Abstract

We present an improved analytical model describing transmittance of a metal-dielectric-metal (MDM) waveguide coupled to an arbitrary number of stubs. The model is built on the well-known analogy between MDM waveguides and microwave transmission lines. This analogy allows one to establish equivalent networks for different MDM-waveguide geometries and to calculate their optical transmission spectra using standard analytical tools of transmission-line theory. A substantial advantage of our model compared to earlier works is that it precisely incorporates the dissipation of surface plasmon polaritons resulting from ohmic losses inside any metal at optical frequencies. We derive analytical expressions for transmittance of MDM waveguides coupled to single and double stubs as well as to N identical stubs with a periodic arrangement. We show that certain phase-matching conditions must be satisfied to provide optimal filtering characteristics for such waveguides. To check the accuracy of our model, its results are compared with numerical data obtained from the full-blown finite-difference time-domain simulations. Close agreement between the two suggests that our analytical model is suitable for rapid design optimization of MDM-waveguide-based compact photonic devices.

© 2010 Optical Society of America

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2010 (1)

2009 (5)

2008 (3)

2007 (2)

2006 (4)

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

W. L. Barnes, "Surface plasmon-polariton length scales: A route to sub-wavelength optics," J. Opt. A: Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006).
[CrossRef] [PubMed]

K. Y. Kim, Y. K. Cho, H.-S. Tae, and J.-H. Lee, "Light transmission along dispersive plasmonic gap and its subwavelength guidance characteristics," Opt. Express 14, 320-330 (2006).
[CrossRef] [PubMed]

2005 (7)

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett.  95, 046802 (2005).
[CrossRef]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett.  87, 131102 (2005).
[CrossRef]

T. Lee and S. Gray, "Subwavelength light bending by metal slit structures," Opt. Express 13, 9652-9659 (2005).
[CrossRef] [PubMed]

H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, "Surface plasmon polariton propagation and combination in Y-shaped metallic channels," Opt. Express 13, 10795-10800 (2005).
[CrossRef] [PubMed]

2004 (1)

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125409 (2004).
[CrossRef]

2003 (3)

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

S. A. Maier, P. G. Kik, and H. A. Atwater, "Optical pulse propagation in metal nanoparticle chain waveguides," Phys. Rev. B 67, 205402 (2003).
[CrossRef]

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

1998 (1)

1997 (1)

1991 (1)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

1969 (1)

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

Abushagur, M. A. G.

Atwater, H. A.

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Optical pulse propagation in metal nanoparticle chain waveguides," Phys. Rev. B 67, 205402 (2003).
[CrossRef]

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

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,"  Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Baida, F. I.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Barnes, W. L.

W. L. Barnes, "Surface plasmon-polariton length scales: A route to sub-wavelength optics," J. Opt. A: Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

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

Belkhir, A.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Boltasseva, A.

Bozhevolnyi, S. I.

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett.  95, 046802 (2005).
[CrossRef]

Chen, J.

Cho, Y. K.

Deng, Q.

Dereux, A.

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

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett.  95, 046802 (2005).
[CrossRef]

Dionne, J. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,"  Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Djurisic, A. B.

Du, C.

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett.  95, 046802 (2005).
[CrossRef]

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

Economou, E. N.

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

Elazar, J. M.

Fan, S.

G. Veronis, S. E. Kocabas, D. A. B. Miller, and S. Fan, "Modeling of plasmonic waveguide components and networks," J. Comput. Theor. Nanosci. 6, 1808-1826 (2009).
[CrossRef]

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, "Transmission line and equivalent circuit models for plasmonic waveguide components," IEEE J. Sel. Top. Quantum Electron. 14, 1462-1472 (2008).
[CrossRef]

G. Veronis and S. Fan, "Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides," Opt. Express 15, 1211-1221 (2007).
[CrossRef] [PubMed]

G. Veronis and S. Fan, "Modes of subwavelength plasmonic slot waveguides," J. Lightwave Technol. 25, 2511-2521 (2007).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett.  87, 131102 (2005).
[CrossRef]

Fang, G.

