Abstract

We use coupled mode theory (CMT) to analyze a metal-insulator-metal (MIM) plasmonic stub structure, to reveal the existence of asymmetry in its transmittance spectra. Including the effect of the near field contribution for the stub structure, the observed asymmetry is interpreted as Fano-type interference between the quasi-continuum T-junction-resonator local-modes and discrete stub eigenmodes. Based on the asymmetry factor derived from the CMT analysis, methods to control transmittance asymmetry are also demonstrated.

© 2011 OSA

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    [CrossRef]
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    [CrossRef] [PubMed]
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  13. A. A. Reiserer, J. S. Huang, B. Hecht, and T. Brixner, “Subwavelength broadband splitters and switches for femtosecond plasmonic signals,” Opt. Express 18(11), 11810–11820 (2010).
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  14. H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19(4), 2910–2915 (2011).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2011 (3)

2010 (7)

2009 (5)

2008 (2)

2007 (2)

K. Ogusu and K. Takayama, “Transmission characteristics of photonic crystal waveguides with stubs and their application to optical filters,” Opt. Lett. 32(15), 2185–2187 (2007).
[CrossRef] [PubMed]

X. Yang, C. Husko, C. Wong, M. Yu, and D. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91(5), 051113 (2007).
[CrossRef]

2001 (1)

2000 (1)

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, and F. P. H. Van Beckum, “Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters,” Opt. Quantum Electron. 32(6/8), 947–961 (2000).
[CrossRef]

1998 (1)

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Agrawal, G. P.

Borges, B.-H. V.

Bozhevolnyi, S. I.

Brixner, T.

Chen, J.

Dai, Q. F.

De Ridder, R. M.

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, and F. P. H. Van Beckum, “Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters,” Opt. Quantum Electron. 32(6/8), 947–961 (2000).
[CrossRef]

Diniz, L. O.

Fan, S.

Fang, G.

Fano, U.

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Flach, S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

Fukui, M.

Gong, Y.

Han, Z.

Hao, Y.

Haraguchi, M.

Hattori, H. T.

Haus, H. A.

Hecht, B.

Hoekstra, H. J. W. M.

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, and F. P. H. Van Beckum, “Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters,” Opt. Quantum Electron. 32(6/8), 947–961 (2000).
[CrossRef]

Huang, J. S.

Huang, X.

Huang, X. G.

Husko, C.

X. Yang, C. Husko, C. Wong, M. Yu, and D. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91(5), 051113 (2007).
[CrossRef]

Jiang, X.

Jin, X.

Joannopoulos, J. D.

Johnson, S. G.

Kivshar, Y. S.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

Kwong, D.

X. Yang, C. Husko, C. Wong, M. Yu, and D. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91(5), 051113 (2007).
[CrossRef]

Lan, S.

Lin, X.

Lin, X. S.

Liu, J.

Liu, S.

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Surface plasmon reflector based on serial stub structure,” Opt. Express 17(22), 20134–20139 (2009).
[CrossRef] [PubMed]

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

Liu, X.

Lu, H.

Manolatou, C.

Mao, D.

Marega, E.

Matsuzaki, Y.

Min, C.

Miroshnichenko, A. E.

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

Nakagaki, M.

Nunes, F. D.

Ogusu, K.

Okamoto, T.

Pannipitiya, A.

Premaratne, M.

Reiserer, A. A.

Rukhlenko, I. D.

Song, Y.

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

Stoffer, R.

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, and F. P. H. Van Beckum, “Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters,” Opt. Quantum Electron. 32(6/8), 947–961 (2000).
[CrossRef]

Takayama, K.

Tao, J.

Van Beckum, F. P. H.

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, and F. P. H. Van Beckum, “Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters,” Opt. Quantum Electron. 32(6/8), 947–961 (2000).
[CrossRef]

Van Groesen, E.

