Abstract

Low quality (Q) factors of the intrinsic inductive–capacitive (LC) mode as well as the parasitic dipole oscillation mode restrict high-resolution sensing using split-ring resonators (SRR). Although the trapped Fano-mode of the high-Q factor is found in asymmetric SRR, the conventional design limits the scaling down of resonators. As such, excitation and manipulation of multiple trapped modes of SRR is significant for driving innovative designs of terahertz metamaterials and metasurfaces. In this work, we present a novel approach to manipulating multiple terahertz modes by increasing the fractal levels as well as the geometric symmetry of complementary SRR. It is found that the multiple trapped modes become achievable only in the case that the gap of adjacent fractal SRR opposes each other. By increasing the fractal level, the intrinsic resonance modes change slightly, and more trapped modes appear in between the frequency range of the two major intrinsic modes. The map of surface currents and magnetic field distribution reveal that intrinsic LC resonance in the first or second level SRR dominates the intrinsic modes. By contrast, the trapped mode arises from the hybridization of high-order localized dipole oscillation as well as the multiple localized LC resonances. These findings create new design opportunities for scalable metasurfaces across the terahertz spectrum and beyond, with ability to create high-resolution sensors.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Excitation of dark plasmonic modes in symmetry broken terahertz metamaterials

Dibakar Roy Chowdhury, Xiaofang Su, Yong Zeng, Xiaoshuang Chen, Antoinette J. Taylor, and Abul Azad
Opt. Express 22(16) 19401-19410 (2014)

Asymmetric planar terahertz metamaterials

Ranjan Singh, Ibraheem A. I. Al-Naib, Martin Koch, and Weili Zhang
Opt. Express 18(12) 13044-13050 (2010)

Localized terahertz electromagnetically-induced transparency-like phenomenon in a conductively coupled trimer metamolecule

Zhenyu Zhao, Xiaobo Zheng, Wei Peng, Jianbing Zhang, Hongwei Zhao, Zhijian Luo, and Wangzhou Shi
Opt. Express 25(20) 24410-24424 (2017)

References

  • View by:
  • |
  • |
  • |

  1. S. A. Jackson, “The nexus: where science meets society,” Science 310(5754), 1634–1639 (2005).
    [Crossref]
  2. E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
    [Crossref]
  3. N. Liu and A. Pucci, “Plasmonic biosensors: Know your molecules,” Nat. Mater. 11(1), 9–10 (2012).
    [Crossref]
  4. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
    [Crossref]
  5. X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
    [Crossref]
  6. S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
    [Crossref]
  7. L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
    [Crossref]
  8. X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
    [Crossref]
  9. S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
    [Crossref]
  10. Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
    [Crossref]
  11. D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
    [Crossref]
  12. W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
    [Crossref]
  13. 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]
  14. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
    [Crossref]
  15. I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012).
    [Crossref]
  16. R. Singh, I. A. I. Al-Naib, M. Koch, and W. L. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
    [Crossref]
  17. R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
    [Crossref]
  18. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
    [Crossref]
  19. J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
    [Crossref]
  20. J. Wallauer and M. Walther, “Fano line shape and phase reversal in a split-ring resonator based metamaterial,” Phys. Rev. B 88(19), 195118 (2013).
    [Crossref]
  21. D. R. Chowdhury, X. F. Su, Y. Zeng, X. S. Chen, A. J. Taylor, and A. Azad, “Excitation of dark plasmonic modes in symmetry broken terahertz metamaterials,” Opt. Express 22(16), 19401–19410 (2014).
    [Crossref]
  22. D. J. Park, J. H. Shin, K. H. Park, and H. C. Ryu, “Electrically controllable THz asymmetric split-loop resonator with an outer square loop based on VO2,” Opt. Express 26(13), 17397–17406 (2018).
    [Crossref]
  23. S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
    [Crossref]
  24. J. A. Burrow, R. Yahiaoui, A. Sarangan, I. Agha, J. Mathews, and T. A. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25(26), 32540–32549 (2017).
    [Crossref]
  25. E. Bochkova, S. Han, A. D. Lustrac, R. Singh, S. N. Burokur, and A. Lupu, “High-Q Fano resonances via direct excitation of an anti-symmetric dark mode,” Opt. Lett. 43(16), 3818–3821 (2018).
    [Crossref]
  26. W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3370 (2012).
    [Crossref]
  27. Y. K. Srivastava, L. Cong, and R. Singh, “Dual-surface flexible THz Fano metasensor,” Appl. Phys. Lett. 111(20), 201101 (2017).
    [Crossref]
  28. L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7, 1900383 (2019).
    [Crossref]
  29. H. T. Chen, J. F. O’Hara, A. J. Taylor, and R. D. Averitt, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
    [Crossref]
  30. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
    [Crossref]
  31. J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
    [Crossref]
  32. P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
    [Crossref]
  33. Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
    [Crossref]
  34. Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015).
    [Crossref]
  35. H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015).
    [Crossref]
  36. G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
    [Crossref]
  37. G. Volpe, G. Volpe, and R. Quidant, “Fractal plasmonics: subdiffraction focusing and broadband spectral response by a Sierpinski nanocarpet,” Opt. Express 19(4), 3612–3618 (2011).
    [Crossref]
  38. F. Miyamaru, S. Kubota, and M. W. Takeda, “Terahertz response of split-ring resonators with fractal structures,” Appl. Phys. Express 5(7), 072001 (2012).
    [Crossref]
  39. S. Sederberga and A. Y. Elezzabi, “The influence of Hausdorff dimension on plasmonic antennas with Pascal’s triangle geometry,” Appl. Phys. Lett. 98(26), 261105 (2011).
    [Crossref]
  40. X. Q. Huang, S. Y. Xiao, D. X. Ye, J. T. Huangfu, Z. Y. Wang, L. X. Ran, and L. Zhou, “Fractal plasmonic metamaterials for subwavelength imaging,” Opt. Express 18(10), 10377–10387 (2010).
    [Crossref]
  41. F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
    [Crossref]
  42. Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013).
    [Crossref]
  43. B. Mandelbrot, Fractals and Chaos (Springer, 2014) p. 38.
  44. X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
    [Crossref]
  45. J. Neu and C. A. Schmuttenmaer, “Tutorial: An introduction to terahertz time-domain spectroscopy (THz-TDS),” J. Appl. Phys. 124(23), 231101 (2018).
    [Crossref]
  46. Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
    [Crossref]

