Abstract

Local optimization of surface-relief profiles of diffractive high-numerical-aperture imaging lenses is considered in the 1:1 imaging geometry for both linearly polarized illumination and unpolarized illumination by using the transition points of a four-level grating as design parameters. In the imaging geometry the optimized surface profiles differ considerably from those optimized previously for focusing or collimation geometries. Binary surface-relief grating structures are shown to provide high local diffraction efficiencies (up to 95%) in the outer regions of a high-numerical-aperture diffractive imaging lens because of the near-Littrow configuration.

© 2001 Optical Society of America

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References

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  1. H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1987), Vol. XXIV.
  2. R. Petit, ed., Electromagnetic Theory of Gratings (Springer, Berlin, 1980).
  3. E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 31, 5010–5012 (1992).
    [CrossRef]
  4. E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
    [CrossRef]
  5. N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
    [CrossRef]
  6. J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f:1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
    [CrossRef]
  7. J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2000), Vol. XL, Sect. 6.2.
  8. A. W. Lohmann, D. P. Paris, “Binary Fraunhofer holograms, generated by computer,” Appl. Opt. 6, 1739–1748 (1967).
    [CrossRef] [PubMed]
  9. P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
    [CrossRef]
  10. E. Noponen, J. Turunen, “Binary high-frequency-carrier diffractive optical elements: electromagnetic theory,” J. Opt. Soc. Am. A 11, 1097–1109 (1994).
    [CrossRef]

1999 (2)

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

1995 (1)

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f:1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1967 (1)

Bojko, R. J.

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f:1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

Finlan, J. M.

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f:1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

Flood, K. M.

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f:1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

Friberg, A. T.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Kettunen, V.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Kuittinen, M.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2000), Vol. XL, Sect. 6.2.

Laakkonen, P.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

Lautanen, J.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

Lohmann, A. W.

Nishihara, H.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1987), Vol. XXIV.

Noponen, E.

Paris, D. P.

Schirmer, M.

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

Sergienko, N.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Stamnes, J. J.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Suhara, T.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1987), Vol. XXIV.

Turunen, J.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

E. Noponen, J. Turunen, “Binary high-frequency-carrier diffractive optical elements: electromagnetic theory,” J. Opt. Soc. Am. A 11, 1097–1109 (1994).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Parametric optimization of multilevel diffractive optical elements by electromagnetic theory,” Appl. Opt. 31, 5010–5012 (1992).
[CrossRef]

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2000), Vol. XL, Sect. 6.2.

Vahimaa, P.

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

Vasara, A.

Wyrowski, F.

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2000), Vol. XL, Sect. 6.2.

Appl. Opt. (2)

J. Mod. Opt. (2)

P. Laakkonen, J. Lautanen, V. Kettunen, J. Turunen, M. Schirmer, “Analog diffractive elements in SiO2 by electron-beam lithography and proportional etching with negative resist,” J. Mod. Opt. 46, 1295–1307 (1999).
[CrossRef]

N. Sergienko, J. J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. T. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
[CrossRef]

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f:1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

Other (3)

J. Turunen, M. Kuittinen, F. Wyrowski, “Diffractive optics: electromagnetic approach,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2000), Vol. XL, Sect. 6.2.

H. Nishihara, T. Suhara, “Micro Fresnel lenses,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1987), Vol. XXIV.

R. Petit, ed., Electromagnetic Theory of Gratings (Springer, Berlin, 1980).

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Figures (10)

Fig. 1
Fig. 1

Geometrical configuration and definition of parameters that define the imaging geometry.

Fig. 2
Fig. 2

(a) Local grating period d/λ and (b) output-space diffraction angle θ as a function of the radial distance from the optical axis for a four-level diffractive lens in 1:1 imaging geometry when b=10,000λ, and t=1000λ.

Fig. 3
Fig. 3

The four-level profile with the transition points xj, j=1,, 6 treated as optimization parameters.

Fig. 4
Fig. 4

Diffraction efficiency curves for regular four-level diffractive lenses in 1:1 imaging geometry.

Fig. 5
Fig. 5

Transition-point chart for diffractive four-level focusing lenses. The four levels are indicated by gray scales: the black region is the top level, and the white region represents the bottom level.

Fig. 6
Fig. 6

Diffraction efficiency versus local grating period for four-level gratings that are optimized for the focusing geometry but are used in 1:1 imaging geometry.

Fig. 7
Fig. 7

Transition-point chart for diffractive four-level lenses optimized for the 1:1 imaging geometry in TE polarization. The gray lines indicate the transition points of a binary profile.

Fig. 8
Fig. 8

Transition-point chart for diffractive four-level lenses optimized for the 1:1 imaging geometry simultaneously in TE and TM polarization. The gray lines indicate the transition points of a binary profile.

Fig. 9
Fig. 9

Diffraction efficiency versus local grating period for diffractive lenses that are optimized for 1:1 imaging geometry in TE polarization: (a) Efficiency curves in TE polarization, (b) efficiency curves in TM polarization.

Fig. 10
Fig. 10

Same as Fig. 9, but the optimization is performed simultaneously for both TE and TM polarization.

Equations (5)

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

a=b-t/n,
h={a+t[n2+(n2-1) tan2 θ]-1/2}tan θ,
θ= arcsin(n-1sin θ),
θ= -arctan(h/b),
d=λ/|sin θ-n sin θ|

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