Abstract

We investigate the plasmonic nanofocusing of terahertz waves in tapered graphene multilayers separated by dielectrics. The nanofocusing effect is significantly enhanced in the graphene multilayer taper compared with that in a single layer graphene taper due to interlayer coupling between surface plasmon polaritons. The results are optimized by choosing an appropriate layer number of graphene and the field amplitude has been enhanced by 620 folds at λ = 50 μm. Additionally, the structure can slow light to a group velocity ~1/2815 of the light speed in vacuum. Our study provides a unique approach to compress terahertz waves into deep subwavelength scale and may find great applications in terahertz nanodevices for imaging, detecting and spectroscopy.

© 2016 Optical Society of America

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2016 (1)

F. Hui, P. Vajha, Y. Shi, Y. Ji, H. Duan, A. Padovani, L. Larcher, X. R. Li, J. J. Xu, and M. Lanza, “Moving graphene devices from lab to market: advanced graphene-coated nanoprobes,” Nanoscale 8(16), 8466–8473 (2016).
[Crossref] [PubMed]

2015 (8)

H. Hu, K. Wang, H. Long, W. Liu, B. Wang, and P. Lu, “Precise determination of the crystallographic orientations in single ZnS nanowires by second-harmonic generation microscopy,” Nano Lett. 15(5), 3351–3357 (2015).
[Crossref] [PubMed]

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6, 7507 (2015).
[Crossref] [PubMed]

Y. Y. Dai, X. L. Zhu, N. A. Mortersen, J. Zi, and S. S. Xiao, “Nanofocusing in a tapered graphene plasmonic waveguide,” J. Opt. 17(6), 065002 (2015).
[Crossref]

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
[Crossref] [PubMed]

K. Moon, H. Park, J. Kim, Y. Do, S. Lee, G. Lee, H. Kang, and H. Han, “Subsurface nanoimaging by broadband terahertz pulse near-field microscopy,” Nano Lett. 15(1), 549–552 (2015).
[Crossref] [PubMed]

A. Toma, S. Tuccio, M. Prato, F. De Donato, A. Perucchi, P. Di Pietro, S. Marras, C. Liberale, R. Proietti Zaccaria, F. De Angelis, L. Manna, S. Lupi, E. Di Fabrizio, and L. Razzari, “Squeezing terahertz light into nanovolumes: nanoantenna enhanced terahertz spectroscopy (nets) of semiconductor quantum dots,” Nano Lett. 15(1), 386–391 (2015).
[Crossref] [PubMed]

S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic cross-shaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015).
[Crossref] [PubMed]

B. F. Zhu, G. B. Ren, Y. X. Gao, Y. Yang, B. L. Wu, Y. D. Lian, and S. S. Jian, “Nanofocusing in the graphene-coated tapered nanowire infrared probe,” J. Opt. Soc. Am. B 32(5), 955–960 (2015).
[Crossref]

2014 (12)

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

P. Li, T. Wang, H. Böckmann, and T. Taubner, “Graphene-enhanced infrared near-field microscopy,” Nano Lett. 14(8), 4400–4405 (2014).
[Crossref] [PubMed]

B. Zhu, G. Ren, Y. Gao, Y. Yang, Y. Lian, and S. Jian, “Graphene-coated tapered nanowire infrared probe: a comparison with metal-coated probes,” Opt. Express 22(20), 24096–24103 (2014).
[Crossref] [PubMed]

C. Qin, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Low-loss plasmonic supermodes in graphene multilayers,” Opt. Express 22(21), 25324–25332 (2014).
[Crossref] [PubMed]

W. B. Qiu, X. H. Liu, J. Zhao, S. H. He, Y. H. Ma, J. X. Wang, and J. Q. Pan, “Nanofocusing of mid-infrared electromagnetic waves on graphene monolayer,” Appl. Phys. Lett. 104(4), 041109 (2014).
[Crossref]

F. D’Angelo, Z. Mics, M. Bonn, and D. Turchinovich, “Ultra-broadband THz time-domain spectroscopy of common polymers using THz air photonics,” Opt. Express 22(10), 12475–12485 (2014).
[Crossref] [PubMed]

