Abstract

We present a procedure for the design of binary diffractive lenses with pulse-width-modulated subwavelength features. The procedure is based on the combination of two approximate theories, effective medium theory and scalar diffraction theory, and accounts for limitations on feature size and etch depth imposed by fabrication. A design example is presented.

© 1998 Optical Society of America

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References

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  1. M. W. Farn, Appl. Opt. 31, 4453 (1992).
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  2. H. Haidner, J. T. Sheridan, J. Schwider, and N. Streibl, Opt. Commun. 98, 5 (1993).
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  3. D. H. Ranguin, “Subwavelength structured surfaces: theory and application,” Ph.D.??dissertation (University of Rochester, Rochester, New York, 1993).
  4. Z. Zhou and T. J. Drabik, J. Opt. Soc. Am. A 12, 1104 (1995).
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  5. E. Noponen, J. Turunen, and F. Wyrowski, J. Opt. Soc. Am. A 12, 1128 (1995).
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  6. M. Schmitz, R. Bräuer, and O. Bryngdahl, J. Opt. Soc. Am. A 12, 2458 (1995).
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  7. P. Lalanne and D. Lamercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
    [CrossRef]
  8. P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, Opt. Eng. 35, 726 (1996).
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  9. M. Schmitz and O. Bryngdahl, J. Opt. Soc. Am. A 14, 901 (1997).
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  12. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap.??14, pp. 705–708.
  13. S.-H. Lee, ed., Selected Papers on Computer-Generated Holograms and Diffractive Optics, Vol. MS33 of SPIE Milestones Series (SPIE Press, Bellingham, Wash., 1992).
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    [CrossRef]

1998 (1)

1997 (2)

1996 (2)

P. Lalanne and D. Lamercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[CrossRef]

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, Opt. Eng. 35, 726 (1996).
[CrossRef]

1995 (3)

1993 (1)

H. Haidner, J. T. Sheridan, J. Schwider, and N. Streibl, Opt. Commun. 98, 5 (1993).
[CrossRef]

1992 (1)

1985 (1)

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap.??14, pp. 705–708.

Bräuer, R.

Bryngdahl, O.

Collins, J. P.

Collischon, M.

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, Opt. Eng. 35, 726 (1996).
[CrossRef]

Drabik, T. J.

Farn, M. W.

Gaylord, T. K.

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Haidner, H.

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, Opt. Eng. 35, 726 (1996).
[CrossRef]

H. Haidner, J. T. Sheridan, J. Schwider, and N. Streibl, Opt. Commun. 98, 5 (1993).
[CrossRef]

Kipfer, P.

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, Opt. Eng. 35, 726 (1996).
[CrossRef]

Lalanne, P.

P. Lalanne and D. Lamercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[CrossRef]

Lamercier-Lalanne, D.

P. Lalanne and D. Lamercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[CrossRef]

Mait, J. N.

Mirotznik, M. S.

Mirtoznik, M. S.

Moharam, M. G.

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Noponen, E.

Prather, D. W.

Ranguin, D. H.

D. H. Ranguin, “Subwavelength structured surfaces: theory and application,” Ph.D.??dissertation (University of Rochester, Rochester, New York, 1993).

Schmitz, M.

Schwider, J.

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, Opt. Eng. 35, 726 (1996).
[CrossRef]

H. Haidner, J. T. Sheridan, J. Schwider, and N. Streibl, Opt. Commun. 98, 5 (1993).
[CrossRef]

Sheridan, J. T.

H. Haidner, J. T. Sheridan, J. Schwider, and N. Streibl, Opt. Commun. 98, 5 (1993).
[CrossRef]

Streibl, N.

H. Haidner, J. T. Sheridan, J. Schwider, and N. Streibl, Opt. Commun. 98, 5 (1993).
[CrossRef]

Turunen, J.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap.??14, pp. 705–708.

Wyrowski, F.

Zhou, Z.

Appl. Opt. (1)

J. Mod. Opt. (1)

P. Lalanne and D. Lamercier-Lalanne, J. Mod. Opt. 43, 2063 (1996).
[CrossRef]

J. Opt. Soc. Am. A (6)

Opt. Commun. (1)

H. Haidner, J. T. Sheridan, J. Schwider, and N. Streibl, Opt. Commun. 98, 5 (1993).
[CrossRef]

Opt. Eng. (1)

P. Kipfer, M. Collischon, H. Haidner, and J. Schwider, Opt. Eng. 35, 726 (1996).
[CrossRef]

Proc. IEEE (1)

T. K. Gaylord and M. G. Moharam, Proc. IEEE 73, 894 (1985).
[CrossRef]

Other (3)

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1980), Chap.??14, pp. 705–708.

S.-H. Lee, ed., Selected Papers on Computer-Generated Holograms and Diffractive Optics, Vol. MS33 of SPIE Milestones Series (SPIE Press, Bellingham, Wash., 1992).

D. H. Ranguin, “Subwavelength structured surfaces: theory and application,” Ph.D.??dissertation (University of Rochester, Rochester, New York, 1993).

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Figures (2)

Fig. 1
Fig. 1

Binary subwavelength lens design: (a) Substrate profile for 2π continuous-phase lens. (b) Substrate profile for π continuous-phase lens. (c) Index synthesis function. (d) Binary subwavelength profile. (e) Spatially quantized subwavelength profile.

Fig. 2
Fig. 2

Electric-field amplitude response for the lenses represented in Fig.  1.

Tables (1)

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Table 1 Lens Diffraction Efficiencies for the Subwavelength Design

Equations (10)

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tx=dfx,
fx=k=1k oddK rectx-zk+1+zk/2zk+1-zk,
nTE2x=nr2-1gx+1, x=0,W,
gx=fx*1/Δrectx/Δ,
θx=θ0nx-1nr-1.
θ0=2πdn0λnr-1.
gTEx=nr-1θx/θ0+12-1nr2-1.
nTM-2x=nr-2-1gx+1,x=0,W,
gTMx=nr-1θx/θ0+1-2-1nr-2-1.
fx=m=0M-1 rectx-mΔ-gmΔ/2gmΔ,

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