Ford, G. W.

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125409 (2004).
[CrossRef]

Fukui, M.

Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, "Characteristics of gap plasmon waveguide with stub structures," Opt. Express 16, 16314-16325 (2008).
[CrossRef] [PubMed]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

Gao, H.

Gramotnev, D. K.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

Gray, S.

Haraguchi, M.

Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, "Characteristics of gap plasmon waveguide with stub structures," Opt. Express 16, 16314-16325 (2008).
[CrossRef] [PubMed]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

Harel, E.

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

Huang, X.

Huang, X. G.

Jin, X.

Kik, P. G.

S. A. Maier, P. G. Kik, and H. A. Atwater, "Optical pulse propagation in metal nanoparticle chain waveguides," Phys. Rev. B 67, 205402 (2003).
[CrossRef]

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

Kim, K. Y.

Kobayashi, T.

Kocabas, S. E.

G. Veronis, S. E. Kocabas, D. A. B. Miller, and S. Fan, "Modeling of plasmonic waveguide components and networks," J. Comput. Theor. Nanosci. 6, 1808-1826 (2009).
[CrossRef]

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, "Transmission line and equivalent circuit models for plasmonic waveguide components," IEEE J. Sel. Top. Quantum Electron. 14, 1462-1472 (2008).
[CrossRef]

Koel, B. E.

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

Labeke, D. V.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Lamrous, O.

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

Lee, J.-H.

Lee, T.

Leosson, K.

Lin, X.

Liu, J.

Liu, S.

Lu, Z.

Luo, X.

Lv, Y.

Maier, S. A.

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

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

S. A. Maier, P. G. Kik, and H. A. Atwater, "Optical pulse propagation in metal nanoparticle chain waveguides," Phys. Rev. B 67, 205402 (2003).
[CrossRef]

Majewski, M. L.

Matsuo, S.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

Matsuzaki, Y.

Meltzer, S.

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

Miller, D. A. B.

G. Veronis, S. E. Kocabas, D. A. B. Miller, and S. Fan, "Modeling of plasmonic waveguide components and networks," J. Comput. Theor. Nanosci. 6, 1808-1826 (2009).
[CrossRef]

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, "Transmission line and equivalent circuit models for plasmonic waveguide components," IEEE J. Sel. Top. Quantum Electron. 14, 1462-1472 (2008).
[CrossRef]

Morimoto, A.

Mysyrowicz, A.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

Nakagaki, M.

Narimanov, E. E.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

Nikolajsen, T.

Ogawa, T.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

Okamoto, T.

Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, "Characteristics of gap plasmon waveguide with stub structures," Opt. Express 16, 16314-16325 (2008).
[CrossRef] [PubMed]

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

Pile, D. F. P.

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

Polman, A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,"  Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Prade, B.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

Rakic, A. D.

Requicha, A. G.

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

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

Shalaev, V. M.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

Shi, H.

Sweatlock, L. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,"  Phys. Rev. B 73, 035407 (2006).
[CrossRef]

Tae, H.-S.

Takahara, J.

Taki, H.

Tao, J.

Veronis, G.

G. Veronis, S. E. Kocabas, D. A. B. Miller, and S. Fan, "Modeling of plasmonic waveguide components and networks," J. Comput. Theor. Nanosci. 6, 1808-1826 (2009).
[CrossRef]

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, "Transmission line and equivalent circuit models for plasmonic waveguide components," IEEE J. Sel. Top. Quantum Electron. 14, 1462-1472 (2008).
[CrossRef]

G. Veronis and S. Fan, "Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides," Opt. Express 15, 1211-1221 (2007).
[CrossRef] [PubMed]

G. Veronis and S. Fan, "Modes of subwavelength plasmonic slot waveguides," J. Lightwave Technol. 25, 2511-2521 (2007).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett.  87, 131102 (2005).
[CrossRef]

Vinet, J. Y.

