Abstract

The tunneling of surface plasmon-polaritons (SPPs) across an interruption in the metallic film supporting them is numerically investigated in details. Both non-symmetrical and symmetrical geometries are considered. A very high tunneling efficiency is calculated for the long-range surface plasmon in the symmetrical geometry, with an amplitude transmission as high as 80% over a 5 μm gap for a 40 nm thick gold film illuminated at λ=785nm. The transmission is somewhat lower in the non-symmetrical geometry. The coupling between the different SPP modes (radiative and non-radiative) in that geometry is also investigated in detail. This coupling depends periodically upon the length of the gap. Overall, the results indicate that SPPs are not very sensitive to technological imperfections and can survive large waveguide interruptions.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
  6. J. C. Weeber, M. U. Gonzalez, A. L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
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    [CrossRef]
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    [CrossRef]

2006 (4)

I. Breukelaar and P. Berini, "Long-range surface plasmon polariton mode cutoff and radiation in slab waveguides," J. Opt. Soc. Am. A 23, 1971 (2006).
[CrossRef]

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (2006).
[CrossRef]

M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, and A. Dereux, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

G. Gagnon, N. Lahoud, G. A. Mattiussi, and P. Berini, "Thermally activated variable attenuation of long-range surface plasmon-polariton waves," J. Lightwave Technol. 24, 4391 (2006).
[CrossRef]

2005 (6)

J. Seidel, S. Grafström and L. Eng, "Stimulated emission of Surface Plasmons at the interface between a Silver Film and an Optically Pumped Dye Solution," Phys. Rev. Lett.  94, 177401 (2005).
[CrossRef] [PubMed]

R. Charbonneau, N. Lahoud, G. Mattiussi, P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express,  13, 977 (2005).
[CrossRef]

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, "Integrated power monitor for long-range surface plasmon polaritons," Opt. Commun. 255, 51 (2005).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (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]

J. C. Weeber, M. U. Gonzalez, A. L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

2004 (2)

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "Surface plasmon polariton based modulators and switches operating at telecom wavelengths," Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

2003 (3)

R. Nikolajsen, K. Leosson, I. Salakhutdinov and S. I. Bozhevolnyi, "Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

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

J. Seidel, S. Grafström, and L. M. Eng, "Surface plasmon transmission across narrow grooves in thin silver films," Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

2001 (2)

B. Vohnsen and S. I. Bozhevolnyi, "Coupling of surface-plasmon polaritons to directional far-field radiation by an individual surface protrusion," Appl. Opt. 40,6081 (2001).
[CrossRef]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: Bound modes of asymmetric structures," Phys. Rev. B 63, 125417 (2001).
[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]

1999 (1)

J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359 (1999).
[CrossRef]

1995 (2)

S. I. Bozhevolnyi, I. I. Smolyaninov and A. V. Zayats, "Near-field microscopy of surface-plasmon polaritons: Localization and internal interface mapping," Phys. Rev. B 51, 17916 (1995).
[CrossRef]

R. Mittra and U. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microwave Guid. Wave Lett. 5, 84 (1995).
[CrossRef]

1994 (1)

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (2006).
[CrossRef]

Baida, F. I.

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

Barnes, W. L.

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

Baudrion, A. L.

M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, and A. Dereux, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J. C. Weeber, M. U. Gonzalez, A. L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

Berenger, J.-P.

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Berini, P.

Bischoff, L.

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

Bozhevolnyi, S. I.

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]

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, "Integrated power monitor for long-range surface plasmon polaritons," Opt. Commun. 255, 51 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "Surface plasmon polariton based modulators and switches operating at telecom wavelengths," Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

R. Nikolajsen, K. Leosson, I. Salakhutdinov and S. I. Bozhevolnyi, "Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

B. Vohnsen and S. I. Bozhevolnyi, "Coupling of surface-plasmon polaritons to directional far-field radiation by an individual surface protrusion," Appl. Opt. 40,6081 (2001).
[CrossRef]

S. I. Bozhevolnyi, I. I. Smolyaninov and A. V. Zayats, "Near-field microscopy of surface-plasmon polaritons: Localization and internal interface mapping," Phys. Rev. B 51, 17916 (1995).
[CrossRef]

Breukelaar, I.

Charbonneau, R.

Dereux, A.

