Abstract

In this paper, the dynamic motion of surface plasmon polaritons, spatial Bloch oscillations, in a kind of nanoscale three-dimensional surface plasmon polaritons metal waveguide arrays is presented. The waveguide arrays are composed of 41 three-dimensional plasmonic waveguides with ultra-small cross section, thus the maximum lateral size of the waveguide arrays is only 6.56µm. The gradient of surface plasmon ploartions propagation constants across the waveguide arrays is realized by gradually changing the refractive index of the dielectric layer in the waveguide arrays. Theoretical results from the coupled wave theory show that surface plasmon polaritons propagate in the three-dimensional metal waveguide arrays as breathing and transverse oscillatory mode Bloch oscillations under the conditions of single and multiple waveguide excitations, respectively. All theoretical results are confirmed by finite-difference time-domain numerical simulations. Through the numerical analysis of fabrication tolerance caused by the metal strips uniform shifts, the designed three-dimensional surface plasmon polaritons metal waveguide arrays can resist certain fabrication errors.

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

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  40. W. Wang, H. Ye, Q. Wang, and W. Lin, “Propagation properties of nanoscale three-dimensional plasmonic waveguide based on hybrid of two fundamental planar optical metal waveguides,” Plasmonics 13(5), 1615–1621 (2018).
    [Crossref]
  41. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  42. W. Wang and W. Lin, “Optical properties of plasmonic components based on nanoscale three-dimensional plasmonic waveguide,” J. Opt. Soc. Am. B 36(8), 2045–2051 (2019).
    [Crossref]
  43. V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92(9), 097401 (2004).
    [Crossref]
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    [Crossref]

2019 (2)

H. Lu, S. Dai, Z. Yue, Y. Fan, H. Cheng, J. Di, D. Mao, E. Li, T. Mei, and J. Zhao, “Sb2Te3 topological insulator: surface plasmon resonance and application in refractive index monitoring,” Nanoscale 11(11), 4759–4766 (2019).
[Crossref]

W. Wang and W. Lin, “Optical properties of plasmonic components based on nanoscale three-dimensional plasmonic waveguide,” J. Opt. Soc. Am. B 36(8), 2045–2051 (2019).
[Crossref]

2018 (2)

W. Wang, H. Ye, Q. Wang, and W. Lin, “Propagation properties of nanoscale three-dimensional plasmonic waveguide based on hybrid of two fundamental planar optical metal waveguides,” Plasmonics 13(5), 1615–1621 (2018).
[Crossref]

C. Tan, Z. Yue, Z. Dai, Q. Bao, X. Wang, H. Lu, and L. Wang, “Nanograting-assisted generation of surface plasmon polaritons in Weyl semimetal WTe2,” Opt. Mater. 86, 421–423 (2018).
[Crossref]

2017 (1)

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photonics Res. 5(3), 162–167 (2017).
[Crossref]

2016 (1)

Q. Wang, W. Hu, J. Wei, and W. Lin, “Controlling diffraction of surface plasmon polaritons in nanoscale metal waveguide arrays,” Plasmonics 11(1), 117–124 (2016).
[Crossref]

2015 (4)

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
[Crossref]

Y. Zhang, M. R. Belić, W. Zhong, F. Wen, Y. Guo, Y. Guo, K. Lu, and Y. Zhang, “Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array,” J. Opt. 17(4), 045703 (2015).
[Crossref]

Z. Li and H. Zhao, “Electromagnetic Bloch-like oscillations in planar quasiperiodic metal-dielectric waveguide arrays,” Europhys. Lett. 111(5), 56005 (2015).
[Crossref]

G. N. Aliev and B. Goller, “Hypersonic phononic stopbands at small angles of wave incidence in porous silicon multilayers,” J. Phys. D: Appl. Phys. 48(32), 325501 (2015).
[Crossref]

2014 (3)

2013 (1)

K. Hassan, A. Bouhelier, T. Bernardin, G. Colas-des-Francs, J. C. Weeber, A. Dereux, and R. E. de Lamaestre, “Momentum-space spectroscopy for advanced analysis of dielectric-loaded surface plasmon polariton coupled and bent waveguides,” Phys. Rev. B 87(19), 195428 (2013).
[Crossref]

2012 (4)

B. Wang, X. Zhang, F. J. Garcia-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]

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D: Appl. Phys. 45(43), 433001 (2012).
[Crossref]