Y. H. Li, A. Rashidinejad, J. M. Wun, D. E. Leaird, J. W. Shi, and A. M. Weiner, “Photonic generation of W-band arbitrary waveforms with high time-bandwidth products enabling 3.9 mm range resolution,” Optica 1(6), 446–454 (2014).
[Crossref]

J. Dai and X. C. Zhang, “Terahertz wave generation from thin metal films excited by asymmetrical optical fields,” Opt. Lett. 39(4), 777–780 (2014).
[Crossref] [PubMed]

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

J. A. Gerber, S. Berweger, B. T. O’Callahan, and M. B. Raschke, “Phase-resolved surface plasmon interferometry of graphene,” Phys. Rev. Lett. 113(5), 055502 (2014).
[Crossref] [PubMed]

R. W. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Nanofocusing of electromagnetic radiation,” Nat. Photonics 8(1), 14–23 (2014).

2013 (7)

C. Martin-Olmos, H. I. Rasool, B. H. Weiller, and J. K. Gimzewski, “Graphene MEMS: AFM probe performance improvement,” ACS Nano 7(5), 4164–4170 (2013).
[Crossref] [PubMed]

S. He, X. Zhang, and Y. He, “Graphene nano-ribbon waveguides of record-small mode area and ultra-high effective refractive indices for future VLSI,” Opt. Express 21(25), 30664–30673 (2013).
[Crossref] [PubMed]

J. H. Jeong, B. J. Kang, J. S. Kim, M. Jazbinsek, S. H. Lee, S. C. Lee, I. H. Baek, H. Yun, J. Kim, Y. S. Lee, J. H. Lee, J. H. Kim, F. Rotermund, and O. P. Kwon, “High-power Broadband Organic THz Generator,” Sci. Rep. 3, 3200 (2013).
[Crossref] [PubMed]

T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. J. Burgess, G. De Los Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7(8), 620–625 (2013).
[Crossref]

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

S. Thongrattanasiri and F. J. García de Abajo, “Optical field enhancement by strong plasmon interaction in graphene nanostructures,” Phys. Rev. Lett. 110(18), 187401 (2013).
[Crossref] [PubMed]

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
[Crossref] [PubMed]

2012 (7)

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12(6), 3308–3314 (2012).
[Crossref] [PubMed]

H. Choo, M. K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–843 (2012).
[Crossref]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
[Crossref] [PubMed]

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6(7), 423–431 (2012).
[Crossref]

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
[Crossref]

P. Tassin, T. Koschny, M. Kafesaki, and C. M. Soukoulis, “A comparison of graphene, superconductors and metals as conductors for metamaterials and plasmonics,” Nat. Photonics 6(4), 259–264 (2012).
[Crossref]

2011 (6)

V. Atanasov and A. Saxena, “Electronic properties of corrugated graphene: the Heisenberg principle and wormhole geometry in the solid state,” J. Phys-Condens. Mat. 23(17), 175301 (2011).

M. Schnell, P. Alonso-Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Q. L. Bao, H. Zhang, B. Wang, Z. H. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref] [PubMed]

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

2010 (3)

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

V. Atanasov and A. Saxena, “Tuning the electronic properties of corrugated graphene: confinement, curvature, and band-gap opening,” Phys. Rev. B 81(20), 205409 (2010).
[Crossref]

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
[Crossref] [PubMed]

2009 (1)

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
[Crossref]

2008 (2)

2007 (2)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

P. K. Mandal and V. Chikan, “Plasmon-phonon coupling in charged n-type CdSe quantum dots: A THz time-domain spectroscopic study,” Nano Lett. 7(8), 2521–2528 (2007).
[Crossref] [PubMed]

2006 (2)

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[Crossref] [PubMed]

A. A. Govyadinov and V. A. Podolskiy, “Metamaterial photonic funnels for subdiffraction light compression and propagation,” Phys. Rev. B 73(15), 155108 (2006).
[Crossref]

2004 (1)

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93(13), 137404 (2004).
[Crossref] [PubMed]

Alaee, R.

