Abstract

We study the propagation of surface plasmon polaritons (SPPs) in nanoscale metal heterowaveguide superlattices and metal waveguide arrays (MWGAs), both realized by gradually increasing the width of guiding regions. Theoretical analysis of the transmission properties of SPPs passing through the metal heterowaveguide superlattices by the transfer matrix method reveals that the SPPs minibands and minigaps in the frequency domain exhibit a spatial tilting, implying the appearance of plasmonic Wannier–Stark ladders and the existence of time-resolved plasmonic Bloch oscillations (BOs) in the superlattices. The analytic results of the coupled wave theory show that SPPs periodically oscillate transversely in the MWGAs under conditions of multiple waveguide excitation as the behavior of spatial BOs. Numerical simulations of the dynamic evolution of SPPs in the superlattices and MWGAs by the finite-difference time-domain method demonstrate the analytical predications well.

© 2009 Optical Society of America

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2009 (2)

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79, 013820 (2009).
[CrossRef]

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

2008 (1)

W. Lin, Y. Gu, and G. P. Wang, “Zener tunneling in plasmonic metal gap waveguide supplattices,” Appl. Phys. Lett. 93, 133118 (2008).
[CrossRef]

2007 (3)

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

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, 243113 (2007).
[CrossRef]

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007), and references therein.
[CrossRef]

2006 (5)

E. Ozbay, “Plasmonics: merging photonics and electronics nanoscale dimensions,” Science 311, 189-193 (2006), and references therein.
[CrossRef] [PubMed]

X. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as Plasmon lenses,” Opt. Lett. 31, 1322-1324 (2006).
[CrossRef] [PubMed]

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, 073901 (2006).
[CrossRef] [PubMed]

G. P. Wang and B. Wang, “Metal heterostructure-based nanophotonic devices: finite-difference time-domain numerical simulations,” J. Opt. Soc. Am. B 23, 1660-1665 (2006).
[CrossRef]

A. Hosseini and Y. Massoud, “A low-loss metal-insulator-metal plasmonic bragg reflector,” Opt. Express 14, 11318-11323 (2006).
[CrossRef]

2005 (2)

B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

X. Wang and K. Kempa, “Negative refraction and subwavelength lensing in a polaritonic crystal,” Phys. Rev. B 71, 233101 (2005).
[CrossRef]

2004 (2)

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

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

2003 (2)

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

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003), and references therein.
[CrossRef] [PubMed]

2002 (1)

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

2001 (1)

G. Malpuech, A. Kavokin, G. Panzarini, and A. D. Carlo, “Theory of photon Bloch oscillations in photonic crystals,” Phys. Rev. B 63, 035108 (2001).
[CrossRef]

2000 (1)

A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000).
[CrossRef]

1999 (3)

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, “Bloch oscillations in an array of curved optical waveguides,” Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

1998 (2)

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701-1703 (1998).
[CrossRef]

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, “Observation of an optical Wannier-Stark ladder,” Phys. Rev. E 57, 2365-2369 (1998).
[CrossRef]

1997 (2)

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671-673 (1997).
[CrossRef]

1992 (1)

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

1991 (1)

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagenic field equation,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

1974 (1)

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

1928 (1)

F. Bloch, “Uber die quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555-600 (1928).

Aitchison, J. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Altewischer, E.

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

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003), and references therein.
[CrossRef] [PubMed]

Bartolini, P.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671-673 (1997).
[CrossRef]

Bloch, F.

F. Bloch, “Uber die quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555-600 (1928).

Brauer, A.

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

Bright, J. N.

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, “Observation of an optical Wannier-Stark ladder,” Phys. Rev. E 57, 2365-2369 (1998).
[CrossRef]

Brophy, L. A. W.

Carlo, A. D.

G. Malpuech, A. Kavokin, G. Panzarini, and A. D. Carlo, “Theory of photon Bloch oscillations in photonic crystals,” Phys. Rev. B 63, 035108 (2001).
[CrossRef]

A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000).
[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, 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, 073901 (2006).
[CrossRef] [PubMed]

Costantino, P.

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

Cunningham, J. E.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Dannberg, P.

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

Davoyan, A. R.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79, 013820 (2009).
[CrossRef]

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

de Sterke, C. M.

