Abstract

Coupled metal ring resonator waveguides filled with optical active materials are proposed to achieve the slow light and tunable time delay. The tunable group index and time delay are realized by the dispersion of the active materials and its interplay with that of the geometric structure of the waveguides. Our results from the transfer matrix analysis and finite-difference time-domain numerical simulation show that the anomalous dispersion of the active materials can help to amplify the group index determined by the waveguide geometry. Based upon this structure, a variable-bit-rate optical time-division-multiplexing system is numerically demonstrated.

© 2009 Optical Society of America

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    [CrossRef]
  25. G. Gantzounis, and N. Stefanou, "Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material," Phys. Rev. B 74,085102 (2006).
    [CrossRef]

2008 (3)

G. Gantzounis, and N. Stefanou, "Tight-binding description of single-mode cavity-plasmon waveguides in the frequency and time domain, " J. Phys.: Condens. Matter 20, 015202 (2008).
[CrossRef]

A. E. Willner, B. Zhang, L. Zhang, L. Yan, and I. Fazal, "Optical signal processing using tunable delay elements based on slow light," IEEE J. Quantum Electron. 14, 691-705 (2008).
[CrossRef]

Y. Shen and G. P. Wang, "Optical bistability in metal gap waveguide nanocavities," Opt. Express 16, 8421-8426 (2008).
[CrossRef] [PubMed]

2007 (3)

2006 (6)

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

A. A. Govyadinov, and V. A. Podolskiy, "Gain-assisted to superluminal group velocity manipulation in nanowaveguides," Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

S. Mookherjea, "Using gain to tune the dispersion relation of coupled-resonator optical waveguides," IEEE Photon. Technol. Lett. 18, 715-717 (2006).
[CrossRef]

B. Wang and G. P. Wang, "Plasmonic waveguide ring resonator at terahertz frequencies," Appl. Phys. Lett. 89, 133106 (2006).
[CrossRef]

G. Gantzounis, and N. Stefanou, "Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material," Phys. Rev. B 74,085102 (2006).
[CrossRef]

J. K. S. Poon, L. Zhu, G. A. DeRose, and A. Yariv, "Transmission and group delay of microring coupled-resonator optical waveguides," Opt. Lett. 31, 456-458 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

2004 (3)

2003 (2)

2001 (1)

G. M. Ribeiro, R. L. Maltez, A. A. Bernussi, D. Ugarte, and W. de Carvalho, Jr., "Seeding of InP islands on InAs quantum dot templates," J. Appl. Phys. 89, 6548-6550 (2001).
[CrossRef]

2000 (1)

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

1999 (1)

1990 (1)

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: a new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

1977 (1)

1974 (1)

Barnes, W. L.

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

Bawendi, M. G.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Bernussi, A. A.

G. M. Ribeiro, R. L. Maltez, A. A. Bernussi, D. Ugarte, and W. de Carvalho, Jr., "Seeding of InP islands on InAs quantum dot templates," J. Appl. Phys. 89, 6548-6550 (2001).
[CrossRef]

Bimberg, D.

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

Borri, P.

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

de Carvalho, W.

G. M. Ribeiro, R. L. Maltez, A. A. Bernussi, D. Ugarte, and W. de Carvalho, Jr., "Seeding of InP islands on InAs quantum dot templates," J. Appl. Phys. 89, 6548-6550 (2001).
[CrossRef]

Dereux, A.

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

DeRose, G. A.

Ding, J.

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).
[CrossRef]

Ebbesen, T. W.

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

Eisler, H. J.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Fazal, I.

Fazal1, I.

Fejer, M. M.

Gallawa, R. L.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: a new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Gantzounis, G.

G. Gantzounis, and N. Stefanou, "Tight-binding description of single-mode cavity-plasmon waveguides in the frequency and time domain, " J. Phys.: Condens. Matter 20, 015202 (2008).
[CrossRef]

G. Gantzounis, and N. Stefanou, "Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material," Phys. Rev. B 74,085102 (2006).
[CrossRef]

Ghatak, A. K.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: a new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Govyadinov, A. A.

A. A. Govyadinov, and V. A. Podolskiy, "Active metamaterials: Sign of refractive index and gain-assisted dispersion management," Appl. Phys. Lett. 91, 191103 (2007).
[CrossRef]

A. A. Govyadinov, and V. A. Podolskiy, "Gain-assisted to superluminal group velocity manipulation in nanowaveguides," Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

Goyal, I. C.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: a new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

Hollingsworth, J. A.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Hong, C. S.

Huang, Y.

Jeong, D. Y.

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).
[CrossRef]

Kaminow, I. P.

Khoo, I. C.

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).
[CrossRef]

Klimov, V. I.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Langbein, W.