R. W. Yu, R. Alaee, F. Lederer, and C. Rockstuhl, “Manipulating the interaction between localized and delocalized surface plasmon-polaritons in graphene,” Phys. Rev. B 90(8), 085409 (2014).
[Crossref]

Alonso-Gonzalez, P.

M. Schnell, P. Alonso-Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

Alonso-González, P.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Alù, A.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Ambacher, O.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Andreani, L. C.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
[Crossref] [PubMed]

Andrews, S. R.

S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[Crossref] [PubMed]

Antes, J.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Arzubiaga, L.

M. Schnell, P. Alonso-Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

Atanasov, V.

V. Atanasov and A. Saxena, “Electronic properties of corrugated graphene: the Heisenberg principle and wormhole geometry in the solid state,” J. Phys-Condens. Mat. 23(17), 175301 (2011).

V. Atanasov and A. Saxena, “Tuning the electronic properties of corrugated graphene: confinement, curvature, and band-gap opening,” Phys. Rev. B 81(20), 205409 (2010).
[Crossref]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
[Crossref] [PubMed]

Baek, I. H.

J. H. Jeong, B. J. Kang, J. S. Kim, M. Jazbinsek, S. H. Lee, S. C. Lee, I. H. Baek, H. Yun, J. Kim, Y. S. Lee, J. H. Lee, J. H. Kim, F. Rotermund, and O. P. Kwon, “High-power Broadband Organic THz Generator,” Sci. Rep. 3, 3200 (2013).
[Crossref] [PubMed]

Bao, J.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Bao, Q. L.

Q. L. Bao, H. Zhang, B. Wang, Z. H. Ni, C. H. Y. X. Lim, Y. Wang, D. Y. Tang, and K. P. Loh, “Broadband graphene polarizer,” Nat. Photonics 5(7), 411–415 (2011).
[Crossref]

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Bek, A.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
[Crossref] [PubMed]

Berweger, S.

J. A. Gerber, S. Berweger, B. T. O’Callahan, and M. B. Raschke, “Phase-resolved surface plasmon interferometry of graphene,” Phys. Rev. Lett. 113(5), 055502 (2014).
[Crossref] [PubMed]

Böckmann, H.

P. Li, T. Wang, H. Böckmann, and T. Taubner, “Graphene-enhanced infrared near-field microscopy,” Nano Lett. 14(8), 4400–4405 (2014).
[Crossref] [PubMed]

Boes, F.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Bokor, J.

H. Choo, M. K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–843 (2012).
[Crossref]

Bonaccorso, F.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Bonn, M.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Nanofocusing of electromagnetic radiation,” Nat. Photonics 8(1), 14–23 (2014).

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, “Highly confined tunable mid-infrared plasmonics in graphene nanoresonators,” Nano Lett. 13(6), 2541–2547 (2013).
[Crossref] [PubMed]

Burgess, J. A. J.

T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. J. Burgess, G. De Los Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7(8), 620–625 (2013).
[Crossref]

Cabrini, S.

H. Choo, M. K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–843 (2012).
[Crossref]

Caldwell, J. D.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6, 7507 (2015).
[Crossref] [PubMed]

Candeloro, P.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
[Crossref] [PubMed]

Carrega, M.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

Casanova, F.

M. Schnell, P. Alonso-Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

Chen, B.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Chen, P. Y.

P. Y. Chen and A. Alù, “Atomically thin surface cloak using graphene monolayers,” ACS Nano 5(7), 5855–5863 (2011).
[Crossref] [PubMed]

Chikan, V.

P. K. Mandal and V. Chikan, “Plasmon-phonon coupling in charged n-type CdSe quantum dots: A THz time-domain spectroscopic study,” Nano Lett. 7(8), 2521–2528 (2007).
[Crossref] [PubMed]

Choi, S. S.

M. A. Seo, H. R. Park, S. M. Koo, D. J. Park, J. H. Kang, O. K. Suwal, S. S. Choi, P. C. M. Planken, G. S. Park, N. K. Park, Q. H. Park, and D. S. Kim, “Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit,” Nat. Photonics 3(3), 152–156 (2009).
[Crossref]

Choo, H.