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, and F. P. H. Van Beckum, “Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters,” Opt. Quantum Electron. 32(6/8), 947–961 (2000).
[CrossRef]

Veronis, G.

Villeneuve, P. R.

Wang, F.

Wang, J.

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

Wang, L.

Wang, M.

Wang, X.

Wang, Y.

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

Weiner, J.

Wong, C.

X. Yang, C. Husko, C. Wong, M. Yu, and D. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91(5), 051113 (2007).
[CrossRef]

Wu, L. J.

Xu, Y.

Yang, J.

Yang, K.

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

Yang, L.

Yang, X.

X. Yang, C. Husko, C. Wong, M. Yu, and D. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91(5), 051113 (2007).
[CrossRef]

Yu, M.

X. Yang, C. Husko, C. Wong, M. Yu, and D. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91(5), 051113 (2007).
[CrossRef]

Zhang, Q.

Zhang, X.

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

Zhang, Y.

Zhao, H.

Zhong, Z. J.

Zhou, H.

Zhou, Q.

Zhu, J. H.

Appl. Phys. Lett. (1)

X. Yang, C. Husko, C. Wong, M. Yu, and D. Kwong, “Observation of femtojoule optical bistability involving Fano resonances in high-Q/Vm silicon photonic crystal nanocavities,” Appl. Phys. Lett. 91(5), 051113 (2007).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (3)

Opt. Express (11)

A. Pannipitiya, I. D. Rukhlenko, M. Premaratne, H. T. Hattori, and G. P. Agrawal, “Improved transmission model for metal-dielectric-metal plasmonic waveguides with stub structure,” Opt. Express 18(6), 6191–6204 (2010).
[CrossRef] [PubMed]

F. Wang, X. Wang, H. Zhou, Q. Zhou, Y. Hao, X. Jiang, M. Wang, and J. Yang, “Fano-resonance-based Mach-Zehnder optical switch employing dual-bus coupled ring resonator as two-beam interferometer,” Opt. Express 17(9), 7708–7716 (2009).
[CrossRef] [PubMed]

Z. J. Zhong, Y. Xu, S. Lan, Q. F. Dai, and L. J. Wu, “Sharp and asymmetric transmission response in metal-dielectric-metal plasmonic waveguides containing Kerr nonlinear media,” Opt. Express 18(1), 79–86 (2010).
[CrossRef] [PubMed]

C. Min and G. Veronis, “Absorption switches in metal-dielectric-metal plasmonic waveguides,” Opt. Express 17(13), 10757–10766 (2009).
[CrossRef] [PubMed]

A. A. Reiserer, J. S. Huang, B. Hecht, and T. Brixner, “Subwavelength broadband splitters and switches for femtosecond plasmonic signals,” Opt. Express 18(11), 11810–11820 (2010).
[CrossRef] [PubMed]

H. Lu, X. Liu, L. Wang, Y. Gong, and D. Mao, “Ultrafast all-optical switching in nanoplasmonic waveguide with Kerr nonlinear resonator,” Opt. Express 19(4), 2910–2915 (2011).
[CrossRef] [PubMed]

J. Tao, X. G. Huang, X. Lin, Q. Zhang, and X. Jin, “A narrow-band subwavelength plasmonic waveguide filter with asymmetrical multiple-teeth-shaped structure,” Opt. Express 17(16), 13989–13994 (2009).
[CrossRef] [PubMed]

J. Liu, G. Fang, H. Zhao, Y. Zhang, and S. Liu, “Surface plasmon reflector based on serial stub structure,” Opt. Express 17(22), 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(21), 16314–16325 (2008).
[CrossRef] [PubMed]

J. Tao, X. G. Huang, and J. H. Zhu, “A wavelength demultiplexing structure based on metal-dielectric-metal plasmonic nano-capillary resonators,” Opt. Express 18(11), 11111–11116 (2010).
[CrossRef] [PubMed]