T. Otsuji, S. A. Boubanga-Tombet, A. Satou, H. Fukidome, M. Suemitsu, E. Sano, V. Popov, M. Ryzhii, and V. Ryzhii, “Graphene-based devices in terahertz science and technology,” J. Phys. D: Appl. Phys. 45(30), 303001 (2012).
[Crossref]

J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D: Appl. Phys. 45(11), 113001 (2012).
[Crossref]

2011 (2)

A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref]

B. H. Cheng and Y. C. Lan, “Bloch oscillations of surface plasmon-like modes in waveguide arrays that comprise perforated perfect conductor layers and dielectric Layers,” Plasmonics 6(2), 427–433 (2011).
[Crossref]

2010 (1)

2009 (2)

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94(16), 161105 (2009).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[Crossref]

2007 (3)

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91(24), 243113 (2007).
[Crossref]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref]

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90(21), 211101 (2007).
[Crossref]

2006 (2)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[Crossref]

2005 (1)

N. D. L. Kimura, A. Fainstein, and B. Jusserand, “Phonon Bloch oscillations in acoustic-cavity structures,” Phys. Rev. B 71(4), 041305 (2005).
[Crossref]

2004 (3)

B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29(17), 1992–1994 (2004).
[Crossref]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92(9), 097401 (2004).
[Crossref]

2003 (2)

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

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91(26), 263902 (2003).
[Crossref]

2002 (2)

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[Crossref]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref]

2001 (1)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref]

1999 (1)

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

1997 (1)

V. G. Lyssenko, G. Valusis, F. Löser, T. Hasche, K. Leo, M. M. Dignam, and K. Köhler, “Direct measurement of the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79(2), 301–304 (1997).
[Crossref]

1996 (1)

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76(24), 4508–4511 (1996).
[Crossref]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1929 (1)

F. Bloch, “Über die quantemechanik der elektronen in kristallgittern,” Z. Phys. 52(7-8), 555–600 (1929).
[Crossref]

Agarwal, V.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92(9), 097401 (2004).
[Crossref]

Aitchison, J. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Aliev, G. N.

G. N. Aliev and B. Goller, “Hypersonic phononic stopbands at small angles of wave incidence in porous silicon multilayers,” J. Phys. D: Appl. Phys. 48(32), 325501 (2015).
[Crossref]

Altewischer, E.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[Crossref]

Bao, Q.

C. Tan, Z. Yue, Z. Dai, Q. Bao, X. Wang, H. Lu, and L. Wang, “Nanograting-assisted generation of surface plasmon polaritons in Weyl semimetal WTe2,” Opt. Mater. 86, 421–423 (2018).
[Crossref]

Barnes, W. L.

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

Bartal, G.

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref]

Belic, M. R.

Y. Zhang, M. R. Belić, W. Zhong, F. Wen, Y. Guo, Y. Guo, K. Lu, and Y. Zhang, “Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array,” J. Opt. 17(4), 045703 (2015).
[Crossref]

Bernardin, T.

K. Hassan, A. Bouhelier, T. Bernardin, G. Colas-des-Francs, J. C. Weeber, A. Dereux, and R. E. de Lamaestre, “Momentum-space spectroscopy for advanced analysis of dielectric-loaded surface plasmon polariton coupled and bent waveguides,” Phys. Rev. B 87(19), 195428 (2013).
[Crossref]

Bleckmann, F.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5(1), 3843 (2014).
[Crossref]

Bloch, F.

F. Bloch, “Über die quantemechanik der elektronen in kristallgittern,” Z. Phys. 52(7-8), 555–600 (1929).
[Crossref]

Block, A.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5(1), 3843 (2014).
[Crossref]

Boubanga-Tombet, S. A.

T. Otsuji, S. A. Boubanga-Tombet, A. Satou, H. Fukidome, M. Suemitsu, E. Sano, V. Popov, M. Ryzhii, and V. Ryzhii, “Graphene-based devices in terahertz science and technology,” J. Phys. D: Appl. Phys. 45(30), 303001 (2012).
[Crossref]

Bouhelier, A.

K. Hassan, A. Bouhelier, T. Bernardin, G. Colas-des-Francs, J. C. Weeber, A. Dereux, and R. E. de Lamaestre, “Momentum-space spectroscopy for advanced analysis of dielectric-loaded surface plasmon polariton coupled and bent waveguides,” Phys. Rev. B 87(19), 195428 (2013).
[Crossref]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Castin, Y.

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76(24), 4508–4511 (1996).
[Crossref]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[Crossref]

Chan, C. T.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91(24), 243113 (2007).
[Crossref]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[Crossref]

Chen, C. M.

