Abstract

We introduce compact wavelength-scale slit-based structures for coupling free space light into metal-dielectric-metal (MDM) subwave-length plasmonic waveguides. We first show that for a single slit structure the coupling efficiency is limited by a trade-off between the light power coupled into the slit, and the transmission of the slit-MDM waveguide junction. We next consider a two-section slit structure, and show that for such a structure the upper slit section enhances the coupling of the incident light into the lower slit section. The optimized two-section slit structure results in ∼ 2.3 times enhancement of the coupling into the MDM plasmonic waveguide compared to the optimized single-slit structure. We finally consider a symmetric double-slit structure, and show that for such a structure the surface plasmons excited at the metal-air interfaces are partially coupled into the slits. Thus, the coupling of the incident light into the slits is greatly enhanced, and the optimized double-slit structure results in ∼ 3.3 times coupling enhancement compared to the optimized single-slit structure. In all cases the coupler response is broadband.

© 2012 OSA

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2011 (1)

2010 (3)

L. Verslegers, Z. Yu, P. B. Catrysse, and S. Fan, “Temporal coupled-mode theory for resonant apertures,” J. Opt. Soc. Am. B 27, 1947–1956 (2010).
[CrossRef]

R. X. Yang, R. A. Wahsheh, Z. L. Lu, and M. A. G. Abushagur, “Efficient light coupling between dielectric slot waveguide and plasmonic slot waveguide,” Opt. Lett. 35, 649–651 (2010).
[CrossRef] [PubMed]

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

2009 (5)

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

J. Tian, S. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

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

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

K. Diest, J. A. Dionne, M. Spain, and H. A. Atwater, “Tunable color filters based on metal-insulator-metal resonators,” Nano Lett. 9, 2579–2583 (2009).
[CrossRef] [PubMed]

2008 (4)

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. Topics Quantum Electron. 14, 1462–1472 (2008).
[CrossRef]

M. J. Preiner, K. T. Shimizu, J. S. White, and N. A. Melosh, “Efficient optical coupling into metal-insulator-metal plasmon modes with subwavelength diffraction gratings,” Appl. Phys. Lett. 92, 113109 (2008).
[CrossRef]

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]

X. S. Lin and X. G. Huang, “Tooth-shaped plasmonic waveguide filters with nanometeric sizes,” Opt. Lett. 33, 2874–2876 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (2)

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

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

2005 (1)

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

2004 (2)

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] [PubMed]

2002 (2)

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
[CrossRef]

S. D. Wu and E. N. Glytsis, “Finite-number-of-periods holographic gratings with finite-width incident beams: analysis using the finite-difference frequency-domain method,” J. Opt. Soc. Am. A 19, 2018–2029 (2002).
[CrossRef]

1989 (1)

K. Krishnakumar, “Micro-genetic algorithms for stationary and non-stationary function optimization,” Proc. SPIE 1196, 289–296 (1989).

1969 (1)

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

Abushagur, M. A. G.

Atwater, H. A.

K. Diest, J. A. Dionne, M. Spain, and H. A. Atwater, “Tunable color filters based on metal-insulator-metal resonators,” Nano Lett. 9, 2579–2583 (2009).
[CrossRef] [PubMed]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

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

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] [PubMed]

Aussenegg, F. R.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Antenna Theory: Analysis and Design, 3rd ed. (Wiley, 2005).

Blaize, S.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Borghs, G.

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

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

S. I. Bozhevolnyi, Plasmonic Nanoguides and Circuits (World Scientific, 2009).

Brongersma, M. L.

Bruyant, A.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Catrysse, P. B.

Chelnokov, A.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Delacour, C.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Devaux, E.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Diest, K.

K. Diest, J. A. Dionne, M. Spain, and H. A. Atwater, “Tunable color filters based on metal-insulator-metal resonators,” Nano Lett. 9, 2579–2583 (2009).
[CrossRef] [PubMed]

Dionne, J. A.

K. Diest, J. A. Dionne, M. Spain, and H. A. Atwater, “Tunable color filters based on metal-insulator-metal resonators,” Nano Lett. 9, 2579–2583 (2009).
[CrossRef] [PubMed]

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

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

Ditlbacher, H.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
[CrossRef]

Dorpe, P. V.

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

Dutton, R. W.

Ebbesen, T. W.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Economou, E. N.

