Abstract

We study the focusing efficiency of multilevel diffractive lenses as a function of f-number. Both scalar and rigorous analyses are performed on two- and three-dimensional lenses. We show that shadowing in lenses with small f-numbers is a critical factor that limits their performance. We show further that scalar analysis does not accurately predict the effects of shadowing for lenses with long f-numbers and large numbers of phase levels.

© 2001 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  2. G. J. Swanson, “Binary optics technoloy: the theory and design of multi-level diffractive optical elements,” (Massachusetts Institute of Technology, Cambridge, Mass., 1989).
  3. G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).
  4. G. J. Swanson, “Binary optics technoloy: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (Massachusetts Institute of Technology, Cambridge, Mass., 1991).
  5. D. A. Gremaux, N. C. Gallagher, “Limits of scalar diffraction theory for conducting gratings,” Appl. Opt. 32, 1948–1953 (1993).
    [CrossRef] [PubMed]
  6. D. A. Pommet, M. G. Moharam, E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994).
    [CrossRef]
  7. A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).
  8. D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1142 (1999).
    [CrossRef]
  9. D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1999).
  10. N. Sergienko, J. Stamnes, V. Kettunen, M. Kuittinen, J. Turunen, P. Vahimaa, A. Friberg, “Comparison of electromagnetic and scalar methods for evaluation of diffractive lenses,” J. Mod. Opt. 46, 65–82 (1999).
  11. J. M. Bendickson, E. N. Glytsis, T. K. Gaylord, “Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses,” J. Opt. Soc. Am. A 15, 1822–1837 (1998).
    [CrossRef]
  12. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Physics 114, 185–200 (1994).
    [CrossRef]

1999 (2)

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

D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1142 (1999).
[CrossRef]

1998 (1)

1994 (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Physics 114, 185–200 (1994).
[CrossRef]

D. A. Pommet, M. G. Moharam, E. B. Grann, “Limits of scalar diffraction theory for diffractive phase elements,” J. Opt. Soc. Am. A 11, 1827–1834 (1994).
[CrossRef]

1993 (1)

Bendickson, J. M.

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Physics 114, 185–200 (1994).
[CrossRef]

Friberg, A.

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

Gallagher, N. C.

Gaylord, T. K.

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Grann, E. B.

Gremaux, D. A.

Kettunen, V.

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

Kuittinen, M.

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

Mirotznik, M. S.

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1999).

Moharam, M. G.

Pommet, D. A.

Prather, D. W.

D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1142 (1999).
[CrossRef]

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1999).

Sergienko, N.

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

Shi, S.

D. W. Prather, S. Shi, “Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements,” J. Opt. Soc. Am. A 16, 1131–1142 (1999).
[CrossRef]

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1999).

Stamnes, J.

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

Swanson, G. J.

G. J. Swanson, “Binary optics technoloy: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (Massachusetts Institute of Technology, Cambridge, Mass., 1991).

G. J. Swanson, “Binary optics technoloy: the theory and design of multi-level diffractive optical elements,” (Massachusetts Institute of Technology, Cambridge, Mass., 1989).

G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).

Taflove, A.

A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).

Turunen, J.

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

Vahimaa, P.

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

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).

Appl. Opt. (1)

J. Comput. Physics (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Physics 114, 185–200 (1994).
[CrossRef]

J. Mod. Opt. (1)

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

J. Opt. Soc. Am. A (3)

Other (6)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

G. J. Swanson, “Binary optics technoloy: the theory and design of multi-level diffractive optical elements,” (Massachusetts Institute of Technology, Cambridge, Mass., 1989).

G. J. Swanson, W. B. Veldkamp, “High-efficiency, multilevel diffractive optical elements,” U.S. patent4,895,790 (23January1990).

G. J. Swanson, “Binary optics technoloy: theoretical limits on the diffraction efficiency of multi-level diffractive optical elements,” (Massachusetts Institute of Technology, Cambridge, Mass., 1991).

A. Taflove, Computational Electromagnetics: The Finite-Difference Time Domain Method (Artech House, Boston, Mass., 1995).

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, SIAM Frontier Book Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1999).

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Figures (7)

Fig. 1
Fig. 1

Illustration of the shadowing effects introduced in the outer zones of a diffractive lens.

Fig. 2
Fig. 2

Focusing efficiency based on a rigorous analysis of four-level spherical lenses.

Fig. 3
Fig. 3

Efficiency of spherical diffractive lenses. Each curve represents the average efficiency of six lenses with different diameters.

Fig. 4
Fig. 4

Efficiency of cylindrical diffractive lenses. Each curve represents the average efficiency of six lenses with different diameters.

Fig. 5
Fig. 5

Efficiency of cylindrical diffractive lenses. Each curve represents the average efficiency of lenses with 2-, 4-, 8-, and 16-phase levels.

Fig. 6
Fig. 6

Averaged efficiencies for rigorously analyzed cylindrical and spherical lenses.

Fig. 7
Fig. 7

Delineation between scalar and electromagnetic models for lens analysis. The difference between predicted efficiencies by use of scalar and electromagnetic models is less than 10% in the scalar region.

Equations (1)

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w=2.44fλ/D,

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