Abstract

In this work we study surface plasmon polariton (SPP) wave-packet dynamics in a new class of plasmonic crystals—plasmonic crystals with monotonically varying-in-space geometrical or optical parameters. Using both a semianalytical approach based on the WKB equations for the SPP dynamics and rigorous electromagnetic modeling [based on the finite-difference time-domain (FDTD) method], we have demonstrated that, by changing the SPP pulse central frequency and spectral bandwidth, it is possible to switch among different important scenarios of the SPP motion: SPP wave-packet acceleration, deceleration, and tunneling to the adjacent plasmonic band. These SPP motion regimes are unique for the considered class of the plasmonic crystals. In addition to that, pronounced broadening of the reflected pulses and significant outburst of absorption in the “slow SPP” region are shown. Aforementioned effects and the fact that they can be easily tuned by variation of the pulse parameters hold a great promise for applications in plasmonic devices.

© 2011 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2010 (6)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef] [PubMed]

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Controllable optical Bloch oscillation in planar graded optical waveguide arrays,” Phys. Rev. A 81, 033829 (2010).
[CrossRef]

M. Levy and P. Kumar, “Nonreciprocal Bloch oscillations in magneto-optic waveguide arrays,” Opt. Lett. 35, 3147–3149(2010).
[CrossRef] [PubMed]

W. Lin and L. Chen, “Plasmonic Bloch oscillations in metal heterowaveguide superlattices and metal waveguide arrays with graded width of guiding regions,” J. Opt. Soc. Am. B 27, 112–117(2010).
[CrossRef]

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, and A. K. Zvezdin, “On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures,” J. Phys. Condens. Matter 22, 395301 (2010).
[CrossRef]

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: the scattering-matrix method,” J. Exp. Theor. Phys. 110, 816–824 (2010).
[CrossRef]

2009 (5)

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Tunable localization and oscillation of coupled plasmon waves in graded plasmonic chains,” J. Appl. Phys. 106, 113307 (2009).
[CrossRef]

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Z. L. Sámson, K. F. MacDonald, and N. I. Zheludev, “Femtosecond active plasmonics: ultrafast control of surface plasmon propagation,” J. Opt. A 11, 114031 (2009).
[CrossRef]

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

2008 (4)

E. Verhagen, A. Polman, and L. K. Kuipers, “Nanofocusing in laterally tapered plasmonic waveguides,” Opt. Express 16, 45–57 (2008).
[CrossRef] [PubMed]

S. E. Yalcin, Y. Wang, and M. Achermann, “Spectral bandwidth and phase effects of resonantly excited ultrafast surface plasmon pulses,” Appl. Phys. Lett. 93, 101103 (2008).
[CrossRef]

Hohenau, A. Drezet, M. Weissenbacher, F. R. Aussenegg, and J. R. Krenn, “Effects of damping on surface-plasmon pulse propagation and refraction,” Phys. Rev. B 78, 155405 (2008).
[CrossRef]

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford, 2008).
[CrossRef]

2007 (7)

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, 2007).

K. Kneipp, “Surface-enhanced Raman scattering,” Phys. Today 60 (11), 40–46 (2007).
[CrossRef]

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer-Verlag, 2007).
[CrossRef]

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[CrossRef] [PubMed]

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sánchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

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

A. Kubo, Y. S. Jung, H. K. Kim, and H. Petek, “Femtosecond microscopy of localized and propagating surface plasmons in silver gratings,” J. Phys. B 40, S259–S272 (2007).
[CrossRef]

2006 (3)

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

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

2005 (1)

R. Rokitski, K. A. Tetz, and Y. Fainman, “Propagation of femtosecond surface plasmon polariton pulses on the surface of a nanostructured metallic film: space-time complex amplitude characterization,” Phys. Rev. Lett. 95, 177401 (2005).
[CrossRef] [PubMed]

2004 (4)

A. Dechant and A. Y. Elezzabi, “Femtosecond optical pulse propagation in subwavelength metallic slits,” Appl. Phys. Lett. 84, 4678–4680 (2004).
[CrossRef]

