Abstract

We directly measure the Gouy phase shift of surface plasmonpolaritons as they evolve through the focus using terahertz (THz) timedomain spectroscopy. This is accomplished by using a semicircular groove inscribed in a metal foil to couple broadband freely propagating THz radiation to a converging propagating surface wave. Since the spatial properties of these waves are not Gaussian, we perform numerical simulations to determine the electric field distribution on the metal surface. The associated Gouy phase shift can be obtained from the transverse spatial distribution of the converging wave. We find excellent agreement between our measurements and expectations based on the numerical simulations. ©2007 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (260.3090) Far-infrared; (120.5050) Phase measurements

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  2. R.P. Van Duyne, "Molecular plasmonics," Science 306, 985-986 (2004).
    [CrossRef] [PubMed]
  3. Z. Liu, J.M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens," NanoLett. 5, 1726-1729 (2005).
    [CrossRef]
  4. W. Nomura, M. Ohtsu, T. Yatsui, "Nanodot coupler with a surface plasmon polaritons condenser for optical far/near-field conversion," Appl. Phys. Lett. 86, 181108 (2005).
    [CrossRef]
  5. L. Yin, V.K. Vlasko-Vlasov, J. Pearson, J.M. Hiller, J. Hua, U. Welp, D.E. Brown, and C.W. Kimball, "Subwavelength focusing and guiding of surface plasmons," NanoLett. 5, 1399-1402 (2005).
    [CrossRef]
  6. I.I. Smoyaninov, Y.-J. Hung, and C.C. Davis, "Surface plasmon dielectric waveguides," Appl. Phys. Lett. 87, 241106 (2005).
    [CrossRef]
  7. I. P. Radko, S. I. Bozhevolnyi, A. B. Evlyukhin, and A. Boltasseva, "Surface plasmon polariton beam focusing with parabolic nanoparticle chains," Opt. Express 15, 6576-6582 (2007).
    [CrossRef] [PubMed]
  8. A. Drezet, A.L. Stepanov, H. Ditlbacher, A. Hohenau, B. Steinberger, F.R. Aussenegg, A. Leitner, and J.R. Krenn, "Surface plasmon propagation in an elliptical corral," Appl. Phys. Lett. 86, 074104 (2005).
    [CrossRef]
  9. T. Thio, K.M. Pellerin, R.A. Linke, H.J. Lezec, T.W. Ebbesen, "Enhanced light transmission through a single subwavelength aperture," Opt. Lett. 26, 1972-1974 (2001).
  10. H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, F. Martin-Moreno, L.J. Garcia-Vidal, and T.W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 220-222 (2002).
    [CrossRef]
  11. A. Nahata, R.A. Linke, T. Ishi, and K. Ohashi, "Enhanced nonlinear optical conversion using periodically nanostructured metal films," Opt. Lett. 28, 423-425 (2003).
    [CrossRef] [PubMed]
  12. M.J. Lockyear, A.P. Hibbins, J.R. Sambles, C.R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture," Appl. Phys. Lett. 84, 2040-2042 (2004).
    [CrossRef]
  13. A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).
  14. B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics (Wiley Interscience, 1991).
    [CrossRef]
  15. A.B. Ruffin, J.V. Rudd, J.F. Whitaker, S. Feng, and H.G. Winful, "Direct observation of the Gouy phase shift with single-cycle terahertz pulses," Phys. Rev. Lett. 83, 3410-3413 (1999).
    [CrossRef]
  16. R.W. McGowan, R.A. Cheville, and D. Grischkowsky, "Direct observation of the Gouy phase shift in THz impulse ranging," Appl. Phys. Lett. 76, 670-672 (2000).
    [CrossRef]
  17. T. Feurer, N.S. Stoyanov, D.W. Ward, and K.A. Nelson, "Direct visualization of the Gouy phase by focusing phonon polaritons," Phys. Rev. Lett. 88, 257402 (2002).
    [CrossRef] [PubMed]
  18. N.C.R. Holme, B.C. Daly, M.T. Myaing, and T.B. Norris, "Gouy phase shift of single-cycle picosecond acoustic pulses," Appl. Phys. Lett. 83, 392-394 (2003).
    [CrossRef]
  19. A.A. Kolomenskii, S.N. Jerebtsov, and H.A. Schuessler, "Focal transformation and the Gouy phase shift of converging one-cycle surface acoustic waves excited by femtosecond laser pulses," Opt. Lett. 30, 2019-2021 (2005).
    [CrossRef] [PubMed]
  20. S. Feng and H.G. Winful, "Physical origin of the Gouy phase shift," Opt. Lett. 26, 485-487 (2001).
    [CrossRef]
  21. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, Jr., and C. A. Ward, "Optical properties of the metals Al, Co, Cu, Au, Fe, Pb, Ni, Pd, Pt, Ag, Ti, and W in the infrared and far infrared," Appl. Opt. 22, 1099-1120 (1983).
    [CrossRef] [PubMed]
  22. A. Agrawal, H. Cao, and A. Nahata, "Time-domain analysis of enhanced transmission through a single subwavelength aperture," Opt. Express 13, 3535-3542 (2005).
    [CrossRef] [PubMed]
  23. A. Agrawal, H. Cao, and A. Nahata, "Excitation and scattering of surface plasmon-polaritons on structured metal films and their application to pulse shaping and enhanced transmission," New J. Phys.  7, 249 (2005).
    [CrossRef]
  24. A. Nahata, A.S. Weling, and T.F. Heinz, "A wide band coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
    [CrossRef]
  25. J. A. Sanchez-Gil, " Surface defect scattering of surface plasmon polaritons: mirrors and light emitters," Appl. Phys. Lett. 73, 3509-3511 (1998).
    [CrossRef]
  26. W. Zhu and A. Nahata, "Electric field vector characterization of terahertz surface plasmons," Opt. Express 15, 5616-5624 (2007).
    [CrossRef] [PubMed]
  27. T.-I. Jeon and D. Grischkowsky, "THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet," Appl. Phys. Lett. 88, 061113 (2006).
    [CrossRef]