2019 (4)

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7, 1900383 (2019).
[Crossref]

P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
[Crossref]

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

2018 (4)

E. Bochkova, S. Han, A. D. Lustrac, R. Singh, S. N. Burokur, and A. Lupu, “High-Q Fano resonances via direct excitation of an anti-symmetric dark mode,” Opt. Lett. 43(16), 3818–3821 (2018).
[Crossref]

D. J. Park, J. H. Shin, K. H. Park, and H. C. Ryu, “Electrically controllable THz asymmetric split-loop resonator with an outer square loop based on VO2,” Opt. Express 26(13), 17397–17406 (2018).
[Crossref]

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

J. Neu and C. A. Schmuttenmaer, “Tutorial: An introduction to terahertz time-domain spectroscopy (THz-TDS),” J. Appl. Phys. 124(23), 231101 (2018).
[Crossref]

2017 (4)

Y. K. Srivastava, L. Cong, and R. Singh, “Dual-surface flexible THz Fano metasensor,” Appl. Phys. Lett. 111(20), 201101 (2017).
[Crossref]

J. A. Burrow, R. Yahiaoui, A. Sarangan, I. Agha, J. Mathews, and T. A. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25(26), 32540–32549 (2017).
[Crossref]

Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
[Crossref]

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

2016 (4)

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
[Crossref]

2015 (5)

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015).
[Crossref]

H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015).
[Crossref]

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
[Crossref]

2014 (1)

2013 (3)

J. Wallauer and M. Walther, “Fano line shape and phase reversal in a split-ring resonator based metamaterial,” Phys. Rev. B 88(19), 195118 (2013).
[Crossref]

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013).
[Crossref]

2012 (6)

F. Miyamaru, S. Kubota, and M. W. Takeda, “Terahertz response of split-ring resonators with fractal structures,” Appl. Phys. Express 5(7), 072001 (2012).
[Crossref]

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012).
[Crossref]

N. Liu and A. Pucci, “Plasmonic biosensors: Know your molecules,” Nat. Mater. 11(1), 9–10 (2012).
[Crossref]

G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
[Crossref]

W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3370 (2012).
[Crossref]

2011 (3)

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

S. Sederberga and A. Y. Elezzabi, “The influence of Hausdorff dimension on plasmonic antennas with Pascal’s triangle geometry,” Appl. Phys. Lett. 98(26), 261105 (2011).
[Crossref]

