Abstract

We launch surface plasmons from one end of a silver nanowire by asymmetric illumination with white light and use plasmon-to-light scattering at the nanowire ends to probe spectroscopically the plasmonic Fabry–Perot wire modes. The spectral positions of the maxima and minima in the scattered intensity from both nanowire ends are found to be either in-phase or out-of-phase, depending on the nanowire length and the spectral range. This behavior can be explained by a generalized Fabry–Perot model. The turnover point between the two regimes is sensitive to the surface plasmon round trip losses and thus opens a new possibility for detecting changes of the optical absorption in the nanowire environment.

© 2012 Optical Society of America

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  1. R. M. Dickson and L. A. Lyon, J. Phys. Chem. B 104, 6095 (2000).
    [CrossRef]
  2. J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).
  3. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, Opt. Lett. 22, 475 (1997).
    [CrossRef]
  4. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).
  5. A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
    [CrossRef]
  6. R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).
  7. Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).
  8. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
    [CrossRef]
  9. T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).
  10. D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
    [CrossRef]
  11. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic Press, Inc., London, 1985).
  12. P. Kusar, C. Gruber, A. Hohenau, and J. R. Krenn, Nano Lett., doi: 10.1021/nl20345cd (2012).
    [CrossRef]
  13. Around this point Is,i has to be independent of k. By equating the coefficients of the cosine functions with identical periodicity in the denominator and numerator of Is,i, one obtains after some algebra Eq. (4).

2011 (2)

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
[CrossRef]

2010 (1)

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

2009 (2)

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

2007 (1)

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

2006 (1)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).

2005 (1)

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

2000 (1)

R. M. Dickson and L. A. Lyon, J. Phys. Chem. B 104, 6095 (2000).
[CrossRef]

1997 (1)

Akimov, A. V.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

Balasubramanian, G.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Bao, K.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Chang, D. E.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).

Chen, D.

D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
[CrossRef]

Chen, J.

D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
[CrossRef]

Dickson, R. M.

R. M. Dickson and L. A. Lyon, J. Phys. Chem. B 104, 6095 (2000).
[CrossRef]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

Dorfmüller, J.

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

Etrich, S.

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

Fang, Y.

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

Grotz, B.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Gruber, C.

P. Kusar, C. Gruber, A. Hohenau, and J. R. Krenn, Nano Lett., doi: 10.1021/nl20345cd (2012).
[CrossRef]

Hao, F.

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

Hemmer, P. R.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

P. Kusar, C. Gruber, A. Hohenau, and J. R. Krenn, Nano Lett., doi: 10.1021/nl20345cd (2012).
[CrossRef]

Huang, Y.

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

Jelezko, F.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Jiang, R.

D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
[CrossRef]

Johansson, P.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Käll, M.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Kern, K.

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

Khunsin, W.

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

Kobayashi, T.

Kolesov, R.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

P. Kusar, C. Gruber, A. Hohenau, and J. R. Krenn, Nano Lett., doi: 10.1021/nl20345cd (2012).
[CrossRef]

Kusar, P.

P. Kusar, C. Gruber, A. Hohenau, and J. R. Krenn, Nano Lett., doi: 10.1021/nl20345cd (2012).
[CrossRef]

Li, Z.

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

Lukin, M. D.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).

Lyon, L. A.

R. M. Dickson and L. A. Lyon, J. Phys. Chem. B 104, 6095 (2000).
[CrossRef]

Miljkovic, V. D.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Morimoto, A.

Mukherjee, A.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

Nicolet, A. A. L.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Nordlander, P.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

Park, H.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

Qiao, X.

D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
[CrossRef]

Qiu, X.

D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
[CrossRef]

Rockstuhl, K.

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

Shegai, T.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Sørensen, A. S.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).

Stöhr, R. J.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Takahara, J.

Taki, H.

Vogelgesang, R.

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

Wachtrup, J.

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

Xu, H.

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

Yamagishi, S.

Yu, C. L.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

Zibrov, A. S.

