Abstract

We analyze the behavior of group and phase velocities in optical waveguides supporting strongly confined propagating modes. We discuss the implications of material absorption for electromagnetic properties of nanoguides and develop an analytical description of the interplay between geometry-induced and materials-induced dispersions. In the limit of strong confinement, the phase velocity of waveguide modes becomes vanishingly small, while group velocity can be modulated from negative to positive values. The modulation of group velocity is enhanced by the factor of λ2R2 with respect to macroscopic systems. Both slow- and fast-light regimes can be achieved in the same nanoguiding structure, and dynamical switching between the two regimes is possible. Applications of the developed formalism lie in the field of ultrafast active nanophotonics.

© 2008 Optical Society of America

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2007 (11)

F. Xia, L. Sekaric, Y. Vlasov, “Subcompact optical buffers on a silicon chip,” Nat. Phot. 1, 65-71 (2007).
[CrossRef]

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,”Phys. Rev. B 76, 245403 (2007).
[CrossRef]

L. Novotny, “Effective wavelength scaling for optical antennas,”Phys. Rev. Lett. 98, 266802 (2007).
[CrossRef] [PubMed]

V. Shalaev, “Optical negative-index metamaterials,” Nature Photonics 1, 41-48 (2007).
[CrossRef]

A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

J. Elser, A. A. Govyadinov, I. Avrustky, I. Salakhutdinov, and V. A. Podolskiy “Plasmonic nanolayer composites: coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomaterials 2007, 79469 (2007).

I. Smolyaninov, Y. Hung, and C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refraction index and gain-assisted dispersion management,” Appl. Phys. Lett. 91, 191103 (2007).
[CrossRef]

L. Deng and M. Payne, “Gain-assisted large and rapidly responding kerr effect using a room-temperature active raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef] [PubMed]

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. A. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402(R) (2007).
[CrossRef]

A. Kapitonov and V. Astratov, “Observation of nanojet-induced modes with small propagation losses in chains of coupled spherical cavities,” Opt. Lett. 32, 409-411 (2007).
[CrossRef] [PubMed]

2006 (5)

M. A. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. E. Small, B. A. Ritzo, V. P. Drachev, and V. M. Shalaev, Opt. Lett. 31, 3022-3024 (2006).
[CrossRef] [PubMed]

L. Alekseyev and E. Narimanov, “Slow light and 3d imaging with non-magnetic negative index systems,” Opt. Express 14, 11184-11193 (2006).
[CrossRef] [PubMed]

A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895-897 (2006).
[CrossRef] [PubMed]

A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity management in nano-waveguides,” Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

2005 (5)

A. Karalis, E. Lidorikis, M. Ibanescu, J. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

V. A. Podolskiy and E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101(R) (2005).
[CrossRef]

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
[CrossRef]

2004 (3)

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

V. Agranovich, Y. Shen, R. Baughman, and A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167-173 (2004).
[CrossRef]

J. B. Jackson and N. J. Halas, “Surface-enhanced Raman scattering on tunable plasmonic nanoparticle substrates,” Proc. Natl. Acad. Sci. U.S.A. 101, 17930 (2004).
[CrossRef] [PubMed]

2003 (2)

M. Bigelow, N. Lepeshkin, and R. Boyd, Science 301, 200-202 (2003).
[CrossRef] [PubMed]

S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
[CrossRef]

2002 (2)

S. Bozhevolnyi, V. Volkov, and K. Leosson, “Localization and waveguiding of surface plasmon polaritons in random nanostructures,” Phys. Rev. Lett. 89, 186801 (2002).
[CrossRef] [PubMed]

M. McCall, A. Lakhtakia, and W. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

2000 (2)

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370-2373 (2000).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1998 (2)

E. Sonnenschein, I. Rutkevich, and D. Censor, “Wave packets, rays, and the role of real group velocity in absorbing media,” Phys. Rev. E 57, 1005-1016 (1998).
[CrossRef]

