Abstract

The focusing properties of the optimized zone plate structures which have upper and lower zones with different thicknesses are studied by the three-dimensional finite-difference time-domain method. Two kinds of materials are chosen, including silver representing metal and BK7 glass representing dielectric. An optimization algorithm is applied to tune the parameters of zone plate structures. Several optimized zone plate structures with smaller circular-shape focus are presented. By using the angular spectrum representation method, we found that the cases with smaller focal sizes have larger high-k components; however, the intensities of side lobes also become larger in comparison with the main beam. It is also found that the phase differences between different spatial field components can have the influences on focusing properties. A special case with two focuses is shown by changing the cost function of the same optimization algorithm. Our findings suggest that the optimized zone plate structures can reconstruct the light intensity distribution and have a great potential for the applications in imaging, lithography, and data storage.

© 2010 OSA

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References

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  1. Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
    [CrossRef]
  2. Y. Fu and W. Zhou, “Modulation of main lobe for superfocusing using subwavelength metallic heterostructures,” Plasmonics 4(2), 141–146 (2009).
    [CrossRef]
  3. Y. Fu, Y. Liu, X. Zhou, Z. Xu, and F. Fang, “Experimental investigation of superfocusing of plasmonic lens with chirped circular nanoslits,” Opt. Express 18(4), 3438–3443 (2010).
    [CrossRef] [PubMed]
  4. A. G. Curto, A. Manjavacas, and F. J. García de Abajo, “Near-field focusing with optical phase antennas,” Opt. Express 17(20), 17801–17811 (2009).
    [CrossRef] [PubMed]
  5. H. C. Kim, H. Ko, and M. Cheng, “Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer,” J. Vac. Sci. Technol. B 26(6), 2197–2203 (2008).
    [CrossRef]
  6. H. C. Kim, H. Ko, and M. Cheng, “High efficient optical focusing of a zone plate composed of metal/dielectric multilayer,” Opt. Express 17(5), 3078–3083 (2009).
    [CrossRef] [PubMed]
  7. Q. Wang, X. Yuan, P. Tan, and D. Zhang, “Phase modulation of surface plasmon polaritons by surface relief dielectric structures,” Opt. Express 16(23), 19271–19276 (2008).
    [CrossRef]
  8. J. Li, Y. Cheng, Y. Chue, C. Lin, and T. W. Sheu, “The influence of propagating and evanescent waves on the focusing properties of zone plate structures,” Opt. Express 17(21), 18462–18468 (2009).
    [CrossRef]
  9. R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, “Near-field focusing properties of zone plates in visible regime - New insights,” Opt. Express 16(13), 9554–9564 (2008).
    [CrossRef] [PubMed]
  10. R. Merlin, “Radiationless electromagnetic interference: Evanescent-field interference lenses and perfect focusing,” Science 317(5840), 927–929 (2007).
    [CrossRef] [PubMed]
  11. A. Grbic, L. Jiang, and R. Merlin, “Near-field plates: Subdiffraction focusing with patterned surfaces,” Science 320(5875), 511–513 (2008).
    [CrossRef] [PubMed]
  12. A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Trans. Antenn. Propag. 56(10), 3159–3165 (2008).
    [CrossRef]
  13. R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
    [CrossRef] [PubMed]
  14. L. E. Helseth, “The almost perfect lens and focusing of evanescent waves,” Opt. Commun. 281(8), 1981–1985 (2008).
    [CrossRef]
  15. L. E. Helseth, “Radiationless electromagnetic interference shaping of evanescent cylindrical vector waves,” Phys. Rev. A 78(1), 013819 (2008).
    [CrossRef]
  16. M. Perez-Molina, L. Carretero, P. Acebal, and S. Blaya, “Optical singularities and power flux in the near-field region of planar evanescent-field superlenses,” J. Opt. Soc. Am. A 25(11), 2865–2874 (2008).
    [CrossRef]
  17. F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
    [CrossRef] [PubMed]
  18. F. L. Pedrotti, S. J. and L. S. Pedrotti, Introduction to Optics (Prentice-Hall International, 2nd ed., 1993), Chap. 18.
  19. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1985).
  20. X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
    [CrossRef]
  21. L. Novotny, and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Chap. 2.