Cheng, B. H.

B. H. Cheng and Y. C. Lan, “Bloch oscillations of surface plasmon-like modes in waveguide arrays that comprise perforated perfect conductor layers and dielectric Layers,” Plasmonics 6(2), 427–433 (2011).
[Crossref]

Cheng, H.

H. Lu, S. Dai, Z. Yue, Y. Fan, H. Cheng, J. Di, D. Mao, E. Li, T. Mei, and J. Zhao, “Sb2Te3 topological insulator: surface plasmon resonance and application in refractive index monitoring,” Nanoscale 11(11), 4759–4766 (2019).
[Crossref]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Colas-des-Francs, G.

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R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

Soergel, E.

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5(1), 3843 (2014).
[Crossref]

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Suemitsu, M.

T. Otsuji, S. A. Boubanga-Tombet, A. Satou, H. Fukidome, M. Suemitsu, E. Sano, V. Popov, M. Ryzhii, and V. Ryzhii, “Graphene-based devices in terahertz science and technology,” J. Phys. D: Appl. Phys. 45(30), 303001 (2012).
[Crossref]

Sukhorukov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94(16), 161105 (2009).
[Crossref]

Sun, C.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Szameit, A.

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
[Crossref]

Tan, C.

C. Tan, Z. Yue, Z. Dai, Q. Bao, X. Wang, H. Lu, and L. Wang, “Nanograting-assisted generation of surface plasmon polaritons in Weyl semimetal WTe2,” Opt. Mater. 86, 421–423 (2018).
[Crossref]

Teng, J.

B. Wang, X. Zhang, F. J. Garcia-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]

Vakil, A.

A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref]

Valusis, G.

V. G. Lyssenko, G. Valusis, F. Löser, T. Hasche, K. Leo, M. M. Dignam, and K. Köhler, “Direct measurement of the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79(2), 301–304 (1997).
[Crossref]

van Exter, M. P.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[Crossref]

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[Crossref]

Vladimirova, M.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92(9), 097401 (2004).
[Crossref]

Wang, B.

Wang, G. P.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91(24), 243113 (2007).
[Crossref]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
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B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29(17), 1992–1994 (2004).
[Crossref]

Wang, K.

Wang, L.

C. Tan, Z. Yue, Z. Dai, Q. Bao, X. Wang, H. Lu, and L. Wang, “Nanograting-assisted generation of surface plasmon polaritons in Weyl semimetal WTe2,” Opt. Mater. 86, 421–423 (2018).
[Crossref]

Wang, Q.

W. Wang, H. Ye, Q. Wang, and W. Lin, “Propagation properties of nanoscale three-dimensional plasmonic waveguide based on hybrid of two fundamental planar optical metal waveguides,” Plasmonics 13(5), 1615–1621 (2018).
[Crossref]

Q. Wang, W. Hu, J. Wei, and W. Lin, “Controlling diffraction of surface plasmon polaritons in nanoscale metal waveguide arrays,” Plasmonics 11(1), 117–124 (2016).
[Crossref]

Wang, W.

W. Wang and W. Lin, “Optical properties of plasmonic components based on nanoscale three-dimensional plasmonic waveguide,” J. Opt. Soc. Am. B 36(8), 2045–2051 (2019).
[Crossref]

W. Wang, H. Ye, Q. Wang, and W. Lin, “Propagation properties of nanoscale three-dimensional plasmonic waveguide based on hybrid of two fundamental planar optical metal waveguides,” Plasmonics 13(5), 1615–1621 (2018).
[Crossref]

Wang, X.

C. Tan, Z. Yue, Z. Dai, Q. Bao, X. Wang, H. Lu, and L. Wang, “Nanograting-assisted generation of surface plasmon polaritons in Weyl semimetal WTe2,” Opt. Mater. 86, 421–423 (2018).
[Crossref]

Weeber, J. C.

K. Hassan, A. Bouhelier, T. Bernardin, G. Colas-des-Francs, J. C. Weeber, A. Dereux, and R. E. de Lamaestre, “Momentum-space spectroscopy for advanced analysis of dielectric-loaded surface plasmon polariton coupled and bent waveguides,” Phys. Rev. B 87(19), 195428 (2013).
[Crossref]

Wei, J.

Q. Wang, W. Hu, J. Wei, and W. Lin, “Controlling diffraction of surface plasmon polaritons in nanoscale metal waveguide arrays,” Plasmonics 11(1), 117–124 (2016).
[Crossref]

Wen, F.

