Abstract

The richer variety of Klein–Gordon basis is already established for discrete breathers in metamatetrials. Based on this attempt, we show various anomalous Fano resonance behaviors that have been experimentally observed, but cannot be explained by nonlinear Schrodinger model. Certain material parameters of Klein–Gordon lattice in metamaterials are related for the first time with characteristics of Fano resonance, which can be utilized for beam filtering and for high-resolution biological sensing technology. Although relations with coupling and other parameters exist, the most remarkable relation is observed with linear permittivity that could control the wave transmission characteristics in metamaterials for applications in optical engineering.

© 2012 Optical Society of America

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  1. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
    [CrossRef]
  2. V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
    [CrossRef]
  3. J. Li, W. D. Schneider, R. Berndt, and B. Delley, “Kondo scattering observed at a single magnetic impurity,” Phys. Rev. Lett. 80, 2893–2896 (1998).
    [CrossRef]
  4. E. Tekman and P. F. Bagwell, “Fano resonances in quasi-one-dimensional electron waveguides,” Phys. Rev. B 48, 2553–2559 (1993).
    [CrossRef]
  5. Z. Shao, W. Porod, and C. S. Lent, “Transmission resonances and zeros in quantum waveguide systems with attached resonators,” Phys. Rev. B 49, 7453–7465 (1994).
    [CrossRef]
  6. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
    [CrossRef]
  7. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
    [CrossRef]
  8. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
    [CrossRef]
  9. A. Rahmani, B. Lukiyanchuk, B. Ng, A. Tavakkoli, Y. F. Liew, and M. H. Hong, “Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic metamaterials,” Opt. Express 19, 4949–4956 (2011).
    [CrossRef]
  10. B. Tang, L. Dai, and C. Jiang, “Transmission enhancement of slow light by subwavelength plasmon-dielectric system,” J. Opt. Soc. Am. B 27, 2433–2437 (2010).
    [CrossRef]
  11. X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
    [CrossRef]
  12. R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19, 6312–6319 (2011).
    [CrossRef]
  13. A. Boardman, N. King, and L. Velasco, “Negative refraction in perspective,” Electromagnetics 25, 365–389 (2005).
    [CrossRef]
  14. A. Alu and N. Enghetta, “Plasmonic materials in transparency and cloaking problems: mechanisms, robustness and physical insights,” Opt. Express 15, 3318–3332 (2007).
    [CrossRef]
  15. 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]
  16. J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Low frequency plasmons in thin-wire Structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
    [CrossRef]
  17. P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
    [CrossRef]
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    [CrossRef]
  20. A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
    [CrossRef]
  21. A. K. Bandyopadhyay, P. C. Ray, and V. Gopalan, “An approach to Klein–Gordon equation for a dynamic study in ferroelectric materials,” J. Phys. Condens. Matter 18, 4093–4099 (2006).
    [CrossRef]
  22. A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc, and A. R. McGurn, “Multiple time-scale analysis for non-linear modes in ferroelectrics LiNbO3,” Phys. Rev. B 81, 0641041 (2010).
    [CrossRef]
  23. B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
    [CrossRef]
  24. S. Flach and A. V. Gorbach, “Discrete breathers-advances in theory and application,” Phys. Rep. 467, 1–116 (2008).
    [CrossRef]
  25. S. Flach, A. E. Miroshchinko, V. Fleurov, and M. V. Fistul, “Fano resonances with discrete breathers,” Phys. Rev. Lett. 90, 084101 (2003).
    [CrossRef]
  26. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
    [CrossRef]
  27. R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a Bose-Einstein condensate in an optical lattice,” Phys. Rev. Lett. 98, 184102 (2007).
    [CrossRef]
  28. S. W. Kim and S. Kim, “Fano resonances in translationally invariant nonlinear chains,” Phys. Rev. B 63, 212301 (2001).
    [CrossRef]
  29. L. S. Schulman, D. Tolkunov, and E. Milhokova, “Structure and time dependence of quantum breathers,” Chem. Phys. 322, 55–74 (2006).
    [CrossRef]
  30. S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
    [CrossRef]