J. Sanchez-Gil and A. Maradudin, “Dynamic near-field calculations of surface-plasmon polariton pulses resonantly scattered at sub-micron metal defects,” Opt. Express 12, 883–894(2004).
[CrossRef] [PubMed]

V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

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

2003 (1)

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]

2002 (1)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

2001 (1)

S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Surface plasmon polariton propagation along a 90° bent line defect in a periodically corrugated metal surface,” Opt. Commun. 196, 41–45 (2001).
[CrossRef]

1999 (1)

G. Sundaram and Q. Niu, “Wave-packet dynamics in slowly perturbed crystals: gradient corrections and Berry-phase effects,” Phys. Rev. B 59, 14915–14925 (1999).
[CrossRef]

1995 (1)

1992 (1)

V. P. Tarakanov, User’s Manual for Code KARAT (Berkeley Research Associates, 1992).

1991 (1)

E. Yablonovitch and K. M. Leung, “Hope for photonic bandgaps,” Nature 351, 278 (1991).
[CrossRef]

1984 (1)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. A 392, 45–57 (1984).
[CrossRef]

1972 (1)

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

1957 (1)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[CrossRef]

1934 (1)

C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. A 145, 523–529 (1934).
[CrossRef]

1929 (1)

F. Bloch, “Über die quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555–600 (1929).
[CrossRef]

Achermann, M.

S. E. Yalcin, Y. Wang, and M. Achermann, “Spectral bandwidth and phase effects of resonantly excited ultrafast surface plasmon pulses,” Appl. Phys. Lett. 93, 101103 (2008).
[CrossRef]

Agarwal, V.

V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef] [PubMed]

Aussenegg, F. R.

Hohenau, A. Drezet, M. Weissenbacher, F. R. Aussenegg, and J. R. Krenn, “Effects of damping on surface-plasmon pulse propagation and refraction,” Phys. Rev. B 78, 155405 (2008).
[CrossRef]

Bartoli, F. J.

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Belotelov, V. I.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, and A. K. Zvezdin, “On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures,” J. Phys. Condens. Matter 22, 395301 (2010).
[CrossRef]

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: the scattering-matrix method,” J. Exp. Theor. Phys. 110, 816–824 (2010).
[CrossRef]

Berry, M. V.

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. A 392, 45–57 (1984).
[CrossRef]

Bloch, F.

F. Bloch, “Über die quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555–600 (1929).
[CrossRef]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford, 2008).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Surface plasmon polariton propagation along a 90° bent line defect in a periodically corrugated metal surface,” Opt. Commun. 196, 41–45 (2001).
[CrossRef]

Brongersma, M. L.

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer-Verlag, 2007).
[CrossRef]

Bykov, D. A.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: the scattering-matrix method,” J. Exp. Theor. Phys. 110, 816–824 (2010).
[CrossRef]

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, and A. K. Zvezdin, “On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures,” J. Phys. Condens. Matter 22, 395301 (2010).
[CrossRef]

Chen, L.

W. Lin and L. Chen, “Plasmonic Bloch oscillations in metal heterowaveguide superlattices and metal waveguide arrays with graded width of guiding regions,” J. Opt. Soc. Am. B 27, 112–117(2010).
[CrossRef]

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Christy, R. W.

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

Coquillat, D.

V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[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]

Davoyan, A. R.

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

Dechant, A.

A. Dechant and A. Y. Elezzabi, “Femtosecond optical pulse propagation in subwavelength metallic slits,” Appl. Phys. Lett. 84, 4678–4680 (2004).
[CrossRef]

del Rio, J. A.

V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

Desyatnikov, A. S.

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

Doskolovich, L. L.

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, and A. K. Zvezdin, “On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures,” J. Phys. Condens. Matter 22, 395301 (2010).
[CrossRef]

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: the scattering-matrix method,” J. Exp. Theor. Phys. 110, 816–824 (2010).
[CrossRef]

Drezet, A.

Hohenau, A. Drezet, M. Weissenbacher, F. R. Aussenegg, and J. R. Krenn, “Effects of damping on surface-plasmon pulse propagation and refraction,” Phys. Rev. B 78, 155405 (2008).
[CrossRef]

Elezzabi, A. Y.