2007 (2)

2006 (2)

T.-I. Jeon and D. Grischkowsky, "THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet," Appl. Phys. Lett. 88, 061113 (2006).
[CrossRef]

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

2005 (8)

A. Drezet, A.L. Stepanov, H. Ditlbacher, A. Hohenau, B. Steinberger, F.R. Aussenegg, A. Leitner, and J.R. Krenn, "Surface plasmon propagation in an elliptical corral," Appl. Phys. Lett. 86, 074104 (2005).
[CrossRef]

Z. Liu, J.M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens," NanoLett. 5, 1726-1729 (2005).
[CrossRef]

W. Nomura, M. Ohtsu, T. Yatsui, "Nanodot coupler with a surface plasmon polaritons condenser for optical far/near-field conversion," Appl. Phys. Lett. 86, 181108 (2005).
[CrossRef]

L. Yin, V.K. Vlasko-Vlasov, J. Pearson, J.M. Hiller, J. Hua, U. Welp, D.E. Brown, and C.W. Kimball, "Subwavelength focusing and guiding of surface plasmons," NanoLett. 5, 1399-1402 (2005).
[CrossRef]

I.I. Smoyaninov, Y.-J. Hung, and C.C. Davis, "Surface plasmon dielectric waveguides," Appl. Phys. Lett. 87, 241106 (2005).
[CrossRef]

A.A. Kolomenskii, S.N. Jerebtsov, and H.A. Schuessler, "Focal transformation and the Gouy phase shift of converging one-cycle surface acoustic waves excited by femtosecond laser pulses," Opt. Lett. 30, 2019-2021 (2005).
[CrossRef] [PubMed]

A. Agrawal, H. Cao, and A. Nahata, "Time-domain analysis of enhanced transmission through a single subwavelength aperture," Opt. Express 13, 3535-3542 (2005).
[CrossRef] [PubMed]

