Abstract

We propose a scheme to induce transparency in one-dimensional disordered multilayers which are composed of negative permittivity and negative permeability metamaterials. First, analytical expressions for transparency condition are derived exactly, providing us a picture that complete tunneling in such kind of multiple-resonance system can be achieved if exponentially growing waves can compensate exponentially decaying waves. Second, a compensating method is used to realize this idea, and both simulations and experiments are performed in the microwave regime to confirm the theoretical analysis. Last, we have a discussion on how the coupling of resonances affects the transport properties of samples.

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    [CrossRef]
  2. P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
    [CrossRef]
  3. J. B. Pendry, “Quasi-extended electron states in strongly disordered systems,” J. Phys. C Solid State Phys. 20(5), 733–742 (1987).
    [CrossRef]
  4. A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, “Hopping conductivity of metal-semiconductor-metal contacts,” Sov. Phys. Semicond. 21, 370–373 (1987).
  5. J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
    [CrossRef] [PubMed]
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2008 (2)

J. B. Pendry, “Light finds a way through maze,” Physics 1, 20 (2008).
[CrossRef]

P. Han, C. T. Chan, and Z. Q. Zhang, “Wave localization in one-dimensional random structures composed of single-negative metamaterials,” Phys. Rev. B 77(11), 115332 (2008).
[CrossRef]

2007 (2)

Y. Weng, Z. G. Wang, and H. Chen, “Band structures of one-dimensional subwavelength photonic crystals containing metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046601 (2007).
[CrossRef] [PubMed]

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

2006 (3)

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, A. Z. Genack, B. Hu, and P. Sebbah, “Localized modes in open one-dimensional dissipative random systems,” Phys. Rev. Lett. 97(24), 243904 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

2005 (1)

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

2004 (1)

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066607 (2004).
[CrossRef] [PubMed]

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(8), 083901 (2003).
[CrossRef] [PubMed]

A. Aù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. 51(10), 2558–2571 (2003).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

2000 (2)

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

1987 (2)

J. B. Pendry, “Quasi-extended electron states in strongly disordered systems,” J. Phys. C Solid State Phys. 20(5), 733–742 (1987).
[CrossRef]

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, “Hopping conductivity of metal-semiconductor-metal contacts,” Sov. Phys. Semicond. 21, 370–373 (1987).

1977 (1)

1958 (1)

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[CrossRef]

Anderson, P. W.

P. W. Anderson, “Absence of diffusion in certain random lattices,” Phys. Rev. 109(5), 1492–1505 (1958).
[CrossRef]

Asatryan, A. A.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Aù, A.

A. Aù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. 51(10), 2558–2571 (2003).
[CrossRef]

Bertolotti, J.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Bliokh, K. Y.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, A. Z. Genack, B. Hu, and P. Sebbah, “Localized modes in open one-dimensional dissipative random systems,” Phys. Rev. Lett. 97(24), 243904 (2006).
[CrossRef] [PubMed]

Bliokh, Y. P.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, A. Z. Genack, B. Hu, and P. Sebbah, “Localized modes in open one-dimensional dissipative random systems,” Phys. Rev. Lett. 97(24), 243904 (2006).
[CrossRef] [PubMed]

Botten, L. C.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Byrne, M. A.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Chan, C. T.

P. Han, C. T. Chan, and Z. Q. Zhang, “Wave localization in one-dimensional random structures composed of single-negative metamaterials,” Phys. Rev. B 77(11), 115332 (2008).
[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(8), 083901 (2003).
[CrossRef] [PubMed]

Chen, H.

Y. Weng, Z. G. Wang, and H. Chen, “Band structures of one-dimensional subwavelength photonic crystals containing metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046601 (2007).
[CrossRef] [PubMed]

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066607 (2004).
[CrossRef] [PubMed]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Engheta, N.

A. Aù and N. Engheta, “Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency,” IEEE Trans. Antenn. Propag. 51(10), 2558–2571 (2003).
[CrossRef]

Fistul, M. V.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, “Hopping conductivity of metal-semiconductor-metal contacts,” Sov. Phys. Semicond. 21, 370–373 (1987).

Freilikher, V.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, A. Z. Genack, B. Hu, and P. Sebbah, “Localized modes in open one-dimensional dissipative random systems,” Phys. Rev. Lett. 97(24), 243904 (2006).
[CrossRef] [PubMed]

Freilikher, V. D.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Genack, A. Z.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, A. Z. Genack, B. Hu, and P. Sebbah, “Localized modes in open one-dimensional dissipative random systems,” Phys. Rev. Lett. 97(24), 243904 (2006).
[CrossRef] [PubMed]

Ghulinyan, M.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Gottardo, S.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Gredeskul, S. A.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Han, P.

P. Han, C. T. Chan, and Z. Q. Zhang, “Wave localization in one-dimensional random structures composed of single-negative metamaterials,” Phys. Rev. B 77(11), 115332 (2008).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Hong, C.