T. Klar, M. Perner, S. Grosse, G. von Plessen, and W. Spirkl, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

1994 (2)

E. Bolda, J. Garrison, and R. Chiao, “Optical pulse propagation at negative group velocities due to nearby gain line,” Phys. Rev. A 49, 2938-2947 (1994).
[CrossRef] [PubMed]

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071-2075 (1994).
[CrossRef] [PubMed]

1989 (1)

W. E. Moerner and L. Kador, “Optical detection and spectroscopy of single molecules in a solid,” Phys. Rev. Lett. 62, 2535-2538 (1989).
[CrossRef] [PubMed]

1988 (1)

V. M. Agranovich and T. A. Leskova, “Diffraction methods in the spectroscopy of thin films in the vicinity of resonances,” Progress in Surf. Sci. 29, 169-327 (1988).

1982 (1)

I. Pockrand, A. Brillante, and D. Mobius, “Exciton-surface plasmon coupling: an experimental investigation,” J. Chem. Phys. 77, 6289-9295 (1982).
[CrossRef]

Adegoke, J.

Agranovich, V.

V. Agranovich, Y. Shen, R. Baughman, and A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167-173 (2004).
[CrossRef]

Agranovich, V. M.

V. M. Agranovich and T. A. Leskova, “Diffraction methods in the spectroscopy of thin films in the vicinity of resonances,” Progress in Surf. Sci. 29, 169-327 (1988).

Alekseyev, L.

A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

L. Alekseyev and E. Narimanov, “Slow light and 3d imaging with non-magnetic negative index systems,” Opt. Express 14, 11184-11193 (2006).
[CrossRef] [PubMed]

Astratov, V.

Atwater, H.

S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
[CrossRef]

Avrustky, I.

J. Elser, A. A. Govyadinov, I. Avrustky, I. Salakhutdinov, and V. A. Podolskiy “Plasmonic nanolayer composites: coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomaterials 2007, 79469 (2007).

Avrutsky, I.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. A. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402(R) (2007).
[CrossRef]

Bahoura, M.

Barsi, C.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895-897 (2006).
[CrossRef] [PubMed]

Baughman, R.

V. Agranovich, Y. Shen, R. Baughman, and A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167-173 (2004).
[CrossRef]

Bigelow, M.

M. Bigelow, N. Lepeshkin, and R. Boyd, Science 301, 200-202 (2003).
[CrossRef] [PubMed]

Bolda, E.

E. Bolda, J. Garrison, and R. Chiao, “Optical pulse propagation at negative group velocities due to nearby gain line,” Phys. Rev. A 49, 2938-2947 (1994).
[CrossRef] [PubMed]

Boyd, R.

M. Bigelow, N. Lepeshkin, and R. Boyd, Science 301, 200-202 (2003).
[CrossRef] [PubMed]

Boyd, R. W.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895-897 (2006).
[CrossRef] [PubMed]

Bozhevolnyi, S.

S. Bozhevolnyi, V. Volkov, and K. Leosson, “Localization and waveguiding of surface plasmon polaritons in random nanostructures,” Phys. Rev. Lett. 89, 186801 (2002).
[CrossRef] [PubMed]

Brillante, A.

I. Pockrand, A. Brillante, and D. Mobius, “Exciton-surface plasmon coupling: an experimental investigation,” J. Chem. Phys. 77, 6289-9295 (1982).
[CrossRef]

Censor, D.

E. Sonnenschein, I. Rutkevich, and D. Censor, “Wave packets, rays, and the role of real group velocity in absorbing media,” Phys. Rev. E 57, 1005-1016 (1998).
[CrossRef]

Chang-Hasnain, C.

P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
[CrossRef]

Chiao, R.

E. Bolda, J. Garrison, and R. Chiao, “Optical pulse propagation at negative group velocities due to nearby gain line,” Phys. Rev. A 49, 2938-2947 (1994).
[CrossRef] [PubMed]

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071-2075 (1994).
[CrossRef] [PubMed]

Chuang, S.

