Abstract

Subwavelength surface plasmon polariton optical filters based on metal–insulator–metal slot nanocavites are proposed and analyzed by using coupled mode theory and a finite element method. Simulation results reveal that a single slot cavity coupled with two access waveguides possesses a bandpass-filtering characteristic with its performance affected by its geometric parameters. To further improve the filtering performance, we explore coupled slot cavities as high-order plasmonic filters. When the slot cavities are side-coupled, the bandpass filtering spectrum is dependent on the positions of the access waveguides. The two slot cavities can also be set orthogonal, leading to strong mutual coupling. With careful tuning of the relative length between the two cavities, improved filtering spectrum can be obtained. Given the subwavelength footprint of the proposed plasmonic filters, they can be used in an ultradense plasmonic integrated circuit for optical signal processing.

© 2013 Optical Society of America

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References

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    [CrossRef]
  2. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, “Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides,” Nat. Mater. 2, 229–232 (2003).
    [CrossRef]
  3. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
    [CrossRef]
  4. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010).
    [CrossRef]
  5. P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
    [CrossRef]
  6. D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30, 1186–1188 (2005).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (1)

2011 (2)

2010 (5)

2009 (6)

2008 (3)

2007 (3)

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal–insulator–metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

2006 (4)

A. Hosseini and Y. Massoud, “A low-loss metal–insulator–metal plasmonic Bragg reflector,” Opt. Express 14, 11318–11323 (2006).
[CrossRef]

J. Dionne, H. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

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

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

2005 (2)

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30, 1186–1188 (2005).
[CrossRef]

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

2004 (1)

2003 (1)

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

2002 (1)

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714 (2002).
[CrossRef]

2000 (1)

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
[CrossRef]

1969 (1)

E. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[CrossRef]

Abrishamian, M. S.

Abushagur, M. A. G.

Atwater, H.

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

Atwater, H. A.

J. Dionne, H. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

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

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714 (2002).
[CrossRef]

Berini, P.

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Borghs, G.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3, 283–286 (2009).
[CrossRef]

Bozhevolnyi, S. I.

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

Chen, A.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Dalton, L.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

De Vlaminck, I.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3, 283–286 (2009).
[CrossRef]

Dionne, J.

J. Dionne, H. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

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

Economou, E.

E. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[CrossRef]

Fan, S.

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

Forsberg, E.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal–insulator–metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Gong, Y.

Gramotnev, D. K.

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

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30, 1186–1188 (2005).
[CrossRef]

Halas, N. J.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Han, Z.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal–insulator–metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Harel, E.

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

Haus, H. A.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Vol. 1.

He, S.

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal–insulator–metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

Hosseini, A.

A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

A. Hosseini and Y. Massoud, “A low-loss metal–insulator–metal plasmonic Bragg reflector,” Opt. Express 14, 11318–11323 (2006).
[CrossRef]

Hu, F.

Huang, X. G.

Jin, X.

Jin, X. P.

Kik, P. G.

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

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714 (2002).
[CrossRef]

Kim, H.

Kim, J.

Koel, B. E.

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

Lagae, L.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3, 283–286 (2009).
[CrossRef]

Lal, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Lee, B.

Lezec, H.

J. Dionne, H. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

Lin, X.

Lin, X. S.

Link, S.

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Liu, X.

Liu, Y.

Lu, H.

Lu, Z.

Mahigir, A.

Maier, S. A.

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

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714 (2002).
[CrossRef]

Mao, D.

Massoud, Y.

A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

A. Hosseini and Y. Massoud, “A low-loss metal–insulator–metal plasmonic Bragg reflector,” Opt. Express 14, 11318–11323 (2006).
[CrossRef]

Meltzer, S.

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

Min, C.

Mirnaziry, S. R.

Neutens, P.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3, 283–286 (2009).
[CrossRef]

Ozbay, E.

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Pakizeh, T.

Park, J.

Pile, D. F. P.

Polman, A.

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

Pyayt, A. L.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Requicha, A. A. G.

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

Setayesh, A.

Sweatlock, L.

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

Tao, J.

Van Dorpe, P.

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3, 283–286 (2009).
[CrossRef]

Veronis, G.

