Abstract

We propose and analyze a new plasmonic lens allowing the simultaneous focusing of both short and long range surface plasmons polaritons. The considered geometry is circularly symmetric and the SPP excitation is radially polarized. The long range and the short range modes are compared and found to have very different focusing properties. The trade-offs between the modes are discussed. The interplay between these two modes is used to demonstrate a practical focusing scenario providing a smaller spot size compared with previous version of plasmonic lenses, and a large depth of focus simultaneously.

© 2009 Optical Society of America

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  1. Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing surface plasmons with a plasmonic lens," Nano Lett. 5, 1726-1729 (2005).
    [CrossRef] [PubMed]
  2. W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
    [CrossRef]
  3. Q. Zhan, "Evanescent Bessel beam generation via surface plasmon resonance excitation by a radially polarized beam," Opt. Lett. 31, 1726-1728 (2006).
    [CrossRef] [PubMed]
  4. A. Yanai and U. Levy, "Plasmonic focusing with a coaxial structure illuminated by radially polarized light," Opt. Express 17, 924-932 (2009).
    [CrossRef] [PubMed]
  5. W. Chen and Q. Zhan, "Realization of an evanescent Bessel beam via surface plasmon interference excited by a radially polarized beam," Opt. Lett. 34, 722-724 (2009).
    [CrossRef] [PubMed]
  6. G. Lerman, A. Yanai and U. Levy, "Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light," Nano Lett. 9, 2139-2143 (2009).
    [CrossRef] [PubMed]
  7. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).
  8. D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
    [CrossRef]
  9. P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
    [CrossRef]
  10. R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005).
    [CrossRef] [PubMed]
  11. A. Degiron and D. Smith, "Numerical simulations of long-range plasmons," Opt. Express 14, 1611-1625 (2006).
    [CrossRef] [PubMed]
  12. K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006).
    [CrossRef] [PubMed]
  13. M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
    [CrossRef] [PubMed]
  14. D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys.B Lasers Opt. 86, 7-17 (2007).
  15. D. Gramotnev, M. Vogel, and M. Stockman, "Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods," J. Appl. Phys. 104, 034311 (2008).
    [CrossRef]
  16. E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons," Phys. Rev. Lett. 100, 023901-1-4 (2008).
    [CrossRef] [PubMed]
  17. K. Kurihara, K. Yamamoto, J. Takahara and A. Otomo,"Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables," J. Phys. A Math.Theor. 41295401 (2008).
    [CrossRef]
  18. E. Verhagen, A. Polman, and L. Kuipers, "Nanofocusing in laterally taperd plasmonic waveguides," Opt. Express 16, 45-57 (2008).
    [CrossRef] [PubMed]
  19. L. Feng, D. Van Orden, M. Abashin, Q. Wang, Y. Chen, V. Lomakin, and Y. Fainman, "Nanoscale optical field localization by resonantly focused plasmons," Opt. Express 17, 4824-4832 (2009).
    [CrossRef] [PubMed]
  20. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
    [CrossRef] [PubMed]
  21. http://ab-initio.mit.edu/meep/

2009 (4)

2008 (4)

D. Gramotnev, M. Vogel, and M. Stockman, "Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods," J. Appl. Phys. 104, 034311 (2008).
[CrossRef]

K. Kurihara, K. Yamamoto, J. Takahara and A. Otomo,"Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables," J. Phys. A Math.Theor. 41295401 (2008).
[CrossRef]

E. Verhagen, A. Polman, and L. Kuipers, "Nanofocusing in laterally taperd plasmonic waveguides," Opt. Express 16, 45-57 (2008).
[CrossRef] [PubMed]

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

2007 (1)

D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys.B Lasers Opt. 86, 7-17 (2007).

2006 (4)

2005 (2)

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

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005).
[CrossRef] [PubMed]

2004 (1)

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

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, 10484-10503 (2000).
[CrossRef]

1981 (1)

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Abashin, M.

Berini, P.

R. Charbonneau, N. Lahoud, G. Mattiussi, and P. Berini, "Demonstration of integrated optics elements based on long-ranging surface plasmon polaritons," Opt. Express 13, 977-984 (2005).
[CrossRef] [PubMed]

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

Bermel, P.

Bogy, C.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

Boltasseva, A.

Bozhevolnyi, S. I.