G. Volpe, G. Volpe, and R. Quidant, “Fractal plasmonics: subdiffraction focusing and broadband spectral response by a Sierpinski nanocarpet,” Opt. Express 19(4), 3612–3618 (2011).
[Crossref]

2010 (4)

X. Q. Huang, S. Y. Xiao, D. X. Ye, J. T. Huangfu, Z. Y. Wang, L. X. Ran, and L. Zhou, “Fractal plasmonic metamaterials for subwavelength imaging,” Opt. Express 18(10), 10377–10387 (2010).
[Crossref]

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

R. Singh, I. A. I. Al-Naib, M. Koch, and W. L. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
[Crossref]

2008 (1)

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

2007 (3)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref]

H. T. Chen, J. F. O’Hara, A. J. Taylor, and R. D. Averitt, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[Crossref]

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

2006 (1)

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref]

2005 (1)

S. A. Jackson, “The nexus: where science meets society,” Science 310(5754), 1634–1639 (2005).
[Crossref]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000).
[Crossref]

Agha, I.

Ahn, Y. H.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Al-Naib, I. A. I.

W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3370 (2012).
[Crossref]

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

R. Singh, I. A. I. Al-Naib, M. Koch, and W. L. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
[Crossref]

Appugliese, F.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Averitt, R. D.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

H. T. Chen, J. F. O’Hara, A. J. Taylor, and R. D. Averitt, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007).
[Crossref]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref]

Azad, A.

Barron, L. D.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Bochkova, E.

Brolo, G.

G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

Burokur, S. N.

Burrow, J. A.

Cao, W.

W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3370 (2012).
[Crossref]

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Carpy, T.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Chen, H.

Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
[Crossref]

Chen, H. T.

Chen, H.-T.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

Chen, X. S.

Cheng, Q.

G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
[Crossref]

Choi, S. J.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Chowdhury, D. R.

D. R. Chowdhury, X. F. Su, Y. Zeng, X. S. Chen, A. J. Taylor, and A. Azad, “Excitation of dark plasmonic modes in symmetry broken terahertz metamaterials,” Opt. Express 22(16), 19401–19410 (2014).
[Crossref]

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Cong, L.

L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7, 1900383 (2019).
[Crossref]

Y. K. Srivastava, L. Cong, and R. Singh, “Dual-surface flexible THz Fano metasensor,” Appl. Phys. Lett. 111(20), 201101 (2017).
[Crossref]

Cui, H.-L.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Cui, T. J.

G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
[Crossref]

H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015).
[Crossref]

J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
[Crossref]

Dokmeci, M. R.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Dong, H. Y.

G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
[Crossref]

Du, C.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Du, Q.

Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013).
[Crossref]

Elezzabi, A. Y.

S. Sederberga and A. Y. Elezzabi, “The influence of Hausdorff dimension on plasmonic antennas with Pascal’s triangle geometry,” Appl. Phys. Lett. 98(26), 261105 (2011).
[Crossref]

Faist, J.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Fan, Z.

Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
[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 broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref]

Forn-Díaz, P.

P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
[Crossref]

Fu, W.

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

Gadegaard, N.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Gao, W.

L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
[Crossref]

García de Abajo, F. J.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

Geng, Z.

Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
[Crossref]

Gu, C.

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Gu, C. Z.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Gu, Z.

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

Haase, J.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Han, S.

Han, S. T.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

He, M.

He, X.

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Hendry, E.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Highstrete, C.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref]

Hong, J. T.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Hou, B.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Huang, B.

G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
[Crossref]

Huang, X. Q.

Huangfu, J. T.

Jackson, S. A.

S. A. Jackson, “The nexus: where science meets society,” Science 310(5754), 1634–1639 (2005).
[Crossref]

Jiang, W. X.

J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
[Crossref]

Jiang, X.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Johnston, J.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Kadodwala, M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Kang, J.-H.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Kapitanova, P. V.

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012).
[Crossref]

Keller, J.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Kelly, S. M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Kim, D. S.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Kim, H. S.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Kim, J. H.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Kivshar, Y. S.

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012).
[Crossref]

Koch, M.

Kono, J.

P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
[Crossref]

L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
[Crossref]

Kubota, S.

F. Miyamaru, S. Kubota, and M. W. Takeda, “Terahertz response of split-ring resonators with fractal structures,” Appl. Phys. Express 5(7), 072001 (2012).
[Crossref]

Kwon, J.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Lamata, L.

P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
[Crossref]

Lapthorn, A. J.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Lee, D.-K.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Lee, J.-S.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Lee, M.