G. Lenz, I. Talanina, and C. M. de Sterke, “Bloch oscillations in an array of curved optical waveguides,” Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, “Observation of an optical Wannier-Stark ladder,” Phys. Rev. E 57, 2365-2369 (1998).
[CrossRef]

C. M. de Sterke, J. E. Sipe, and L. A. W. Brophy, “Electromagnetic Stark ladders in waveguide geometries,” Opt. Lett. 16, 1141-1143 (1991).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003), and references therein.
[CrossRef] [PubMed]

Dignam, M. M.

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003), and references therein.
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Elflein, W.

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

Fan, X.

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, 073901 (2006).
[CrossRef] [PubMed]

X. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as Plasmon lenses,” Opt. Lett. 31, 1322-1324 (2006).
[CrossRef] [PubMed]

Fang, N.

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

Feldmann, J.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Ghulinyan, M.

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

Gu, Y.

W. Lin, Y. Gu, and G. P. Wang, “Zener tunneling in plasmonic metal gap waveguide supplattices,” Appl. Phys. Lett. 93, 133118 (2008).
[CrossRef]

Hammon, T. E.

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, “Observation of an optical Wannier-Stark ladder,” Phys. Rev. E 57, 2365-2369 (1998).
[CrossRef]

Hasche, T.

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

Hosseini, A.

Joannopoulos, J. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Kaminow, I. P.

Kavokin, A.

G. Malpuech, A. Kavokin, G. Panzarini, and A. D. Carlo, “Theory of photon Bloch oscillations in photonic crystals,” Phys. Rev. B 63, 035108 (2001).
[CrossRef]

A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000).
[CrossRef]

Kempa, K.

X. Wang and K. Kempa, “Negative refraction and subwavelength lensing in a polaritonic crystal,” Phys. Rev. B 71, 233101 (2005).
[CrossRef]

Kivshar, Yu. S.

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

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79, 013820 (2009).
[CrossRef]

Kohler, K.

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

Krug, P. A.

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, “Observation of an optical Wannier-Stark ladder,” Phys. Rev. E 57, 2365-2369 (1998).
[CrossRef]

Lagendijk, A.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671-673 (1997).
[CrossRef]

Lederer, F.

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

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701-1703 (1998).
[CrossRef]

Lee, J. C. W.

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, 073901 (2006).
[CrossRef] [PubMed]

Lenz, G.

G. Lenz, I. Talanina, and C. M. de Sterke, “Bloch oscillations in an array of curved optical waveguides,” Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

Leo, K.

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Lin, W.

W. Lin, Y. Gu, and G. P. Wang, “Zener tunneling in plasmonic metal gap waveguide supplattices,” Appl. Phys. Lett. 93, 133118 (2008).
[CrossRef]

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, 243113 (2007).
[CrossRef]

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

Loser, F.

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

Lugli, P.

A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000).
[CrossRef]

Luo, Q.

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

Lyssenko, V. G.

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

Malpuech, G.

G. Malpuech, A. Kavokin, G. Panzarini, and A. D. Carlo, “Theory of photon Bloch oscillations in photonic crystals,” Phys. Rev. B 63, 035108 (2001).
[CrossRef]

A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000).
[CrossRef]

Mammel, W. L.

Massoud, Y.

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Meier, T.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Miller, D. A. B.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Morandotti, R.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagenic field equation,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

Oton, C. J.

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

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics nanoscale dimensions,” Science 311, 189-193 (2006), and references therein.
[CrossRef] [PubMed]

Panzarini, G.

G. Malpuech, A. Kavokin, G. Panzarini, and A. D. Carlo, “Theory of photon Bloch oscillations in photonic crystals,” Phys. Rev. B 63, 035108 (2001).
[CrossRef]

Pavesi, L.

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

Pertsch, T.

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

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701-1703 (1998).
[CrossRef]

Peschel, U.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

U. Peschel, T. Pertsch, and F. Lederer, “Optical Bloch oscillations in waveguide arrays,” Opt. Lett. 23, 1701-1703 (1998).
[CrossRef]

Plessen, G. V.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, 1988), Chap. 2, p. 6.

Righini, R.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671-673 (1997).
[CrossRef]

Rossi, F.

A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000).
[CrossRef]

Sapienza, R.

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

Schmitt-Rink, S.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Schulze, A.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Shadrivov, I. V.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79, 013820 (2009).
[CrossRef]

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

Shah, J.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007), and references therein.
[CrossRef]

Silberberg, Y.

