Abstract

The refractive and the diffractive properties of planar micro-optical elements are investigated. The transition between purely refractive and purely diffractive planar microlenses is numerically simulated for the example of differently designed phase-matched Fresnel elements. Results obtained from numerical simulations and experiments show that the refractive and diffractive types exhibit a distinctly different behavior in the presence of small fabrication errors or wavelength deviations. Based on these results, design rules for various applications, including low- and high-numerical-aperture lenses and hybrid refractive–diffractive elements, are derived. For a high-numerical-aperture (f/# = 1.0) lens the experimental characterization of the irradiance distribution in the image space is presented and shown to agree well with theoretical predictions.

© 1995 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989), Chap. 3.1.
  2. R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
    [CrossRef]
  3. W. T. Welford, Aberrations of Optical Systems (Hilger, London, 1986), Chap. 2.1.
  4. M. Rossi, R. E. Kunz, G. L. Bona, “Phase-matched Fresnel elements for optical interconnects,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp 321–324.
  5. J. A. Futhey, M. Fleming, “Superzone diffractive lenses,” in Diffractive Optics: Design, Fabrication and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp 9–6.
  6. J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).
  7. D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
    [CrossRef] [PubMed]
  8. L. N. Hazra, Y. Han, C. Delisle, “Plane kinoform lenses for axial stigmatism in finite conjugate imaging,” Opt. Commun. 91, 1–4 (1992).
    [CrossRef]
  9. J. S. Fender, R. A. Carreras, “Demonstration of an optical phased telescope array,” Opt. Eng. 27, 706–711 (1988).
  10. M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
    [CrossRef]
  11. D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).
  12. G. J. Swanson, W. B. Veldkamp, “Diffractive optical elements for use in infrared systems,” Opt. Eng. 28, 605–608 (1989).
  13. H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).
  14. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap.5.1.
  15. S. Sinzinger, M. Testorf, W. Singer, “The transition between diffractive and refractive micro-optical components,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 143–146.
  16. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap.10.2.
  17. K. Miyamoto, “The phase Fresnel lens,” J. Opt. Soc. Am. 51, 17–20 (1961).
    [CrossRef]
  18. J. J. Stamnes, Waves in Focal Regions (Hilger, London, 1986), Chap.12.1.
  19. Ref. 1, Chap. 8.8.
  20. G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.
  21. Ref. 3, Chap. 11.3.
  22. Ref. 3, Chap. 10.2.
  23. E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1987), Chap.6.3.
  24. E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
    [CrossRef]

1994 (1)

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

1993 (2)

1992 (1)

L. N. Hazra, Y. Han, C. Delisle, “Plane kinoform lenses for axial stigmatism in finite conjugate imaging,” Opt. Commun. 91, 1–4 (1992).
[CrossRef]

1989 (2)

D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
[CrossRef] [PubMed]

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

1988 (1)

J. S. Fender, R. A. Carreras, “Demonstration of an optical phased telescope array,” Opt. Eng. 27, 706–711 (1988).

1970 (1)

H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).

1961 (1)

Angell, D. K.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

Bona, G. L.

M. Rossi, R. E. Kunz, G. L. Bona, “Phase-matched Fresnel elements for optical interconnects,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp 321–324.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989), Chap. 3.1.

Buralli, D. A.

Carreras, R. A.

J. S. Fender, R. A. Carreras, “Demonstration of an optical phased telescope array,” Opt. Eng. 27, 706–711 (1988).

Cress, B. C.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

Dammann, H.

H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).

Daschner, W.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

Delisle, C.

L. N. Hazra, Y. Han, C. Delisle, “Plane kinoform lenses for axial stigmatism in finite conjugate imaging,” Opt. Commun. 91, 1–4 (1992).
[CrossRef]

Faklis, D.

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

Fan, J.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

Fender, J. S.

J. S. Fender, R. A. Carreras, “Demonstration of an optical phased telescope array,” Opt. Eng. 27, 706–711 (1988).

Fleming, M.

J. A. Futhey, M. Fleming, “Superzone diffractive lenses,” in Diffractive Optics: Design, Fabrication and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp 9–6.

Futhey, J. A.