A. Agrawal, H. Cao, and A. Nahata, "Excitation and scattering of surface plasmon-polaritons on structured metal films and their application to pulse shaping and enhanced transmission," New J. Phys.  7, 249 (2005).
[CrossRef]

2004 (2)

M.J. Lockyear, A.P. Hibbins, J.R. Sambles, C.R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture," Appl. Phys. Lett. 84, 2040-2042 (2004).
[CrossRef]

R.P. Van Duyne, "Molecular plasmonics," Science 306, 985-986 (2004).
[CrossRef] [PubMed]

2003 (2)

A. Nahata, R.A. Linke, T. Ishi, and K. Ohashi, "Enhanced nonlinear optical conversion using periodically nanostructured metal films," Opt. Lett. 28, 423-425 (2003).
[CrossRef] [PubMed]

N.C.R. Holme, B.C. Daly, M.T. Myaing, and T.B. Norris, "Gouy phase shift of single-cycle picosecond acoustic pulses," Appl. Phys. Lett. 83, 392-394 (2003).
[CrossRef]

2002 (2)

H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, F. Martin-Moreno, L.J. Garcia-Vidal, and T.W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 220-222 (2002).
[CrossRef]

T. Feurer, N.S. Stoyanov, D.W. Ward, and K.A. Nelson, "Direct visualization of the Gouy phase by focusing phonon polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (1)

R.W. McGowan, R.A. Cheville, and D. Grischkowsky, "Direct observation of the Gouy phase shift in THz impulse ranging," Appl. Phys. Lett. 76, 670-672 (2000).
[CrossRef]

1999 (1)

A.B. Ruffin, J.V. Rudd, J.F. Whitaker, S. Feng, and H.G. Winful, "Direct observation of the Gouy phase shift with single-cycle terahertz pulses," Phys. Rev. Lett. 83, 3410-3413 (1999).
[CrossRef]

1998 (1)

J. A. Sanchez-Gil, " Surface defect scattering of surface plasmon polaritons: mirrors and light emitters," Appl. Phys. Lett. 73, 3509-3511 (1998).
[CrossRef]

1996 (1)

A. Nahata, A.S. Weling, and T.F. Heinz, "A wide band coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

1983 (1)

Appl. Opt. (1)

Appl. Phys. Lett. (9)

A. Nahata, A.S. Weling, and T.F. Heinz, "A wide band coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69, 2321-2323 (1996).
[CrossRef]

J. A. Sanchez-Gil, " Surface defect scattering of surface plasmon polaritons: mirrors and light emitters," Appl. Phys. Lett. 73, 3509-3511 (1998).
[CrossRef]

T.-I. Jeon and D. Grischkowsky, "THz Zenneck surface wave (THz surface plasmon) propagation on a metal sheet," Appl. Phys. Lett. 88, 061113 (2006).
[CrossRef]

W. Nomura, M. Ohtsu, T. Yatsui, "Nanodot coupler with a surface plasmon polaritons condenser for optical far/near-field conversion," Appl. Phys. Lett. 86, 181108 (2005).
[CrossRef]

I.I. Smoyaninov, Y.-J. Hung, and C.C. Davis, "Surface plasmon dielectric waveguides," Appl. Phys. Lett. 87, 241106 (2005).
[CrossRef]

A. Drezet, A.L. Stepanov, H. Ditlbacher, A. Hohenau, B. Steinberger, F.R. Aussenegg, A. Leitner, and J.R. Krenn, "Surface plasmon propagation in an elliptical corral," Appl. Phys. Lett. 86, 074104 (2005).
[CrossRef]

M.J. Lockyear, A.P. Hibbins, J.R. Sambles, C.R. Lawrence, "Surface-topography-induced enhanced transmission and directivity of microwave radiation through a subwavelength circular metal aperture," Appl. Phys. Lett. 84, 2040-2042 (2004).
[CrossRef]

R.W. McGowan, R.A. Cheville, and D. Grischkowsky, "Direct observation of the Gouy phase shift in THz impulse ranging," Appl. Phys. Lett. 76, 670-672 (2000).
[CrossRef]