2010 (1)

2009 (7)

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
[CrossRef] [PubMed]

H. C. Kim, H. Ko, and M. Cheng, “High efficient optical focusing of a zone plate composed of metal/dielectric multilayer,” Opt. Express 17(5), 3078–3083 (2009).
[CrossRef] [PubMed]

A. G. Curto, A. Manjavacas, and F. J. García de Abajo, “Near-field focusing with optical phase antennas,” Opt. Express 17(20), 17801–17811 (2009).
[CrossRef] [PubMed]

J. Li, Y. Cheng, Y. Chue, C. Lin, and T. W. Sheu, “The influence of propagating and evanescent waves on the focusing properties of zone plate structures,” Opt. Express 17(21), 18462–18468 (2009).
[CrossRef]

Y. Fu and W. Zhou, “Modulation of main lobe for superfocusing using subwavelength metallic heterostructures,” Plasmonics 4(2), 141–146 (2009).
[CrossRef]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[CrossRef] [PubMed]

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

2008 (8)

R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, “Near-field focusing properties of zone plates in visible regime - New insights,” Opt. Express 16(13), 9554–9564 (2008).
[CrossRef] [PubMed]

M. Perez-Molina, L. Carretero, P. Acebal, and S. Blaya, “Optical singularities and power flux in the near-field region of planar evanescent-field superlenses,” J. Opt. Soc. Am. A 25(11), 2865–2874 (2008).
[CrossRef]

Q. Wang, X. Yuan, P. Tan, and D. Zhang, “Phase modulation of surface plasmon polaritons by surface relief dielectric structures,” Opt. Express 16(23), 19271–19276 (2008).
[CrossRef]

H. C. Kim, H. Ko, and M. Cheng, “Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer,” J. Vac. Sci. Technol. B 26(6), 2197–2203 (2008).
[CrossRef]

A. Grbic, L. Jiang, and R. Merlin, “Near-field plates: Subdiffraction focusing with patterned surfaces,” Science 320(5875), 511–513 (2008).
[CrossRef] [PubMed]

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Trans. Antenn. Propag. 56(10), 3159–3165 (2008).
[CrossRef]

L. E. Helseth, “The almost perfect lens and focusing of evanescent waves,” Opt. Commun. 281(8), 1981–1985 (2008).
[CrossRef]

L. E. Helseth, “Radiationless electromagnetic interference shaping of evanescent cylindrical vector waves,” Phys. Rev. A 78(1), 013819 (2008).
[CrossRef]

2007 (2)

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

R. Merlin, “Radiationless electromagnetic interference: Evanescent-field interference lenses and perfect focusing,” Science 317(5840), 927–929 (2007).
[CrossRef] [PubMed]

Acebal, P.

Blaya, S.

Carretero, L.

Cheng, M.

H. C. Kim, H. Ko, and M. Cheng, “High efficient optical focusing of a zone plate composed of metal/dielectric multilayer,” Opt. Express 17(5), 3078–3083 (2009).
[CrossRef] [PubMed]

H. C. Kim, H. Ko, and M. Cheng, “Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer,” J. Vac. Sci. Technol. B 26(6), 2197–2203 (2008).
[CrossRef]

Cheng, Y.

Chue, Y.

Curto, A. G.

Du, C. L.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Fang, F.

Fu, Y.

Y. Fu, Y. Liu, X. Zhou, Z. Xu, and F. Fang, “Experimental investigation of superfocusing of plasmonic lens with chirped circular nanoslits,” Opt. Express 18(4), 3438–3443 (2010).
[CrossRef] [PubMed]

Y. Fu and W. Zhou, “Modulation of main lobe for superfocusing using subwavelength metallic heterostructures,” Plasmonics 4(2), 141–146 (2009).
[CrossRef]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Gao, X.

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

García de Abajo, F. J.

Gordon, R.

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
[CrossRef] [PubMed]

Grbic, A.

A. Grbic, L. Jiang, and R. Merlin, “Near-field plates: Subdiffraction focusing with patterned surfaces,” Science 320(5875), 511–513 (2008).
[CrossRef] [PubMed]

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Trans. Antenn. Propag. 56(10), 3159–3165 (2008).
[CrossRef]

He, X.

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

Helseth, L. E.

L. E. Helseth, “The almost perfect lens and focusing of evanescent waves,” Opt. Commun. 281(8), 1981–1985 (2008).
[CrossRef]

L. E. Helseth, “Radiationless electromagnetic interference shaping of evanescent cylindrical vector waves,” Phys. Rev. A 78(1), 013819 (2008).
[CrossRef]

Huang, F. M.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[CrossRef] [PubMed]

Jiang, L.