2012

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

2011

P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
[CrossRef]

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

A. Rahmani, B. Lukiyanchuk, B. Ng, A. Tavakkoli, Y. F. Liew, and M. H. Hong, “Generation of pronounced Fano resonances and tuning of subwavelength spatial light distribution in plasmonic metamaterials,” Opt. Express 19, 4949–4956 (2011).
[CrossRef]

R. Singh, I. A. I. Al-Naib, M. Koch, and W. Zhang, “Sharp Fano resonances in THz metamaterials,” Opt. Express 19, 6312–6319 (2011).
[CrossRef]

2010

B. Tang, L. Dai, and C. Jiang, “Transmission enhancement of slow light by subwavelength plasmon-dielectric system,” J. Opt. Soc. Am. B 27, 2433–2437 (2010).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc, and A. R. McGurn, “Multiple time-scale analysis for non-linear modes in ferroelectrics LiNbO3,” Phys. Rev. B 81, 0641041 (2010).
[CrossRef]

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

2008

S. Flach and A. V. Gorbach, “Discrete breathers-advances in theory and application,” Phys. Rep. 467, 1–116 (2008).
[CrossRef]

A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
[CrossRef]

2007

R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a Bose-Einstein condensate in an optical lattice,” Phys. Rev. Lett. 98, 184102 (2007).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
[CrossRef]

A. Alu and N. Enghetta, “Plasmonic materials in transparency and cloaking problems: mechanisms, robustness and physical insights,” Opt. Express 15, 3318–3332 (2007).
[CrossRef]

2006

L. S. Schulman, D. Tolkunov, and E. Milhokova, “Structure and time dependence of quantum breathers,” Chem. Phys. 322, 55–74 (2006).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, and V. Gopalan, “An approach to Klein–Gordon equation for a dynamic study in ferroelectric materials,” J. Phys. Condens. Matter 18, 4093–4099 (2006).
[CrossRef]

N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete breathers in nonlinear magnetic metamaterials,” Phys. Rev. Lett. 97, 157406–157409 (2006).
[CrossRef]

2005

A. Boardman, N. King, and L. Velasco, “Negative refraction in perspective,” Electromagnetics 25, 365–389 (2005).
[CrossRef]

2003

S. Flach, A. E. Miroshchinko, V. Fleurov, and M. V. Fistul, “Fano resonances with discrete breathers,” Phys. Rev. Lett. 90, 084101 (2003).
[CrossRef]

2001

S. W. Kim and S. Kim, “Fano resonances in translationally invariant nonlinear chains,” Phys. Rev. B 63, 212301 (2001).
[CrossRef]

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]

1998

J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Low frequency plasmons in thin-wire Structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
[CrossRef]

J. Li, W. D. Schneider, R. Berndt, and B. Delley, “Kondo scattering observed at a single magnetic impurity,” Phys. Rev. Lett. 80, 2893–2896 (1998).
[CrossRef]

1994

Z. Shao, W. Porod, and C. S. Lent, “Transmission resonances and zeros in quantum waveguide systems with attached resonators,” Phys. Rev. B 49, 7453–7465 (1994).
[CrossRef]

1993

E. Tekman and P. F. Bagwell, “Fano resonances in quasi-one-dimensional electron waveguides,” Phys. Rev. B 48, 2553–2559 (1993).
[CrossRef]

1961

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Adato, R.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Adhikari, S.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

Al-Naib, I. A. I.

Altug, H.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Alu, A.

Arju, N.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Bagwell, P. F.

E. Tekman and P. F. Bagwell, “Fano resonances in quasi-one-dimensional electron waveguides,” Phys. Rev. B 48, 2553–2559 (1993).
[CrossRef]

Bandyopadhyay, A. K.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc, and A. R. McGurn, “Multiple time-scale analysis for non-linear modes in ferroelectrics LiNbO3,” Phys. Rev. B 81, 0641041 (2010).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, and V. Gopalan, “An approach to Klein–Gordon equation for a dynamic study in ferroelectric materials,” J. Phys. Condens. Matter 18, 4093–4099 (2006).
[CrossRef]

Basu, R.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

Berndt, R.