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

Fan, S.

Fedeli, J. M.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Feigenbaum, E.

Fukui, M.

Glytsis, E. N.

Grosse, P.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Haraguchi, M.

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] [PubMed]

Hosseini, A.

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

Huang, X. G.

Jin, J.

J. Jin, The Finite Element Method in Electromagnetics (Wiley, New York, 2002).

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] [PubMed]

Kocabas, S. E.

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. Topics 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. 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] [PubMed]

Krenn, J. R.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
[CrossRef]

Krishnakumar, K.

K. Krishnakumar, “Micro-genetic algorithms for stationary and non-stationary function optimization,” Proc. SPIE 1196, 289–296 (1989).

Lagae, L.

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

Laluet, J. Y.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

Lamprecht, B.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
[CrossRef]

Leitner, A.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
[CrossRef]

Lerondel, G.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Lezec, H. J.

H. J. Lezec, J. A. Dionne, and H. A. Atwater, “Negative refraction at visible frequencies,” Science 316, 430–432 (2007).
[CrossRef] [PubMed]

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

Lin, X. S.

Lu, Z. L.

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] [PubMed]

Massoud, Y.

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

Matsuzaki, Y.

Melosh, N. A.

M. J. Preiner, K. T. Shimizu, J. S. White, and N. A. Melosh, “Efficient optical coupling into metal-insulator-metal plasmon modes with subwavelength diffraction gratings,” Appl. Phys. Lett. 92, 113109 (2008).
[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] [PubMed]

Miller, D. A. B.

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. Topics Quantum Electron. 14, 1462–1472 (2008).
[CrossRef]

Min, C.

Nakagaki, M.

Neutens, P.

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

Okamoto, T.

Orenstein, M.

Palik, E. D.

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

Pozar, D. M.

D. M. Pozar, Microwave Engineering (Wiley, New York, 1998).

Preiner, M. J.

M. J. Preiner, K. T. Shimizu, J. S. White, and N. A. Melosh, “Efficient optical coupling into metal-insulator-metal plasmon modes with subwavelength diffraction gratings,” Appl. Phys. Lett. 92, 113109 (2008).
[CrossRef]

Qiu, M.

J. Tian, S. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

Ramo, S.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1994).

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] [PubMed]

Salas-Montiel, R.

C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10, 2922–2926 (2010).
[CrossRef] [PubMed]

Salerno, M.

J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
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K. Diest, J. A. Dionne, M. Spain, and H. A. Atwater, “Tunable color filters based on metal-insulator-metal resonators,” Nano Lett. 9, 2579–2583 (2009).
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S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1994).

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

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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508–511 (2006).
[CrossRef] [PubMed]

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S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics (Wiley, New York, 1994).

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M. J. Preiner, K. T. Shimizu, J. S. White, and N. A. Melosh, “Efficient optical coupling into metal-insulator-metal plasmon modes with subwavelength diffraction gratings,” Appl. Phys. Lett. 92, 113109 (2008).
[CrossRef]

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Yan, W.

J. Tian, S. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

Yang, L.

Yang, R. X.

Yu, S.

J. Tian, S. Yu, W. Yan, and M. Qiu, “Broadband high-efficiency surface-plasmon-polariton coupler with silicon-metal interface,” Appl. Phys. Lett. 95, 013504 (2009).
[CrossRef]

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[CrossRef]

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[CrossRef]

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J. R. Krenn, B. Lamprecht, H. Ditlbacher, G. Schider, M. Salerno, A. Leitner, and F. R. Aussenegg, “Non-diffraction-limited light transport by gold nanowires,” Europhys. Lett. 60, 663–669 (2002).
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Figures (6)

Fig. 1
Fig. 1

(a) Schematic of a structure consisting of a single slit for incoupling a normally incident plane wave from free space into the fundamental mode of a MDM plasmonic waveguide. (b) Transmission cross section σT of the MDM plasmonic waveguide in units of w for the structure of Fig. 1(a) as a function of the slit width d and length h calculated using FDFD. Results are shown for a silver-silica-silver structure with w = 50 nm at λ0 =1.55 μm. (c) Transmission cross section σT for the structure of Fig. 1(a) as a function of the slit length h calculated using FDFD (red circles) and scattering matrix theory (black solid line). Results are shown for d = 220 nm. All other parameters are as in Fig. 1(b). (d) Profile of the magnetic field amplitude for the structure of Fig. 1(a) for d = 250 nm and h = 205 nm, normalized with respect to the field amplitude of the incident plane wave. All other parameters are as in Fig. 1(b).