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

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

Wahsheh, R. A.

Wang, B.

Wang, G. P.

Wang, H. Z.

Wang, L.

Wang, T. B.

Wen, X. W.

Wiley, B.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Xia, Y.

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Yi, H.

Yin, C. P.

Zand, I.

Zhang, Q.

Zhou, Z.

Zhu, J. H.

Appl. Phys. Lett. (3)

S. A. Maier, P. G. Kik, and H. A. Atwater, “Observation of coupled plasmon-polariton modes in Au nanoparticle chain waveguides of different lengths: estimation of waveguide loss,” Appl. Phys. Lett. 81, 1714 (2002).
[CrossRef]

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

A. Hosseini and Y. Massoud, “Nanoscale surface plasmon based resonator using rectangular geometry,” Appl. Phys. Lett. 90, 181102 (2007).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

Z. Han, E. Forsberg, and S. He, “Surface plasmon Bragg gratings formed in metal–insulator–metal waveguides,” IEEE Photon. Technol. Lett. 19, 91–93 (2007).
[CrossRef]

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

Nano Lett. (1)

J. Dionne, H. Lezec, and H. A. Atwater, “Highly confined photon transport in subwavelength metallic slot waveguides,” Nano Lett. 6, 1928–1932 (2006).
[CrossRef]

Nat. Mater. (1)

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

Nat. Nanotechnol. (1)

A. L. Pyayt, B. Wiley, Y. Xia, A. Chen, and L. Dalton, “Integration of photonic and silver nanowire plasmonic waveguides,” Nat. Nanotechnol. 3, 660–665 (2008).
[CrossRef]

Nat. Photonics (3)

P. Neutens, P. Van Dorpe, I. De Vlaminck, L. Lagae, and G. Borghs, “Electrical detection of confined gap plasmons in metal–insulator–metal waveguides,” Nat. Photonics 3, 283–286 (2009).
[CrossRef]

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

S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1, 641–648 (2007).
[CrossRef]

Opt. Express (11)

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

Y. Liu and J. Kim, “Characteristics of plasmonic Bragg reflectors with insulator width modulated in sawtooth profiles,” Opt. Express 18, 11589–11598 (2010).
[CrossRef]

A. Hosseini and Y. Massoud, “A low-loss metal–insulator–metal plasmonic Bragg reflector,” Opt. Express 14, 11318–11323 (2006).
[CrossRef]

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

H. Lu, X. Liu, D. Mao, L. Wang, and Y. Gong, “Tunable band-pass plasmonic waveguide filters with nanodisk resonators,” Opt. Express 18, 17922–17927 (2010).
[CrossRef]

T. B. Wang, X. W. Wen, C. P. Yin, and H. Z. Wang, “The transmission characteristics of surface plasmon polaritons in ring resonator,” Opt. Express 17, 24096–24101 (2009).
[CrossRef]

I. Zand, A. Mahigir, T. Pakizeh, and M. S. Abrishamian, “Selective-mode optical nanofilters based on plasmonic complementary split-ring resonators,” Opt. Express 20, 7516–7525 (2012).
[CrossRef]

J. Park, H. Kim, and B. Lee, “High order plasmonic Bragg reflection in the metal–insulator–metal waveguide Bragg grating,” Opt. Express 16, 413–425 (2008).
[CrossRef]

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, 13989–13994 (2009).
[CrossRef]

Q. Zhang, X. G. Huang, X. S. Lin, J. Tao, and X. P. Jin, “A subwavelength coupler-type MIM optical filter,” Opt. Express 17, 7549–7555 (2009).
[CrossRef]

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, 11111–11116 (2010).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. (1)

E. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539 (1969).
[CrossRef]

Phys. Rev. B (2)

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

P. Berini, “Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures,” Phys. Rev. B 61, 10484 (2000).
[CrossRef]

Science (1)

E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189–193 (2006).
[CrossRef]

Other (1)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984), Vol. 1.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic structure of the plasmonic filter based on a single SPP slot cavity.

Fig. 2.
Fig. 2.