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref]

Lee, S.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Li, J. J.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Liu, L.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Liu, N.

N. Liu and A. Pucci, “Plasmonic biosensors: Know your molecules,” Nat. Mater. 11(1), 9–10 (2012).
[Crossref]

Liu, X.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Liu, Y.

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

Liu, Z.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Lu, X.

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Luo, Y.

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

Lupu, A.

Lustrac, A. D.

Lv, T.

Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013).
[Crossref]

Lv, X.

Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
[Crossref]

Ma, H. F.

J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
[Crossref]

Ma, Y.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

MacNaughton, S.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Maissen, C.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Mandelbrot, B.

B. Mandelbrot, Fractals and Chaos (Springer, 2014) p. 38.

Mao, H.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Maslovski, S. I.

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012).
[Crossref]

Mathews, J.

Mikhaylovskiy, R. V.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Miyamaru, F.

F. Miyamaru, S. Kubota, and M. W. Takeda, “Terahertz response of split-ring resonators with fractal structures,” Appl. Phys. Express 5(7), 072001 (2012).
[Crossref]

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Morandotti, R.

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (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(18), 4184–4187 (2000).
[Crossref]

Neu, J.

J. Neu and C. A. Schmuttenmaer, “Tutorial: An introduction to terahertz time-domain spectroscopy (THz-TDS),” J. Appl. Phys. 124(23), 231101 (2018).
[Crossref]

O’Hara, J. F.

Ozaki, T.

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Padilla, W. J.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[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(18), 4184–4187 (2000).
[Crossref]

Pan, X.

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[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 broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref]

Paravicini-Bagliani, G. L.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Park, D. J.

Park, J. Y.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Park, K. H.

Park, Q.-H.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Park, S. J.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Park, W. K.

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

Peng, W.

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015).
[Crossref]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Popland, M.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[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 broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref]

Pucci, A.

N. Liu and A. Pucci, “Plasmonic biosensors: Know your molecules,” Nat. Mater. 11(1), 9–10 (2012).
[Crossref]

Quan, B.

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Quidant, R.

Rajabali, S.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Ran, L. X.

Rico, E.

P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
[Crossref]

Rockstuh, C.

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[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 broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref]

Ryu, H. C.

Saito, Y.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Sarangan, A.

Scalari, G.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Schmuttenmaer, C. A.

J. Neu and C. A. Schmuttenmaer, “Tutorial: An introduction to terahertz time-domain spectroscopy (THz-TDS),” J. Appl. Phys. 124(23), 231101 (2018).
[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(18), 4184–4187 (2000).
[Crossref]

Searles, T. A.

Sederberga, S.

S. Sederberga and A. Y. Elezzabi, “The influence of Hausdorff dimension on plasmonic antennas with Pascal’s triangle geometry,” Appl. Phys. Lett. 98(26), 261105 (2011).
[Crossref]

Selvarasah, S.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Seo, M.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Shadrivov, I. V.

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012).
[Crossref]

Sheng, P.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Shi, J. H.

J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
[Crossref]

Shi, W.

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015).
[Crossref]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Shin, J. H.

Shrekenhamer, D. B.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Shu, Jie

L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
[Crossref]

Singh, R.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7, 1900383 (2019).
[Crossref]

E. Bochkova, S. Han, A. D. Lustrac, R. Singh, S. N. Burokur, and A. Lupu, “High-Q Fano resonances via direct excitation of an anti-symmetric dark mode,” Opt. Lett. 43(16), 3818–3821 (2018).
[Crossref]

Y. K. Srivastava, L. Cong, and R. Singh, “Dual-surface flexible THz Fano metasensor,” Appl. Phys. Lett. 111(20), 201101 (2017).
[Crossref]

W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3370 (2012).
[Crossref]

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

R. Singh, I. A. I. Al-Naib, M. Koch, and W. L. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
[Crossref]

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(18), 4184–4187 (2000).
[Crossref]

Solano, E.

P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
[Crossref]

Song, C.-S.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Song, G. Y.

G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
[Crossref]

Song, Z.

Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015).
[Crossref]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Sonkusale, S.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Srivastava, Y. K.

Y. K. Srivastava, L. Cong, and R. Singh, “Dual-surface flexible THz Fano metasensor,” Appl. Phys. Lett. 111(20), 201101 (2017).
[Crossref]

Su, X. F.

Takeda, M. W.