A. Grbic, L. Jiang, and R. Merlin, “Near-field plates: Subdiffraction focusing with patterned surfaces,” Science 320(5875), 511–513 (2008).
[CrossRef] [PubMed]

Kim, H. C.

H. C. Kim, H. Ko, and M. Cheng, “High efficient optical focusing of a zone plate composed of metal/dielectric multilayer,” Opt. Express 17(5), 3078–3083 (2009).
[CrossRef] [PubMed]

H. C. Kim, H. Ko, and M. Cheng, “Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer,” J. Vac. Sci. Technol. B 26(6), 2197–2203 (2008).
[CrossRef]

Ko, H.

H. C. Kim, H. Ko, and M. Cheng, “High efficient optical focusing of a zone plate composed of metal/dielectric multilayer,” Opt. Express 17(5), 3078–3083 (2009).
[CrossRef] [PubMed]

H. C. Kim, H. Ko, and M. Cheng, “Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer,” J. Vac. Sci. Technol. B 26(6), 2197–2203 (2008).
[CrossRef]

Lau, S. P.

Li, J.

Li, X.

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

Lim, L. E. N.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Lin, C.

Liu, Y.

Luo, X. G.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Manjavacas, A.

Merlin, R.

A. Grbic, L. Jiang, and R. Merlin, “Near-field plates: Subdiffraction focusing with patterned surfaces,” Science 320(5875), 511–513 (2008).
[CrossRef] [PubMed]

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Trans. Antenn. Propag. 56(10), 3159–3165 (2008).
[CrossRef]

R. Merlin, “Radiationless electromagnetic interference: Evanescent-field interference lenses and perfect focusing,” Science 317(5840), 927–929 (2007).
[CrossRef] [PubMed]

Mote, R. G.

Ng, B. K.

Perez-Molina, M.

Sheu, T. W.

Tan, P.

Wang, Q.

Wu, J.

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

Wu, L.

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

Xu, Z.

Yu, S. F.

Yuan, X.

Zhang, D.

Zhao, L.

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

Zheludev, N. I.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[CrossRef] [PubMed]

Zhou, W.

Y. Fu and W. Zhou, “Modulation of main lobe for superfocusing using subwavelength metallic heterostructures,” Plasmonics 4(2), 141–146 (2009).
[CrossRef]

R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, “Near-field focusing properties of zone plates in visible regime - New insights,” Opt. Express 16(13), 9554–9564 (2008).
[CrossRef] [PubMed]

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Zhou, X.

Appl. Phys. Lett. (1)

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: Superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[CrossRef]

Appl. Surf. Sci. (1)

X. He, J. Wu, X. Li, X. Gao, L. Zhao, and L. Wu, “Synthesis and properties of silicon dioxide films prepared by pulsed laser deposition using ceramic SiO2 target,” Appl. Surf. Sci. 256(1), 231–234 (2009).
[CrossRef]

IEEE Trans. Antenn. Propag. (1)

A. Grbic and R. Merlin, “Near-field focusing plates and their design,” IEEE Trans. Antenn. Propag. 56(10), 3159–3165 (2008).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. B (1)

H. C. Kim, H. Ko, and M. Cheng, “Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer,” J. Vac. Sci. Technol. B 26(6), 2197–2203 (2008).
[CrossRef]

Nano Lett. (1)

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Lett. 9(3), 1249–1254 (2009).
[CrossRef] [PubMed]

Opt. Commun. (1)

L. E. Helseth, “The almost perfect lens and focusing of evanescent waves,” Opt. Commun. 281(8), 1981–1985 (2008).
[CrossRef]

Opt. Express (6)

Phys. Rev. A (1)

L. E. Helseth, “Radiationless electromagnetic interference shaping of evanescent cylindrical vector waves,” Phys. Rev. A 78(1), 013819 (2008).
[CrossRef]

Phys. Rev. Lett. (1)

R. Gordon, “Proposal for superfocusing at visible wavelengths using radiationless interference of a plasmonic array,” Phys. Rev. Lett. 102(20), 207402 (2009).
[CrossRef] [PubMed]

Plasmonics (1)