A. Dechant and A. Y. Elezzabi, “Femtosecond optical pulse propagation in subwavelength metallic slits,” Appl. Phys. Lett. 84, 4678–4680 (2004).
[CrossRef]

Fainman, Y.

R. Rokitski, K. A. Tetz, and Y. Fainman, “Propagation of femtosecond surface plasmon polariton pulses on the surface of a nanostructured metallic film: space-time complex amplitude characterization,” Phys. Rev. Lett. 95, 177401 (2005).
[CrossRef] [PubMed]

Gan, Q.

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[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]

Gil, B.

V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

Gippius, N. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Hohenau,

Hohenau, A. Drezet, M. Weissenbacher, F. R. Aussenegg, and J. R. Krenn, “Effects of damping on surface-plasmon pulse propagation and refraction,” Phys. Rev. B 78, 155405 (2008).
[CrossRef]

Ishihara, T.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

Johnson, P. B.

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[CrossRef]

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V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: the scattering-matrix method,” J. Exp. Theor. Phys. 110, 816–824 (2010).
[CrossRef]

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V. Agarwal, J. A. del Rio, 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, 097401 (2004).
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A. Kubo, Y. S. Jung, H. K. Kim, and H. Petek, “Femtosecond microscopy of localized and propagating surface plasmons in silver gratings,” J. Phys. B 40, S259–S272 (2007).
[CrossRef]

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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, 161105 (2009).
[CrossRef]

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

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
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H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sánchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

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Hohenau, A. Drezet, M. Weissenbacher, F. R. Aussenegg, and J. R. Krenn, “Effects of damping on surface-plasmon pulse propagation and refraction,” Phys. Rev. B 78, 155405 (2008).
[CrossRef]

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H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

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A. Kubo, Y. S. Jung, H. K. Kim, and H. Petek, “Femtosecond microscopy of localized and propagating surface plasmons in silver gratings,” J. Phys. B 40, S259–S272 (2007).
[CrossRef]

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[CrossRef] [PubMed]

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Kumar, P.

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H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

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S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Surface plasmon polariton propagation along a 90° bent line defect in a periodically corrugated metal surface,” Opt. Commun. 196, 41–45 (2001).
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Z. L. Sámson, K. F. MacDonald, and N. I. Zheludev, “Femtosecond active plasmonics: ultrafast control of surface plasmon propagation,” J. Opt. A 11, 114031 (2009).
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V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

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Muljarov, E. A.

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

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H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
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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]

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

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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]

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H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

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H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

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A. Kubo, Y. S. Jung, H. K. Kim, and H. Petek, “Femtosecond microscopy of localized and propagating surface plasmons in silver gratings,” J. Phys. B 40, S259–S272 (2007).
[CrossRef]

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[CrossRef] [PubMed]

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G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

Polman, A.

Pontius, N.

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[CrossRef] [PubMed]

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Reinisch, R.

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R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[CrossRef]

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R. Rokitski, K. A. Tetz, and Y. Fainman, “Propagation of femtosecond surface plasmon polariton pulses on the surface of a nanostructured metallic film: space-time complex amplitude characterization,” Phys. Rev. Lett. 95, 177401 (2005).
[CrossRef] [PubMed]

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Z. L. Sámson, K. F. MacDonald, and N. I. Zheludev, “Femtosecond active plasmonics: ultrafast control of surface plasmon propagation,” J. Opt. A 11, 114031 (2009).
[CrossRef]

Sánchez-Dehesa, J.

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sánchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

Sanchez-Gil, J.

Sanchis-Alepuz, H.

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sánchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

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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]

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V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

Shadrivov, I. V.

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

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

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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, 161105 (2009).
[CrossRef]

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

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

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G. Sundaram and Q. Niu, “Wave-packet dynamics in slowly perturbed crystals: gradient corrections and Berry-phase effects,” Phys. Rev. B 59, 14915–14925 (1999).
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V. P. Tarakanov, User’s Manual for Code KARAT (Berkeley Research Associates, 1992).

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R. Rokitski, K. A. Tetz, and Y. Fainman, “Propagation of femtosecond surface plasmon polariton pulses on the surface of a nanostructured metallic film: space-time complex amplitude characterization,” Phys. Rev. Lett. 95, 177401 (2005).
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S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

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H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
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Vladimirova, M.