J. A. Futhey, M. Fleming, “Superzone diffractive lenses,” in Diffractive Optics: Design, Fabrication and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp 9–6.

Gale, M. T.

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap.10.2.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap.5.1.

Han, Y.

L. N. Hazra, Y. Han, C. Delisle, “Plane kinoform lenses for axial stigmatism in finite conjugate imaging,” Opt. Commun. 91, 1–4 (1992).
[CrossRef]

Hazra, L. N.

L. N. Hazra, Y. Han, C. Delisle, “Plane kinoform lenses for axial stigmatism in finite conjugate imaging,” Opt. Commun. 91, 1–4 (1992).
[CrossRef]

Hecht, E.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1987), Chap.6.3.

Kunz, R. E.

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
[CrossRef]

M. Rossi, R. E. Kunz, G. L. Bona, “Phase-matched Fresnel elements for optical interconnects,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp 321–324.

Larsson, M.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

Lee, S. H.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

Marron, J. C.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

Miyamoto, K.

Morris, G. M.

D. A. Buralli, G. M. Morris, J. R. Rogers, “Optical performance of holographic kinoforms,” Appl. Opt. 28, 976–983 (1989).
[CrossRef] [PubMed]

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

Noponen, E.

Pedersen, J.

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Rogers, J. R.

Rossi, M.

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
[CrossRef]

M. Rossi, R. E. Kunz, G. L. Bona, “Phase-matched Fresnel elements for optical interconnects,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp 321–324.

Schütz, H.

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Singer, W.

S. Sinzinger, M. Testorf, W. Singer, “The transition between diffractive and refractive micro-optical components,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 143–146.

Sinzinger, S.

S. Sinzinger, M. Testorf, W. Singer, “The transition between diffractive and refractive micro-optical components,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 143–146.

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, London, 1986), Chap.12.1.

Swanson, G. J.

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

Tai, A. M.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

Testorf, M.

S. Sinzinger, M. Testorf, W. Singer, “The transition between diffractive and refractive micro-optical components,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 143–146.

Turunen, J.

Urquhart, K. S.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

Vasara, A.

Veldkamp, W. B.

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

Welford, W. T.

W. T. Welford, Aberrations of Optical Systems (Hilger, London, 1986), Chap. 2.1.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989), Chap. 3.1.

Zajac, A.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1987), Chap.6.3.

Zaleta, D.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (2)

L. N. Hazra, Y. Han, C. Delisle, “Plane kinoform lenses for axial stigmatism in finite conjugate imaging,” Opt. Commun. 91, 1–4 (1992).
[CrossRef]

R. E. Kunz, M. Rossi, “Phase-matched Fresnel elements,” Opt. Commun. 97, 6–10 (1993).
[CrossRef]

Opt. Eng. (3)

J. S. Fender, R. A. Carreras, “Demonstration of an optical phased telescope array,” Opt. Eng. 27, 706–711 (1988).

M. T. Gale, M. Rossi, J. Pedersen, H. Schütz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

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

Optik (1)

H. Dammann, “Blazed synthetic phase-only holograms,” Optik 31, 95–104 (1970).

Other (15)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chap.5.1.

S. Sinzinger, M. Testorf, W. Singer, “The transition between diffractive and refractive micro-optical components,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 143–146.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978), Chap.10.2.

J. J. Stamnes, Waves in Focal Regions (Hilger, London, 1986), Chap.12.1.

Ref. 1, Chap. 8.8.

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

Ref. 3, Chap. 11.3.

Ref. 3, Chap. 10.2.

E. Hecht, A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1987), Chap.6.3.

D. Zaleta, W. Daschner, M. Larsson, B. C. Cress, J. Fan, K. S. Urquhart, S. H. Lee, “Diffractive optics fabricated by electron-beam direct write methods,” in Diffractive and Miniaturized Optics, S. H. Lee, ed., Proc. Soc. Photo-Opt. Instrum. Eng.CR49, 117–137 (1993).

W. T. Welford, Aberrations of Optical Systems (Hilger, London, 1986), Chap. 2.1.

M. Rossi, R. E. Kunz, G. L. Bona, “Phase-matched Fresnel elements for optical interconnects,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp 321–324.

