Abstract

A method is proposed to modulate phase using variant square holes in a metallic film based on a fundamental mode approximation model. Phase retardation through square holes in a subwavelength scale in a thin metal film has been analyzed and calculated. Based on the model, a structured lens with a numerical aperture of 0.583 and a focal length of 240μm formed by a 2D square hole array in a metallic film is designed. Numerical simulation using the finite-difference time-domain method is carried out, and the results agree with the theoretical analysis. A focal spot close to the diffraction limit can be obtained.

© 2008 Optical Society of America

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  1. L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
    [CrossRef] [PubMed]
  2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
    [CrossRef]
  3. J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
    [CrossRef]
  4. T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
    [CrossRef]
  5. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
    [CrossRef] [PubMed]
  6. L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
    [CrossRef] [PubMed]
  7. F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, Phys. Rev. Lett. 95, 103901 (2005).
    [CrossRef] [PubMed]
  8. J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 93, 227401 (2004).
    [CrossRef] [PubMed]
  9. E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).
    [CrossRef]
  10. J. M. Brok and H. P. Urbach, Opt. Express 14, 2552 (2006).
    [CrossRef] [PubMed]
  11. Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
    [CrossRef]
  12. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
    [CrossRef] [PubMed]
  13. X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
    [CrossRef]
  14. J. R. Suckling, Phys. Rev. Lett. 92, 147401 (2004).
    [CrossRef] [PubMed]

2006 (1)

2005 (3)

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef] [PubMed]

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

2004 (3)

J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 93, 227401 (2004).
[CrossRef] [PubMed]

J. R. Suckling, Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

2002 (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

2001 (3)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

2000 (1)

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).
[CrossRef]

1999 (1)

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Bravo-Abad, J.

J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 93, 227401 (2004).
[CrossRef] [PubMed]

Brok, J. M.

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Dong, X.

Du, C.

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef] [PubMed]

Ebbesen, T. W.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Enoch, S.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).
[CrossRef]

Fu, Y.

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

Gao, H.

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 93, 227401 (2004).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Garcia-Vidal, L. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Kim, H. K.

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Li, H.

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

Luo, X.

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef] [PubMed]

Ma, J.

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

Martin-Moreno, F.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

Martin-Moreno, L.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 93, 227401 (2004).
[CrossRef] [PubMed]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

Moreno, E.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

Neviere, M.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).
[CrossRef]

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, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

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, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Popov, E.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).
[CrossRef]

Porto, J. A.

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

Reinisch, R.

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).
[CrossRef]

Shi, H.

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef] [PubMed]

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

Suckling, J. R.

J. R. Suckling, Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Sun, Z.

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Thio, T.

T. Thio, K. M. Pellerin, R. A. Linke, H. J. Lezec, and T. W. Ebbesen, Opt. Lett. 26, 1972 (2001).
[CrossRef]

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Urbach, H. P.

Wang, C.

H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, Opt. Express 13, 6815 (2005).
[CrossRef] [PubMed]

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

Wolff, P. A.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

Z. Sun and H. K. Kim, Appl. Phys. Lett. 85, 642 (2004).
[CrossRef]

Nature (2)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and P. A. Wolff, Nature 414, 184 (2001).
[CrossRef] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, Nature 391, 667 (1998).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

E. Popov, M. Neviere, S. Enoch, and R. Reinisch, Phys. Rev. B 62, 16100 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

L. Martin-Moreno, F. J. Garcia-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, Phys. Rev. Lett. 86, 1114 (2001).
[CrossRef] [PubMed]

F. J. Garcia-Vidal, E. Moreno, J. A. Porto, and L. Martin-Moreno, Phys. Rev. Lett. 95, 103901 (2005).
[CrossRef] [PubMed]

J. Bravo-Abad, F. J. Garcia-Vidal, and L. Martin-Moreno, Phys. Rev. Lett. 93, 227401 (2004).
[CrossRef] [PubMed]

J. A. Porto, F. J. Garcia-Vidal, and J. B. Pendry, Phys. Rev. Lett. 83, 2845 (1999).
[CrossRef]

J. R. Suckling, Phys. Rev. Lett. 92, 147401 (2004).
[CrossRef] [PubMed]

Proc. SPIE (1)

X. Luo, C. Wang, C. Du, H. Shi, H. Gao, J. Ma, Y. Fu, and H. Li, Proc. SPIE 5927, 59270 X-1 (2005).
[CrossRef]

Science (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, F. Martin-Moreno, L. J. Garcia-Vidal, and T. W. Ebbesen, Science 297, 820 (2002).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Diagram of single rectangular hole of side a x and a y perforated on a thin metal film of thickness h. The film is illuminated by a p-polarized plane wave with its angle of incidence with respect to the normal being θ. (H is parallel to the Y axis and E is in the X Z plane.)

Fig. 2
Fig. 2

Phase retardation of a single square hole in a metallic film as a function of the hole size a for several values of the thickness h of the films; both a and h are in units of wavelength λ. Normal incidence and p polarization is assumed for the incident plane wave (see Fig. 1). Note that the phase retardation can be fully modulated from π to π. The inset shows normalized-to-area transmittance ( T ) versus hole size a when the thickness is h = 1.8 λ .

Fig. 3
Fig. 3

Schematic of the structured lens with a focus length f. The film is perforated with square holes of different sizes in an orderly sequence; the gray part indicates metal, and the white part indicates air. The holes can be centered at any position r so long as the holes do not overlap. It is illuminated by a plane wave with E polariton in the X direction.

Fig. 4
Fig. 4

(a) Numerical calculation of intensity distribution in the Y Z plane at distance 180 to 420 μ m from the exit surface of the metal film. (b) Intensity distribution along the Z axis, indicating the focus position Z = 232 μ m . (c) Intensity distribution in the X Y plane at Z = 232 μ m . (d) Cross section of (c) at Y = 0 , spot size (FWHM) δ = 11.2 μ m .

Equations (3)

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

( G Σ ) E i G v E o = I 0 ,
G v E i + ( G Σ ) E o = 0 ,
φ ( x , y ) = 2 m π + 2 π ( x 2 + y 2 + f 2 f ) λ ,

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