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

Langrock, C.

Leatherdale, C. A.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Lee, R. K.

Malko, A.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Maltez, R. L.

G. M. Ribeiro, R. L. Maltez, A. A. Bernussi, D. Ugarte, and W. de Carvalho, Jr., "Seeding of InP islands on InAs quantum dot templates," J. Appl. Phys. 89, 6548-6550 (2001).
[CrossRef]

Mammel, W. L.

Mikhailovsky, A.A.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Mookherjea, S.

S. Mookherjea, "Using gain to tune the dispersion relation of coupled-resonator optical waveguides," IEEE Photon. Technol. Lett. 18, 715-717 (2006).
[CrossRef]

J. K. S. Poon, J. Scheuer, S. Mookherjea, G. T. Paloczi, Y. Huang, and A. Yariv, "Matrix analysis of microring coupled-resonator optical waveguides," Opt. Express 12, 90-103 (2004).
[CrossRef] [PubMed]

Nuccio, S.

Ouang, D.

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

Ozbay, E.

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

Paloczi, G. T.

Podolskiy, V. A.

A. A. Govyadinov, and V. A. Podolskiy, "Active metamaterials: Sign of refractive index and gain-assisted dispersion management," Appl. Phys. Lett. 91, 191103 (2007).
[CrossRef]

A. A. Govyadinov, and V. A. Podolskiy, "Gain-assisted to superluminal group velocity manipulation in nanowaveguides," Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

Poon, J. K. S.

Ribeiro, G. M.

G. M. Ribeiro, R. L. Maltez, A. A. Bernussi, D. Ugarte, and W. de Carvalho, Jr., "Seeding of InP islands on InAs quantum dot templates," J. Appl. Phys. 89, 6548-6550 (2001).
[CrossRef]

Scherer, A.

Scheuer, J.

Schneider, S.

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

Sellin, R. L.

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

Shen, Y.

Stefanou, N.

G. Gantzounis, and N. Stefanou, "Tight-binding description of single-mode cavity-plasmon waveguides in the frequency and time domain, " J. Phys.: Condens. Matter 20, 015202 (2008).
[CrossRef]

G. Gantzounis, and N. Stefanou, "Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material," Phys. Rev. B 74,085102 (2006).
[CrossRef]

Ugarte, D.

G. M. Ribeiro, R. L. Maltez, A. A. Bernussi, D. Ugarte, and W. de Carvalho, Jr., "Seeding of InP islands on InAs quantum dot templates," J. Appl. Phys. 89, 6548-6550 (2001).
[CrossRef]

Wang, B.

B. Wang and G. P. Wang, "Plasmonic waveguide ring resonator at terahertz frequencies," Appl. Phys. Lett. 89, 133106 (2006).
[CrossRef]

Wang, G. P.

Y. Shen and G. P. Wang, "Optical bistability in metal gap waveguide nanocavities," Opt. Express 16, 8421-8426 (2008).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, "Plasmonic waveguide ring resonator at terahertz frequencies," Appl. Phys. Lett. 89, 133106 (2006).
[CrossRef]

Weber, H. P.

Willner, A. E.

Woggon, U.

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

Xu, S.

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Xu, Y.

Yan, L.

A. E. Willner, B. Zhang, L. Zhang, L. Yan, and I. Fazal, "Optical signal processing using tunable delay elements based on slow light," IEEE J. Quantum Electron. 14, 691-705 (2008).
[CrossRef]

Yan, L. S.

Yang1, J. Y.

Yariv, A.

Ye, Y. H.

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).
[CrossRef]

Yeh, P.

Yilmaz, O.

Zhang, B.

Zhang, L.

A. E. Willner, B. Zhang, L. Zhang, L. Yan, and I. Fazal, "Optical signal processing using tunable delay elements based on slow light," IEEE J. Quantum Electron. 14, 691-705 (2008).
[CrossRef]

B. Zhang, L. Zhang, L. S. Yan, I. Fazal1, J. Y. Yang1, and A. E. Willner, "Continuously-tunable, bit-rate variable OTDM using broadband SBS slow-light delay line," Opt. Express 15, 8317-8322 (2007).
[CrossRef] [PubMed]

Zhang, Q. M.

