Abstract

By using the effective-index method (EIM) and the finite element methods (FEM), a surface plasmon polariton (SPP) waveguide structured by a dielectric ridge placed on monolayer black phosphorus is proposed and analyzed in the infrared spectral region. It is found that the strong anisotropic dispersion of the black phosphorus (BP) gives rise to direction-dependent waveguide modes in a dielectric-loaded black phosphorus waveguide (DLBPW). The effective mode index, propagation loss and cutoff wavelength of higher order modes are investigated along the armchair (AC) and the zigzag (ZZ) directions of the black phosphorus. Moreover, the propagation characteristics of single-mode are investigated for different widths of the dielectric ridge and different polarization directions of the black phosphorus. Via tuning the carrier density, the electromagnetic field propagation features can be effectively modified. Also, the coupling effect by adding more dielectric bridges can tune the propagation properties. These results will lead to great applications in black phosphorus-based optical integrated devices.

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

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2018 (2)

2017 (2)

Y. Q. Liu and P. K. Liu, “Excitation of surface plasmon polaritons by electron beam with graphene ribbon arrays,” J. Appl. Phys. 121(11), 113104 (2017).
[Crossref]

H. Lu, Y. Gong, D. Mao, X. Gan, and J. Zhao, “Strong plasmonic confinement and optical force in phosphorene pairs,” Opt. Express 25(5), 5255–5263 (2017).
[Crossref] [PubMed]

2016 (2)

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
[Crossref] [PubMed]

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

2015 (3)

2014 (8)

X. Zhou, T. Zhang, L. Chen, W. Hong, and X. Li, “A graphene-based hybrid plasmonic waveguide with ultra-deep subwavelength confinement,” J. Lightwave Technol. 32(21), 3597–3601 (2014).

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B Condens. Matter Mater. Phys. 89(23), 235319 (2014).
[Crossref]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

Y. Du, H. Liu, Y. Deng, and P. D. Ye, “Device perspective for black phosphorus field-effect transistors: contact resistance, ambipolar behavior, and scaling,” ACS Nano 8(10), 10035–10042 (2014).
[Crossref] [PubMed]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

2013 (3)

P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove waveguides,” Opt. Express 21(26), 32432–32440 (2013).
[Crossref] [PubMed]

J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref] [PubMed]

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

2012 (1)

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

2011 (2)

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

2010 (3)

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. 96(22), 221103 (2010).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

2009 (3)

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009).
[Crossref] [PubMed]

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 80(24), 245435 (2009).
[Crossref]

J. Dintinger and O. J. F. Martin, “Channel and wedge plasmon modes of metallic V-grooves with finite metal thickness,” Opt. Express 17(4), 2364–2374 (2009).
[Crossref] [PubMed]

2007 (1)

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B Condens. Matter Mater. Phys. 75(42), 245405 (2007).
[Crossref]

2006 (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

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]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[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]

Avouris, P.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

Aydin, K.

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
[Crossref] [PubMed]

Bai, P.

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. 96(22), 221103 (2010).
[Crossref]

Balendhran, S.

S. Balendhran, S. Walia, H. Nili, S. Sriram, and M. Bhaskaran, “Elemental analogues of graphene: silicene, germanene, stanene, and phosphorene,” Small 11(6), 640–652 (2015).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Bartal, G.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009).
[Crossref] [PubMed]

Bhaskaran, M.

S. Balendhran, S. Walia, H. Nili, S. Sriram, and M. Bhaskaran, “Elemental analogues of graphene: silicene, germanene, stanene, and phosphorene,” Small 11(6), 640–652 (2015).
[Crossref] [PubMed]

Blanter, S. I.

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B Condens. Matter Mater. Phys. 75(42), 245405 (2007).
[Crossref]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

Brongersma, M. L.

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 80(24), 245435 (2009).
[Crossref]

Buscema, M.

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref] [PubMed]

Cai, W.

Carvalho, A.

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

Castellanos-Gomez, A.

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref] [PubMed]

Chang, D. E.

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Chen, L.

Christensen, J.

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

Chu, H. S.

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. 96(22), 221103 (2010).
[Crossref]

de Abajo, F. J.

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

Deng, Y.

Y. Du, H. Liu, Y. Deng, and P. D. Ye, “Device perspective for black phosphorus field-effect transistors: contact resistance, ambipolar behavior, and scaling,” ACS Nano 8(10), 10035–10042 (2014).
[Crossref] [PubMed]

Dereux, A.