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[CrossRef]

Sipe, J. E.

Srituravanich, W.

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

Sukhorukov, A. A.

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79, 013820 (2009).
[CrossRef]

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

Sun, C.

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

Talanina, I.

G. Lenz, I. Talanina, and C. M. de Sterke, “Bloch oscillations in an array of curved optical waveguides,” Phys. Rev. Lett. 83, 963-966 (1999).
[CrossRef]

Thomas, P.

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

Tian, T.

F. Y. Ye, T. Tian, and X. Q. Yang, Higher Mathematics, 2nd ed. (Higher Education Press, 1990), Chap. 11, p. 284.

Valusis, G.

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 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, 304-306 (2002).
[CrossRef] [PubMed]

Wang, B.

Wang, G. P.

W. Lin, Y. Gu, and G. P. Wang, “Zener tunneling in plasmonic metal gap waveguide supplattices,” Appl. Phys. Lett. 93, 133118 (2008).
[CrossRef]

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, 243113 (2007).
[CrossRef]

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (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, 073901 (2006).
[CrossRef] [PubMed]

X. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as Plasmon lenses,” Opt. Lett. 31, 1322-1324 (2006).
[CrossRef] [PubMed]

G. P. Wang and B. Wang, “Metal heterostructure-based nanophotonic devices: finite-difference time-domain numerical simulations,” J. Opt. Soc. Am. B 23, 1660-1665 (2006).
[CrossRef]

B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

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

Wang, X.

X. Wang and K. Kempa, “Negative refraction and subwavelength lensing in a polaritonic crystal,” Phys. Rev. B 71, 233101 (2005).
[CrossRef]

Weber, H. P.

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, 263902 (2003).
[CrossRef]

Wiersma, D. S.

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671-673 (1997).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

Woerdman, J. P.

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

Yang, X. Q.

F. Y. Ye, T. Tian, and X. Q. Yang, Higher Mathematics, 2nd ed. (Higher Education Press, 1990), Chap. 11, p. 284.

Ye, F. Y.

F. Y. Ye, T. Tian, and X. Q. Yang, Higher Mathematics, 2nd ed. (Higher Education Press, 1990), Chap. 11, p. 284.

Zhang, X.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4, 1085-1088 (2004).
[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, 243113 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

B. Wang and G. P. Wang, “Plasmon Bragg reflectors and nanocavities on flat metallic surfaces,” Appl. Phys. Lett. 87, 013107 (2005).
[CrossRef]

W. Lin and G. P. Wang, “Metal heterowaveguide superlattices for a plasmonic analog to electronic Bloch oscillations,” Appl. Phys. Lett. 91, 143121 (2007).
[CrossRef]

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, 243113 (2007).
[CrossRef]

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

W. Lin, Y. Gu, and G. P. Wang, “Zener tunneling in plasmonic metal gap waveguide supplattices,” Appl. Phys. Lett. 93, 133118 (2008).
[CrossRef]

IEEE Trans. Electromagn. Compat. (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagenic field equation,” IEEE Trans. Electromagn. Compat. 23, 377-382 (1981).
[CrossRef]

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

Nano Lett. (1)

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

Nat. Photonics (1)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41-48 (2007), and references therein.
[CrossRef]

Nature (3)

D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671-673 (1997).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003), and references therein.
[CrossRef] [PubMed]

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

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. A (1)

A. R. Davoyan, I. V. Shadrivov, A. A. Sukhorukov, and Yu. S. Kivshar, “Beam oscillations and curling in chirped periodic structures with metamaterials,” Phys. Rev. A 79, 013820 (2009).
[CrossRef]

Phys. Rev. B (4)

A. Kavokin, G. Malpuech, A. D. Carlo, P. Lugli, and F. Rossi, “Photonic Bloch oscillations in laterally confined Bragg mirrors,” Phys. Rev. B 61, 4413-4416 (2000).
[CrossRef]

G. Malpuech, A. Kavokin, G. Panzarini, and A. D. Carlo, “Theory of photon Bloch oscillations in photonic crystals,” Phys. Rev. B 63, 035108 (2001).
[CrossRef]

J. Feldmann, K. Leo, J. Shah, D. A. B. Miller, J. E. Cunningham, T. Meier, G. V. Plessen, A. Schulze, P. Thomas, and S. Schmitt-Rink, “Optical investigation of Bloch oscillations in a semiconductor superlattice,” Phys. Rev. B 46, 7252-7255 (1992).
[CrossRef]