P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
[CrossRef]

Crankshaw, S.

P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
[CrossRef]

Davis, C.

I. Smolyaninov, Y. Hung, and C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699-1701 (2007).
[CrossRef] [PubMed]

Deng, L.

L. Deng and M. Payne, “Gain-assisted large and rapidly responding kerr effect using a room-temperature active raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef] [PubMed]

Drachev, V. P.

Elser, J.

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. A. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402(R) (2007).
[CrossRef]

J. Elser, A. A. Govyadinov, I. Avrustky, I. Salakhutdinov, and V. A. Podolskiy “Plasmonic nanolayer composites: coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomaterials 2007, 79469 (2007).

Eng, L.

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Engheta, N.

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,”Phys. Rev. B 76, 245403 (2007).
[CrossRef]

Franz, K. J.

A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Fromm, D. P.

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

Garrison, J.

E. Bolda, J. Garrison, and R. Chiao, “Optical pulse propagation at negative group velocities due to nearby gain line,” Phys. Rev. A 49, 2938-2947 (1994).
[CrossRef] [PubMed]

Gehring, G. M.

G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895-897 (2006).
[CrossRef] [PubMed]

Glasgow, S. A.

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370-2373 (2000).
[CrossRef] [PubMed]

Gmachl, C.

A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Govyadinov, A.

A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity management in nano-waveguides,” Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

Govyadinov, A. A.

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refraction index and gain-assisted dispersion management,” Appl. Phys. Lett. 91, 191103 (2007).
[CrossRef]

J. Elser, A. A. Govyadinov, I. Avrustky, I. Salakhutdinov, and V. A. Podolskiy “Plasmonic nanolayer composites: coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomaterials 2007, 79469 (2007).

Grafstrom, S.

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Grosse, S.

T. Klar, M. Perner, S. Grosse, G. von Plessen, and W. Spirkl, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

Halas, N. J.

J. B. Jackson and N. J. Halas, “Surface-enhanced Raman scattering on tunable plasmonic nanoparticle substrates,” Proc. Natl. Acad. Sci. U.S.A. 101, 17930 (2004).
[CrossRef] [PubMed]

Harel, E.

S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
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A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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I. Smolyaninov, Y. Hung, and C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699-1701 (2007).
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A. Karalis, E. Lidorikis, M. Ibanescu, J. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
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A. Karalis, E. Lidorikis, M. Ibanescu, J. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
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A. Karalis, E. Lidorikis, M. Ibanescu, J. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
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S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
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P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
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S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
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G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895-897 (2006).
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A. Karalis, E. Lidorikis, M. Ibanescu, J. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
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L. Landau, E. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Vol. 8 of Landau and Lifshitz Course of Theoretical Physics2nd ed. (Reed, 1984)

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S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
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M. McCall, A. Lakhtakia, and W. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353-359 (2002).
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J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

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S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
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I. Pockrand, A. Brillante, and D. Mobius, “Exciton-surface plasmon coupling: an experimental investigation,” J. Chem. Phys. 77, 6289-9295 (1982).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
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W. E. Moerner and L. Kador, “Optical detection and spectroscopy of single molecules in a solid,” Phys. Rev. Lett. 62, 2535-2538 (1989).
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P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
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V. A. Podolskiy and E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101(R) (2005).
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A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refraction index and gain-assisted dispersion management,” Appl. Phys. Lett. 91, 191103 (2007).
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P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
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L. Deng and M. Payne, “Gain-assisted large and rapidly responding kerr effect using a room-temperature active raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
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J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370-2373 (2000).
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J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
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T. Klar, M. Perner, S. Grosse, G. von Plessen, and W. Spirkl, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249-4252 (1998).
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Pitaevskii, L. P.