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

Dintinger, J.

Du, Y.

Y. Du, H. Liu, Y. Deng, and P. D. Ye, “Device perspective for black phosphorus field-effect transistors: contact resistance, ambipolar behavior, and scaling,” ACS Nano 8(10), 10035–10042 (2014).
[Crossref] [PubMed]

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Forati, E.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Gan, X.

García de Abajo, F. J.

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

García-Vidal, F. J.

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]

Genov, D. A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009).
[Crossref] [PubMed]

Gong, Y.

Gosciniak, J.

J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref] [PubMed]

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Groenendijk, D. J.

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref] [PubMed]

Guinea, F.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

Hanson, G. W.

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

Hassan, K.

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

Hegde, R.

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. 96(22), 221103 (2010).
[Crossref]

Holmgaard, T.

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B Condens. Matter Mater. Phys. 75(42), 245405 (2007).
[Crossref]

Hong, W.

Ishikawa, A.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009).
[Crossref] [PubMed]

Jablan, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 80(24), 245435 (2009).
[Crossref]

Jia, Y.

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

Jiang, Y.

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

Koppens, F. H.

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

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Kriezis, E.

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

Lan, G.

Li, E. P.

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. 96(22), 221103 (2010).
[Crossref]

Li, X.

Liang, Y.

V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B Condens. Matter Mater. Phys. 89(23), 235319 (2014).
[Crossref]

Liu, H.

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

Y. Du, H. Liu, Y. Deng, and P. D. Ye, “Device perspective for black phosphorus field-effect transistors: contact resistance, ambipolar behavior, and scaling,” ACS Nano 8(10), 10035–10042 (2014).
[Crossref] [PubMed]

Liu, K.

Liu, P.

Liu, P. K.

Y. Q. Liu and P. K. Liu, “Excitation of surface plasmon polaritons by electron beam with graphene ribbon arrays,” J. Appl. Phys. 121(11), 113104 (2017).
[Crossref]

Liu, Y. Q.

Y. Q. Liu and P. K. Liu, “Excitation of surface plasmon polaritons by electron beam with graphene ribbon arrays,” J. Appl. Phys. 121(11), 113104 (2017).
[Crossref]

Liu, Z.

P. Wan, C. Yang, and Z. Liu, “Channel hybrid plasmonic modes in dielectric-loaded graphene groove waveguides,” Opt. Commun. 420, 72–77 (2018).
[Crossref]

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
[Crossref] [PubMed]

Low, T.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

Lu, H.

Lu, J.

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

Lu, Q. S.

Lu, Y.

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

Ma, Z.

Maier, S. A.

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]

Manjavacas, A.

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

Mao, D.

Markey, L.

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

Martin, O. J. F.

Martín-Moreno, L.

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]

Moreno, L. M.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

Neto, A. C.

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

Nili, H.

S. Balendhran, S. Walia, H. Nili, S. Sriram, and M. Bhaskaran, “Elemental analogues of graphene: silicene, germanene, stanene, and phosphorene,” Small 11(6), 640–652 (2015).
[Crossref] [PubMed]

Nong, J.

Pitilakis, A.

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

Qin, S. Q.

Rodin, A.

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

Roldán, R.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

Shalaev, V. M.

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

Shang, Z.

Soklaski, R.

V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B Condens. Matter Mater. Phys. 89(23), 235319 (2014).
[Crossref]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 80(24), 245435 (2009).
[Crossref]

Sow, C. H.

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

Sriram, S.

S. Balendhran, S. Walia, H. Nili, S. Sriram, and M. Bhaskaran, “Elemental analogues of graphene: silicene, germanene, stanene, and phosphorene,” Small 11(6), 640–652 (2015).
[Crossref] [PubMed]

Steele, G. A.

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

Tan, D. T.

J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref] [PubMed]

Tang, L.

Thongrattanasiri, S.

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

Tran, V.

V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B Condens. Matter Mater. Phys. 89(23), 235319 (2014).
[Crossref]

Tsilipakos, O.

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

van der Zant, H. S.

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

Walia, S.

S. Balendhran, S. Walia, H. Nili, S. Sriram, and M. Bhaskaran, “Elemental analogues of graphene: silicene, germanene, stanene, and phosphorene,” Small 11(6), 640–652 (2015).
[Crossref] [PubMed]

Wan, P.