Fig. 2
Fig. 2

(a) Schematic defining the transmission cross section σT1 of a semi-infinite MDM waveguide when a plane wave is normally incident on it. (b) Schematic defining the reflection coefficient r1, and transmission coefficient t1 when the fundamental TM mode of a metal-air-metal waveguide is incident at the junction with a metal-dielectric-metal waveguide. (c) Schematic defining the reflection coefficient r2 of the fundamental TM mode of a MDM waveguide at the waveguide/air interface. (d) Schematic defining the transmission cross section σT2 of two semi-infinite MDM waveguides when a plane wave is normally incident on them. (e) Schematic defining the reflection coefficient r3, and transmission coefficients t2, t3 when the fundamental TM mode of a metal-dielectric-metal waveguide is incident at the junction with a metal-air-metal waveguide. (f) Schematic of a structure consisting of two semi-infinite MDM waveguides defining the reflection coefficient r4 of the fundamental TM mode of one of the MDM waveguides at the waveguide/air interface, and the transmission coefficient t4 into the other MDM waveguide.

Fig. 3
Fig. 3

Transmission cross sections (in units of w = 50 nm) of a single silver-air-silver MDM waveguide σT1 (Fig. 2(a)), and of a double silver-air-silver MDM waveguide σT2 (Fig. 2(d)), as a function of their total air core thickness (d for the single and 2d for the double waveguide). The total width of the double waveguide is 2d + D = 1.1μm.

Fig. 4
Fig. 4

(a) Schematic of a structure consisting of a two-section slit for incoupling a normally incident plane wave from free space into the fundamental mode of a MDM plasmonic waveguide. (b) Profile of the magnetic field amplitude for the optimized structure of Fig. 4(a) with d1 = 410 nm, d2 = 1100 nm, h1 = 230 nm, and h2 = 540 nm, normalized with respect to the field amplitude of the incident plane wave. All other parameters are as in Fig. 1(b).

Fig. 5
Fig. 5

(a) Schematic of a double-slit structure for incoupling a normally incident plane wave from free space into the fundamental mode of a MDM plasmonic waveguide. (b) Transmission cross section σT of the MDM plasmonic waveguide in units of w for the structure of Fig. 5(a) as a function of the slit width d and length h calculated using FDFD. The total width of the incoupling structure is 2d + D = 1.1μm. All other parameters are as in Fig. 1(b). (c) Transmission cross section σT for the structure of Fig. 5(a) as a function of the slit length h calculated using FDFD (red circles) and scattering matrix theory (black solid line). Results are shown for d = 220 nm. All other parameters are as in Fig. 5(b). (d) Profile of the magnetic field amplitude for the structure of Fig. 5(a) for d = 200 nm and h = 250 nm, normalized with respect to the field amplitude of the incident plane wave. All other parameters are as in Fig. 5(b).

Fig. 6
Fig. 6

Transmission cross section σT spectra in units of w for the three optimized incoupling structures in Figs. 1(a) (single slit), 4(a) (two-section slit), and 5(a) (double slit). Results are shown for the structure of Fig. 1(a) with d = 250 nm, h = 205 nm (black line), for the structure of Fig. 4(a) with d1 = 410 nm, d2 = 1100 nm, h1 = 230 nm, and h2 = 540 nm (red line), and for the structure of Fig. 5(a) with d = 200 nm, h = 250 nm (blue line). Also shown are the transmission cross section σT spectra for the double-slit structure (Fig. 5(a)), if the metal in the MDM waveguide is lossless (blue dashed line). All other parameters are as in Fig. 1(b).

Tables (1)

Tables Icon

Table 1 Transmission cross sections σT1/2 and σT in units of w, power transmission coefficient of the T-shaped junction Tsplitter, and resonance enhancement factors ηres1/2 calculated using scattering matrix theory. Results are shown for the optimized single slit, two-section slit, and double-slit structures of Figs. 1(a), 4(a), and 5(a), respectively.

Equations (2)

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σ T = σ T 1 η res 1 T splitter ,
σ T = σ T 2 η res 2 T splitter ,

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