K. Leosson, T. Nikolajsen, A. Boltasseva, and S. I. Bozhevolnyi, "Long-range surface plasmon polariton nanowire waveguides for device applications," Opt. Express 14, 314-319 (2006).
[CrossRef] [PubMed]

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons," Phys. Rev. Lett. 100, 023901-1-4 (2008).
[CrossRef] [PubMed]

Burr, G. W.

Charbonneau, R.

Chen, W.

Chen, Y.

Degiron, A.

Fainman, Y.

Farjadpour, A.

Feng, L.

Garcia-Vidal, F. J.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons," Phys. Rev. Lett. 100, 023901-1-4 (2008).
[CrossRef] [PubMed]

Gramotnev, D.

D. Gramotnev, M. Vogel, and M. Stockman, "Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods," J. Appl. Phys. 104, 034311 (2008).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys.B Lasers Opt. 86, 7-17 (2007).

Ibanescu, M.

Joannopoulos, J. D.

Johnson, S. G.

Kuipers, L.

Kurihara, K.

K. Kurihara, K. Yamamoto, J. Takahara and A. Otomo,"Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables," J. Phys. A Math.Theor. 41295401 (2008).
[CrossRef]

Lahoud, N.

Leosson, K.

Lerman, G.

G. Lerman, A. Yanai and U. Levy, "Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light," Nano Lett. 9, 2139-2143 (2009).
[CrossRef] [PubMed]

Levy, U.

G. Lerman, A. Yanai and U. Levy, "Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light," Nano Lett. 9, 2139-2143 (2009).
[CrossRef] [PubMed]

A. Yanai and U. Levy, "Plasmonic focusing with a coaxial structure illuminated by radially polarized light," Opt. Express 17, 924-932 (2009).
[CrossRef] [PubMed]

Liu, Z. W.

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

Lomakin, V.

Martin-Moreno, L.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons," Phys. Rev. Lett. 100, 023901-1-4 (2008).
[CrossRef] [PubMed]

Mattiussi, G.

Moreno, E.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons," Phys. Rev. Lett. 100, 023901-1-4 (2008).
[CrossRef] [PubMed]

Nikolajsen, T.

Otomo, A.

K. Kurihara, K. Yamamoto, J. Takahara and A. Otomo,"Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables," J. Phys. A Math.Theor. 41295401 (2008).
[CrossRef]

Pan, L.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

Pikus, Y.

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

Polman, A.

Rodrigo, S. G.

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons," Phys. Rev. Lett. 100, 023901-1-4 (2008).
[CrossRef] [PubMed]

Rodriguez, A.

Roundy, D.

Sarid, D.

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Smith, D.

Srituravanich, W.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

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

Steele, J. M.

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

Stockman, M.

D. Gramotnev, M. Vogel, and M. Stockman, "Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods," J. Appl. Phys. 104, 034311 (2008).
[CrossRef]

Stockman, M. I.

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

Sun, C.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

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

Takahara, J.

K. Kurihara, K. Yamamoto, J. Takahara and A. Otomo,"Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables," J. Phys. A Math.Theor. 41295401 (2008).
[CrossRef]

Van Orden, D.

Verhagen, E.

Vernon, K. C.

D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys.B Lasers Opt. 86, 7-17 (2007).

Vogel, M.

D. Gramotnev, M. Vogel, and M. Stockman, "Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods," J. Appl. Phys. 104, 034311 (2008).
[CrossRef]

Wang, Q.

Wang, Y.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

Yamamoto, K.

K. Kurihara, K. Yamamoto, J. Takahara and A. Otomo,"Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables," J. Phys. A Math.Theor. 41295401 (2008).
[CrossRef]

Yanai, A.

A. Yanai and U. Levy, "Plasmonic focusing with a coaxial structure illuminated by radially polarized light," Opt. Express 17, 924-932 (2009).
[CrossRef] [PubMed]

G. Lerman, A. Yanai and U. Levy, "Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light," Nano Lett. 9, 2139-2143 (2009).
[CrossRef] [PubMed]

Zhan, Q.

Zhang, X.

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

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

B Lasers Opt. (1)

D. K. Gramotnev and K. C. Vernon, "Adiabatic nano-focusing of plasmons by sharp metallic wedges," Appl. Phys.B Lasers Opt. 86, 7-17 (2007).