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).
[CrossRef]

Zhu, L.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

B. Wang and G. P. Wang, "Plasmonic waveguide ring resonator at terahertz frequencies," Appl. Phys. Lett. 89, 133106 (2006).
[CrossRef]

A. A. Govyadinov, and V. A. Podolskiy, "Active metamaterials: Sign of refractive index and gain-assisted dispersion management," Appl. Phys. Lett. 91, 191103 (2007).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. E. Willner, B. Zhang, L. Zhang, L. Yan, and I. Fazal, "Optical signal processing using tunable delay elements based on slow light," IEEE J. Quantum Electron. 14, 691-705 (2008).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

S. Schneider, P. Borri, W. Langbein, U. Woggon, R. L. Sellin, D. Ouang, and D. Bimberg, "Excited-state gain dynamics in InGaAs quantum-dot amplifiers," IEEE Photon. Technol. Lett. 17, 2014-2016 (2005).
[CrossRef]

S. Mookherjea, "Using gain to tune the dispersion relation of coupled-resonator optical waveguides," IEEE Photon. Technol. Lett. 18, 715-717 (2006).
[CrossRef]

J. Appl. Phys. (1)

G. M. Ribeiro, R. L. Maltez, A. A. Bernussi, D. Ugarte, and W. de Carvalho, Jr., "Seeding of InP islands on InAs quantum dot templates," J. Appl. Phys. 89, 6548-6550 (2001).
[CrossRef]

J. Lightwave Technol. (1)

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, "Bent planar waveguides and whispering gallery modes: a new method of analysis," J. Lightwave Technol. 8, 768-774 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

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

J. Phys.: Condens. Matter (1)

G. Gantzounis, and N. Stefanou, "Tight-binding description of single-mode cavity-plasmon waveguides in the frequency and time domain, " J. Phys.: Condens. Matter 20, 015202 (2008).
[CrossRef]

Nature (1)

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

Opt. Express (5)

Opt. Lett. (2)

Phys. Rev. B (1)

G. Gantzounis, and N. Stefanou, "Cavity-plasmon waveguides: Multiple scattering calculations of dispersion in weakly coupled dielectric nanocavities in a metallic host material," Phys. Rev. B 74,085102 (2006).
[CrossRef]

Phys. Rev. E (1)

Y. H. Ye, J. Ding, D. Y. Jeong, I. C. Khoo, and Q. M. Zhang, "Finite-size effect on one-dimensional coupled-resonator optical waveguides," Phys. Rev. E 69, 056604 (2004).
[CrossRef]

Phys. Rev. Lett. (1)

A. A. Govyadinov, and V. A. Podolskiy, "Gain-assisted to superluminal group velocity manipulation in nanowaveguides," Phys. Rev. Lett. 97, 223902 (2006).
[CrossRef] [PubMed]

Science (2)

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

V. I. Klimov, A.A. Mikhailovsky, S. Xu, A. Malko, J. A. Hollingsworth, C. A. Leatherdale, H. J. Eisler, M. G. Bawendi, "Optical gain and stimulated emission in nanocrystal quantum dots," Science 290, 314-317 (2000).
[CrossRef] [PubMed]

Other (1)

E. D. Palik, Handbook of Optical Constants of Solids (Academic, London, 1985).

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Figures (4)

Fig. 1.
Fig. 1.

(color online) (a)Scheme of the plasmonic CROW. (b)–(c) Real (top) and imaginary (bottom) parts of the (b) εd and (c) neff as the optical gain strength of the active materials A is -0.011 (red solid curve), -0.007 (blue dashed curve), and 0 (green dotted curve), respectively.

Fig. 2.
Fig. 2.

(color online) TMM calculated (a) transmittance, (b) dispersion relation, and (c) group index of the plasmonic CROW as the optical gain strength of the active materials A is -0.011 (red solid curve), -0.007 (blue dashed curve), and 0 (green dotted curve), respectively. Inset of (c), group index for lossless plasmonic-CROW [A=0 and Im(neff )=0].

Fig. 3.
Fig. 3.

(color online) Time evolution of an input pulse (black solid curve) passing through the plasmonic CROW as the optical gain strength of the active materials A=-0.011 (red dashed curve, magnified by 20 times) and A=-0.007 (blue dotted curve, magnified by 200 times), respectively.

Fig. 4.
Fig. 4.

(color online) Time evolution of two different input bit-rate data pulses incident into the plasmonic CROW from the bottom of both the input- and output-waveguides [Fig. 1(a)] at the same time as the optical gain coefficient A=-0.011 (a) and A=-0.007 (b), respectively. The input pulses from the bottom of input- and output-waveguides are drawn in red dashed curves and black dotted-dashed curves, while the outputs in red dotted curves and black solid curves, respectively.

Equations (6)

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εd=εd +A · ω02 (ω02ω2jγdω)
βspp(ω)=neff(εd)·ωc .
Q(ω)=[0eiβspp(ω)Rπeiβspp(ω)Rπ0]
tN(ω)=tNr (ω) +j tNi (ω) =TN(ω) ejϕN
KN(N1)Λ=t a n1 [tNi(ω)tNr(ω)]
ng=cυg=c·dKNdω=c(N1)Λddω[tan1(tNitNr)]

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