V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

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S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Surface plasmon polariton propagation along a 90° bent line defect in a periodically corrugated metal surface,” Opt. Commun. 196, 41–45 (2001).
[CrossRef]

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L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[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]

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S. E. Yalcin, Y. Wang, and M. Achermann, “Spectral bandwidth and phase effects of resonantly excited ultrafast surface plasmon pulses,” Appl. Phys. Lett. 93, 101103 (2008).
[CrossRef]

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Hohenau, A. Drezet, M. Weissenbacher, F. R. Aussenegg, and J. R. Krenn, “Effects of damping on surface-plasmon pulse propagation and refraction,” Phys. Rev. B 78, 155405 (2008).
[CrossRef]

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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]

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G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

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M. J. Zheng, J. J. Xiao, and K. W. Yu, “Controllable optical Bloch oscillation in planar graded optical waveguide arrays,” Phys. Rev. A 81, 033829 (2010).
[CrossRef]

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Tunable localization and oscillation of coupled plasmon waves in graded plasmonic chains,” J. Appl. Phys. 106, 113307 (2009).
[CrossRef]

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E. Yablonovitch and K. M. Leung, “Hope for photonic bandgaps,” Nature 351, 278 (1991).
[CrossRef]

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S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
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S. E. Yalcin, Y. Wang, and M. Achermann, “Spectral bandwidth and phase effects of resonantly excited ultrafast surface plasmon pulses,” Appl. Phys. Lett. 93, 101103 (2008).
[CrossRef]

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M. J. Zheng, J. J. Xiao, and K. W. Yu, “Controllable optical Bloch oscillation in planar graded optical waveguide arrays,” Phys. Rev. A 81, 033829 (2010).
[CrossRef]

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Tunable localization and oscillation of coupled plasmon waves in graded plasmonic chains,” J. Appl. Phys. 106, 113307 (2009).
[CrossRef]

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V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

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G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

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C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. A 145, 523–529 (1934).
[CrossRef]

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Z. L. Sámson, K. F. MacDonald, and N. I. Zheludev, “Femtosecond active plasmonics: ultrafast control of surface plasmon propagation,” J. Opt. A 11, 114031 (2009).
[CrossRef]

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M. J. Zheng, J. J. Xiao, and K. W. Yu, “Controllable optical Bloch oscillation in planar graded optical waveguide arrays,” Phys. Rev. A 81, 033829 (2010).
[CrossRef]

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Tunable localization and oscillation of coupled plasmon waves in graded plasmonic chains,” J. Appl. Phys. 106, 113307 (2009).
[CrossRef]

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V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: the scattering-matrix method,” J. Exp. Theor. Phys. 110, 816–824 (2010).
[CrossRef]

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, and A. K. Zvezdin, “On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures,” J. Phys. Condens. Matter 22, 395301 (2010).
[CrossRef]

Appl. Phys. Lett. (4)

S. E. Yalcin, Y. Wang, and M. Achermann, “Spectral bandwidth and phase effects of resonantly excited ultrafast surface plasmon pulses,” Appl. Phys. Lett. 93, 101103 (2008).
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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, 161105 (2009).
[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]

J. Appl. Phys. (1)

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Tunable localization and oscillation of coupled plasmon waves in graded plasmonic chains,” J. Appl. Phys. 106, 113307 (2009).
[CrossRef]

J. Exp. Theor. Phys. (1)

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, A. N. Kalish, and A. K. Zvezdin, “Giant transversal Kerr effect in magneto-plasmonic heterostructures: the scattering-matrix method,” J. Exp. Theor. Phys. 110, 816–824 (2010).
[CrossRef]

J. Opt. A (1)

Z. L. Sámson, K. F. MacDonald, and N. I. Zheludev, “Femtosecond active plasmonics: ultrafast control of surface plasmon propagation,” J. Opt. A 11, 114031 (2009).
[CrossRef]

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

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

J. Phys. B (1)

A. Kubo, Y. S. Jung, H. K. Kim, and H. Petek, “Femtosecond microscopy of localized and propagating surface plasmons in silver gratings,” J. Phys. B 40, S259–S272 (2007).
[CrossRef]