M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, and A. Dereux, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J. C. Weeber, M. U. Gonzalez, A. L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824 (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]

Ditlbacher, H.

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (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 (2003).
[CrossRef] [PubMed]

Eng, L.

J. Seidel, S. Grafström and L. Eng, "Stimulated emission of Surface Plasmons at the interface between a Silver Film and an Optically Pumped Dye Solution," Phys. Rev. Lett.  94, 177401 (2005).
[CrossRef] [PubMed]

Eng, L. M.

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

J. Seidel, S. Grafström, and L. M. Eng, "Surface plasmon transmission across narrow grooves in thin silver films," Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

Gagnon, G.

Gonzalez, M. U.

M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, and A. Dereux, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J. C. Weeber, M. U. Gonzalez, A. L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

Grafström, S.

J. Seidel, S. Grafström and L. Eng, "Stimulated emission of Surface Plasmons at the interface between a Silver Film and an Optically Pumped Dye Solution," Phys. Rev. Lett.  94, 177401 (2005).
[CrossRef] [PubMed]

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

J. Seidel, S. Grafström, and L. M. Eng, "Surface plasmon transmission across narrow grooves in thin silver films," Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

Guizal, B.

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

Jakopic, G.

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (2006).
[CrossRef]

Krenn, J. R.

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (2006).
[CrossRef]

Lahoud, N.

Lamprecht, B.

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (2006).
[CrossRef]

Leising, G.

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (2006).
[CrossRef]

Leosson, K.

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, "Integrated power monitor for long-range surface plasmon polaritons," Opt. Commun. 255, 51 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "Surface plasmon polariton based modulators and switches operating at telecom wavelengths," Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

R. Nikolajsen, K. Leosson, I. Salakhutdinov and S. I. Bozhevolnyi, "Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359 (1999).
[CrossRef]

Mattiussi, G.

Mattiussi, G. A.

Mittra, R.

R. Mittra and U. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microwave Guid. Wave Lett. 5, 84 (1995).
[CrossRef]

Nikolajsen, R.

R. Nikolajsen, K. Leosson, I. Salakhutdinov and S. I. Bozhevolnyi, "Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Nikolajsen, T.

S. I. Bozhevolnyi, T. Nikolajsen, and K. Leosson, "Integrated power monitor for long-range surface plasmon polaritons," Opt. Commun. 255, 51 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "Surface plasmon polariton based modulators and switches operating at telecom wavelengths," Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

Pekel, U.

R. Mittra and U. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microwave Guid. Wave Lett. 5, 84 (1995).
[CrossRef]

Salakhutdinov, I.

R. Nikolajsen, K. Leosson, I. Salakhutdinov and S. I. Bozhevolnyi, "Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

Sanchez-Gil, J. A.

J. A. Sanchez-Gil and A. A. Maradudin, "Near-field and far-field scattering of surface plasmon polaritons by one-dimensional surface defects," Phys. Rev. B 60, 8359 (1999).
[CrossRef]

Seidel, J.

J. Seidel, S. Grafström and L. Eng, "Stimulated emission of Surface Plasmons at the interface between a Silver Film and an Optically Pumped Dye Solution," Phys. Rev. Lett.  94, 177401 (2005).
[CrossRef] [PubMed]

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

J. Seidel, S. Grafström, and L. M. Eng, "Surface plasmon transmission across narrow grooves in thin silver films," Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

S. I. Bozhevolnyi, I. I. Smolyaninov and A. V. Zayats, "Near-field microscopy of surface-plasmon polaritons: Localization and internal interface mapping," Phys. Rev. B 51, 17916 (1995).
[CrossRef]

Van Labeke, D.

J. Seidel, F. I. Baida, L. Bischoff, B. Guizal, S. Grafström, D. Van Labeke, and L. M. Eng, "Coupling between surface plasmon modes on metal films," Phys. Rev. B 69, 121405 (2004).
[CrossRef]

Vohnsen, B.

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]

Weeber, J. C.