Hu, B.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, A. Z. Genack, B. Hu, and P. Sebbah, “Localized modes in open one-dimensional dissipative random systems,” Phys. Rev. Lett. 97(24), 243904 (2006).
[CrossRef] [PubMed]

Jiang, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066607 (2004).
[CrossRef] [PubMed]

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Li, H.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066607 (2004).
[CrossRef] [PubMed]

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(8), 083901 (2003).
[CrossRef] [PubMed]

McPhedran, R. C.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Pavesi, L.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, “Light finds a way through maze,” Physics 1, 20 (2008).
[CrossRef]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

J. B. Pendry, “Quasi-extended electron states in strongly disordered systems,” J. Phys. C Solid State Phys. 20(5), 733–742 (1987).
[CrossRef]

Raikh, M. E.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, “Hopping conductivity of metal-semiconductor-metal contacts,” Sov. Phys. Semicond. 21, 370–373 (1987).

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Ruzin, I. M.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, “Hopping conductivity of metal-semiconductor-metal contacts,” Sov. Phys. Semicond. 21, 370–373 (1987).

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

Sebbah, P.

K. Y. Bliokh, Y. P. Bliokh, V. Freilikher, A. Z. Genack, B. Hu, and P. Sebbah, “Localized modes in open one-dimensional dissipative random systems,” Phys. Rev. Lett. 97(24), 243904 (2006).
[CrossRef] [PubMed]

Shadrivov, I. V.

A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, “Suppression of Anderson localization in disordered metamaterials,” Phys. Rev. Lett. 99(19), 193902 (2007).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

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(8), 083901 (2003).
[CrossRef] [PubMed]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312(5781), 1780–1782 (2006).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science 314(5801), 977–980 (2006).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech. 47(11), 2075–2084 (1999).
[CrossRef]

Tartakovskii, A. V.

A. V. Tartakovskii, M. V. Fistul, M. E. Raikh, and I. M. Ruzin, “Hopping conductivity of metal-semiconductor-metal contacts,” Sov. Phys. Semicond. 21, 370–373 (1987).

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(18), 4184–4187 (2000).
[CrossRef] [PubMed]

Wang, Z. G.

Y. Weng, Z. G. Wang, and H. Chen, “Band structures of one-dimensional subwavelength photonic crystals containing metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046601 (2007).
[CrossRef] [PubMed]

Weng, Y.

Y. Weng, Z. G. Wang, and H. Chen, “Band structures of one-dimensional subwavelength photonic crystals containing metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75(4), 046601 (2007).
[CrossRef] [PubMed]

Wiersma, D. S.

J. Bertolotti, S. Gottardo, D. S. Wiersma, M. Ghulinyan, and L. Pavesi, “Optical necklace states in Anderson localized 1D systems,” Phys. Rev. Lett. 94(11), 113903 (2005).
[CrossRef] [PubMed]

Yariv, A.

Yeh, P.

Zhang, Y.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066607 (2004).
[CrossRef] [PubMed]

Zhang, Z. Q.

P. Han, C. T. Chan, and Z. Q. Zhang, “Wave localization in one-dimensional random structures composed of single-negative metamaterials,” Phys. Rev. B 77(11), 115332 (2008).
[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(8), 083901 (2003).
[CrossRef] [PubMed]

Zhu, S.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066607 (2004).
[CrossRef] [PubMed]

Zi, J.

H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(6), 066607 (2004).
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Figures (4)

Fig. 1
Fig. 1

Calculated transmittance as a function of frequency for the sample before compensation (dash-dot line) and after compensation (solid line).

Fig. 2
Fig. 2

Intensity distributions inside the sample before compensation (a) and after compensation (b) corresponding to Fig. 1.

Fig. 3
Fig. 3

Numerical simulations (solid lines) and experimental results (open circles), showing resonance tunneling states in reflection spectra. (a) Reflectance of the sample before compensation. (b) Reflectance after compensation.

Fig. 4
Fig. 4

Tunneling behaviors in different disordered samples. Top panels: calculated transmission spectrum (a) and field intensity distribution (b) for the first sample. Inset: transmission spectrum for periodic AB pairs. Bottom panels: transmission spectrum (c) and field intensity distribution (d) for the second sample.

Equations (7)

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( E j H j ) = M j ( E j + 1 H j + 1 ) ,
M j = ( 1 1 Z j 1 Z j 1 ) ( exp ( α j d j ) 0 0 exp ( α j d j ) ) ( 1 1 Z j 1 Z j 1 ) 1 .
T ( ν 0 ) = 1 1 + 1 4 [ ( Z S | Z A | + | Z B | Z S ) sin h ( N A α A d A N B α B d B ) ] 2 ,
N A α A d A N B α B d B = 0.
N A α A d A N B α B d B ± α C d C = 0.
ε A = 3.57 13.08 ν 2 , μ A = 1
ε B = 3.57 , μ B = 1 3.66 ν 2

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