P. Wan, C. Yang, and Z. Liu, “Channel hybrid plasmonic modes in dielectric-loaded graphene groove waveguides,” Opt. Commun. 420, 72–77 (2018).
[Crossref]

Wang, H.

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

Wang, L.

Wang, W.

Weeber, J. C.

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

Wei, W.

Xia, F.

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

Xu, J.

Xu, W.

Yang, C.

P. Wan, C. Yang, and Z. Liu, “Channel hybrid plasmonic modes in dielectric-loaded graphene groove waveguides,” Opt. Commun. 420, 72–77 (2018).
[Crossref]

Yang, J.

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

Yang, L.

V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B Condens. Matter Mater. Phys. 89(23), 235319 (2014).
[Crossref]

Ye, P. D.

Y. Du, H. Liu, Y. Deng, and P. D. Ye, “Device perspective for black phosphorus field-effect transistors: contact resistance, ambipolar behavior, and scaling,” ACS Nano 8(10), 10035–10042 (2014).
[Crossref] [PubMed]

Yi, J.

Yuan, X. D.

Zhang, J. F.

Zhang, S.

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009).
[Crossref] [PubMed]

Zhang, T.

Zhang, X.

P. Liu, X. Zhang, Z. Ma, W. Cai, L. Wang, and J. Xu, “Surface plasmon modes in graphene wedge and groove waveguides,” Opt. Express 21(26), 32432–32440 (2013).
[Crossref] [PubMed]

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009).
[Crossref] [PubMed]

Zhao, J.

Zhou, X.

Zhu, Z. H.

Acc. Chem. Res. (1)

J. Lu, J. Yang, A. Carvalho, H. Liu, Y. Lu, and C. H. Sow, “Light–matter interactions in phosphorene,” Acc. Chem. Res. 49(9), 1806–1815 (2016).
[Crossref] [PubMed]

ACS Nano (2)

Y. Du, H. Liu, Y. Deng, and P. D. Ye, “Device perspective for black phosphorus field-effect transistors: contact resistance, ambipolar behavior, and scaling,” ACS Nano 8(10), 10035–10042 (2014).
[Crossref] [PubMed]

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

Appl. Phys. Lett. (3)

E. Forati and G. W. Hanson, “Surface plasmon polaritons on soft-boundary graphene nanoribbons and their application in switching/demultiplexing,” Appl. Phys. Lett. 103(13), 133104 (2013).
[Crossref]

K. Hassan, J. C. Weeber, L. Markey, A. Dereux, A. Pitilakis, O. Tsilipakos, and E. Kriezis, “Thermo-optic plasmo-photonic mode interference switches based on dielectric loaded waveguides,” Appl. Phys. Lett. 99(24), 241110 (2011).
[Crossref]

H. S. Chu, E. P. Li, P. Bai, and R. Hegde, “Optical performance of single-mode hybrid dielectric-loaded plasmonic waveguide-based components,” Appl. Phys. Lett. 96(22), 221103 (2010).
[Crossref]

J. Appl. Phys. (1)

Y. Q. Liu and P. K. Liu, “Excitation of surface plasmon polaritons by electron beam with graphene ribbon arrays,” J. Appl. Phys. 121(11), 113104 (2017).
[Crossref]

J. Lightwave Technol. (1)

Nano Lett. (3)

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref] [PubMed]

F. H. Koppens, D. E. Chang, and F. J. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11(8), 3370–3377 (2011).
[Crossref] [PubMed]

Nanotechnology (1)

J. Gosciniak and D. T. Tan, “Graphene-based waveguide integrated dielectric-loaded plasmonic electro-absorption modulators,” Nanotechnology 24(18), 185202 (2013).
[Crossref] [PubMed]

Nat. Commun. (2)

F. Xia, H. Wang, and Y. Jia, “Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics,” Nat. Commun. 5(1), 4458 (2014).
[Crossref] [PubMed]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos-Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref] [PubMed]

Nat. Photonics (1)

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[Crossref]

Nature (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440(7083), 508–511 (2006).
[Crossref] [PubMed]

Opt. Commun. (1)

P. Wan, C. Yang, and Z. Liu, “Channel hybrid plasmonic modes in dielectric-loaded graphene groove waveguides,” Opt. Commun. 420, 72–77 (2018).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B Condens. Matter Mater. Phys. (4)