X. Wang and K. Kempa, “Negative refraction and subwavelength lensing in a polaritonic crystal,” Phys. Rev. B 71, 233101 (2005).
[CrossRef]

Phys. Rev. E (1)

C. M. de Sterke, J. N. Bright, P. A. Krug, and T. E. Hammon, “Observation of an optical Wannier-Stark ladder,” Phys. Rev. E 57, 2365-2369 (1998).
[CrossRef]

Phys. Rev. Lett. (6)

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

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Experimental observation of linear and nonlinear optical Bloch oscillations,” Phys. Rev. Lett. 83, 4756-4759 (1999).
[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, 263902 (2003).
[CrossRef]

V. G. Lyssenko, G. Valusis, F. Loser, T. Hasche, K. Leo, M. M. Dignam, and K. Kohler, “Direct measurement of the spatial displacement of bloch-oscillating electrons in semiconductor superlattices,” Phys. Rev. Lett. 79, 301-304 (1997).
[CrossRef]

G. Lenz, I. Talanina, and C. M. de Sterke, “Bloch oscillations in an array of curved optical waveguides,” Phys. Rev. Lett. 83, 963-966 (1999).
[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, 073901 (2006).
[CrossRef] [PubMed]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics nanoscale dimensions,” Science 311, 189-193 (2006), and references therein.
[CrossRef] [PubMed]

Z. Phys. (1)

F. Bloch, “Uber die quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555-600 (1928).

Other (4)

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic crystals: Molding the Flow of Light, 2nd ed. (Princeton Univ., 2008).

H. Raether, Surface Plasmons (Springer-Verlag, 1988), Chap. 2, p. 6.

E.D.Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985), Part 2, Chap. 1, p. 356.

F. Y. Ye, T. Tian, and X. Q. Yang, Higher Mathematics, 2nd ed. (Higher Education Press, 1990), Chap. 11, p. 284.

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Figures (5)

Fig. 1
Fig. 1

Scheme of (a) SPP coupled microcavities and (b) metal heterowavedguide superlattices realized by gradually increasing the gap width of ECCs. (c) Plasmonic band structure of metal heterowaveguide superlattices with g = 14.27 % . White areas represent the allowed minibands, and black area represent minigaps. (d) Transmission spectrum of SPPs passing through the superlattices. (e) Scattering states maps of SPPs inside the superlattices. In (c), (d) and (e), the area between the two dotted–dashed lines indicates the Wannier–Stark ladders region.

Fig. 2
Fig. 2

Dynamic evolutions of SPP field ( | H y | 2 ) with time in the metal heterowaveguide superlattices as a time-domain Gaussian pulse is incident into the superlattices ( g = 14.27 % ) .

Fig. 3
Fig. 3

(a) Scheme of MWGAs composed of 71 pieces of waveguides with 15 nm thick Ag film and fixed dielectric ( Si O 2 ) in guide region. The Arrow direction indicates the decrease of propagation constants of SPPs. Inset, guide width of each guide. (b) Coupling coefficients (dashed curve) and propagation constants (solid curve) of SPPs in the MWGAs for the incident light with λ = 532 nm .

Fig. 4
Fig. 4

(a) Theoretical analysed and (b) FDTD-simulated | H y | 2 distribution of SPPs in the MWGAs by multiple guides excitation with incident light at λ = 532 nm . (c) Phase wavefront of SPPs in the MWGAs.

Fig. 5
Fig. 5

(a) FDTD-simulated | H y | 2 distribution of SPPs in the MWGAs by multiple guides excitation with incident light at λ = 650 nm . (b) Dependence of FDTD-simulated BO periods of SPPs on the wavelengths of incident light ( λ = 532 , 546 , 578 , 600 , 633 , 650 nm ) .

Equations (4)

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

d a m ( z ) d z = i C m 1 , m a m 1 ( z ) + i β m a m ( z ) + i C m , m + 1 a m + 1 ( z ) ,
a m ( z ) = j = 1 M η j e χ j z Q j ( m ) ,
a m ( 0 ) = exp [ ( m 15 ) 2 ( 10 ) 2 ] ( m = 6 , 7 , 25 ) ,
a m ( 0 ) = 0 ( m < 6 , m > 25 ) .

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