N.C.R. Holme, B.C. Daly, M.T. Myaing, and T.B. Norris, "Gouy phase shift of single-cycle picosecond acoustic pulses," Appl. Phys. Lett. 83, 392-394 (2003).
[CrossRef]

NanoLett. (2)

Z. Liu, J.M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens," NanoLett. 5, 1726-1729 (2005).
[CrossRef]

L. Yin, V.K. Vlasko-Vlasov, J. Pearson, J.M. Hiller, J. Hua, U. Welp, D.E. Brown, and C.W. Kimball, "Subwavelength focusing and guiding of surface plasmons," NanoLett. 5, 1399-1402 (2005).
[CrossRef]

New J. Phys. (1)

A. Agrawal, H. Cao, and A. Nahata, "Excitation and scattering of surface plasmon-polaritons on structured metal films and their application to pulse shaping and enhanced transmission," New J. Phys.  7, 249 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. Lett. (2)

T. Feurer, N.S. Stoyanov, D.W. Ward, and K.A. Nelson, "Direct visualization of the Gouy phase by focusing phonon polaritons," Phys. Rev. Lett. 88, 257402 (2002).
[CrossRef] [PubMed]

A.B. Ruffin, J.V. Rudd, J.F. Whitaker, S. Feng, and H.G. Winful, "Direct observation of the Gouy phase shift with single-cycle terahertz pulses," Phys. Rev. Lett. 83, 3410-3413 (1999).
[CrossRef]

Science (3)

H.J. Lezec, A. Degiron, E. Devaux, R.A. Linke, F. Martin-Moreno, L.J. Garcia-Vidal, and T.W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 220-222 (2002).
[CrossRef]

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

R.P. Van Duyne, "Molecular plasmonics," Science 306, 985-986 (2004).
[CrossRef] [PubMed]

Other (2)

A. E. Siegman, Lasers (University Science Books, Sausalito, 1986).

B.E.A. Saleh, M.C. Teich, Fundamentals of Photonics (Wiley Interscience, 1991).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Schematic diagram of the experimental setup for measuring the Gouy phase shift (a) a (110) ZnTe crystal is used as the detection medium, λ/4 corresponds to a quarter-wave plate, WP corresponds to a Wollaston prism, and differential detection is used for improved sensitivity. (b) the optical probe beam and the SPP direction co-propagate. The position of the ZnTe crystal can be changed with respect to the center of the semicircular groove to measure the relative phase change or spatial properties of the SPP beam.

Fig. 2.
Fig. 2.

(a) Time-domain waveforms of the SPP measured at x=-10mm (upper blue curve) and x=0 mm (middle black curve), and x=+10 mm (lower red curve) for a semicircular groove. (b) The relative phase shift difference between the waveform obtain for x=-10 mm and for x=+10 mm. When a linear groove is used, we observe no phase shift over the same propagation distance.

Fig. 3.
Fig. 3.

(a) FDTD simulated steady-state field distribution of the z-component of the SPP electric field at 0.3 THz shown on a log scale, with the corresponding color map shown on the right hand side. The measured (filled circles) and simulated (solid line) cross-section of the electric field distribution is shown for (b) x=0 mm; (c) x=1 mm; and (d) x=2 mm. The measured field magnitude values at 0.3 THz are taken from Fourier transforms of the corresponding time-domain waveforms.

Fig. 4.
Fig. 4.

The measured and simulated phase shift at 0.3 THz for a SPP focused using a semicircular groove. The total phase shift is ~π/2. The filled triangles represent the measured phase shift at 0.3 THz retrieved by the Fourier transforms of time-domain waveforms measured at different positions. The solid curve represents the simulated phase transition based on the spatial field distribution calculated from FDTD simulations.

Equations (3)

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

F ( k y , x ) = 1 2 π E z ( x , y ) exp ( ik y y ) dy .
k y 2 = k y 2 F ( k y , x ) 2 dk y F ( k y , x ) 2 dk y
ϕ G ( x ) = λ 2 π 0 x k y 2 dx ,

Metrics