J. Li, W. D. Schneider, R. Berndt, and B. Delley, “Kondo scattering observed at a single magnetic impurity,” Phys. Rev. Lett. 80, 2893–2896 (1998).
[CrossRef]

Bhattacharjee, A. K.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

Biswas, A.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

Boardman, A.

A. Boardman, N. King, and L. Velasco, “Negative refraction in perspective,” Electromagnetics 25, 365–389 (2005).
[CrossRef]

Boardman, A. D.

A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
[CrossRef]

Brand, J.

R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a Bose-Einstein condensate in an optical lattice,” Phys. Rev. Lett. 98, 184102 (2007).
[CrossRef]

Chen, W.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
[CrossRef]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Choudhary, K.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
[CrossRef]

Crommie, M. F.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
[CrossRef]

Dai, L.

Delley, B.

J. Li, W. D. Schneider, R. Berndt, and B. Delley, “Kondo scattering observed at a single magnetic impurity,” Phys. Rev. Lett. 80, 2893–2896 (1998).
[CrossRef]

Egan, P.

A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
[CrossRef]

Eleftheriou, M.

N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete breathers in nonlinear magnetic metamaterials,” Phys. Rev. Lett. 97, 157406–157409 (2006).
[CrossRef]

Enghetta, N.

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Fedotov, V. A.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
[CrossRef]

Fistul, M. V.

S. Flach, A. E. Miroshchinko, V. Fleurov, and M. V. Fistul, “Fano resonances with discrete breathers,” Phys. Rev. Lett. 90, 084101 (2003).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

S. Flach and A. V. Gorbach, “Discrete breathers-advances in theory and application,” Phys. Rep. 467, 1–116 (2008).
[CrossRef]

R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a Bose-Einstein condensate in an optical lattice,” Phys. Rev. Lett. 98, 184102 (2007).
[CrossRef]

S. Flach, A. E. Miroshchinko, V. Fleurov, and M. V. Fistul, “Fano resonances with discrete breathers,” Phys. Rev. Lett. 90, 084101 (2003).
[CrossRef]

Fleurov, V.

S. Flach, A. E. Miroshchinko, V. Fleurov, and M. V. Fistul, “Fano resonances with discrete breathers,” Phys. Rev. Lett. 90, 084101 (2003).
[CrossRef]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Giri, P.

P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
[CrossRef]

Gopalan, V.

A. K. Bandyopadhyay, P. C. Ray, and V. Gopalan, “An approach to Klein–Gordon equation for a dynamic study in ferroelectric materials,” J. Phys. Condens. Matter 18, 4093–4099 (2006).
[CrossRef]

Gorbach, A. V.

S. Flach and A. V. Gorbach, “Discrete breathers-advances in theory and application,” Phys. Rep. 467, 1–116 (2008).
[CrossRef]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Low frequency plasmons in thin-wire Structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Hong, M. H.

Jamneala, T.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
[CrossRef]

Jiang, C.

Khanikaev, A. B.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Kim, S.

S. W. Kim and S. Kim, “Fano resonances in translationally invariant nonlinear chains,” Phys. Rev. B 63, 212301 (2001).
[CrossRef]

Kim, S. W.

S. W. Kim and S. Kim, “Fano resonances in translationally invariant nonlinear chains,” Phys. Rev. B 63, 212301 (2001).
[CrossRef]

King, N.

A. Boardman, N. King, and L. Velasco, “Negative refraction in perspective,” Electromagnetics 25, 365–389 (2005).
[CrossRef]

King, N. J.

A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
[CrossRef]

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Koch, M.

Lazarides, N.

N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete breathers in nonlinear magnetic metamaterials,” Phys. Rev. Lett. 97, 157406–157409 (2006).
[CrossRef]

Lent, C. S.

Z. Shao, W. Porod, and C. S. Lent, “Transmission resonances and zeros in quantum waveguide systems with attached resonators,” Phys. Rev. B 49, 7453–7465 (1994).
[CrossRef]

Li, J.