L. Landau, E. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media, Vol. 8 of Landau and Lifshitz Course of Theoretical Physics2nd ed. (Reed, 1984)

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I. Pockrand, A. Brillante, and D. Mobius, “Exciton-surface plasmon coupling: an experimental investigation,” J. Chem. Phys. 77, 6289-9295 (1982).
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Podolskiy, V. A.

J. Elser, A. A. Govyadinov, I. Avrustky, I. Salakhutdinov, and V. A. Podolskiy “Plasmonic nanolayer composites: coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomaterials 2007, 79469 (2007).

A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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I. Avrutsky, I. Salakhutdinov, J. Elser, and V. A. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402(R) (2007).
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A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refraction index and gain-assisted dispersion management,” Appl. Phys. Lett. 91, 191103 (2007).
[CrossRef]

A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity management in nano-waveguides,” Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

V. A. Podolskiy and E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101(R) (2005).
[CrossRef]

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S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
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Ritzo, B. A.

Rutkevich, I.

E. Sonnenschein, I. Rutkevich, and D. Censor, “Wave packets, rays, and the role of real group velocity in absorbing media,” Phys. Rev. E 57, 1005-1016 (1998).
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I. Avrutsky, I. Salakhutdinov, J. Elser, and V. A. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402(R) (2007).
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J. Elser, A. A. Govyadinov, I. Avrustky, I. Salakhutdinov, and V. A. Podolskiy “Plasmonic nanolayer composites: coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomaterials 2007, 79469 (2007).

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J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,”Phys. Rev. B 76, 245403 (2007).
[CrossRef]

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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
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G. M. Gehring, A. Schweinsberg, C. Barsi, N. Kostinski, and R. W. Boyd, “Observation of backward pulse propagation through a medium with a negative group velocity,” Science 312, 895-897 (2006).
[CrossRef] [PubMed]

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P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
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J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
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F. Xia, L. Sekaric, Y. Vlasov, “Subcompact optical buffers on a silicon chip,” Nat. Phot. 1, 65-71 (2007).
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V. Shalaev, “Optical negative-index metamaterials,” Nature Photonics 1, 41-48 (2007).
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V. Agranovich, Y. Shen, R. Baughman, and A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167-173 (2004).
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A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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Small, C. E.

Smolyaninov, I.

I. Smolyaninov, Y. Hung, and C. Davis, “Magnifying superlens in the visible frequency range,” Science 315, 1699-1701 (2007).
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A. Karalis, E. Lidorikis, M. Ibanescu, J. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

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E. Sonnenschein, I. Rutkevich, and D. Censor, “Wave packets, rays, and the role of real group velocity in absorbing media,” Phys. Rev. E 57, 1005-1016 (1998).
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T. Klar, M. Perner, S. Grosse, G. von Plessen, and W. Spirkl, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249-4252 (1998).
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A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071-2075 (1994).
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M. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
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P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
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F. Xia, L. Sekaric, Y. Vlasov, “Subcompact optical buffers on a silicon chip,” Nat. Phot. 1, 65-71 (2007).
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S. Bozhevolnyi, V. Volkov, and K. Leosson, “Localization and waveguiding of surface plasmon polaritons in random nanostructures,” Phys. Rev. Lett. 89, 186801 (2002).
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T. Klar, M. Perner, S. Grosse, G. von Plessen, and W. Spirkl, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249-4252 (1998).
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P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
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J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370-2373 (2000).
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A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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M. McCall, A. Lakhtakia, and W. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353-359 (2002).
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J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

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F. Xia, L. Sekaric, Y. Vlasov, “Subcompact optical buffers on a silicon chip,” Nat. Phot. 1, 65-71 (2007).
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V. Agranovich, Y. Shen, R. Baughman, and A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167-173 (2004).
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Appl. Phys. Lett. (2)

A. A. Govyadinov, V. A. Podolskiy, and M. A. Noginov, “Active metamaterials: sign of refraction index and gain-assisted dispersion management,” Appl. Phys. Lett. 91, 191103 (2007).
[CrossRef]