H. Choo, M. K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal-insulator-metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–843 (2012).
[Crossref]

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

Chuvilin, A.

M. Schnell, P. Alonso-Gonzalez, L. Arzubiaga, F. Casanova, L. E. Hueso, A. Chuvilin, and R. Hillenbrand, “Nanofocusing of mid-infrared energy with tapered transmission lines,” Nat. Photonics 5(5), 283–287 (2011).
[Crossref]

Cocker, T. L.

T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. J. Burgess, G. De Los Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7(8), 620–625 (2013).
[Crossref]

D’Angelo, F.

Dai, J.

Dai, Y. Y.

Y. Y. Dai, X. L. Zhu, N. A. Mortersen, J. Zi, and S. S. Xiao, “Nanofocusing in a tapered graphene plasmonic waveguide,” J. Opt. 17(6), 065002 (2015).
[Crossref]

Das, G.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
[Crossref] [PubMed]

de Abajo, F. J. G.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, “Graphene plasmon waveguiding and hybridization in individual and paired nanoribbons,” ACS Nano 6(1), 431–440 (2012).
[Crossref] [PubMed]

De Angelis, F.

A. Toma, S. Tuccio, M. Prato, F. De Donato, A. Perucchi, P. Di Pietro, S. Marras, C. Liberale, R. Proietti Zaccaria, F. De Angelis, L. Manna, S. Lupi, E. Di Fabrizio, and L. Razzari, “Squeezing terahertz light into nanovolumes: nanoantenna enhanced terahertz spectroscopy (nets) of semiconductor quantum dots,” Nano Lett. 15(1), 386–391 (2015).
[Crossref] [PubMed]

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
[Crossref] [PubMed]

De Donato, F.

A. Toma, S. Tuccio, M. Prato, F. De Donato, A. Perucchi, P. Di Pietro, S. Marras, C. Liberale, R. Proietti Zaccaria, F. De Angelis, L. Manna, S. Lupi, E. Di Fabrizio, and L. Razzari, “Squeezing terahertz light into nanovolumes: nanoantenna enhanced terahertz spectroscopy (nets) of semiconductor quantum dots,” Nano Lett. 15(1), 386–391 (2015).
[Crossref] [PubMed]

De Los Reyes, G.

T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. J. Burgess, G. De Los Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7(8), 620–625 (2013).
[Crossref]

Di Fabrizio, E.

A. Toma, S. Tuccio, M. Prato, F. De Donato, A. Perucchi, P. Di Pietro, S. Marras, C. Liberale, R. Proietti Zaccaria, F. De Angelis, L. Manna, S. Lupi, E. Di Fabrizio, and L. Razzari, “Squeezing terahertz light into nanovolumes: nanoantenna enhanced terahertz spectroscopy (nets) of semiconductor quantum dots,” Nano Lett. 15(1), 386–391 (2015).
[Crossref] [PubMed]

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
[Crossref] [PubMed]

Di Pietro, P.

A. Toma, S. Tuccio, M. Prato, F. De Donato, A. Perucchi, P. Di Pietro, S. Marras, C. Liberale, R. Proietti Zaccaria, F. De Angelis, L. Manna, S. Lupi, E. Di Fabrizio, and L. Razzari, “Squeezing terahertz light into nanovolumes: nanoantenna enhanced terahertz spectroscopy (nets) of semiconductor quantum dots,” Nano Lett. 15(1), 386–391 (2015).
[Crossref] [PubMed]

Do, Y.

K. Moon, H. Park, J. Kim, Y. Do, S. Lee, G. Lee, H. Kang, and H. Han, “Subsurface nanoimaging by broadband terahertz pulse near-field microscopy,” Nano Lett. 15(1), 549–552 (2015).
[Crossref] [PubMed]

Duan, H.

