Abstract

We present preoptimization strategies for improving the design of diffractive lenses in the electromagnetic domain, with few or no electromagnetic analyses. We find that improvements can be substantial, in some cases even to the point that extensive electromagnetic optimization gives only marginal additional improvement.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. 22 of Frontiers in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
    [CrossRef]
  2. D. M. Mackie, D. W. Prather, S. Shi, “Comparison of optimization strategies for subwavelength multilevel DOEs.”
  3. A. Taflove, Computational Electromagnetics: the Finite-Difference Time Domain Method (Artech House, Norwood, Mass., 1995).
  4. 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]
  5. G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
    [CrossRef]
  6. M. Kuittinen, P. Vahimaa, M. Honkanen, J. Turunen, “Beam shaping in the nonparaxial domain of diffractive optics,” Appl. Opt. 36, 2034–2041 (1997).
    [CrossRef] [PubMed]
  7. H. P. Herzig, “Design of refractive and diffractive micro-optics,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 5–6.
  8. K. Ballüder, M. R. Taghizadeh, “Optimized phase quantization for diffractive elements by use of a bias phase,” Opt. Lett. 24, 1756–1758 (1999).
    [CrossRef]
  9. K. Ballüder, M. R. Taghizadeh, “Optimized quantization for diffractive phase elements by use of uneven phase levels,” Opt. Lett. 26, 417–419 (2001).
    [CrossRef]
  10. Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
    [CrossRef]
  11. T. Hessler, “Continuous-relief diffractive optical elements: design, fabrication, and applications,” Ph.D. dissertation (Universite de Neuchâtel, Neuchâtel, Switzerland, 1997).

2001 (1)

1999 (1)

1998 (1)

1997 (1)

1989 (1)

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

1981 (1)

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Ballüder, K.

Bendickson, J. M.

Gaylord, T. K.

Glytsis, E. N.

Herzig, H. P.

H. P. Herzig, “Design of refractive and diffractive micro-optics,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 5–6.

Hessler, T.

T. Hessler, “Continuous-relief diffractive optical elements: design, fabrication, and applications,” Ph.D. dissertation (Universite de Neuchâtel, Neuchâtel, Switzerland, 1997).

Honkanen, M.

Kuittinen, M.

Li, Y.

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Mackie, D. M.

D. M. Mackie, D. W. Prather, S. Shi, “Comparison of optimization strategies for subwavelength multilevel DOEs.”

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, G. Bao, L. Cowsar, W. Masters, eds., Vol. 22 of Frontiers in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
[CrossRef]

Prather, D. W.

D. M. Mackie, D. W. Prather, S. Shi, “Comparison of optimization strategies for subwavelength multilevel DOEs.”

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. 22 of Frontiers in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
[CrossRef]

Shi, S.

D. M. Mackie, D. W. Prather, S. Shi, “Comparison of optimization strategies for subwavelength multilevel DOEs.”

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. 22 of Frontiers in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
[CrossRef]

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Taflove, A.

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

Taghizadeh, M. R.

Turunen, J.

Vahimaa, P.

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Wolf, E.

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Appl. Opt. (1)

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

Opt. Commun. (1)

Y. Li, E. Wolf, “Focal shifts in diffracted converging spherical waves,” Opt. Commun. 39, 211–215 (1981).
[CrossRef]

Opt. Eng. (1)

G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
[CrossRef]

Opt. Lett. (2)

Other (5)

H. P. Herzig, “Design of refractive and diffractive micro-optics,” in Micro-Optics: Elements, Systems and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997), pp. 5–6.

D. W. Prather, M. S. Mirotznik, S. Shi, “Electromagnetic models for finite aperiodic diffractive optical elements,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds., Vol. 22 of Frontiers in Applied Mathematics (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
[CrossRef]

D. M. Mackie, D. W. Prather, S. Shi, “Comparison of optimization strategies for subwavelength multilevel DOEs.”

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

T. Hessler, “Continuous-relief diffractive optical elements: design, fabrication, and applications,” Ph.D. dissertation (Universite de Neuchâtel, Neuchâtel, Switzerland, 1997).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Profiles of an f/0.5 SWDL in glass for an unlimited etch depth (curve) and a 2π etch depth (circles).

Fig. 2
Fig. 2

Profiles for selected overall phase shifts for the f/0.5 SWDL of Table 1.

Fig. 3
Fig. 3

DE versus number of bits for an f/0.5 SWDL with eight-level 0.2 wide bits 2π etched into glass.

Fig. 4
Fig. 4

Profiles for selected numbers of bits for the f/0.5 SWDL of Fig. 3.

Fig. 5
Fig. 5

DE versus axial distance from the lens for the N = 32, f/0.5 SWDL of Fig. 3.

Fig. 6
Fig. 6

DE versus etch depth multiplier for the N = 32, f/0.5 SWDL of Fig. 3.

Fig. 7
Fig. 7

Profiles of the scalar SWDL of Fig. 6 and the vector EM optimized version.

Fig. 8
Fig. 8

Geometries for the Fermat and the phase plate approximations. Rectangles indicate the SWDL profile; heavy lines represent optical paths in air (solid) and the material (dashed).

Fig. 9
Fig. 9

Focal-shift-adjusted profiles of the N = 32, f/0.5 SWDL of Fig. 3 in the standard phase plate approximation and in the Fermat approximation.

Tables (3)

Tables Icon

Table 1 DE Versus Overall Phase Shifta

Tables Icon

Table 2 DE and Focal-Shift Dataa

Tables Icon

Table 3 DE and Focal-Shift Dataa

Equations (2)

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

zr=1n-1f2+R2-f2+r2,
η1,P=sinπ/P/π/P2,

Metrics