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

Volkov, V. S.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett.  95, 046802 (2005).
[CrossRef]

Wahsheh, R. A.

Wang, C.

Weber, W. H.

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125409 (2004).
[CrossRef]

Yamagishi, S.

Yao, H.

Zhang, Q.

Zhang, Y.

Zhao, H.

Appl. Opt. (1)

Appl. Phys. Lett (2)

D. F. P. Pile, T. Ogawa, D. K. Gramotnev, T. Okamoto, M. Haraguchi, M. Fukui, and S. Matsuo, "Theoretical and experimental investigation of strongly localized plasmons on triangular metal wedges for subwavelength waveguiding," Appl. Phys. Lett.  87, 061106 (2005).
[CrossRef]

G. Veronis and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett.  87, 131102 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

S. E. Kocabas, G. Veronis, D. A. B. Miller, and S. Fan, "Transmission line and equivalent circuit models for plasmonic waveguide components," IEEE J. Sel. Top. Quantum Electron. 14, 1462-1472 (2008).
[CrossRef]

J. Appl. Phys (1)

S. A. Maier and H. A. Atwater, "Plasmonics: Localization and guiding of electromagnetic energy in metal/dielectric structures," J. Appl. Phys.  98, 011101 (2005).
[CrossRef]

J. Comput. Theor. Nanosci. (1)

G. Veronis, S. E. Kocabas, D. A. B. Miller, and S. Fan, "Modeling of plasmonic waveguide components and networks," J. Comput. Theor. Nanosci. 6, 1808-1826 (2009).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A: Pure Appl. Opt. (2)

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

W. L. Barnes, "Surface plasmon-polariton length scales: A route to sub-wavelength optics," J. Opt. A: Pure Appl. Opt. 8, S87-S93 (2006).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (2)

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

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

Opt. Express (9)

J. Tao, X. Huang, X. Lin, Q. Zhang, and X. Jin, "A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure," Opt. Express 17, 13989-13994 (2009).
[CrossRef] [PubMed]

R. A. Wahsheh, Z. Lu, and M. A. G. Abushagur, "Nanoplasmonic couplers and splitters," Opt. Express 17, 19033-19040 (2009).
[CrossRef]

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, "Surface plasmon reflector based on serial stub structure," Opt. Express 17, 20134-20139 (2009).
[CrossRef] [PubMed]

Y. Matsuzaki, T. Okamoto, M. Haraguchi, M. Fukui, and M. Nakagaki, "Characteristics of gap plasmon waveguide with stub structures," Opt. Express 16, 16314-16325 (2008).
[CrossRef] [PubMed]

T. Lee and S. Gray, "Subwavelength light bending by metal slit structures," Opt. Express 13, 9652-9659 (2005).
[CrossRef] [PubMed]

H. Gao, H. Shi, C. Wang, C. Du, X. Luo, Q. Deng, Y. Lv, X. Lin, and H. Yao, "Surface plasmon polariton propagation and combination in Y-shaped metallic channels," Opt. Express 13, 10795-10800 (2005).
[CrossRef] [PubMed]

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006).
[CrossRef] [PubMed]

K. Y. Kim, Y. K. Cho, H.-S. Tae, and J.-H. Lee, "Light transmission along dispersive plasmonic gap and its subwavelength guidance characteristics," Opt. Express 14, 320-330 (2006).
[CrossRef] [PubMed]

G. Veronis and S. Fan, "Theoretical investigation of compact couplers between dielectric slab waveguides and two-dimensional metal-dielectric-metal plasmonic waveguides," Opt. Express 15, 1211-1221 (2007).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. (1)

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

Phys. Rev. B (4)