J. Phys. Condens. Matter (1)

V. I. Belotelov, D. A. Bykov, L. L. Doskolovich, and A. K. Zvezdin, “On surface plasmon polariton wavepacket dynamics in metal–dielectric heterostructures,” J. Phys. Condens. Matter 22, 395301 (2010).
[CrossRef]

Nano Lett. (1)

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[CrossRef] [PubMed]

Nat. Mater. (1)

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010).
[CrossRef] [PubMed]

Nature (1)

E. Yablonovitch and K. M. Leung, “Hope for photonic bandgaps,” Nature 351, 278 (1991).
[CrossRef]

Opt. Commun. (1)

S. I. Bozhevolnyi, V. S. Volkov, and K. Leosson, “Surface plasmon polariton propagation along a 90° bent line defect in a periodically corrugated metal surface,” Opt. Commun. 196, 41–45 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. (1)

R. H. Ritchie, “Plasma losses by fast electrons in thin films,” Phys. Rev. 106, 874–881 (1957).
[CrossRef]

Phys. Rev. A (2)

M. J. Zheng, J. J. Xiao, and K. W. Yu, “Controllable optical Bloch oscillation in planar graded optical waveguide arrays,” Phys. Rev. A 81, 033829 (2010).
[CrossRef]

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

Phys. Rev. B (5)

G. Sundaram and Q. Niu, “Wave-packet dynamics in slowly perturbed crystals: gradient corrections and Berry-phase effects,” Phys. Rev. B 59, 14915–14925 (1999).
[CrossRef]

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[CrossRef]

L. Chen, G. P. Wang, Q. Gan, and F. J. Bartoli, “Trapping of surface-plasmon polaritons in a graded Bragg structure: frequency-dependent spatially separated localization of the visible spectrum modes,” Phys. Rev. B 80, 161106 (2009).
[CrossRef]

Hohenau, A. Drezet, M. Weissenbacher, F. R. Aussenegg, and J. R. Krenn, “Effects of damping on surface-plasmon pulse propagation and refraction,” Phys. Rev. B 78, 155405 (2008).
[CrossRef]

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

Phys. Rev. Lett. (7)

H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sánchez-Dehesa, “Acoustic analogue of electronic Bloch oscillations and resonant Zener tunneling in ultrasonic superlattices,” Phys. Rev. Lett. 98, 134301 (2007).
[CrossRef] [PubMed]

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]

H. Trompeter, W. Krolikowski, D. N. Neshev, A. S. Desyatnikov, A. A. Sukhorukov, Y. S. Kivshar, T. Pertsch, U. Peschel, and F. Lederer, “Bloch oscillations and Zener tunneling in two-dimensional photonic lattices,” Phys. Rev. Lett. 96, 053903(2006).
[CrossRef] [PubMed]

V. Agarwal, J. A. del Rio, 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, 097401 (2004).
[CrossRef] [PubMed]

G. A. Wurtz, R. Pollard, and A. V. Zayats, “Optical bistability in nonlinear surface-plasmon polaritonic crystals,” Phys. Rev. Lett. 97, 057402 (2006).
[CrossRef] [PubMed]

R. Rokitski, K. A. Tetz, and Y. Fainman, “Propagation of femtosecond surface plasmon polariton pulses on the surface of a nanostructured metallic film: space-time complex amplitude characterization,” Phys. Rev. Lett. 95, 177401 (2005).
[CrossRef] [PubMed]

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

Phys. Today (1)

K. Kneipp, “Surface-enhanced Raman scattering,” Phys. Today 60 (11), 40–46 (2007).
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Proc. R. Soc. A (2)

M. V. Berry, “Quantal phase factors accompanying adiabatic changes,” Proc. R. Soc. A 392, 45–57 (1984).
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C. Zener, “A theory of the electrical breakdown of solid dielectrics,” Proc. R. Soc. A 145, 523–529 (1934).
[CrossRef]

Science (1)

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

Z. Phys. (1)

F. Bloch, “Über die quantenmechanik der elektronen in kristallgittern,” Z. Phys. 52, 555–600 (1929).
[CrossRef]

Other (4)

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (Pan Stanford, 2008).
[CrossRef]

M. L. Brongersma and P. G. Kik, Surface Plasmon Nanophotonics (Springer-Verlag, 2007).
[CrossRef]

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer-Verlag, 2007).