F. Hui, P. Vajha, Y. Shi, Y. Ji, H. Duan, A. Padovani, L. Larcher, X. R. Li, J. J. Xu, and M. Lanza, “Moving graphene devices from lab to market: advanced graphene-coated nanoprobes,” Nanoscale 8(16), 8466–8473 (2016).
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Durach, M.

Engheta, N.

A. Vakil and N. Engheta, “Transformation optics using graphene,” Science 332(6035), 1291–1294 (2011).
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Fang, W.

W. Li, B. Chen, C. Meng, W. Fang, Y. Xiao, X. Li, Z. Hu, Y. Xu, L. Tong, H. Wang, W. Liu, J. Bao, and Y. R. Shen, “Ultrafast all-optical graphene modulator,” Nano Lett. 14(2), 955–959 (2014).
[Crossref] [PubMed]

Fernández-Domínguez, A. I.

A. Wiener, A. I. Fernández-Domínguez, A. P. Horsfield, J. B. Pendry, and S. A. Maier, “Nonlocal effects in the nanofocusing performance of plasmonic tips,” Nano Lett. 12(6), 3308–3314 (2012).
[Crossref] [PubMed]

Ferrari, A. C.

F. Bonaccorso, Z. Sun, T. Hasan, and A. C. Ferrari, “Graphene photonics and optoelectronics,” Nat. Photonics 4(9), 611–622 (2010).
[Crossref]

Freeman, M. R.

T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. J. Burgess, G. De Los Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7(8), 620–625 (2013).
[Crossref]

Freude, W.

S. Koenig, D. Lopez-Diaz, J. Antes, F. Boes, R. Henneberger, A. Leuther, A. Tessmann, R. Schmogrow, D. Hillerkuss, R. Palmer, T. Zwick, C. Koos, W. Freude, O. Ambacher, J. Leuthold, and I. Kallfass, “Wireless sub-THz communication system with high data rate,” Nat. Photonics 7(12), 977–981 (2013).
[Crossref]

Galli, M.

F. De Angelis, G. Das, P. Candeloro, M. Patrini, M. Galli, A. Bek, M. Lazzarino, I. Maksymov, C. Liberale, L. C. Andreani, and E. Di Fabrizio, “Nanoscale chemical mapping using three-dimensional adiabatic compression of surface plasmon polaritons,” Nat. Nanotechnol. 5(1), 67–72 (2010).
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Gan, C. H.

C. H. Gan, “Analysis of surface plasmon excitation at terahertz frequencies with highly doped graphene sheets via attenuated total reflection,” Appl. Phys. Lett. 101(11), 111609 (2012).
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Gao, Y.

A. Woessner, M. B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, and F. H. L. Koppens, “Highly confined low-loss plasmons in graphene-boron nitride heterostructures,” Nat. Mater. 14(4), 421–425 (2014).
[Crossref] [PubMed]

B. Zhu, G. Ren, Y. Gao, Y. Yang, Y. Lian, and S. Jian, “Graphene-coated tapered nanowire infrared probe: a comparison with metal-coated probes,” Opt. Express 22(20), 24096–24103 (2014).
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Gao, Y. X.

García de Abajo, F. J.

S. Thongrattanasiri and F. J. García de Abajo, “Optical field enhancement by strong plasmon interaction in graphene nanostructures,” Phys. Rev. Lett. 110(18), 187401 (2013).
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García-Vidal, F. J.

B. Wang, X. Zhang, F. J. García-Vidal, X. Yuan, and J. Teng, “Strong coupling of surface plasmon polaritons in monolayer graphene sheet arrays,” Phys. Rev. Lett. 109(7), 073901 (2012).
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S. A. Maier, S. R. Andrews, L. Martín-Moreno, and F. J. García-Vidal, “Terahertz surface plasmon-polariton propagation and focusing on periodically corrugated metal wires,” Phys. Rev. Lett. 97(17), 176805 (2006).
[Crossref] [PubMed]

Gaussmann, F.

P. Li, M. Lewin, A. V. Kretinin, J. D. Caldwell, K. S. Novoselov, T. Taniguchi, K. Watanabe, F. Gaussmann, and T. Taubner, “Hyperbolic phonon-polaritons in boron nitride for near-field optical imaging and focusing,” Nat. Commun. 6, 7507 (2015).
[Crossref] [PubMed]

Geim, A. K.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Gerber, J. A.