J. Li, W. D. Schneider, R. Berndt, and B. Delley, “Kondo scattering observed at a single magnetic impurity,” Phys. Rev. Lett. 80, 2893–2896 (1998).
[CrossRef]

Li, S.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Liew, Y. F.

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Lukiyanchuk, B.

Madhavan, V.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
[CrossRef]

Maier, S. A.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

Mandal, B.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

Mandal, D.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

Mandal, S. J.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

McGurn, A. R.

P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc, and A. R. McGurn, “Multiple time-scale analysis for non-linear modes in ferroelectrics LiNbO3,” Phys. Rev. B 81, 0641041 (2010).
[CrossRef]

Milhokova, E.

L. S. Schulman, D. Tolkunov, and E. Milhokova, “Structure and time dependence of quantum breathers,” Chem. Phys. 322, 55–74 (2006).
[CrossRef]

Miroshchinko, A. E.

S. Flach, A. E. Miroshchinko, V. Fleurov, and M. V. Fistul, “Fano resonances with discrete breathers,” Phys. Rev. Lett. 90, 084101 (2003).
[CrossRef]

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Mitchell-Thomas, R. C.

A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
[CrossRef]

Miyamaru, F.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (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]

Ng, B.

Nordlander, P.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[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]

Papasimakis, N.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
[CrossRef]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Low frequency plasmons in thin-wire Structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Porod, W.

Z. Shao, W. Porod, and C. S. Lent, “Transmission resonances and zeros in quantum waveguide systems with attached resonators,” Phys. Rev. B 49, 7453–7465 (1994).
[CrossRef]

Prosvirnin, S. L.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
[CrossRef]

Rahmani, A.

Rapoport, Y. G.

A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
[CrossRef]

Ray, P. C.

A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc, and A. R. McGurn, “Multiple time-scale analysis for non-linear modes in ferroelectrics LiNbO3,” Phys. Rev. B 81, 0641041 (2010).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, and V. Gopalan, “An approach to Klein–Gordon equation for a dynamic study in ferroelectric materials,” J. Phys. Condens. Matter 18, 4093–4099 (2006).
[CrossRef]

Robins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Low frequency plasmons in thin-wire Structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Rose, M.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
[CrossRef]

Schneider, W. D.

J. Li, W. D. Schneider, R. Berndt, and B. Delley, “Kondo scattering observed at a single magnetic impurity,” Phys. Rev. Lett. 80, 2893–2896 (1998).
[CrossRef]

Schulman, L. S.

L. S. Schulman, D. Tolkunov, and E. Milhokova, “Structure and time dependence of quantum breathers,” Chem. Phys. 322, 55–74 (2006).
[CrossRef]

Schultz, S.

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]

Sengupta, A.

P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
[CrossRef]

Shao, Z.

Z. Shao, W. Porod, and C. S. Lent, “Transmission resonances and zeros in quantum waveguide systems with attached resonators,” Phys. Rev. B 49, 7453–7465 (1994).
[CrossRef]

Sheng, P.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Shvets, G.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Singh, R.

Smith, D. R.

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]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Low frequency plasmons in thin-wire Structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

Takeda, M. W.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Tang, B.

Tavakkoli, A.

Tekman, E.

E. Tekman and P. F. Bagwell, “Fano resonances in quasi-one-dimensional electron waveguides,” Phys. Rev. B 48, 2553–2559 (1993).
[CrossRef]

Tolkunov, D.

L. S. Schulman, D. Tolkunov, and E. Milhokova, “Structure and time dependence of quantum breathers,” Chem. Phys. 322, 55–74 (2006).
[CrossRef]

Tsironis, G. P.

N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete breathers in nonlinear magnetic metamaterials,” Phys. Rev. Lett. 97, 157406–157409 (2006).
[CrossRef]

Velasco, L.

A. Boardman, N. King, and L. Velasco, “Negative refraction in perspective,” Electromagnetics 25, 365–389 (2005).
[CrossRef]

Vicencio, R. A.

R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a Bose-Einstein condensate in an optical lattice,” Phys. Rev. Lett. 98, 184102 (2007).
[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]

Vu-Quoc, L.

