Abstract

In this study, we describe characteristics of plasmonic filters based on stubs coupled perpendicularly to metal–insulator–metal waveguides. To achieve a desirable filter, a designing procedure is proposed based on impedance curves, which lead to responses with great accordance to those obtained by numeric techniques. We study the impact of stub lengths and distance between stubs on bandgap width and filter sharpening. In addition, we illustrate the existence of trade-off between filter dimensions and filter parameters, which lead to a discussion about advantages and disadvantages of these structures. Validation of analytic results is confirmed with the finite-difference time-domain method.

© 2011 Optical Society of America

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References

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  2. 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]
  3. 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]
  4. 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] [PubMed]
  5. D. F. P. Pile and D. K. Gramotev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29, 1069–1071 (2004).
    [CrossRef] [PubMed]
  6. D. K. Gramotev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel Plasmon-polaritons in triangular,” Appl. Phys. Lett. 85, 6323–6325 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2011 (1)

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, “Numerical investigation of tunable band-pass plasmonic filter with hollow-core ring resonator,” J. Opt. 13035004 (2011).
[CrossRef]

2010 (2)

2009 (3)

2008 (1)

2007 (1)

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

2006 (2)

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

S. S. Xiao, L. Liu, and M. Qiu, “Resonator channel drop filters in a plasmon–polaritons metal,” Opt. Express 14, 2932–2937(2006).
[CrossRef] [PubMed]

2005 (3)

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

M. A. Parker, Physics of Optoelectronics (CRC Press, 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] [PubMed]

2004 (2)

D. K. Gramotev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel Plasmon-polaritons in triangular,” Appl. Phys. Lett. 85, 6323–6325 (2004).
[CrossRef]

D. F. P. Pile and D. K. Gramotev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29, 1069–1071 (2004).
[CrossRef] [PubMed]

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]

1984 (1)

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinenann, 1984).

Abrishamian, M. S.

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, “Numerical investigation of tunable band-pass plasmonic filter with hollow-core ring resonator,” J. Opt. 13035004 (2011).
[CrossRef]

Agrawal, G. P.

Atwater, H. A.

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407(2006).
[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]

Barnes, W. L.

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

Bozhevolnyi, S. I.

D. K. Gramotev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[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] [PubMed]

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] [PubMed]

Dionne, J. A.

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

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] [PubMed]

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

Fan, S.

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

Fang, G.

Fukui, M.

Geluk, E. J.

Gramotev, D. K.

D. K. Gramotev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

D. F. P. Pile and D. K. Gramotev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29, 1069–1071 (2004).
[CrossRef] [PubMed]

D. K. Gramotev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel Plasmon-polaritons in triangular,” Appl. Phys. Lett. 85, 6323–6325 (2004).
[CrossRef]

Haraguchi, M.

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]

Hattori, H. T.

Hill, M. T.

Huang, X.

Karouta, F.

Kik, P. 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]

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]

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]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinenann, 1984).

Leong, E. S. P.

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinenann, 1984).

Lin, X.

Liu, J.

Liu, L.

Liu, S.

Maier, S. A.

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

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]

Marell, M.

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]

Mirnaziry, S. R.

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, “Numerical investigation of tunable band-pass plasmonic filter with hollow-core ring resonator,” J. Opt. 13035004 (2011).
[CrossRef]

Nakagaki, M.

Ning, C.-Z.

Oei, Y.-S.

Okamoto, T.

Pannipitiya, A.

Parker, M. A.

M. A. Parker, Physics of Optoelectronics (CRC Press, 2005).
[CrossRef]

Peter, J.

Pile, D. F. P.

D. K. Gramotev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel Plasmon-polaritons in triangular,” Appl. Phys. Lett. 85, 6323–6325 (2004).
[CrossRef]

D. F. P. Pile and D. K. Gramotev, “Channel plasmon-polariton in a triangular groove on a metal surface,” Opt. Lett. 29, 1069–1071 (2004).
[CrossRef] [PubMed]

Polman, A.

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

Premaratne, M.

Qiu, M.

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]

Richard, N.

Rukhlenko, I. D.

Setayesh, A.

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, “Numerical investigation of tunable band-pass plasmonic filter with hollow-core ring resonator,” J. Opt. 13035004 (2011).
[CrossRef]

Smalbragge, B.

Smit, M. K.

Sun, M.

Sweatlock, L. A.

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

Van, V.

Veronis, G.

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

Xiao, S. S.

Zhang, Y.

Zhao, H.

Zhu, Y.

Appl. Phys. Lett. (2)

D. K. Gramotev and D. F. P. Pile, “Single-mode subwavelength waveguide with channel Plasmon-polaritons in triangular,” Appl. Phys. Lett. 85, 6323–6325 (2004).
[CrossRef]

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

J. Opt. (1)

A. Setayesh, S. R. Mirnaziry, and M. S. Abrishamian, “Numerical investigation of tunable band-pass plasmonic filter with hollow-core ring resonator,” J. Opt. 13035004 (2011).
[CrossRef]

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

Nat. Photon. (1)

D. K. Gramotev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photon. 4, 83–91 (2010).
[CrossRef]

Nature (2)

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, 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]

Opt. Express (5)

Opt. Lett. (1)

Phys. Rev. B (2)

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]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407(2006).
[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] [PubMed]

Other (3)

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

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Butterworth-Heinenann, 1984).