Y. Zhang, M. R. Belić, W. Zhong, F. Wen, Y. Guo, Y. Guo, K. Lu, and Y. Zhang, “Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array,” J. Opt. 17(4), 045703 (2015).
[Crossref]

Wiersma, D.

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91(26), 263902 (2003).
[Crossref]

Woerdman, J. P.

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[Crossref]

Xu, W.

J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D: Appl. Phys. 45(11), 113001 (2012).
[Crossref]

Ye, H.

W. Wang, H. Ye, Q. Wang, and W. Lin, “Propagation properties of nanoscale three-dimensional plasmonic waveguide based on hybrid of two fundamental planar optical metal waveguides,” Plasmonics 13(5), 1615–1621 (2018).
[Crossref]

Yu, Z.

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[Crossref]

Yuan, X.

B. Wang, X. Zhang, F. J. Garcia-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]

Yue, Z.

H. Lu, S. Dai, Z. Yue, Y. Fan, H. Cheng, J. Di, D. Mao, E. Li, T. Mei, and J. Zhao, “Sb2Te3 topological insulator: surface plasmon resonance and application in refractive index monitoring,” Nanoscale 11(11), 4759–4766 (2019).
[Crossref]

C. Tan, Z. Yue, Z. Dai, Q. Bao, X. Wang, H. Lu, and L. Wang, “Nanograting-assisted generation of surface plasmon polaritons in Weyl semimetal WTe2,” Opt. Mater. 86, 421–423 (2018).
[Crossref]

Zamfirescu, M.

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92(9), 097401 (2004).
[Crossref]

Zayats, A. V.

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90(21), 211101 (2007).
[Crossref]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref]

Zhang, J.

J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D: Appl. Phys. 45(11), 113001 (2012).
[Crossref]

Zhang, L.

J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D: Appl. Phys. 45(11), 113001 (2012).
[Crossref]

Zhang, X.

B. Wang, X. Zhang, F. J. Garcia-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]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Zhang, Y.

Y. Zhang, M. R. Belić, W. Zhong, F. Wen, Y. Guo, Y. Guo, K. Lu, and Y. Zhang, “Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array,” J. Opt. 17(4), 045703 (2015).
[Crossref]

Y. Zhang, M. R. Belić, W. Zhong, F. Wen, Y. Guo, Y. Guo, K. Lu, and Y. Zhang, “Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array,” J. Opt. 17(4), 045703 (2015).
[Crossref]

Zhao, H.

Z. Li and H. Zhao, “Electromagnetic Bloch-like oscillations in planar quasiperiodic metal-dielectric waveguide arrays,” Europhys. Lett. 111(5), 56005 (2015).
[Crossref]

Zhao, J.

H. Lu, S. Dai, Z. Yue, Y. Fan, H. Cheng, J. Di, D. Mao, E. Li, T. Mei, and J. Zhao, “Sb2Te3 topological insulator: surface plasmon resonance and application in refractive index monitoring,” Nanoscale 11(11), 4759–4766 (2019).
[Crossref]

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photonics Res. 5(3), 162–167 (2017).
[Crossref]

Zhong, W.

Y. Zhang, M. R. Belić, W. Zhong, F. Wen, Y. Guo, Y. Guo, K. Lu, and Y. Zhang, “Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array,” J. Opt. 17(4), 045703 (2015).
[Crossref]

Zhou, X.

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91(24), 243113 (2007).
[Crossref]

Appl. Phys. Lett. (3)

W. Lin, X. Zhou, G. P. Wang, and C. T. Chan, “Spatial Bloch oscillations of plasmons in nanoscale metal waveguide arrays,” Appl. Phys. Lett. 91(24), 243113 (2007).
[Crossref]

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Plasmonic Bloch oscillations in chirped metal-dielectric structures,” Appl. Phys. Lett. 94(16), 161105 (2009).
[Crossref]

A. V. Krasavin and A. V. Zayats, “Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides,” Appl. Phys. Lett. 90(21), 211101 (2007).
[Crossref]

Europhys. Lett. (1)

Z. Li and H. Zhao, “Electromagnetic Bloch-like oscillations in planar quasiperiodic metal-dielectric waveguide arrays,” Europhys. Lett. 111(5), 56005 (2015).
[Crossref]

J. Opt. (1)

Y. Zhang, M. R. Belić, W. Zhong, F. Wen, Y. Guo, Y. Guo, K. Lu, and Y. Zhang, “Beam splitter and combiner based on Bloch oscillation in a spatially modulated waveguide array,” J. Opt. 17(4), 045703 (2015).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. D: Appl. Phys. (4)