P. Palinginis, S. Crankshaw, F. Sedgwick, E. Kim, M. Moewe, C. Chang-Hasnain, H. Wang, and S. Chuang, “Ultraslow light (<200 m/s) propagation in a semiconductor nanostructure,” Appl. Phys. Lett. 87, 171102 (2005).
[CrossRef]

Eur. J. Phys. (1)

M. McCall, A. Lakhtakia, and W. Weiglhofer, “The negative index of refraction demystified,” Eur. J. Phys. 23, 353-359 (2002).
[CrossRef]

J. Chem. Phys. (1)

I. Pockrand, A. Brillante, and D. Mobius, “Exciton-surface plasmon coupling: an experimental investigation,” J. Chem. Phys. 77, 6289-9295 (1982).
[CrossRef]

J. Lumin. (1)

V. Agranovich, Y. Shen, R. Baughman, and A. Zakhidov, “Optical bulk and surface waves with negative refraction,” J. Lumin. 110, 167-173 (2004).
[CrossRef]

J. Nanomaterials (1)

J. Elser, A. A. Govyadinov, I. Avrustky, I. Salakhutdinov, and V. A. Podolskiy “Plasmonic nanolayer composites: coupled plasmon polaritons, effective-medium response, and subdiffraction light manipulation,” J. Nanomaterials 2007, 79469 (2007).

Nat. Phot. (1)

F. Xia, L. Sekaric, Y. Vlasov, “Subcompact optical buffers on a silicon chip,” Nat. Phot. 1, 65-71 (2007).
[CrossRef]

Nature Mater. (2)

A. Hoffman, A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

S. Maier, P. Kik, H. Atwater, S. Meltzer, E. Harel, B. Koel, and A. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nature Mater. 2, 229-232 (2003).
[CrossRef]

Nature Photonics (1)

V. Shalaev, “Optical negative-index metamaterials,” Nature Photonics 1, 41-48 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. A (2)

E. Bolda, J. Garrison, and R. Chiao, “Optical pulse propagation at negative group velocities due to nearby gain line,” Phys. Rev. A 49, 2938-2947 (1994).
[CrossRef] [PubMed]

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071-2075 (1994).
[CrossRef] [PubMed]

Phys. Rev. B (4)

I. Avrutsky, I. Salakhutdinov, J. Elser, and V. A. Podolskiy, “Highly confined optical modes in nanoscale metal-dielectric multilayers,” Phys. Rev. B 75, 241402(R) (2007).
[CrossRef]

V. A. Podolskiy and E. Narimanov, “Strongly anisotropic waveguide as a nonmagnetic left-handed system,” Phys. Rev. B 71, 201101(R) (2005).
[CrossRef]

J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,”Phys. Rev. B 76, 245403 (2007).
[CrossRef]

A. Govyadinov and V. A. Podolskiy, “Meta-material photonic funnels for sub-diffraction light compression and propagation,” Phys. Rev. B 73, 155108 (2006).
[CrossRef]

Phys. Rev. E (1)

E. Sonnenschein, I. Rutkevich, and D. Censor, “Wave packets, rays, and the role of real group velocity in absorbing media,” Phys. Rev. E 57, 1005-1016 (1998).
[CrossRef]

Phys. Rev. Lett. (12)

L. Novotny, “Effective wavelength scaling for optical antennas,”Phys. Rev. Lett. 98, 266802 (2007).
[CrossRef] [PubMed]

T. Klar, M. Perner, S. Grosse, G. von Plessen, and W. Spirkl, “Surface-plasmon resonances in single metallic nanoparticles,” Phys. Rev. Lett. 80, 4249-4252 (1998).
[CrossRef]

P. J. Schuck, D. P. Fromm, A. Sundaramurthy, G. S. Kino, and W. E. Moerner, “Improving the mismatch between light and nanoscale objects with gold bowtie nanoantennas,” Phys. Rev. Lett. 94, 017402 (2005).
[CrossRef] [PubMed]