J. A. Futhey, M. Fleming, “Superzone diffractive lenses,” in Diffractive Optics: Design, Fabrication and Applications, Vol. 9 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp 9–6.

J. C. Marron, D. K. Angell, A. M. Tai, “Higher-order kinoforms,” in Computer and Optically Formed Holographic Optics, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1211, 62–66 (1990).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1989), Chap. 3.1.

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Figures (10)

Fig. 1
Fig. 1

Definitions of PMFE segments and focal points of different orders.

Fig. 2
Fig. 2

Schematic design examples for (a) top-aligned and (b) bottom-aligned PMFE microstructures.

Fig. 3
Fig. 3

Axial position of higher- and lower-order foci for PMFE's with different phase-matching numbers.

Fig. 4
Fig. 4

PMFE surface-relief elements for numerical simulations.

Fig. 5
Fig. 5

Calculated distributions of irradiance (dashed curves) and encircled energy (solid curves) along the optical axis z = z 12 for PMFE's with (a) M = 1, (b) M = 2, (c) M = 4, (d) M = 6, and (e) M = 8, all with a depth scaling factor of μ = 0.9; (f) the curves for an element with M = 4 and NA = 0.1. The vertical lines show the positions and the efficiencies of the focal points calculated with Eqs. (11) and (12).

Fig. 6
Fig. 6

Wavelength dependence of (a) focal length l′ and (b) encircled energy. The dashed line in (a) shows the values for a purely diffractive lens calculated with Eq. (11).

Fig. 7
Fig. 7

Hybrid (refractive–diffractive) lens.

Fig. 8
Fig. 8

Hybrid achromat (M = 1): number of diffractive segments versus focal length.

Fig. 9
Fig. 9

Measured irradiance distribution in the image space of an f/1 PMFE.

Fig. 10
Fig. 10

Calculated axial distribution of the encircled energy of an f/1 lens with a depth scaling factor of μ = 0.9.

Tables (1)

Tables Icon

Table 1 Focus Width (FWHM a values) for Phase-Matched Fresnel Elements with Varying Values for M and μ

Equations (22)

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Δ W j = W ( OS j + 1 P ) ¯ W ( OS j P ) ¯ = M j λ ,
r j 2 = 2 j M j λ 0 l ,
Φ j ( r ) = α M j 2 π ( j r 2 2 M j λ 0 l ) , r j r r j + 1 ,
α = λ 0 [ n ( λ 1 ) 1 ] λ 1 [ n ( λ 0 ) 1 ]
h ( r ) = μ h ( r ) .
h ( r ) = λ 0 2 π [ n ( λ 0 ) 1 ] Φ ( r ) ,
t ( ξ ) = N = exp [ i π ( α μ M N ) ] sinc ( α μ M N ) × exp ( i 2 π N ξ )
t ( r ) = N = exp [ i π ( α μ M N ) ] sinc ( α μ M N ) × exp [ i π N r 2 M λ 0 l ] ,
sinc ( x ) = sin ( π x ) π x .
t ( r ) = exp ( i π r 2 λ 1 f ) .
l N = M l N λ 0 λ 1 .
η N = sinc 2 ( α μ M N ) .
u 2 ( x , y ) = u 1 ( x e , y e ) ( z 12 i λ r 12 2 ) exp ( jkr 12 ) d x e d y e = u 1 ( x e , y e ) × exp { ikz 12 [ 1 + ( x x e z 12 ) + ( y y e z 12 ) 2 ] 1 / 2 } i λ z 12 [ 1 + ( x x e z 12 ) + ( y y e z 12 ) 2 ] × d x e d y e .
1 f = 1 f r + 1 f d ,
f r ν r + f d ν d = 0 ,
ν r = n 1 1 n 2 n 3 ,
ν d = λ 1 λ 2 λ 3 .
f d = f ( 1 ν r ν d ) .
Φ ( r ) = 2 π λ 1 r 2 2 f d .
Q = Φ ( a ) 2 π M = 1 λ 1 a 2 2 f d M .
Q = f 8 λ M ( f / # ) 2 ν d ν d ν r .
Q l ( NA ) 2 2 M λ 0 .

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