M. U. Gonzalez, J. C. Weeber, A. L. Baudrion, and A. Dereux, "Design, near-field characterization, and modeling of 45° surface-plasmon Bragg mirrors," Phys. Rev. B 73, 155416 (2006).
[CrossRef]

J. C. Weeber, M. U. Gonzalez, A. L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep. 408, 131 (2005).
[CrossRef]

S. I. Bozhevolnyi, I. I. Smolyaninov and A. V. Zayats, "Near-field microscopy of surface-plasmon polaritons: Localization and internal interface mapping," Phys. Rev. B 51, 17916 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

J. Seidel, S. Grafström, and L. M. Eng, "Surface plasmon transmission across narrow grooves in thin silver films," Appl. Phys. Lett. 82, 1368 (2003).
[CrossRef]

R. Nikolajsen, K. Leosson, I. Salakhutdinov and S. I. Bozhevolnyi, "Polymer-based surface-plasmon polariton stripe waveguides at telecommunication wavelengths," Appl. Phys. Lett. 82, 668 (2003).
[CrossRef]

H. Ditlbacher, F. R. Aussenegg, J. R. Krenn, B. Lamprecht, G. Jakopic, G. Leising, "Organic diodes as monolithically integrated surface plasmon polariton detectors," Appl. Phys. Lett. 89, 161101 (2006).
[CrossRef]

J. C. Weeber, M. U. Gonzalez, A. L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005).
[CrossRef]

T. Nikolajsen, K. Leosson, S. I. Bozhevolnyi, "Surface plasmon polariton based modulators and switches operating at telecom wavelengths," Appl. Phys. Lett. 85, 5833 (2004).
[CrossRef]

IEEE Microwave Guid. Wave Lett. (1)

R. Mittra and U. Pekel, "A new look at the perfectly matched layer (PML) concept for the reflectionless absorption of electromagnetic waves," IEEE Microwave Guid. Wave Lett. 5, 84 (1995).
[CrossRef]

J. Comput. Phys. (1)

J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185 (1994).
[CrossRef]

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Supplementary Material (2)

» Media 1: AVI (542 KB)     
» Media 2: AVI (466 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Sketch of a metallic waveguide with thickness t and an interruption d. Two SPP modes can propagate in that system. (a) Excitation with an air mode and (b) with a substrate mode. For clarity, modes reflected backwards at the interfaces are not shown.

Fig. 2.
Fig. 2.

Amplitude of magnetic field when an air SPP mode is propagating on a t=50 nm thick gold film with a d=700 nm interruption, see Fig. 1(a). The movie shows the field distribution for interruptions between d=50 nm and d=4.7 μm. [Media 1]

Fig. 3.
Fig. 3.

Amplitude of the magnetic field (a) 5 nm below and (b) 5 nm above the metallic film (see the dashed lines in Fig. 3).

Fig. 4.
Fig. 4.

Relative average amplitude of the field transmitted through the gap measured (a) 5 nm above and (b) 5 nm below the metallic film, as a function of the interruption length d in the film. The air mode is used for excitation, see Fig. 1(a).

Fig. 5.
Fig. 5.

Relative average amplitude of the field transmitted through the gap measured 5 nm below the metallic film, as a function of the interruption length d in the film. Two different substrates are considered, with respective index n=1.47 and n=1.8.

Fig. 6.
Fig. 6.

Relative average amplitude of the field transmitted through the gap measured (a) 5 nm above and (b) 5 nm below the metallic film, as a function of the interruption length d in the film. The glass mode is used for excitation, see Fig. 1(b).

Fig. 7.
Fig. 7.

Symmetrical geometry where a metallic waveguide with thickness t and an interruption d is embedded in two similar dielectrics. Two SPP modes can propagate in that system: (a) long-range mode and (b) short-range mode. The amplitude of the magnetic field is sketched and any reflected mode is omitted for clarity.

Fig. 8.
Fig. 8.

Amplitude of magnetic field when a LR SPP mode is propagating on a t=40 nm thick gold film with a d=700 nm interruption, see Fig. 7(a). The movie shows the field distribution for interruptions between d=50 nm and d=4.7 μm.

Fig. 9.
Fig. 9.

Amplitude of the magnetic field 5 nm above the t=40 nm thick metallic film (see the dashed lines in Fig. 7) for long-range (LR) and short-range (SR) excitations. The film has a d=700 nm long interruption.

Fig. 10.
Fig. 10.

Relative average amplitude of the field transmitted through the gap measured 5 nm above the metallic film, as a function of the interruption length d in the film. Both excitations with LR and SR modes are investigated.

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