W. E. Moerner and L. Kador, “Optical detection and spectroscopy of single molecules in a solid,” Phys. Rev. Lett. 62, 2535-2538 (1989).
[CrossRef] [PubMed]

A. Karalis, E. Lidorikis, M. Ibanescu, J. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength light in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

A. Govyadinov and V. A. Podolskiy, “Gain-assisted slow to superluminal group velocity management in nano-waveguides,” Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

L. Deng and M. Payne, “Gain-assisted large and rapidly responding kerr effect using a room-temperature active raman gain medium,” Phys. Rev. Lett. 98, 253902 (2007).
[CrossRef] [PubMed]

J. Peatross, S. A. Glasgow, and M. Ware, “Average energy flow of optical pulses in dispersive media,” Phys. Rev. Lett. 84, 2370-2373 (2000).
[CrossRef] [PubMed]

S. Bozhevolnyi, V. Volkov, and K. Leosson, “Localization and waveguiding of surface plasmon polaritons in random nanostructures,” Phys. Rev. Lett. 89, 186801 (2002).
[CrossRef] [PubMed]

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

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmons at the interface between a silver film and an optically pumped dye solution,” Phys. Rev. Lett. 94, 177401 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. B. Jackson and N. J. Halas, “Surface-enhanced Raman scattering on tunable plasmonic nanoparticle substrates,” Proc. Natl. Acad. Sci. U.S.A. 101, 17930 (2004).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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[CrossRef] [PubMed]

Surf. Sci. (1)

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Other (6)

As shown in Ref. , the solution of Eq. can be approximated with logarithmic precision as x0≃−2ε2/ε1/(ln−4ε1/ε2−γ) with γ≃0.577 being Euler's constant

C. Kittel, Introduction to Solid State Physics (Wiley, 2004).

Im[vg] may also lead to pulse reshaping

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A. E. Siegman, Lasers (University Science Books, 1986).

J. Joannopoulos, R. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

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Figures (5)

Fig. 1
Fig. 1

Schematic geometries of (a) anisotropy-based photonic funnel, (c) plasmonic nanorod waveguide , and radial profiles of the field in (b) TM 01 modes in the funnel and (d) in a plasmonic nanorod . The profiles are calculated for R = 20 nm and λ = 575 nm ; material parameters are provided in the text.

Fig. 2
Fig. 2

Dispersion of TM 01 mode in a photonic funnel structure; in each figure part, solid curves correspond to Re ω k z mapping; dashed and dashed-dotted curves correspond to Re k z ω mapping; each 4-graph section represents a single panel of the figure; right top section of each panel represents the relationship between real parts of ω and k z ; the two adjacent sections represent imaginary parts, with remaining graph providing the zoom of the behavior of the system in the proximity to dielectric resonance; (a) dispersion of both materials neglected; (b),(c) dispersion of metal neglected; (d) dispersion of both metal and dielectric included; (a,c,d) correspond to R = 10 nm ; (b) represents R = 90 nm .

Fig. 3
Fig. 3

Dispersion of TM 01 mode in a plasmonic nanorod; in all figure parts, solid lines correspond to Re ω k z mapping; dashed and dashed-dotted lines correspond to Re k z ω mapping; (a) dispersion of both materials neglected; (b),(c) dispersion of metal neglected; (d) dispersion of both metal and dielectric included; (a,c,d) correspond to R = 5 nm ; (b) represents R = 100 nm .

Fig. 4
Fig. 4

Phase (dashed-dotted curves) and group (dashed curves) velocities of TM 01 mode plasmonic nanorod (a,b) and in photonic funnels (c,d) as functions of waveguide radius; ε m = 10 + 0.1 i . Frequencies correspond to weak-dispersion regime (away from the dielectric resonance) λ = 575 nm (a,c) and dispersion-dominated regime λ = 535 nm (b,d); note non-monotonic behavior of group velocity in the regime of weak dispersion. Thin lines correspond to Eqs. (19) and (17); dots in (a,c) correspond to idealized system with material dispersion neglected; velocities are shown in units of c; real part of v p and v g is shown.

