Abstract

We propose and analyze a plasmonic lens that is illuminated by a radially polarized light. The lens is made of a coax-like geometry consisting of an annular dielectric slit surrounded by metal. Focusing efficiency is enhanced by the use of a circular grating assisting the coupling of light into surface plasmons. Further enhancement is obtained by introducing a circular Bragg grating on top of the structure, reflecting the surface plasmon modes that are propagating in the counter-focus direction. Using the Finite-Difference Time-Domain approach we investigate the transmission and the focusing mechanisms, and study the effect of structural parameters on the performance of the plasmonic lens.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2008 (4)

2007 (5)

2006 (6)

2005 (4)

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

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]

Wulin Jia, Xiaohan Liu, "Mechanism of the superenhanced light transmission through 2D subwavelength coaxial hole arrays," Phys. Lett. A,  344 (6), 451-456 (2005).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

2004 (1)

2003 (2)

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a Radially Polarized Light Beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, "Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit," Phys. Rev. Lett. 90, 213901-1 - 213901-4 (2003).
[CrossRef]

2002 (1)

2001 (2)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

2000 (2)

S. Quabis, R. Dorn, M. Eberler, O. Glöckl and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

K. S. Youngworth and T. G. Brown, "Focusing of high numerical aperture cylindrical vector beams," Opt. Express 7, 77-87 (2000).
[CrossRef] [PubMed]

Bermel, P.

Brown, D. E.

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

Brown, T. G.

Burr, G. W.

Chang, C. K.

D. Z. Lin, C.H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens", Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Chen, C.H.

D. Z. Lin, C.H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens", Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Chen, W.

W. Chen and Q. Zhan, "Optimal plasmonic focusing with radial polarization," Proc. SPIE,  6450, 64500D (2007)
[CrossRef]

Cheng, T. D.

D. Z. Lin, C.H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens", Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a Radially Polarized Light Beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Ebbesen, T. W.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, "Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit," Phys. Rev. Lett. 90, 213901-1 - 213901-4 (2003).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Eberler, M.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Fainman, Y.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, "Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves," Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

U. Levy, C. H. Tsai, L. Pang and Y. Fainman, "Engineering space-variant inhomogeneous media for polarization control," Opt. Lett. 29, 1718-1720 (2004).
[CrossRef] [PubMed]

Farjadpour, A.

Feng, L.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, "Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves," Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, "Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit," Phys. Rev. Lett. 90, 213901-1 - 213901-4 (2003).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Ginzburg, P.

Glöckl, O.

S. Quabis, R. Dorn, M. Eberler, O. Glöckl and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Gordon, R.

Hahn, J.

Hao, B.

Hiller, J. M.

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

Hua, J.

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

Hugonin, J. P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Approximate model for surface-plasmon generation at slit apertures," J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Ibanescu, M.

Jia, Wulin

Wulin Jia, Xiaohan Liu, "Mechanism of the superenhanced light transmission through 2D subwavelength coaxial hole arrays," Phys. Lett. A,  344 (6), 451-456 (2005).
[CrossRef]

Joannopoulos, J. D.

Johnson, S. G.

Kempa, K.

Kim, H.

Kimball, C. W.

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

Kozawa, Y.

Lalanne, P.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Approximate model for surface-plasmon generation at slit apertures," J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Lee, B.

Lee, C. K.

D. Z. Lin, C.H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens", Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Lee, H.

Z.W. Liu, J. M. Steele, H. Lee, and X. Zhang, "Tuning the focus of a plasmonic lens by the incident angle," Appl. Phys. Lett. 88171108 (2006).
[CrossRef]

Leger, J.

Leger, J. R.

Lerman, G. M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a Radially Polarized Light Beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Levy, U.

Lezec, H. J.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, "Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit," Phys. Rev. Lett. 90, 213901-1 - 213901-4 (2003).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Lin, D. Z.

D. Z. Lin, C.H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens", Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Liu, Xiaohan

Wulin Jia, Xiaohan Liu, "Mechanism of the superenhanced light transmission through 2D subwavelength coaxial hole arrays," Phys. Lett. A,  344 (6), 451-456 (2005).
[CrossRef]

Liu, Z.

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]

Liu, Z.W.

Z.W. Liu, J. M. Steele, H. Lee, and X. Zhang, "Tuning the focus of a plasmonic lens by the incident angle," Appl. Phys. Lett. 88171108 (2006).
[CrossRef]

Lomakin, V.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, "Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves," Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Marthandam, P.