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B Condens. Matter Mater. Phys. 80(24), 245435 (2009).
[Crossref]

T. Low, A. Rodin, A. Carvalho, Y. Jiang, H. Wang, F. Xia, and A. C. Neto, “Tunable optical properties of multilayer black phosphorus thin films,” Phys. Rev. B Condens. Matter Mater. Phys. 90(7), 075434 (2014).
[Crossref]

V. Tran, R. Soklaski, Y. Liang, and L. Yang, “Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus,” Phys. Rev. B Condens. Matter Mater. Phys. 89(23), 235319 (2014).
[Crossref]

T. Holmgaard and S. I. Bozhevolnyi, “Theoretical analysis of dielectric-loaded surface plasmon-polariton waveguides,” Phys. Rev. B Condens. Matter Mater. Phys. 75(42), 245405 (2007).
[Crossref]

Phys. Rev. Lett. (3)

A. Ishikawa, S. Zhang, D. A. Genov, G. Bartal, and X. Zhang, “Deep subwavelength terahertz waveguides using gap magnetic plasmon,” Phys. Rev. Lett. 102(4), 043904 (2009).
[Crossref] [PubMed]

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]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref] [PubMed]

Science (1)

M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for plasmonics,” Science 328(5977), 440–441 (2010).
[Crossref] [PubMed]

Small (1)

S. Balendhran, S. Walia, H. Nili, S. Sriram, and M. Bhaskaran, “Elemental analogues of graphene: silicene, germanene, stanene, and phosphorene,” Small 11(6), 640–652 (2015).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 Effective mode indices N eff of the SP modes in DLBPW with a width of 200 nm: (a) Real part, θ= 0 , (b) Imaginary part, θ= 0 , (c) Real part, θ=9 0 , (d) Imaginary part, θ=9 0 . The insets of (a) and (b) show the amplitudes of E y at different wavelength. The solid lines correspond to the EIM, and the symbols correspond to the FEM calculations. The dashed blue lines indicate N clad and N core . (e) and (f) show the schematic of DLBPW. (e) The armchair (AC) direction of BP is along the x-axis. (f) The zigzag (ZZ) direction is along the x-axis.
Fig. 2
Fig. 2 The fundamental mode and multi-modes operation regions calculated by Eq. (8) as a function of the strip width and the wavelength. The numbers of modes supported by the DLBPW are labeled. (a) θ= 0 , (b) θ=9 0 .
Fig. 3
Fig. 3 Effective fundamental mode refractive indices in DLBPW as a function of the rotation angle of the BP layer. (a) N eff , (b) Im( β/ k 0 ) .
Fig. 4
Fig. 4 Effective fundamental mode indices of the fundamental mode in DLBPW as functions of the height and various widths of the dielectric ridge. (a) N eff , (b) Im( β/ k 0 ).(c)–(j) | E |profiles of the fundamental T M 00 modes with different geometric configurations.
Fig. 5
Fig. 5 The real part of the effective refractive indices of the fundamental mode in DLBPW versus various wavelength at different carrier densities. (a) θ= 0 , (b) θ=9 0 .
Fig. 6
Fig. 6 The effective refractive indices of the fundamental mode in the DLBPW as a function of gap separation s: (a) Real part, (b) Imaginary part, θ= 0 , λ=50nm. (c) Real part, (d) Imaginary part, θ=9 0 , λ=30nm. The insets show the amplitudes of E y at different s. The dotted red line is N eff for only one bridge in the DLBPW.

Equations (8)

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

σ j j = i D j j π(ω+iη/)
σ( θ )= σ AC sin 2 θ+ σ ZZ cos 2 θ
H x ={ H 2 e γ 2 y H 1 e γ 1 y y<0 y0
E z ={ i γ 2 ε r2 ω ε 0 H 2 e γ 2 y i γ 1 ε r1 ω ε 0 H 1 e γ 1 x y<0 y0
{ H x 1 H x 2 =σ( θ ) E z E z 1 = E z 2 y=0
ε r1 γ 1 + ε r2 γ 2 + iσ( θ ) ω ε 0 =0
tan( ξ 1 Wmπ 2 )= ξ 2 ξ 1
λ cut m =Re( 2W m N core 2 N clad 2 )

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