Fig. 5
Fig. 5

Phase (dashed-dotted curves) and group (dashed curves) velocities of TM 01 mode plasmonic nanorod (a,b) and in photonic funnels (c,d) as functions of waveguide radius; ε m described by Drude model. Frequencies correspond to dispersion-compensated regime λ = 535 nm (a,c) and dispersion-dominated regime λ = 575 nm (b,d). Thin lines correspond to Eqs. (19) and (17); velocities are shown in units of c; real part of v p and v g is shown.

Equations (22)

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{ E r TE = i ω r κ TE 2 c B z φ E φ TE = i ω κ TE 2 c B z r B r TE = i k z κ TE 2 B z r B φ TE = i k z r κ TE 2 B z φ , } ,
{ E r TM = i k z κ TM 2 ε z ε r φ E z r E φ TM = i k z r κ TM 2 ε z ε r φ E z φ B r TM = i ε z ω r κ TM 2 c E z φ B φ TM = i ε z ω κ TM 2 c E z r } ,
E z = { J m ( κ 1 r ) e i ω t + i k z z + i m φ , r R 0 , r > R }
D 1 AN = ω 2 c 2 k z 2 ε r φ κ 1 2 ε z = 0 .
D AN = J m ( κ 1 R ) = 0.
k z 2 = ε r φ [ ω 2 c 2 X 0 2 R 2 ε z ] ,
k z ± ε r φ ε z X 0 R .
E z = { I 0 ( κ 1 r ) I 0 ( κ 1 R ) e i ω t + i k z z , r R K 0 ( κ 2 r ) K 0 ( κ 2 R ) e i ω t + i k z z , r > R }
D 1 SPP = ε 1 ω 2 c 2 k z 2 + κ 1 2 = 0 ,
D 2 SPP = ε 2 ω 2 c 2 k z 2 + κ 2 2 = 0 .
D S P P = ε 1 ε 2 I 1 ( κ 1 R ) κ 1 I 0 ( κ 1 R ) + K 1 ( κ 2 R ) κ 2 K 0 ( κ 2 R ) = 0 .
k z x 0 R ( 1 + δ z ) ,
δ z = ω 2 R 2 2 c 2 x 0 2 ε 1 2 α 1 + ε 2 2 α 2 ε 1 α 1 + ε 2 α 2 1 ,
ε 1 I 1 ( x 0 ) I 0 ( x 0 ) + ε 2 K 1 ( x 0 ) K 0 ( x 0 ) = 0 ,
ε m = ε ω p 2 ω 2 + i Γ ω
ε d = ε ( 0 ) + A ω 0 2 ω 0 2 ω 2 i γ 0 ω ,
v p = ω k z ,
v g = d ω d k z ,
v g = i D κ i ( D i κ i ) 1 D i k z D k z i D κ i ( D i κ i ) 1 D i ω D ω .
v g v p = c 2 ε r φ [ 1 + ω 2 ε r φ d ε r φ d ω ] c 2 ε r φ X 0 2 2 ω ε z R 2 ( 1 ε r φ d ε r φ d ω 1 ε z d ε z d ω ) ,
v g v p = c 2 ( i = 1 2 D SPP κ i 1 κ i ) [ i = 1 2 D SPP κ i 1 κ i ( ε i + ω 2 d ε i d ω ) c 2 ω ε 1 ε 2 I 1 ( κ 1 R ) κ 1 I 0 ( κ 1 R ) ( 1 ε 1 d ε 1 d ω 1 ε 2 d ε 2 d ω ) ] 1 .
v g v p c 2 α i ε i α i ε i 2 [ 1 + ω 2 ε i d ε i d ω ] ε 1 x 0 c 2 ω R 2 I 1 ( x 0 ) I 0 ( x 0 ) ( 1 ε 1 d ε 1 d ω 1 ε 2 d ε 2 d ω ) .

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