures,” Prog. Electromagnet. Res. B 1, 197–208 (2008).

Srivastava, S. K.

S. K. Srivastava and S. P. Ojha, “Enhancement of omnidirectional reflection bands in one-dimentional photonic crystals with left-handed materials,” Prog. Electromagn. Res. 68, 91–111 (2007).
[CrossRef]

Stewart, W. J.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
[CrossRef]

Togo, H.

T. Sakata, H. Togo, and F. Shimokawa, “Reflection-type 2×2 optical waveguide switch using the Goos–Hänchen shift effect,” Appl. Phys. Lett. 76, 2841–2843 (2000).
[CrossRef]

Tse, W. S.

Wang, L. G.

Wang, Y.

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
[CrossRef]

Yariv, A.

P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
[CrossRef]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Yeh, P.

P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
[CrossRef]

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984).

Yin, X. B.

X. B. Yin and L. Hesselink, “Goos-Hänchen shift surface plasmon resonance sensor,” Appl. Phys. Lett. 89, 261108 (2006).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773–4776 (1996).
[CrossRef]

Yu, T.

Y. Wang, H. Li, Z. Cao, T. Yu, Q. Shen, and Y. He, “Oscillating wave sensor based on the Goos-Hänchen effect,” Appl. Phys. Lett. 92, 061117 (2008).
[CrossRef]

Zhang, Y. W.

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

Zhang, Z. F.

X. Chen, M. Sheng, Z. F. Zhang, and C. F. Li, “Tunable lateral shift and polarization beam splitting of the transmitted light beam through electro-optic crystals,” Appl. Phys. 104, 123101 (2008).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 16617–16619 (2004).
[CrossRef]

V. Shadrivov, A. A. Zharov, and Y. S. Kivshar, “Giant Goos-Hänchen 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.

L. G. Wang and S. Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31, 101–103 (2006).
[CrossRef]

L. G. Wang, H. Chen, and S. Y. Zhu, “Large negative Goos-Hänchen shift from a weakly absorbing dielectric slab,” Opt. Lett. 30, 2936–2938 (2005).
[CrossRef]

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

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

Zi, J.

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Figures (6)

Fig. 1.
Fig. 1.

Schematic diagrams of the configuration under study. The parameters are as follows: d1=6mm, d2=8mm, μd=1, εd=12.25, and μ0=ε0=±1.

Fig. 2.
Fig. 2.

Existence regions of (a) TE-polarized surface modes for CEM structure and (b) TM-polarized surface modes for DEM structure. Here, we take β=1.85, dc=3d1 (solid blue curves), dc=d1 (dashed green curves), and dc=0.01d1 (dotted red curves). Dispersion property of (c) the TE-polarized and (d) TM-polarized surface modes at the second bandgaps of the layered structure for the different thickness of the cap layer. We choose d1=6mm and d2=8mm.

Fig. 3.
Fig. 3.

The transverse profiles of the surface waves versus coordinate z for CEM structure (μ0=ε0=+1) are shown in (a) and (b) and for DEM structure (μ0=ε0=1) are shown in (c) and (d). We take β=1.5, ω=5GHz and dc=d1 in (a) and (c), dc=3d1 in (b) and (d).

Fig. 4.
Fig. 4.

Relative GH shifts versus (a) angle of incident beam for different thickness of conventional layer of CEM structure (b) thickness of conventional layer of CEM structure, and (c) thickness of DNG layer of DEM structure.

Fig. 5.
Fig. 5.

Relative GH shifts versus the incidence angle for (a) the CEM structure corresponding to forward surface states and (b) the DEM structure corresponding to backward surface states. Here L=7.38mm.

Fig. 6.
Fig. 6.

Profiles of the reflected (solid) and incident (dotted) beams shown as the field amplitude versus coordinate x for incidence angle of beam θ=25.3 (a) in the case of forward surface state and presence of conventional layer and (b) in the case of backward surface state and presence of DNG layer in structure. Field distribution of the surface states are shown in (c) and (d) corresponding to (a) and (b). Here d=d1+d2.

Equations (5)

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

εENG=1ωep2ω2,μENG=3,εMNG=3,μMNG=1ωmp2ω2,
Ei(x)=exp[(x/a)2ikx0x],
Δr=dφ/dkx,
Er(x)=12πR(kx)E¯i(kx)eikxxdkx,
Δn=anxn|Er(x)|2dx(|Er(x)|2dx)1.

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