V. P. Tarakanov, User’s Manual for Code KARAT (Berkeley Research Associates, 1992).

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Figures (5)

Fig. 1
Fig. 1

(a) Dispersion diagram for SPP in the plasmonic crystal (see inset) of a smooth metal (Ag) and a dielectric grating of the period d = 280 nm , the slit width r = 60 nm and different heights h of 10 nm (solid red curve), 100 nm (dashed green curve), and 200 nm (dotted–dashed blue curve). The inclined dotted straight black lines are borders of the light cone in air, the horizontal dashed black line indicates the low-frequency border for the region of the wave-packet coupling to the far-field radiation. (b) Top graph: derivative of ω / h at κ = π / d versus h. Bottom graph: frequencies of upper edge of the first plasmonic band (solid curve) and lower edge of the second plasmonic band (dashed curve) versus h.

Fig. 2
Fig. 2

Time dependence of the position of the wave-packet center expressed via h 0 . Initially, h 0 ( 0 ) = 30 nm . Three different cases are considered: (i) propagation without reflection ( ω 0 = 0.97 eV , red dotted–dashed curve), (ii) propagation with partial reflection and tunneling ( ω 0 = 1.27 eV , green solid curve), and (iii) propagation with reflection and without tunneling ω 0 = 1.14 eV (black dashed curve). The dielectric grating period is d = 280 nm , and the slit width is r = 60 nm . The dielectric wedge angle is α = 0.4 ° . Inset: the plasmonic crystal considered.

Fig. 3
Fig. 3

(a) Time dependences of the velocity v of the wave-packet center normalized to the vacuum light velocity c calculated as a solution of Eq. (3) (red solid curve) and found from the FDTD modeling for the pulse duration of 40 fs (dashed green curve). (b) Dielectric grating height h 0 at the position of the wave-packet center versus time calculated from Eq. (3) (red solid curve) and found from the FDTD modeling for the SPP pulses of duration τ = 40 fs (green curve with squares) and τ = 70 fs (black curve with triangles). ω 0 = 1.43 eV ; grating wedge angle is α = 0.2 ° ; all other grating pa rameters are the same as those for Fig. 2. Gaussian type of the time dependence of the wave-packet envelope function is assumed.

Fig. 4
Fig. 4

Plasmonic pulse envelopes at different time moments: (i), 10 fs (black curve); (ii), 135 fs (red curve); (iii), 180 fs (blue curve); (iv)  240 fs (green curve). Gaussian type of the time dependence of the incident wave-packet envelope function is assumed with τ = 20 fs . Absolute value of the magnetic field of the pulse | H y | is normalized to its maximum value of the incident pulse. The reflection point of the central frequency is indicated by the vertical dashed line. Arrows show direction of the pulse group velocity; ω 0 = 1.43 eV ; the wedge angle is α = 0.2 ° ; all other grating parameters are the same as those for Fig. 2.

Fig. 5
Fig. 5

Transmission (T), reflection (R), and absorption (A) coefficients for the propagation of the SPP pulse through the Bragg barrier versus the pulse duration τ (the wedge angle is α = 0.4 ° ). All other grating parameters are the same as those for Fig. 2. ω 0 = 1.33 eV , x in = 0 , x out = 20 μm [see Eqs. (4, 5)], h ( x in ) = 30 nm .

Equations (5)

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H ( WP ) ( r , t ) = H ( r , t ) exp ( i ω 0 t ) ,
H ( r , t ) = d 3 κ C ( κ , t ) h κ , r 0 ( r , t ) .
κ ˙ 0 = ω r 0 + T ^ rr r ˙ 0 + T ^ r κ κ ˙ 0 , r ˙ 0 = ω κ 0 T ^ κ r r ˙ 0 T ^ κ κ κ ˙ 0 ,
T = | Z , Δ t out S x ( x out ) d z d t Z , Δ t in S x ( x in ) d z d t | ,
R = | Z , Δ t refl S x ( x in ) d z d t Z , Δ t in S x ( x in ) d z d t | .

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