G. N. Aliev and B. Goller, “Hypersonic phononic stopbands at small angles of wave incidence in porous silicon multilayers,” J. Phys. D: Appl. Phys. 48(32), 325501 (2015).
[Crossref]

S. Hayashi and T. Okamoto, “Plasmonics: visit the past to know the future,” J. Phys. D: Appl. Phys. 45(43), 433001 (2012).
[Crossref]

T. Otsuji, S. A. Boubanga-Tombet, A. Satou, H. Fukidome, M. Suemitsu, E. Sano, V. Popov, M. Ryzhii, and V. Ryzhii, “Graphene-based devices in terahertz science and technology,” J. Phys. D: Appl. Phys. 45(30), 303001 (2012).
[Crossref]

J. Zhang, L. Zhang, and W. Xu, “Surface plasmon polaritons: physics and applications,” J. Phys. D: Appl. Phys. 45(11), 113001 (2012).
[Crossref]

Nano Lett. (1)

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[Crossref]

Nanoscale (1)

H. Lu, S. Dai, Z. Yue, Y. Fan, H. Cheng, J. Di, D. Mao, E. Li, T. Mei, and J. Zhao, “Sb2Te3 topological insulator: surface plasmon resonance and application in refractive index monitoring,” Nanoscale 11(11), 4759–4766 (2019).
[Crossref]

Nat. Commun. (2)

M. Lebugle, M. Gräfe, R. Heilmann, A. Perez-Leija, S. Nolte, and A. Szameit, “Experimental observation of N00N state Bloch oscillations,” Nat. Commun. 6(1), 8273 (2015).
[Crossref]

A. Block, C. Etrich, T. Limboeck, F. Bleckmann, E. Soergel, C. Rockstuhl, and S. Linden, “Bloch oscillations in plasmonic waveguide arrays,” Nat. Commun. 5(1), 3843 (2014).
[Crossref]

Nature (2)

E. Altewischer, M. P. van Exter, and J. P. Woerdman, “Plasmon-assisted transmission of entangled photons,” Nature 418(6895), 304–306 (2002).
[Crossref]

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

Opt. Lett. (4)

Opt. Mater. (1)

C. Tan, Z. Yue, Z. Dai, Q. Bao, X. Wang, H. Lu, and L. Wang, “Nanograting-assisted generation of surface plasmon polaritons in Weyl semimetal WTe2,” Opt. Mater. 86, 421–423 (2018).
[Crossref]

Photonics Res. (1)

H. Lu, X. Gan, D. Mao, and J. Zhao, “Graphene-supported manipulation of surface plasmon polaritons in metallic nanowaveguides,” Photonics Res. 5(3), 162–167 (2017).
[Crossref]

Phys. Rev. B (3)

K. Hassan, A. Bouhelier, T. Bernardin, G. Colas-des-Francs, J. C. Weeber, A. Dereux, and R. E. de Lamaestre, “Momentum-space spectroscopy for advanced analysis of dielectric-loaded surface plasmon polariton coupled and bent waveguides,” Phys. Rev. B 87(19), 195428 (2013).
[Crossref]

N. D. L. Kimura, A. Fainstein, and B. Jusserand, “Phonon Bloch oscillations in acoustic-cavity structures,” Phys. Rev. B 71(4), 041305 (2005).
[Crossref]

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[Crossref]

Phys. Rev. Lett. (13)

V. Agarwal, J. A. del Río, G. Malpuech, M. Zamfirescu, A. Kavokin, D. Coquillat, D. Scalbert, M. Vladimirova, and B. Gil, “Photon Bloch oscillations in porous silicon optical superlattices,” Phys. Rev. Lett. 92(9), 097401 (2004).
[Crossref]

M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76(24), 4508–4511 (1996).
[Crossref]

R. Sapienza, P. Costantino, D. Wiersma, M. Ghulinyan, C. J. Oton, and L. Pavesi, “Optical analogue of electronic Bloch oscillations,” Phys. Rev. Lett. 91(26), 263902 (2003).
[Crossref]

T. Pertsch, P. Dannberg, W. Elflein, A. Bräuer, and F. Lederer, “Optical Bloch oscillations in temperature tuned waveguide arrays,” Phys. Rev. Lett. 83(23), 4752–4755 (1999).
[Crossref]

Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Subwavelength discrete solitons in nonlinear metamaterials,” Phys. Rev. Lett. 99(15), 153901 (2007).
[Crossref]

B. Wang, X. Zhang, F. J. Garcia-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]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[Crossref]

L. Verslegers, P. B. Catrysse, Z. Yu, and S. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[Crossref]

V. G. Lyssenko, G. Valusis, F. Löser, T. Hasche, K. Leo, M. M. Dignam, and K. Köhler, “Direct measurement of the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79(2), 301–304 (1997).
[Crossref]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[Crossref]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, “Diffraction management,” Phys. Rev. Lett. 85(9), 1863–1866 (2000).
[Crossref]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, “Self-focusing and defocusing in waveguide arrays,” Phys. Rev. Lett. 86(15), 3296–3299 (2001).
[Crossref]

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88(9), 093901 (2002).
[Crossref]

Plasmonics (3)

B. H. Cheng and Y. C. Lan, “Bloch oscillations of surface plasmon-like modes in waveguide arrays that comprise perforated perfect conductor layers and dielectric Layers,” Plasmonics 6(2), 427–433 (2011).
[Crossref]

W. Wang, H. Ye, Q. Wang, and W. Lin, “Propagation properties of nanoscale three-dimensional plasmonic waveguide based on hybrid of two fundamental planar optical metal waveguides,” Plasmonics 13(5), 1615–1621 (2018).
[Crossref]

Q. Wang, W. Hu, J. Wei, and W. Lin, “Controlling diffraction of surface plasmon polaritons in nanoscale metal waveguide arrays,” Plasmonics 11(1), 117–124 (2016).
[Crossref]

Science (2)

A. Vakil and N. Engheta, “Transformation Optics Using Graphene,” Science 332(6035), 1291–1294 (2011).
[Crossref]

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311(5758), 189–193 (2006).
[Crossref]

Z. Phys. (1)

F. Bloch, “Über die quantemechanik der elektronen in kristallgittern,” Z. Phys. 52(7-8), 555–600 (1929).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. (a) Top view of the TDPW based TDSPPWGAs in the xy plane. (b) The cross section of the waveguide arrays along the dashed line in (a).
Fig. 2.
Fig. 2. The field distributions in the TDPW-based TDSPPWGAs with D of (a) 40 nm, (b) 60 nm, (c) 80 nm, (d)100 nm, (e) 120 nm, and (f) 140 nm, respectively. (g) The coupling coefficient depends on the edge-to-edge distance.
Fig. 3.
Fig. 3. (a) The cross section of 41 guides hetero-TDSPPWGAs with refractive index of dielectric layer linearly varying from the −20th-guide to the 20th-guide by a step of Δn. (b) The Cm,m+1 and βm of the hetero-TDSPPWGAs as the refractive index of the dielectric in guide(−20) is 1.5 and Δn is 0.05 at wavelength of 1550 nm.
Fig. 4.
Fig. 4. Theoretical predicted BOs effect of different wavelength. (a)-(e) single waveguide exciting mode. (f)-(j) multiple waveguides exciting mode.
Fig. 5.
Fig. 5. FDTD simulation single waveguide exciting BOs effect (breathing mode)
Fig. 6.
Fig. 6. (a)-(e) FDTD simulated multiple waveguide exciting BOs effect (transverse Oscillatory mode). (f) Dependence of the theoretic and simulated PBO on the wavelengths of incident light.
Fig. 7.
Fig. 7. (a)-(d) The cross section of 41 guides hetero-TDSPPWGAs with no metal strips shift, shift to right side, shift to left side, and shift to center, respectively. (e)-(g) FDTD simulated results for fabrication tolerance of metal strips shift corresponding to (b)-(d), respectively.

Equations (6)

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

a m ( x ) = ( i ) m exp ( i β x ) J m ( 2 C x ) ,
i d a m ( x ) d x + β a m ( x ) + C [ a m 1 ( x ) + a m + 1 ( x ) ] = 0 ,
d a m ( x ) d x = i C m 1 , m a m 1 ( x ) + i β m a m ( x ) + i C m , m + 1 a m + 1 ( x ) .
M = i ( β 20 C 20 , 19 C 20 , 19 β 19 C 19 , 18 C 1 , 0 β 0 C 0 , 1 C 18 , 19 β 19 C 19 , 20 C 19 , 20 β 20 ) .
a m ( x ) = j = 20 20 η j e χ j x Q j ( m ) ,
P BO = 2 π Δ β = λ 0 Δ n e f f .

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