M. A. Parker, Physics of Optoelectronics (CRC Press, 2005).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

(a) Schematic of an MIM waveguide and the field orientation corresponding to the odd TM mode. (b) Electric field ratio of an antisymmetric TM mode inside an MIM waveguide. Inset shows the profile of electric field components of the odd TM mode at λ = 0.8 μm .

Fig. 2
Fig. 2

(a) Profile of energy density at different locations for four wavelengths. Plots are normalized to the maximum value of energy density at each wavelength. (b) Comparison between contributions of electric field components at total energy over the optical spectrum.

Fig. 3
Fig. 3

(a) Schematic of a single-stub filter with stub length L stub , stub width W stub , and main waveguide width of W MIM . (b) Equivalent transmission line model for a single-stub filter.

Fig. 4
Fig. 4

Normalized real part of stub impedance with W stub = 100 nm (red dashed curve) and normalized real part of input impedance obtained by paralleling stub impedance and characteristic impedance. The main waveguide is Ag–air–Ag with W MIM = 100 nm .

Fig. 5
Fig. 5

Transmission spectra of a single-stub structure designed with stub length corresponding to the (a) first and (b) second trough of the input impedance curve for filtering λ = 1 μm . All widths are assumed 100 nm .

Fig. 6
Fig. 6

Comparison between two different designs of a single-stub filter. The blue solid curve is obtained by using the stub length found from the input impedance curve, and the red dashed curve is obtained from Eq. (10). Stub width and waveguide width in both designs are fixed to 100 nm .

Fig. 7
Fig. 7

(a) Schematic of a two-stub filter with stub lengths L stub1 and L stub 2 . Stub widths are W stub1 and W stub2 , respectively. The distance between two stubs is D. (b) Transmission line model for a two-stub filter.

Fig. 8
Fig. 8

Transmission spectra of a designed two-stub filter for reflecting (a)  λ = 0.8 μm and (b)  λ = 1.25 μm . All widths for both (a) and (b) are fixed to 100 nm .

Fig. 9
Fig. 9

Variation effect of distance between two stubs on the real part of transferred impedance. Transferred impedance has been normalized. All widths are considered 100 nm .

Fig. 10
Fig. 10

Transmission spectra of a two-stub filter designed for constructing a narrow bandgap at λ = 1.2 μm . All widths are considered 100 nm .

Fig. 11
Fig. 11

Effect of choosing different distances between two stubs on the transmission spectra of a two-stub filter. The dotted red (dashed blue) curve is achieved by using the distance obtained with respect to the first (second) trough of input impedance curve. The stub width and the main waveguide width are both assumed to be 100 nm .

Fig. 12
Fig. 12

Normalized input impedance curves of a two-stub filter with respect to stub lengths. The red dashed curve is obtained at λ = 0.8 μm , and the blue solid curve is obtained at λ = 1.2 μm . All widths are 100 nm .

Fig. 13
Fig. 13

Transmission spectra of a two-stub filter designed to construct a bandgap at λ = 0.8 μm while passing λ = 1.2 μm . All widths are fixed at 100 nm .

Fig. 14
Fig. 14

(a) Transmission spectra of a three-stub filter designed to construct a bandgap at λ = 1 μm . (b) Transmission spectra of a two-stub filter designed to construct a narrow-width bandgap at λ = 1 μm .

Tables (2)

Tables Icon

Table 1 Comparison between the Stub Lengths Obtained by Eq. (10) and Those Obtained by Impedance Curve for Three Wavelengths λ = 0.8 , 1 , 1.5 μm a

Tables Icon

Table 2 Comparison between Filter Dimensions and Bandgap Width a

Equations (13)

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

E x = i A 1 ω ε 0 ε 1 k 1 e i β x e k 1 z + i B 1 ω ε 0 ε 1 k 1 e i β x e k 1 z ,
E z = A β ω ε 0 ε 1 e i β x e k 1 z + B β ω ε 0 ε 1 e i β x e k 1 z ,
tanh ( k 1 W MIM 2 ) = ( k 2 ε 1 k 1 ε 2 ) .
| E x E z | = | k 1 β | tanh ( k 1 z ) .
U = 0.5 ( E . D + H . B ) ,
U = 0.5 ( Re ( ω ε 2 ω ) E . E + H . B ) .
Z MIM = V I E z W MIM H y = β ( W MIM ) W MIM ω ε 0 ε r .
Z L = Z MIM ε 2 ε 1 .
Z stub = Z MIM Z L i Z MIM tan ( β ( W stub ) L stub ) Z MIM i Z L tan ( β ( W stub ) L stub ) .
Z in = Z stub Z MIM Z stub + Z MIM ,
L stub = ( π 2 β ( W stub ) ) .
T = | 1 + Z MIM 2 Z stub | 2 e ( L L spp ) ,
T = | ( 1 + Z MIM 2 Z stub 1 ) ( 1 + Z MIM 2 Z stub 2 ) Z MIM 2 4 Z stub1 Z stub2 e ( 2 i β D ) | 2 exp ( L L spp ) .

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