Y. Fu and W. Zhou, “Modulation of main lobe for superfocusing using subwavelength metallic heterostructures,” Plasmonics 4(2), 141–146 (2009).
[CrossRef]

Science (2)

R. Merlin, “Radiationless electromagnetic interference: Evanescent-field interference lenses and perfect focusing,” Science 317(5840), 927–929 (2007).
[CrossRef] [PubMed]

A. Grbic, L. Jiang, and R. Merlin, “Near-field plates: Subdiffraction focusing with patterned surfaces,” Science 320(5875), 511–513 (2008).
[CrossRef] [PubMed]

Other (3)

F. L. Pedrotti, S. J. and L. S. Pedrotti, Introduction to Optics (Prentice-Hall International, 2nd ed., 1993), Chap. 18.

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, San Diego, 1985).

L. Novotny, and B. Hecht, Principles of Nano-Optics (Cambridge University Press, 2006), Chap. 2.

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Figures (7)

Fig. 1
Fig. 1

A cartoon of the investigated zone plate structure with different thickness in each zone, where (a) is the top view and (b) is the cross view.

Fig. 2
Fig. 2

The cost function values c(tu , tl ) = fx + fy verse the number of simulation during the proposed optimization procedures. The circles are the final optimized zone plate structures.

Fig. 3
Fig. 3

(a), (c), (e), (g), and (i) are the simulated Pz (x, y) for the cases standard, 1, 2, 3, and 4 in Table 1, and (b), (d), (f), (h), (j) are the zoom-in plots of (a), (c), (e), (g), and (i) where the white dashed lines are the contours of half intensity of the focus.

Fig. 4
Fig. 4

The simulated normalized Pz (x, y) divided by its maximum along the lines of (a) y = 0 and (b) x = 0 in the focal planes (z = 1 μm) for the cases tabulated in Table 1.

Fig. 5
Fig. 5

The simulated normalized Pz (kx , ky ) divided by its maximum along the lines of (a) ky = 0 and (b) kx = 0 in the focal planes (z = 1 μm) for the cases tabulated in Table 1.

Fig. 6
Fig. 6

The predicted values of the normalized | E x ( x , y = 0 ) | along the line y = 0 for different combinations of the field components in the k-domain. The field in case 1 (blue line) is all in phase: 10 ten-time intensity of 0 k x 2 + k y 2 ( 0.1 k 0 ) 2 with one-time intensity of other components including ( 0.2 k 0 ) 2 k x 2 + k y 2 ( 0.3 k 0 ) 2 , ( 0.4 k 0 ) 2 k x 2 + k y 2 ( 0.5 k 0 ) 2 , ( 0.6 k 0 ) 2 k x 2 + k y 2 ( 0.7 k 0 ) 2 , and ( 0.8 k 0 ) 2 k x 2 + k y 2 ( 1.1 k 0 ) 2 . The case 2 (red line), case 3 (green line) and case 4 (yellow line): there are phase differences π 4 , π 2 , and 3 π 4 between 0 k x 2 + k y 2 ( 0.1 k 0 ) 2 and other spatial field components, respectively. The case 5 (black line): the intensities of all other components double the intensities except 0 k x 2 + k y 2 ( 0.1 k 0 ) 2 as comparing to the conditions in case 1. The case 6 (magenta line): the intensity of the component ( 0.8 k 0 ) 2 k x 2 + k y 2 ( 1.1 k 0 ) 2 doubles the intensity as comparing to the conditions in case 1.

Fig. 7
Fig. 7

Two-focus case: (a) The simulated Pz (x, y) which is normalized to the incident plane wave, and (b) is the zoom-in plot of (a) where the white dashed lines are the contours of half intensity of the focuses.

Tables (1)

Tables Icon

Table 1 The zone thicknesses (tu and tl ), FWHMs (fx and fy ), the maximum of z-component of average power density normalized by the incident plane wave (max. Pz ), and the focal size for the standard zone plate structure and the optimized structures

Equations (4)

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c ( t u , t l ) = f x + f y
| f x f y | < w 1 × max ( f x , f y )
max ( P z ( x , y f , z = 1 μ m ) ) < w 2 × max ( P z ( x , y f , z = 1 μ m ) ) ,
P z = ( 1 2 Re ( E x × H y * E y × H x * ) ) / ( 1 2 Re ( E i x × H i y * ) ) ,

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