J. A. Gerber, S. Berweger, B. T. O’Callahan, and M. B. Raschke, “Phase-resolved surface plasmon interferometry of graphene,” Phys. Rev. Lett. 113(5), 055502 (2014).
[Crossref] [PubMed]

Gimzewski, J. K.

C. Martin-Olmos, H. I. Rasool, B. H. Weiller, and J. K. Gimzewski, “Graphene MEMS: AFM probe performance improvement,” ACS Nano 7(5), 4164–4170 (2013).
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Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, “Graphene plasmonics for tunable terahertz metamaterials,” Nat. Nanotechnol. 6(10), 630–634 (2011).
[Crossref] [PubMed]

Govyadinov, A. A.

A. A. Govyadinov and V. A. Podolskiy, “Metamaterial photonic funnels for subdiffraction light compression and propagation,” Phys. Rev. B 73(15), 155108 (2006).
[Crossref]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Nanofocusing of electromagnetic radiation,” Nat. Photonics 8(1), 14–23 (2014).

Gu, M.

H. Lu, C. Zeng, Q. Zhang, X. Liu, M. M. Hossain, P. Reineck, and M. Gu, “Graphene-based active slow surface plasmon polaritons,” Sci. Rep. 5, 8443 (2015).
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Gupta, M.

T. L. Cocker, V. Jelic, M. Gupta, S. J. Molesky, J. A. J. Burgess, G. De Los Reyes, L. V. Titova, Y. Y. Tsui, M. R. Freeman, and F. A. Hegmann, “An ultrafast terahertz scanning tunnelling microscope,” Nat. Photonics 7(8), 620–625 (2013).
[Crossref]

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Figures (10)