F. Miyamaru, S. Kubota, and M. W. Takeda, “Terahertz response of split-ring resonators with fractal structures,” Appl. Phys. Express 5(7), 072001 (2012).
[Crossref]

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Tang, C.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Tang, L.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

Tao, H.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Tao, Z.

H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015).
[Crossref]

Taylor, A. J.

Totachawattana, A.

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[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(18), 4184–4187 (2000).
[Crossref]

Volpe, G.

Wallauer, J.

J. Wallauer and M. Walther, “Fano line shape and phase reversal in a split-ring resonator based metamaterial,” Phys. Rev. B 88(19), 195118 (2013).
[Crossref]

Walther, M.

J. Wallauer and M. Walther, “Fano line shape and phase reversal in a split-ring resonator based metamaterial,” Phys. Rev. B 88(19), 195118 (2013).
[Crossref]

Wang, C.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

Wang, G. M.

H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015).
[Crossref]

Wang, H.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Wang, L.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Wang, S.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Wang, X.

Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013).
[Crossref]

Wang, Y. J.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Wang, Z. X.

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Wang, Z. Y.

Wei, D.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Wen, W.

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Woo, D. H.

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

Wu, X.

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Xia, L.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Xia, X. X.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Xiao, S. Y.

Xie, L.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
[Crossref]

Xu, H. X.

H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015).
[Crossref]

Xu, X.

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Xua, W.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

Yahiaoui, R.

Yan, S.

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

Yang, H.

Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013).
[Crossref]

Yang, K.

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

Yang, S. Y.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Yang, X.

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

Yang, Y. P.

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Ye, D. X.

Ying, Y.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
[Crossref]

Yiwen, E.

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

Zeng, Y.

Zhang, J.

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

Zhang, W.

Zhang, W. L.

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

R. Singh, I. A. I. Al-Naib, M. Koch, and W. L. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010).
[Crossref]

Zhang, X.

Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
[Crossref]

Zhao, H.

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Zhao, X.

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

Zhao, Z.

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015).
[Crossref]

Zheludev, N. I.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[Crossref]

Zhou, L.

Zhu, J.

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

Zhu, Z.

J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
[Crossref]

Adv. Opt. Mater. (2)

L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7, 1900383 (2019).
[Crossref]

J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018).
[Crossref]

Appl. Phys. Express (1)

F. Miyamaru, S. Kubota, and M. W. Takeda, “Terahertz response of split-ring resonators with fractal structures,” Appl. Phys. Express 5(7), 072001 (2012).
[Crossref]

Appl. Phys. Lett. (4)

S. Sederberga and A. Y. Elezzabi, “The influence of Hausdorff dimension on plasmonic antennas with Pascal’s triangle geometry,” Appl. Phys. Lett. 98(26), 261105 (2011).
[Crossref]

X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010).
[Crossref]

Y. K. Srivastava, L. Cong, and R. Singh, “Dual-surface flexible THz Fano metasensor,” Appl. Phys. Lett. 111(20), 201101 (2017).
[Crossref]

R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011).
[Crossref]

Biosens. Bioelectron. (1)

X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013).
[Crossref]

Carbon (1)

W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019).
[Crossref]

IEEE Photonics Technol. Lett. (1)

S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016).
[Crossref]

J. Appl. Phys. (5)

J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012).
[Crossref]

Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019).
[Crossref]

Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015).
[Crossref]

J. Neu and C. A. Schmuttenmaer, “Tutorial: An introduction to terahertz time-domain spectroscopy (THz-TDS),” J. Appl. Phys. 124(23), 231101 (2018).
[Crossref]

Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015).
[Crossref]

Nat. Mater. (1)

N. Liu and A. Pucci, “Plasmonic biosensors: Know your molecules,” Nat. Mater. 11(1), 9–10 (2012).
[Crossref]

Nat. Nanotechnol. (1)

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010).
[Crossref]

Nat. Photonics (1)

G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012).
[Crossref]

Opt. Commun. (1)

Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013).
[Crossref]

Opt. Express (7)

Opt. Lett. (2)

Phys. Rev. B (3)

S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016).
[Crossref]

J. Wallauer and M. Walther, “Fano line shape and phase reversal in a split-ring resonator based metamaterial,” Phys. Rev. B 88(19), 195118 (2013).
[Crossref]

F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008).
[Crossref]

Phys. Rev. Lett. (4)

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007).
[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(18), 4184–4187 (2000).
[Crossref]

W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006).
[Crossref]

I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012).
[Crossref]