J. Appl. Phys. (1)

D. Gramotnev, M. Vogel, and M. Stockman, "Optimized nonadiabatic nanofocusing of plasmons by tapered metal rods," J. Appl. Phys. 104, 034311 (2008).
[CrossRef]

Nano Lett. (2)

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

G. Lerman, A. Yanai and U. Levy, "Demonstration of nano focusing by the use of plasmonic lens illuminated with radially polarized light," Nano Lett. 9, 2139-2143 (2009).
[CrossRef] [PubMed]

Nature Nanotech. (1)

W. Srituravanich, L. Pan, Y. Wang, C. Sun, C. Bogy, and X. Zhang, "Flying plasmonic lens in the near field for high-speed nanolithography," Nature Nanotech. 3, 733 - 737 (2008).
[CrossRef]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. B (1)

P. Berini, "Plasmon-polariton waves guided by thin lossy metal films of finite width: bound modes of symmetric structures," Phys. Rev. B 61, 10484-10503 (2000).
[CrossRef]

Phys. Rev. Lett. (2)

D. Sarid, "Long-range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

Theor. (1)

K. Kurihara, K. Yamamoto, J. Takahara and A. Otomo,"Superfocusing modes of surface plasmon polaritons in a wedge-shaped geometry obtained by quasi-separation of variables," J. Phys. A Math.Theor. 41295401 (2008).
[CrossRef]

Other (3)

E. Moreno, S. G. Rodrigo, S. I. Bozhevolnyi, L. Martin-Moreno, and F. J. Garcia-Vidal, "Guiding and focusing of electromagnetic fields with wedge plasmon-polaritons," Phys. Rev. Lett. 100, 023901-1-4 (2008).
[CrossRef] [PubMed]

http://ab-initio.mit.edu/meep/

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, New York, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

Schematics of the cylindrical metallic disk and its resulting intensity patterns: (a) structure geometry. (b) Schematic pattern of ∣Ez 2 corresponding to Eq. (11). (c) Schematic pattern of ∣Er 2 corresponding to Eq. (12).

Fig. 2.
Fig. 2.

SPP lateral field intensity distribution on the surface of the thin metallic disk embedded in a dielectric with n=1.33. The fields are calculated in the air. (a) SRSPP mode with metallic layer thickness h=15 nm. (b) SRSPP mode, h=10 nm. (c) LRSPP mode, h=15 nm.

Fig. 3.
Fig. 3.

FOMs of the PL. The left and the right columns correspond to LRSPP and SRSPP excitations respectively. (a)-(e) λSPP , SPSZ, DOF, NA eff and the propagation length respectively, as a function of the excitation wavelength λ 0. (f) Legend for (a)-(e) specifying the refractive index nD surrounding the metal.

Fig. 4.
Fig. 4.

(a) SPSZ Normalized by (λ 0/nD ) as a function of the metal thickness. (b) SPSZ Normalized by (λSPP /nD ) as a function of the metal thickness. (c) Legend for (a)-(b) specifying the refractive index nD surrounding the metal.

Fig. 5.
Fig. 5.

(a) Schematic diagram of the cross-section of the circular wedge (b) 3-D view of the circular wedge

Fig. 6.
Fig. 6.

FDTD simulation showing the total electric energy density (logarithmic color scaling) for: (a) excitation of a pure symmetric mode. The region designated by the purple rectangle is dominated by the energy density of the SRSPP. The region designated by the white rectangle is dominated by energy density originated from diffraction and radiation from the wedge. (b) excitation of a pure anti-symmetric mode

Fig. 7.
Fig. 7.

(a) Electric energy density (logarithmic color scaling) resulted by excitation of LRSPP and SRSPP modes using radially polarized light illumination. (b) Zoom of Fig. 7(a) in the vicinity of the focal region (c) The resulting SPSZ as a function of the distance (along the z axis) from the center of the metallic layer. (d) The normalized electric energy density at the center as a function of the distance from the metallic surface.

Equations (16)

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

ErzEzr=jωμHθ
1rHzθHθz=ε0εiEr
1rHθ+Hθr1rHrθ=ε0εiEz
Hr=Eθ=Hz=0
z=kD,r=,θ=0,kD2=β2ω2ε0εDμ
Hθz=ε0εiEr
1rHθ+Hθr=ε0εiEz
1r[ErzEzr]+[ErzEzr]r=ω2με0εiEz
2Ezr2+1rEzr+β2Ez=0
Er=jkDβ2Ezr
Ez(r,z)=AJ0(βr)exp(kDz)
Er(r,z)=AjkDβJ1(βr)exp(kDz)
Ez(r,z)=BJ0(βr)exp(kMz)
Er(r,z)=BjkMβJ1(βr)exp(kMz)
tanh(12kMh)=kDεMkMεD
tanh(12kMh)=kMεDkDεM

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