A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc, and A. R. McGurn, “Multiple time-scale analysis for non-linear modes in ferroelectrics LiNbO3,” Phys. Rev. B 81, 0641041 (2010).
[CrossRef]

Wen, W.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Wingreen, N. S.

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
[CrossRef]

Wu, C.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Wu, J.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Xiao, X.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Yanik, A. A.

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Zhang, M.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Zhang, W.

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
[CrossRef]

Appl. Phys. Lett.

X. Xiao, J. Wu, F. Miyamaru, M. Zhang, S. Li, M. W. Takeda, W. Wen, and P. Sheng, “Fano effect of metamaterial resonance in terahertz extraordinary transmission,” Appl. Phys. Lett. 98, 011911 (2011).
[CrossRef]

Chem. Phys.

L. S. Schulman, D. Tolkunov, and E. Milhokova, “Structure and time dependence of quantum breathers,” Chem. Phys. 322, 55–74 (2006).
[CrossRef]

Electromagnetics

A. Boardman, N. King, and L. Velasco, “Negative refraction in perspective,” Electromagnetics 25, 365–389 (2005).
[CrossRef]

J. Appl. Phys.

S. J. Mandal, K. Choudhary, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Quantum breathers in Klein–Gordon lattice: Non-periodic boundary condition approach,” J. Appl. Phys. 110, 124106 (2011).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Condens. Matter

J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, “Low frequency plasmons in thin-wire Structures,” J. Phys. Condens. Matter 10, 4785–4809 (1998).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, and V. Gopalan, “An approach to Klein–Gordon equation for a dynamic study in ferroelectric materials,” J. Phys. Condens. Matter 18, 4093–4099 (2006).
[CrossRef]

Nat. Mater.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9, 707–715 (2010).
[CrossRef]

C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymmetric metamaterials for ultrasensitive spectroscopy and identification of molecular monolayer,” Nat. Mater. 11, 69–75 (2012).
[CrossRef]

Opt. Express

Phys. Rep.

S. Flach and A. V. Gorbach, “Discrete breathers-advances in theory and application,” Phys. Rep. 467, 1–116 (2008).
[CrossRef]

Phys. Rev.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866–1878 (1961).
[CrossRef]

Phys. Rev. B

S. W. Kim and S. Kim, “Fano resonances in translationally invariant nonlinear chains,” Phys. Rev. B 63, 212301 (2001).
[CrossRef]

A. K. Bandyopadhyay, P. C. Ray, L. Vu-Quoc, and A. R. McGurn, “Multiple time-scale analysis for non-linear modes in ferroelectrics LiNbO3,” Phys. Rev. B 81, 0641041 (2010).
[CrossRef]

P. Giri, K. Choudhary, A. Sengupta, A. K. Bandyopadhyay, and A. R. McGurn, “Klein–Gordon equation approach to non-linear split-ring resonator based metamaterials: 1D systems,” Phys. Rev. B 84, 155429–155440 (2011).
[CrossRef]

E. Tekman and P. F. Bagwell, “Fano resonances in quasi-one-dimensional electron waveguides,” Phys. Rev. B 48, 2553–2559 (1993).
[CrossRef]

Z. Shao, W. Porod, and C. S. Lent, “Transmission resonances and zeros in quantum waveguide systems with attached resonators,” Phys. Rev. B 49, 7453–7465 (1994).
[CrossRef]

Phys. Rev. Lett.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broad structural symmetry,” Phys. Rev. Lett. 99, 147401–147404 (2007).
[CrossRef]

N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete breathers in nonlinear magnetic metamaterials,” Phys. Rev. Lett. 97, 157406–157409 (2006).
[CrossRef]

S. Flach, A. E. Miroshchinko, V. Fleurov, and M. V. Fistul, “Fano resonances with discrete breathers,” Phys. Rev. Lett. 90, 084101 (2003).
[CrossRef]

J. Li, W. D. Schneider, R. Berndt, and B. Delley, “Kondo scattering observed at a single magnetic impurity,” Phys. Rev. Lett. 80, 2893–2896 (1998).
[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]

R. A. Vicencio, J. Brand, and S. Flach, “Fano blockade by a Bose-Einstein condensate in an optical lattice,” Phys. Rev. Lett. 98, 184102 (2007).
[CrossRef]

Phys. Scr.