B. Prade, J. Y. Vinet, and A. Mysyrowicz, "Guided optical waves in planar heterostructures with negative dielectric constant," Phys. Rev. B 44, 13556-13572 (1991).
[CrossRef]

F. I. Baida, A. Belkhir, D. V. Labeke, and O. Lamrous, "Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes," Phys. Rev. B 74, 205419 (2006).
[CrossRef]

W. H. Weber and G. W. Ford, "Propagation of optical excitations by dipolar interactions in metal nanoparticle chains," Phys. Rev. B 70, 125409 (2004).
[CrossRef]

S. A. Maier, P. G. Kik, and H. A. Atwater, "Optical pulse propagation in metal nanoparticle chain waveguides," Phys. Rev. B 67, 205402 (2003).
[CrossRef]

Phys. Rev. Lett (1)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, "Channel plasmon-polariton guiding by subwavelength metal grooves," Phys. Rev. Lett.  95, 046802 (2005).
[CrossRef]

Other (9)

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

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, "Plasmon slot waveguides: Towards chipscale propagation with subwavelength-scale localization,"  Phys. Rev. B 73, 035407 (2006).
[CrossRef]

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[CrossRef]

G. Veronis and S. Fan, "Subwavelength plasmonic waveguide structures based on slots in thin metal films," Proc. SPIE 6123, 612308(1-10) (2006).

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Figures (8)

Fig. 1.
Fig. 1.

Left panel: Schematic of an MDM waveguide with dielectric layer of thickness h and permitivity ε1 separating two metallic layers of permittivity ε2. Right panel: Density plots of longitudinal (Ex) and transverse (Ey) electric fields (in arbitrary units) corresponding to the fundamental antisymmetric SPP mode.

Fig. 2.
Fig. 2.

Left panel: Real and imaginary parts of the dielectric permittivity of silver. Open circles show the experimental data and the solid curves show the fit with the 7-pole Drude–Lorentz model. Right panel: Real part of the effective refractive index and propagation length of SPPs for four thicknesses of the air layer in the Ag–air–Ag-waveguide.

Fig. 3.
Fig. 3.

Schematic of an MDM waveguide with a single stub of width w and length d coupled perpendicular to the waveguide axis (a). The equivalent transmission-line representation (b), its simplified circuit model (c), and details of the notations employed. ZMDM and ZS are the characteristic impedances of transmission lines corresponding to the MDM waveguide and the stub; ZL accounts for the reflection of SPPs from the stub end; Zstub is the effective stub impedance.

Fig. 4.
Fig. 4.

Transmission spectra of the Ag–air–Ag waveguide coupled to a 300-nm stub (left panel) and the evolution of the waveguide transmittance with the stub length for λ = 850 nm (right panel). The red, blue, and green curves show the results of our improved model [Eq. (8)], FDTD simulations, and the lossless model, respectively. The waveguide parameters are: h = w = 50 nm and L = 400 nm.

Fig. 5.
Fig. 5.

Schematic of (a) an MDM waveguide coupled to two stubs separated by distance Δ and (b) the corresponding transmission-line model.

Fig. 6.
Fig. 6.

Comparison between the analytic (red and green curves) and numerically calculated (blue curves) transmission spectra of the Ag–air–Ag-waveguide shown in Fig. 5(a). The left and right panels correspond to identical and different stubs, respectively. In all cases, w = h = 50 nm.

Fig. 7.
Fig. 7.

Schematic of MDM waveguide coupled to N stubs. The position, width, and length of the jth stub are given by lj, wj, and dj, respectively; Δ j is the distance between (j-1)th and jth stubs.

Fig. 8.
Fig. 8.

Transmittance of Ag–air–Ag–waveguide as a function of frequency for three (left panel) and four (right panel) equal stubs coupled perpendicular to the waveguide axis. In both panels, h = w = 50 nm.