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

J. Mater. Sci.: Mater. Electron. (1)

D. Chen, X. Qiao, X. Qiu, J. Chen, and R. Jiang, J. Mater. Sci.: Mater. Electron. 22, 6 (2011).
[CrossRef]

J. Phys. Chem. B (1)

R. M. Dickson and L. A. Lyon, J. Phys. Chem. B 104, 6095 (2000).
[CrossRef]

Nano Lett. (3)

J. Dorfmüller, R. Vogelgesang, W. Khunsin, K. Rockstuhl, S. Etrich, and K. Kern, Nano Lett. 10, 3596 (2010).

T. Shegai, V. D. Miljkovic, K. Bao, H. Xu, P. Nordlander, P. Johansson, and M. Käll, Nano Lett. 11, 706 (2011).

Z. Li, F. Hao, Y. Huang, Y. Fang, P. Nordlander, and H. Xu, Nano Lett. 9, 4383 (2009).

Nat. Phys. (1)

R. Kolesov, B. Grotz, G. Balasubramanian, R. J. Stöhr, A. A. L. Nicolet, P. R. Hemmer, F. Jelezko, and J. Wachtrup, Nat. Phys. 5, 470 (2009).

Nature (1)

A. V. Akimov, A. Mukherjee, C. L. Yu, D. E. Chang, A. S. Zibrov, P. R. Hemmer, H. Park, and M. D. Lukin, Nature 450, 402 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (2)

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, Phys. Rev. Lett. 97, 053002 (2006).

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef]

Other (3)

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic Press, Inc., London, 1985).

P. Kusar, C. Gruber, A. Hohenau, and J. R. Krenn, Nano Lett., doi: 10.1021/nl20345cd (2012).
[CrossRef]

Around this point Is,i has to be independent of k. By equating the coefficients of the cosine functions with identical periodicity in the denominator and numerator of Is,i, one obtains after some algebra Eq. (4).

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Figures (3)

Fig. 1.
Fig. 1.

Sketch of a silver nanowire on glass substrate. The nanowire was illuminated from the glass substrate in total internal reflection geometry (thick, green arrows). The light scattered from the input (I) and distal (D) end of the wire is collected by a microscope objective and imaged on the input of a spectrograph. Ai,n and As,n are the amplitudes of the light incident and scattered from the input (n=I) or distal (n=D) end. AP+ and AP are the amplitudes of the excited right and left propagating SP mode, respectively, and r and t are the reflection, transmission and scattering efficiencies as described in the text.

Fig. 2.
Fig. 2.

(a,b): Experimentally recorded scattering spectra of a (a) 19 μm and (b) 5 μm long silver nanowire of the input (lower, black curves) and distal (upper, red curves) ends. (c,d): Theoretical scattering spectra calculated by a generalized FP model for a (c) 19 μm and (d) 5 μm long nanowire (see text).

Fig. 3.
Fig. 3.

Calculated spectra of Is,I around the phase-flip point for a 5 μm long nanowire. The SP end-cap reflectivity is assumed as R=|r|2=0.4 (upper, black curve) and R=0.392 (lower, red curve). The resulting spectral shift of the phase-flip point leads to a pronounced qualitative difference between the curves around this point.

Equations (7)

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

Ai,It˜I+APrI=AP+Ai,Dt˜D+AP+eikLrD=APeikLAs,D=AP+eikLtD+Ai,Dr˜DAs,I=APtI+Ai,Ir˜I.
As,I=Ai,Ir˜I+eikLAi,Dt˜DtI+Ai,IrDtIt˜IeikL1rIrDe2ikL,As,D=Ai,Dr˜D+eikLAi,It˜ItD+Ai,DrItDt˜De2ikL1rIrDe2ikL.
Is,D|As,D|2Ii|t˜It1r2e2ikL|2,Is,I|As,I|2Ii|r˜I|2|1(r2rtt˜I/r˜I)e2ikL1r2e2ikL|2.
r˜I=tt˜Irξ21ξ2
ξ2=r˜Irt˜It+r˜Ir
Is,I=Ii|r˜I|21ξ2,
|APrAi,Ir˜I|=1+1ξ.

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