Z. Han and S. I. Bozhevolnyi, “Plasmon-induced transparency with detuned ultracompact Fabry-Perot resonators in integrated plasmonic devices,” Opt. Express 19(4), 3251–3257 (2011).
[CrossRef] [PubMed]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

R. Stoffer, H. J. W. M. Hoekstra, R. M. De Ridder, E. Van Groesen, and F. P. H. Van Beckum, “Numerical studies of 2D photonic crystals: Waveguides, coupling between waveguides and filters,” Opt. Quantum Electron. 32(6/8), 947–961 (2000).
[CrossRef]

Optik (Stuttg.) (1)

J. Wang, Y. Wang, X. Zhang, K. Yang, Y. Wang, S. Liu, and Y. Song, “A transmission line model for subwavelength metallic grating with single cut,” Optik (Stuttg.) . in press, doi:.

Phys. Rev. (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124(6), 1866–1878 (1961).
[CrossRef]

Rev. Mod. Phys. (1)

A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010).
[CrossRef]

Other (3)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

L. O. Diniz, F. D. Nunes, E. Marega, Jr., and B. H. V. Borges, “A novel subwavelength plasmon-polariton optical filter based on tilted coupled structures,” in Proc. META’ 10 2nd Int. Conf. Metamaterials, Photonic Crystals and Plasmonics, Cairo, Egypt, 106–110 (2010).

D. M. Pozar, Microwave Engineering (John Wiley & Sons, 2005).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematics of stub structure. W is the width of stub / waveguide, and L is stub length. (b) Analytic equivalent model for CMT with an effective low-Q resonator in the junction region

Fig. 2
Fig. 2

Field patterns of plasmonic MIM (Ag-Si-Ag) stub structures, at the operation frequency ωT = 193THz. Waveguide width W was set to 30 nm. Stub length L = (5/4λspp and 9/4λspp ) - δskin-depth for FDTD was set at, (a) 440 nm and (b) 810 nm. Corresponding transmittance spectra are shown in (c) and (d), calculated either with CMT (marks) or FDTD numerical analysis (lines). AR = 0 for PEC and −0.8 for real metal.

Fig. 3
Fig. 3

Stub structures (Ag-Si-Ag) with different refractive index n in the junction resonator region; (a) n = 1, (b) n = 3.46, and (c) n = 5. Transmittance spectra from stub (a)~(c) are shown in (d)~(f). Insets show the zoomed-in local mode profiles around the junction resonator. The values of AR used in the CMT was 0 (for n = 1), −0.8 (for n = 3.46), and −1.7 (for n = 5), respectively.

Fig. 4
Fig. 4

Stub structures (Ag-Si-Ag) and field profiles at different operation frequencies; (a) ωT = 150 THz, (L = 580 nm), (b) ωT = 193 THz (L = 440 nm), and (c) ωT = 300 THz (L = 260 nm). Transmittance spectra from the stub structures of (a) ~(c) are shown in (d) ~(f). The values of asymmetry factor AR used in the CMT calculation were −0.5, −0.8, and −1.2, respectively.

Equations (9)

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

d a d t = ( j ω R 1 τ 1 1 τ 2 1 τ 3 ) a + κ 1 s 1 + + κ 2 s 2 + + κ 3 s 3 + )
s 1 = s 1 + + κ 1 a ,
s 2 = s 2 + + κ 2 a ,
s 3 = s 3 + + κ 3 a .
s 3 + = s 3 e j φ ,
t = s 2 s 1 + = κ 1 κ 2 j ( ω ω R ) 1 τ 1 1 τ 2 1 τ 3 + κ 3 2 1 + e j φ
t = 2 j ( ω ω R ) τ 0 + 3 2 1 + e j φ
A R ( ω ω R ) τ 0 = 2 ( ω ω R ) / Γ 0
T = | t | 2 = 4 ( cos φ + 1 ) ( A R 2 + 3 ) ( cos φ + 1 ) + 2 + 2 A R sin φ

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