Tables (1)

Tables Icon

Table 1. Parameters of the Drude–Lorentz model for silver

Equations (28)

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

U j x y t = U j ( y ) exp [ i ( βx ωt ) ] ,
n eff = β k = λ λ MDM + i λ 4 π L SPP ,
tanh ( i k 1 h 2 ) = ( ε 2 ε 1 k 1 k 2 ) ± 1 ,
ε 2 ( ω ) = 1 ω p 2 ω ( ω i γ ) + n = 1 5 f n ω n 2 ω n 2 ω 2 i ω γ n ,
z MDM ( h ) E 1 y h H 1 z = β ( h ) h ω ε 0 ε 1 ,
Z S ( w ) = Z MDM ( w ) = β ( w ) w ω ε 0 ε 1 .
Γ = Z L Z S Z L + Z S = ε 2 ε 1 ε 2 + ε 1 ,
Z L ( w ) = ε 2 ε 1 Z S ( w ) .
Z stub = Z S Z L i Z S tan ( β d ) Z S i Z L tan ( β d ) ,
V in ( x ) = V in + exp ( i β x ) + V in exp ( i β x ) , V out ( x ) = V out + exp [ i β ( x L ) ] ,
V in + V in = T V out + 0 ,
A ( x ) = ( exp ( i β x ) 0 0 exp ( i β x ) ) , B ( Z stub ) = ( 1 + Z MDM 2 Z stub Z MDM 2 Z stub Z MDM 2 Z stub 1 Z MDM 2 Z stub ) .
T 1 = V out + V in + 2 = 1 + Z MDM 2 Z stub 2 exp ( L L SPP ) .
Z stub ( j ) = Z S ( w j ) Z L ( w j ) i Z S ( w j ) tan [ β ( w j ) d j ] Z S ( w j ) i Z L ( w j ) tan [ β ( w j ) d j ] ,
T = A ( l 1 ) B ( Z stub ( 1 ) ) A ( Δ ) B ( Z stub ( 1 ) ) A ( L l 2 ) .
T 2 = ( 1 + Z MDM 2 Z stub ( 1 ) ) ( 1 + Z MDM 2 Z stub ( 2 ) ) Z MDM 2 4 Z stub ( 1 ) Z stub ( 2 ) exp ( 2 i β Δ ) 2 exp ( L L SPP ) .
T 1 = 1 + Z MDM Z stub 2 exp ( L L SPP ) .
β ( ω n ) ( d 1 + d 2 ) = π P n for Δ = p q ( d 1 + d 2 ) and
β ( ω n ) d 1 = π Q n for d 1 d 2 = p q ,
T = A ( l 1 ) B ( Z stub ( 1 ) ) ( j = 2 N A ( Δ j ) B ( Z stub ( j ) ) ) A ( L l N ) .
min j [ 2 , N ] Δ j 2 Im k 2 .
T N = Φ + N 1 G + Φ N 1 G 2 exp ( L L SPP ) ,
Φ ± = 1 2 [ 1 + Z MDM 2 Z stub + ( 1 Z MDM 2 Z stub ) exp ( 2 Δ ) ± Q ] ,
G ± = 1 2 Q { ( 1 + Z MDM 2 Z stub ) 2 [ 1 + ( Z MDM 2 Z stub ) 2 ] exp ( 2 Δ ) } ± 1 2 ( 1 + Z MDM 2 Z stub ) ,
Q = { [ 1 + Z MDM 2 Z stub + ( 1 Z MDM 2 Z stub ) exp ( 2 Δ ) ] 2 4 exp ( 2 Δ ) } 1 / 2 .
T N = 1 + Z MDM 2 Z stub 2 N exp ( L L SPP ) .
T N = 1 + N Z MDM 2 Z stub 2 = { 1 + N 2 4 [ ε 1 + ε 2 tan ( πd / Δ ) ε 2 + ε 1 tan ( πd / Δ ) ] 2 } 1 .
d Δ = n 1 π tan 1 ε 1 ε 2 ,

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