Fig. 1
Fig. 1 (a) Schematic for plasmonic nanofocusing of THz wave in tapered graphene multilayers. (b) xz and xy cross sections of the graphene multilayer taper. The geometric parameters of the taper are labelled in the xz cross section. The graphene monolayers and dielectric areas are respectively labelled with black and red numbers in the xy cross section.
Fig. 2
Fig. 2 Plasmonic nanofocusing of THz wave in a single layer graphene taper. (a) Plot of calculated effective index along the taper. The red and green curves represent the real part (Re[neff]) and imaginary part (Im[neff]), respectively. (b) Plot of adiabatic parameter variation along the taper. (c) Normalized modal profiles of Er (left) and |E|/|E0| over the area labelled by red dashed line (right) calculated by numerical simulation. (d) Normalized field amplitude |E|/|E0| on the exterior surface of graphene taper calculated with adiabatic approximation (red dashed curve) and numerical simulation (green curve). (e) Field amplitude enhancement (|Etip|/|E0|) as a function of the tip radius Rb. Inset: Plot of SPPs mode lateral extent lspp as a function of tip radius Rb. (f) Field amplitude enhancement (|Etip|/|E0|) as a function of the taper length L. Without specifications, the taper structure parameters are set as Ra = 1 μm, Rb = 5 nm, L = 3 μm.
Fig. 3
Fig. 3 (a)-(c) Theoretical calculated mode profiles of Er for graphene scrolls, N = 1, 2, 3 respectively. (d) Real part and (e) imaginary part of the effective indices. The red circles denote the modes with the largest Re(neff) (s = N). For all the scrolls, Rb = 5 nm, Rb1 = 4 nm.
Fig. 4
Fig. 4 Plasmonic nanofocusing in graphene two-layer taper. (a) Real part and (b) imaginary part of the effective indices for modes s = 1 and s = 2 along the taper. (c) The variation of adiabatic parameter for mode s = 2 along the taper. (d) Normalized filed distributions of Er component (left) and |E|/|E0| over the dashed line labelled area (right)calculated by simulation. (e) Normalized field amplitude |E|/|E0| on the surface of the inner layer graphene calculated by adiabatic approximation (red dashed curve) and numerical simulation (green curve). (f) Field amplitude enhancement |Etip|/|E0| as a function of taper length as ΔRb = 1 nm and 2 nm, respectively. Without specifications, the taper structure parameters are set as Ra = 1 μm, Rb = 5 nm, Rb1 = 4 nm, L = 3 μm.
Fig. 5
Fig. 5 Plasmonic nanofocusing in graphene multilayer taper. (a)-(c) Plots of calculated field enhancement |Etip|/|E0| as functions of taper length for the 3, 4, 5-layer graphene taper, respectively. (d)-(f) The corresponding field distributions of Er component and |E|/|E0| for the 3, 4, 5-layer graphene taper. The taper lengths are labelled with arrows in (a)-(c). (g) Plot of field amplitude enhancement |Etip|/|E0| dependence on the graphene layer number N. (h) Plot of inverse of normalized effective mode area (1/ Aeff) at the taper tip (red dots) and propagation loss η (green dots) as functions of the graphene layer number N. Ra = 1 μm, Rb = 5 nm, Rb1 = 4 nm.
Fig. 6
Fig. 6 Plasmonic nanofocusing of THz wave dependent on wavelength and graphene chemical potential. (a)-(c) Mappings of field amplitude enhancement |Etip|/|E0| as functions of wavelength and graphene chemical potential for 1, 2, and 3-layer graphene taper, respectively. Ra = 1 μm, Rb = 5 nm, Rb1 = 4 nm, L = 3 μm.
Fig. 7
Fig. 7 (a) Schematic for the SPPs field superposition between interlayer graphene. (b)Schematic for the field of SPPs propagating and reflecting in the tapered waveguide.
Fig. 8
Fig. 8 Influence of bending induced geometric potential on the plasmonic nanofocusing. (a) Plot of graphene chemical potential as a function of curvature radius R. (b) Plot of effective index along the SPPs propagation direction for single layer graphene taper with (Red line) and without (Blue line) considering the influence of geometric potential. (c) Plot of normalized field distribution |E|/|E0| for single graphene taper with (Red line) and without (Blue line) considering the influence of geometric potential.
Fig. 9
Fig. 9 Calculated reflection coefficients for graphene scroll port, N = 1 and 2 respectively. (a) Plot of reflection coefficients for a single layer graphene scroll as function of scroll radius R. (b) Real part and (c) imaginary part of the reflection coefficients for graphene two-layer scroll as function of scroll sizes. R1 and R2 are the radius of the inner layer scroll and the interlayer space between of the two layers, respectively.
Fig. 10
Fig. 10 Comparison of nanofocusing for modes s = 1 and s = 2. Field distributions of Er and |E|/|E0| for (a)(b) s = 1 and (c)(d) s = 2, respectively. (e) Plot of effective indices for modes s = 1 and s = 2. Inset shows the plot of Im(neff). (f) The normalized field amplitude |E|/|E0| for modes s = 1 (Green) and s = 2 (Red) on the inner-layer graphene surface. Ra = 1 μm, Rb = 5 nm, Rb1 = 4 nm, L = 3 μm.

Equations (22)

