Abstract

A multiresolution direct binary search iterative procedure is used to design small dielectric irregular diffractive optical elements that have subwavelength features and achieve near-field focusing below the diffraction limit. Designs with a single focus or with two foci, depending on wavelength or polarization, illustrate the possible functionalities available from the large number of degrees of freedom. These examples suggest that the concept of such elements may find applications in near-field lithography, wavelength-division multiplexing, spectral analysis, and polarization beam splitters.

© 2006 Optical Society of America

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References

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    [CrossRef]
  2. M. Yang, J. Li, and K. J. Webb, Appl. Phys. Lett. 83, 2736 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  5. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef] [PubMed]
  6. L. Zhang and C. Yang, IEEE Photon. Technol. Lett. 16, 1670 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  8. E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
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    [CrossRef]
  10. G. A. Swartzlander, Opt. Lett. 26, 497 (2001).
    [CrossRef]

2005 (1)

2004 (2)

L. Zhang and C. Yang, IEEE Photon. Technol. Lett. 16, 1670 (2004).
[CrossRef]

M. Yang, J. Li, and K. J. Webb, IEEE Trans. Microwave Theory Tech. 52, 161 (2004).
[CrossRef]

2003 (1)

M. Yang, J. Li, and K. J. Webb, Appl. Phys. Lett. 83, 2736 (2003).
[CrossRef]

2001 (2)

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley-IEEE, 2001).
[CrossRef]

G. A. Swartzlander, Opt. Lett. 26, 497 (2001).
[CrossRef]

1998 (1)

T. Haq, K. J. Webb, and N. C. Gallagher, IEEE Trans. Microwave Theory Tech. 46, 1856 (1998).
[CrossRef]

1987 (2)

1985 (1)

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

Allebach, J. P.

Chen, H.

Chuang, S. L.

Cueva, G. R.

Gallagher, N. C.

T. Haq, K. J. Webb, and N. C. Gallagher, IEEE Trans. Microwave Theory Tech. 46, 1856 (1998).
[CrossRef]

Haq, T.

T. Haq, K. J. Webb, and N. C. Gallagher, IEEE Trans. Microwave Theory Tech. 46, 1856 (1998).
[CrossRef]

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley-IEEE, 2001).
[CrossRef]

Li, J.

M. Yang, J. Li, and K. J. Webb, IEEE Trans. Microwave Theory Tech. 52, 161 (2004).
[CrossRef]

M. Yang, J. Li, and K. J. Webb, Appl. Phys. Lett. 83, 2736 (2003).
[CrossRef]

Minin, S.

Palik, E. D.

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

Seldowitz, M. A.

Swartzlander, G. A.

Sweeney, D. W.

Webb, K. J.

M. Yang, H. Chen, K. J. Webb, S. Minin, S. L. Chuang, and G. R. Cueva, Opt. Lett. 31, 383 (2005).
[CrossRef]

M. Yang, J. Li, and K. J. Webb, IEEE Trans. Microwave Theory Tech. 52, 161 (2004).
[CrossRef]

M. Yang, J. Li, and K. J. Webb, Appl. Phys. Lett. 83, 2736 (2003).
[CrossRef]

T. Haq, K. J. Webb, and N. C. Gallagher, IEEE Trans. Microwave Theory Tech. 46, 1856 (1998).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Yang, C.

L. Zhang and C. Yang, IEEE Photon. Technol. Lett. 16, 1670 (2004).
[CrossRef]

Yang, M.

M. Yang, H. Chen, K. J. Webb, S. Minin, S. L. Chuang, and G. R. Cueva, Opt. Lett. 31, 383 (2005).
[CrossRef]

M. Yang, J. Li, and K. J. Webb, IEEE Trans. Microwave Theory Tech. 52, 161 (2004).
[CrossRef]

M. Yang, J. Li, and K. J. Webb, Appl. Phys. Lett. 83, 2736 (2003).
[CrossRef]

Zhang, L.

L. Zhang and C. Yang, IEEE Photon. Technol. Lett. 16, 1670 (2004).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Yang, J. Li, and K. J. Webb, Appl. Phys. Lett. 83, 2736 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

L. Zhang and C. Yang, IEEE Photon. Technol. Lett. 16, 1670 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

T. Haq, K. J. Webb, and N. C. Gallagher, IEEE Trans. Microwave Theory Tech. 46, 1856 (1998).
[CrossRef]

M. Yang, J. Li, and K. J. Webb, IEEE Trans. Microwave Theory Tech. 52, 161 (2004).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. Lett. (1)

E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef] [PubMed]

Other (2)

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

R. F. Harrington, Time-Harmonic Electromagnetic Fields (Wiley-IEEE, 2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Incident field and region containing the two-dimensional IDOE.

Fig. 2
Fig. 2

IDOE with Si scatterers in free space that focuses a normally incident TE (E out of the page) plane wave from the top to a plane 0.1 λ 0 below the structure ( z λ 0 = 0.26 ) . (a) Structure; the shaded region is Si and the nonshaded region is free space. (b) Normalized Poynting vector, S z S i , over a portion of the computation domain. × marks the focal point. (c) S z S i in the focal plane.

Fig. 3
Fig. 3

Si IDOE that focuses normally incident TE plane waves from the top at λ 0 and 1.001 λ 0 to different focus points 0.1 λ 0 below the structure ( z λ 0 = 0.26 ) . (a) Structure, (b) S z S i at λ 0 , (c) S z S i at 1.001 λ 0 . The scale for S z S i in (b) and (c) has been saturated at ± 10 to permit better visualization of the foci, which are marked by × for λ 0 and + for 1.001 λ 0 . (d) S z S i in the focal plane: solid curve, λ 0 ; dashed curve, 1.001 λ 0 .

Fig. 4
Fig. 4

Si IDOE that focuses normally incident TE and TM plane waves from the top at λ 0 to different focus points 0.1 λ 0 below the structure ( z λ 0 = 0.26 ) . (a) Structure, (b) S z S i for an incident TE plane wave, (c) S z S i for an incident TM plane wave. The focus point for the TE field is marked by ×, and that for the TM field by + in (b) and (c). (d) S z S i in the focal plane: solid curve, TE field; dashed curve, TM field.

Equations (3)

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c ( g ) = x f S z ( x ; g ) d x ,
c ( g ) = c λ 1 ( g ) + c λ 2 ( g ) ,
c λ i ( g ) = 1 t x f i S z , λ i ( x ; g ) d x + 1 t x f j S z , λ i ( x ; g ) d x + 1 w 2 t x f o S z , λ i ( x ; g ) d x ,

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