Martin-Moreno, L.

F. J. Garcia-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martin-Moreno, "Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit," Phys. Rev. Lett. 90, 213901-1 - 213901-4 (2003).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Orenstein, M.

Pang, L.

Pearson, J.

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

Pellerin, K. M.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Pendry, J. B.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Peng, Y.

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]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, "Sharper Focus for a Radially Polarized Light Beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

S. Quabis, R. Dorn, M. Eberler, O. Glöckl and G. Leuchs, "Focusing light to a tighter spot," Opt. Commun. 179, 1-7 (2000).
[CrossRef]

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Approximate model for surface-plasmon generation at slit apertures," J. Opt. Soc. Am. A 23, 1608-1615 (2006).
[CrossRef]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, "Theory of surface plasmon generation at nanoslit apertures," Phys. Rev. Lett. 95, 263902 (2005).
[CrossRef]

Rodriguez, A.

Roundy, D.

Sato, S.

Slutsky, B.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, "Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves," Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Srituravanich, 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]

Steele, J. M.

J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, "Resonant and non-resonant generation and focusing of surface plasmons with circular gratings," Opt. Express 14, 5664-5670 (2006).
[CrossRef] [PubMed]

Z.W. Liu, J. M. Steele, H. Lee, and X. Zhang, "Tuning the focus of a plasmonic lens by the incident angle," Appl. Phys. Lett. 88171108 (2006).
[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]

Sun, C.

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]

Takakura, Y.

Y. Takakura, "Optical Resonance in a Narrow Slit in a Thick Metallic Screen," Phys. Rev. Lett. 86, 5601-5603 (2001).
[CrossRef] [PubMed]

Tetz, K. A.

L. Feng, K. A. Tetz, B. Slutsky, V. Lomakin, and Y. Fainman, "Fourier plasmonics: Diffractive focusing of in-plane surface plasmon polariton waves," Appl. Phys. Lett. 91, 081101 (2007).
[CrossRef]

Thio, T.

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Tsai, C. H.

Vlasko-Vlasov, V. K.

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

Wang, X.

Wang, Y.

Welp, U.

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," Nano Lett.  5,1399-1402 (2005).
[CrossRef] [PubMed]

Yeh, C. S.

D. Z. Lin, C.H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens", Appl. Phys. Lett. 92, 233106 (2008).
[CrossRef]

Yin, L.

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Supplementary Material (2)

» Media 1: MOV (265 KB)     
» Media 2: MOV (935 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Structure layout and parameters. (a) structure cross-section. (b) structure top view

Fig. 2.
Fig. 2.

(a) Frame excerpt from (Media 1) showing the energy density, for a structure with a Bragg reflector placed in region C. Counter focus propagation is diminished and energy density at the focal region (around r=0) is high. (b) Frame from (Media 2), for a structure with no Bragg reflector. Counter focus propagation can be observed. Also, the difference in energy density around the focus region is clearly observed. Image produced by an FDTD simulation which will be discussed in section 4. The color scaling is saturated and linear, and identical in both insets.

Fig. 3.
Fig. 3.

(a)-(f) Contributions to the energy density of the various SPP field components. The color scaling of all insets is logarithmic, and non-saturated. For (a)–(c), and for (d)–(f) separately, each color intensity corresponds to the same power density, so it can be seen that the ER component is weak compared to EZ and Hφ. We used values of d=1200 nm, and hB=360 nm. No gratings are applied. (g)–(h) schematic illustration showing the propagation of the ER and EZ components from two opposite points on the slit circumference. In (g), because the ER components are excited in antiphase and accumulate the same phase until they arrive at the center, destructive interference is obtained. In (h), the EZ components are generated in phase and accumulate the same phase along their propagation towards the center. Therefore, these components interfere constructively. The colors of the arrows in (g)-(h) represent the accumulated phase.

Fig. 4.
Fig. 4.

Electric power density averaged over a full period of the optical wavelength. Color scaling is logarithmic and non-saturated, and equal in all insets. Calculated for d=1200 nm, hB=360 nm. (a) no gratings are applied. (b) gratings are shifted from the slit with λ SPP,C/2. The enhanced radiation surrounding the slit can be clearly observed. In (c) where the shift is λ SPP,C/4, the radiation is minimal and the energy density at the focus is the strongest.

Fig. 5.
Fig. 5.

Focusing efficiency as function of the outer disc radius, in units of λ SPP.. d=1200 nm and hB=350 nm. All other parameters are as in section 4.1.

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