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[ A n B n ] = m n 1 m n 1 [ A n 1 B n 1 ] ,
m n = [ K 0 ( κ n R n ) ε n κ n K 1 ( κ n R n ) I 0 ( κ n R n ) ε n κ n I 1 ( κ n R n ) ] ,
m n 1 = [ K 0 ( κ n 1 R n ) ε n - 1 κ n 1 K 1 ( κ n 1 R n ) + σ g η 0 j k 0 K 0 ( κ n 1 R n ) I 0 ( κ n 1 R n ) ε n - 1 κ n 1 I 1 ( κ n 1 R n ) + σ g η 0 j k 0 I 0 ( κ n 1 R n ) ] .
Φ ( x , y , z ) = exp ( i k 0 0 z n e f f d z ) 1 exp ( 2 i k 0 0 L n e f f d z ) r a r b ( n e f f ( 0 ) n e f f ( z ) ) [ 1 ± r b exp ( 2 i k 0 z L n e f f d z ) ] Φ 0 ( x , y , z ) ,
l S P P = 1 / Re [ k 0 ( n e f f 2 1 ) ] 1 / [ k 0 Re ( n e f f ) ] .
E z = { A n 1 k 0 ( κ n 1 r ) + B n 1 I 0 ( κ n 1 r ) R n 1 < r < R n A n k 0 ( κ n r ) + B n I 0 ( κ n r ) R n < r < R n + 1 ,
E r = i β κ i 2 E z r = { i β κ n 1 [ A n 1 k 1 ( κ n 1 r ) B n 1 I 0 ( κ n 1 r ) ] R n 1 < r < R n i β κ n [ A n k 0 ( κ n r ) B n I 0 ( κ n r ) ] R n < r < R n + 1 ,
H φ = i k 0 ε i η 0 κ i 2 E z r = { i k 0 ε n 1 η 0 κ n 1 [ A n 1 k 1 ( κ n 1 r ) B n 1 I 0 ( κ n 1 r ) ] R n 1 < r < R n i k 0 ε n η 0 κ n [ A n k 0 ( κ n r ) B n I 0 ( κ n r ) ] R n < r < R n + 1 ,
[ A n B n ] = m n 1 m n 1 [ A n 1 B n 1 ] ,
m n = [ K 0 ( κ n R n ) I 0 ( κ n R n ) ε n κ n K 1 ( κ n R n ) ε n κ n I 1 ( κ n R n ) ] ,
m n 1 = [ K 0 ( κ n R n ) I 0 ( κ n 1 R n ) ε n 1 κ n 1 K 1 ( κ n 1 R n ) + σ g η 0 j k 0 I 0 ( κ n 1 R n ) ε n 1 κ n 1 I 1 ( κ n 1 R n ) + σ g η 0 j k 0 I 0 ( κ n 1 R n ) ] .
2 E z = ( x , y , z ) + n 2 ( x , y , z ) k 0 2 E z ( x , y , z ) = 0.
t 2 Ψ ( x , y , z ) + n 2 ( x , y , z ) k 0 2 Ψ ( x , y , z ) = n e f f 2 ( z ) k 0 2 Ψ ( x , y , z ) ,
d 2 Θ ( z ) d z 2 + n e f f 2 ( z ) k 0 2 Θ ( z ) = 0.
φ ( z ) = z n e f f ( z ) k 0 d z + z i n e f f d n e f f = k 0 z n e f f ( z ) d z + i ln ( n e f f ( z ) n e f f ( 0 ) ) .
Θ ( z ) = A exp [ i ϕ ( z ) ] = A ( n e f f ( z ) n e f f ( 0 ) ) 1 exp [ i k 0 z n e f f ( z ) d z ] .
E z ( x , y , z ) = A Ψ ( x , y , z ) ( n e f f ( z ) n e f f ( 0 ) ) 1 exp [ i k 0 z n e f f ( z ) d z ] .
Φ ( x , y , z ) = A Φ 0 ( x , y , z ) ( n e f f ( z ) n e f f ( 0 ) ) 1 exp [ i k 0 z n e f f ( z ) d z ] .
E a = Φ 0 + E b exp ( L 0 i k 0 n e f f d z ) n e f f ( 0 ) n e f f ( L ) r a , E b = E a exp ( 0 L i k 0 n e f f d z ) n e f f ( L ) n e f f ( 0 ) r b ,
Φ ( z ) = E a exp ( 0 z i k 0 n e f f d z ) ( n e f f ( z ) n e f f ( 0 ) ) 1 ± E b exp ( L z i k 0 n e f f d z ) ( n e f f ( z ) n e f f ( 0 ) ) 1 ) .
Φ ( x , y , z ) = exp ( i k 0 0 z n e f f d z ) 1 exp ( 2 i k 0 0 L n e f f d z ) r a r b ( n e f f ( 0 ) n e f f ( z ) ) [ 1 ± r b exp ( 2 i k 0 z L n e f f d z ) ] Φ 0 ( x , y , z ) ,
μ c = μ c 0 ν F R ,

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