(a) Reflection and (b) transmission spectra of the plasmonic filter based on a single SPP slot cavity for various coupling gap sizes. (c) Filter central wavelength versus coupling gap. (d) Filter insertion loss and bandwidth versus coupling gap.

Fig. 3.
Fig. 3.

(a) Reflection and (b) transmission spectra of the plasmonic filter based on a single SPP slot cavity for various cavity widths. (c) Filter central wavelength versus coupling gap. (d) Filter insertion loss and bandwidth versus coupling gap.

Fig. 4.
Fig. 4.

Schematic structures of plasmonic filters based on two side-coupled SPP slot cavities. The output waveguide can either be directly coupled with (a) the first cavity (type I) or (b) the second cavity (type II).

Fig. 5.
Fig. 5.

(a)–(c) Reflection and transmission spectra of the plasmonic filter based on side-coupled SPP slot cavities (type I) for various cavity length differences. The intercavity gap is gc=70nm. (d)–(f) Reflection and transmission spectra for various intercavity gap sizes. The cavity length difference is dLc=5nm. (g) Magnetic field Hy, (h) electric field Ex, and (i) time-averaged power flow magnitude Pav distributions at the filter central wavelength with dLc=5nm and gc=100nm.

Fig. 6.
Fig. 6.

(a) Reflection and (b) transmission spectra of plasmonic filter based on side-coupled SPP slot cavities (type II) for various intercavity gap sizes. (c) Magnetic-field Hy, (d) electric-field Ex, and (e) time-averaged power flow magnitude Pav distributions at the filter central wavelength with gc=70nm.

Fig. 7.
Fig. 7.

Schematic structure of the plasmonic filter based on two cross-coupled SPP slot cavities.

Fig. 8.
Fig. 8.

(a) Reflection and (b) transmission spectra of the plasmonic filter based on cross-coupled SPP slot cavities (Lc1=Lc2) and a single vertical cavity. (c)–(e) Magnetic-field Hy distributions in the filter corresponding to three wavelengths of interest: (c) notch A, (d) peak B, and (e) peak C. Their spectral positions are indicated in (b).

Fig. 9.
Fig. 9.

(a) Reflection and (b) transmission spectra of the plasmonic filter based on cross-coupled SPP slot cavities. The vertical cavity length is varied. (c) Magnetic-field Hy, (d) electric-field Ex, and (e) time-averaged power flow magnitude Pav distributions at the filter central wavelength indicated by the dotted curves in (a) and (b) for dLc=124nm. (f)–(h) are the distribution for dLc=148nm.

Equations (14)

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εdpεmk=1ekW1+ekW.
k=k0βspp2εdk02;p=k0βspp2εmk02,
εm(ω)=εωpω(ω+iγ),
P=[Re(E×H*)dS]/2.
dadt=(jω01τ01τe11τe2)a+κ1s+1,
s1=s+1+κ1*as2=κ2*a.
R=s1s+1=j(ωωo)1τo+1τe11τe2j(ωωo)+1τo+1τe1+1τe2,
T=s2s+1=2τe1τe2ej(θ1θ2)j(ωωo)+1τo+1τe1+1τe2.
da1dt=(jω11τ101τe11τe2)a1+κ1s+1jμa2da2dt=(jω21τ20)a2jμa1,
R=s1s+1=[j(ωω1)+1τ101τe1+1τe2][j(ωω2)+1τ20]+μ2[j(ωω1)+1τ10+1τe1+1τe2][j(ωω2)+1τ20]+μ2,
T=s2s+1=2τe1τe2ej(θ1θ2)[j(ωω2)+1τ20][j(ωω1)+1τ10+1τe1+1τe2][j(ωω2)+1τ20]+μ2.
da1dt=(jω11τ101τe1)a1+κ1s+1jμa2da2dt=(jω21τ201τe2)a2jμa1.
R=s1s+1=[j(ωω1)+1τ101τe1][j(ωω2)+1τ20+1τe2]+μ2[j(ωω1)+1τ10+1τe1][j(ωω2)+1τ20+1τe2]+μ2,
T=s2s+1=2μτe1τe2ej(θ1θ2π/2)[j(ωω1)+1τ10+1τe1][j(ωω2)+1τ20+1τe2]+μ2.

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