B. Mandal, S. Adhikari, R. Basu, K. Choudhary, S. J. Mandal, A. Biswas, A. K. Bandyopadhyay, A. K. Bhattacharjee, and D. Mandal, “Role of coupling of discrete breathers in SRR based metamaterials,” Phys. Scr. 86, 015601 (2012).
[CrossRef]

Proc. SPIE

A. D. Boardman, P. Egan, R. C. Mitchell-Thomas, Y. G. Rapoport, and N. J. King, “Weakly and strongly nonlinear waves in negative phase metamaterials,” Proc. SPIE 7029, F1–F14 (2008).
[CrossRef]

Rev. Mod. Phys.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82, 2257–2298 (2010).
[CrossRef]

Science

V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, “Tunneling into single magnetic atom: Spectroscopic evidence of Kondo resonance,” Science 280, 567–569 (1998).
[CrossRef]

Other

Nonlinearities in Periodic Structures and Metamaterials, C. Denz, S. Flach, and Yu. S. Kivshar, eds. (Springer, 2009), pp. 242.

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Figures (5)

Fig. 1.
Fig. 1.

λ=0.04, α=1, ε1=10, k=π/2 to 5π/2 is chosen to show the complete behavior. It shows asymmetric peaks, which are due to the Fano resonance arising out of the presence of discrete breathers in the system that act similar to impurity.

Fig. 2.
Fig. 2.

(a) Circles for λ=+0.04 and triangles for λ=0.04. In both cases, α=1, ε1=10; (b) Circles for α=1 and stars for α=1. In both cases, ε1=10, λ=0.04.

Fig. 3.
Fig. 3.

Squares are for λ=0.03, circles for λ=0.04 (α=1, ε1=10).

Fig. 4.
Fig. 4.

Circles for ε1=10, stars for ε1=15 (λ=0.04, α=1).

Fig. 5.
Fig. 5.

(a) ε1=1, λ=0.04 and α=1; (b) ε1=50, λ=0.04 and α=1.

Equations (21)

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

q¨n+λ(q¨n+1+q¨n1)+qn3αεl|qn|2qnΛq˙ncos(Ωτ)=0,
ωz2=[1+2λcosz]1.
qn=qn,0eiωbτ+cc,
ωb2[qn,0+λ(qn+1,0+qn1,0)]+qn,03αεl|qn,0|2qn,0=0,
ωb2=(3αεl)[1+2λ(coshz)]1,
qn,0=An=ezn,
ωb2[An+λ(An+1+An1)]+An3αεl|An|2An=0.
qn,t=qn,t+Ψn,t,
[Ψ¨n+λ(Ψ¨n+1+Ψ¨n1)+Ψn]3αεl(2|qn|2Ψn+qnΨn*qn)=0.
[Ψ¨n+λ(Ψ¨n+1+Ψ¨n1)+Ψn]3αεl(2|q0|2Ψ0+|q0|2Ψ0*ei(ω+2ωb)τ)δn,0=0,
[Ψ¨n+λ(Ψ¨n+1+Ψ¨n1)+Ψn]3αεl(2Ψ0+Ψ0*e2iωbτ)δn,0=0.
Ψn,t=Xneiωτ+Yn*ei(ω+2ωb)τ,
(1ω2)Xn+λ(Xn+1+Xn1)3αεl(2X0+Y0)δn,0=0,
[1+(ω+2ωB)2]Yn+λ(Yn+1+Yn1)3αεl(2Y0+X0)δn,0=0.
Xn=Ieikn+ρeiknforn<0,
Xn=Γeiknforn0,
Yn=y0r|n|
T=λ2cos2kλ2cos2k+[[((1ω2)λ(cosk)6αεl)]9α2εl2[11+(2ωb+ω)2+2λr6αεl]]2+2λcosk,
r=[1+(ω+2ωb)2]±[1+(ω+2ωb)2]24λ22λ.
ω=ωF=2ωb±2λ2+9α2εl21,
F(αF)=(αF+f)2αF2+β,

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