Rev. Mod. Phys. (2)

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[Crossref]

P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019).
[Crossref]

Sci. Rep. (6)

H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015).
[Crossref]

G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016).
[Crossref]

Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017).
[Crossref]

D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017).
[Crossref]

S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015).
[Crossref]

L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015).
[Crossref]

Science (1)

S. A. Jackson, “The nexus: where science meets society,” Science 310(5754), 1634–1639 (2005).
[Crossref]

Trends Biotechnol. (1)

X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016).
[Crossref]

Other (1)

B. Mandelbrot, Fractals and Chaos (Springer, 2014) p. 38.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. Schematic representation of CSRR design. (a) Fractal meta-atoms of CSRR under different symmetric conditions: O-gap, U-gap, and C-gap, respectively, and fractal levels. (b) Pattern direction of fractal meta-atom, of which the z direction is the <100>-crystallographic orientation of SI-GaAs. P: lattice period, g: gap-size, r1: outer-radius, r2: inner-radius. (c) The top-view optical image of meta-atom. (d) Diagram of terahertz transmission spectroscopy
Fig. 2.
Fig. 2. Transmittance from simulation and measurement when excited with Ex-polarised terahertz waves. Simulated (blue solid line) and measured (red solid line) transmittance (a) O-gap; (b) U-gap; and (c) C-gap meta-atoms. Dashed line represents the central position of resonance modes.
Fig. 3.
Fig. 3. Complex permittivity based on symmetry of meta-atoms with Ex-polarized incident terahertz waves. Dielectric spectra of (a) O-gap, (b) U-gap, and (c) C-gap meta-atom for Ex-polarized incident terahertz waves. Red solid line: imaginary part of permittivity. Blue solid line: solid part of permittivity. Dashed line: the central frequencies of resonance modes.
Fig. 4.
Fig. 4. Surface current and magnetic field distribution at resonance modes. Surface currents at resonance modes for (a) O-gap, (b) U-gap, (c) C-gap; Magnetic field distribution of resonance modes of meta-atom in the layout of (d) O-gap, (e) U-gap, (f) C-gap. Where polarization of electric field is parallel to split gaps. Color bars denote the relative strength of surface current and magnetic field accordingly.
Fig. 5.
Fig. 5. Transmittance from simulation and measurement when excited with Ey-polarised terahertz waves. Simulated (blue solid line) and measured (red solid line) transmittance for (a) O-gap, (b) U-gap, and (c) C-gap meta-atoms. Dashed line: the central position of resonance modes
Fig. 6.
Fig. 6. Complex permittivity based on symmetry of meta-atoms with Ey-polarized incident terahertz waves. Dielectric spectra of (a) O-gap, (b) U-gap, and (c) C-gap meta-atom in the case of Ey-polarization. Red solid line: imaginary part of permittivity. Blue solid line: solid part of permittivity. Dashed line: the central position of resonance modes.
Fig. 7.
Fig. 7. Surface current and magnetic fields distribution at resonance modes. (a) Surface currents and (b) magnetic field at resonance modes of O-gap meta-atom. Where polarization of electric field is perpendicular to the split gaps. Color bars denotes the relative strength of surface current and magnetic field accordingly. I refers to the intrinsic modes. T refers to the trapped modes.
Fig. 8.
Fig. 8. Surface current and magnetic fields distribution for different fractal levels of U-gap meta-atom, at resonance modes. (a) Surface currents and (b) magnetic field at resonance modes of meta-atom in the layout of U-gap. Color bars: the relative strength of surface current and magnetic field accordingly. I refers to the intrinsic modes.

Tables (4)

Tables Icon

Table 1. The resonance modes of fractal metamaterial excited by Ex-linearly polarized terahertz waves.

Tables Icon

Table 2. Q factors of resonance modes of fractal meta-atoms excited with Ex-polarized terahertz waves.

Tables Icon

Table 3. The resonance modes of fractal meta-atoms excited by Ey-polarized terahertz waves.

Tables Icon

Table 4. The Q factors of fractal meta-atoms excited by Ey-polarized terahertz waves.

Equations (3)

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

F = lg ( N ) / lg ( N ) lg ( 1 / 1 S S ) lg ( 1 / 1 S S ) ,
T ~ ( ν ) = | E s a m p l e ( ν ) / E s a m p l e ( ν ) E r e f ( ν ) E r e f ( ν ) | ,
ε ( v ) = ε r ( v ) + i ε i ( v ) ,