Abstract

We present a fast and general iterative design method for both diffractive and nondiffractive two-dimensional optical elements. The method is based on a finite-thickness model in combination with the Yang–Gu phase-retrieval algorithm. A rigorous electromagnetic analysis (boundary element method) is used to appraise the designed results. We calculate the transverse-intensity distributions, diffraction efficiency, and spot size of the designed microlenses at the focusing plane for microlenses designed using the presented method and the conventional zero-thickness model. The main findings show the superiority of the presented method over the conventional method, especially for nondiffractive optical elements.

© 2007 Optical Society of America

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  1. K. Hirayama, E. N. Glytsis, T. K. Gaylord, and D. W. Wilson, "Rigorous electromagnetic analysis of diffractive cylindrical lenses," J. Opt. Soc. Am. A 13, 2219-2231 (1996).
    [CrossRef]
  2. J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors," J. Opt. Soc. Am. A 16, 113-130 (1999).
    [CrossRef]
  3. K. Hirayama, K. Igarashi, Y. Hayashi, E. N. Glytsis, and T. K. Gaylord, "Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods," J. Opt. Soc. Am. A 16, 1294-1302 (1999).
    [CrossRef]
  4. P. Blattner and H. P. Herzig, "Rigorous diffraction theory applied to microlenses," J. Mod. Opt. 45, 1395-1403 (1998).
    [CrossRef]
  5. D. W. Prather, S. Shi, and J. S. Bergey, "Field stitching algorithm for the analysis of electrically large diffractive optical elements," Opt. Lett. 24, 273-275 (1999).
    [CrossRef]
  6. D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 8, 34-43 (1997).
    [CrossRef]
  7. D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, "Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements," J. Opt. Soc. Am. A 15, 1599-1607 (1998).
    [CrossRef]
  8. D. Feng, Y. B. Yan, G. Jin, and S. Fan, "Design and fabrication of continuous-profile diffractive micro-optical elements as a beam splitter," Appl. Opt. 43, 5476-5480 (2004).
    [CrossRef] [PubMed]
  9. J. M. Bendickson. E. N. Glytsis, and 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]
  10. D. A. Buralli, G. M. Morris, and J. R. Rogers, "Optical performance of holographic kinoforms," Appl. Opt. 28, 976-983 (1989).
    [CrossRef] [PubMed]
  11. M. Rossi. R. E. Kunz, and H. P. Herzig, "Refractive and diffractive properties of planar micro-optical elements," Appl. Opt. 34, 5996-6007 (1995).
    [CrossRef] [PubMed]
  12. V. Moreno. J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
    [CrossRef]
  13. J.-S. Ye, B.-Y. Gu, B.-Z. Dong, and S.-T. Liu, "Improved first Rayleigh-Sommerfeld method for analysis of cylindrical microlenses with small f-numbers," Opt. Lett. 29, 2345-2347 (2004).
    [CrossRef] [PubMed]
  14. J.-S. Ye, B.-Y. Gu, B.-Z. Dong, and S.-T. Liu, "Applications of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers," J. Opt. Soc. Am. A 22, 862-869 (2005).
    [CrossRef]
  15. J.-S. Ye and S.-T. Liu, "Applying the finite-thickness model to designs of cylindrical microlenses with small f-numbers," Optik (Stuttgart) 117, 225-230 (2005).
    [CrossRef]
  16. B.-Y. Gu, G.-Z. Yang, and B. Z. Dong, "General theory for performing an optical transform," Appl. Opt. 25, 3197-3206 (1986).
    [CrossRef] [PubMed]
  17. G.-Z. Yang, B. Z. Dong, B.-Y. Gu, J. Y. Zhuang, and O. K. Ersoy, "Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison," Appl. Opt. 33, 209-218 (1994).
    [CrossRef] [PubMed]
  18. M. Bass, E. M. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Vol. II, Devices, Measurements and Properties (McGraw-Hill, 1995).

2005 (2)

2004 (2)

1999 (3)

1998 (3)

1997 (2)

D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 8, 34-43 (1997).
[CrossRef]

V. Moreno. J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

1989 (1)

1986 (1)

Bass, M.

M. Bass, E. M. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Vol. II, Devices, Measurements and Properties (McGraw-Hill, 1995).

Bendickson, J. M.

Bergey, J. S.

Blattner, P.

P. Blattner and H. P. Herzig, "Rigorous diffraction theory applied to microlenses," J. Mod. Opt. 45, 1395-1403 (1998).
[CrossRef]

Buralli, D. A.

Collins, J. P.

Dong, B. Z.

Dong, B.-Z.

Ersoy, O. K.

Fan, S.

Feng, D.

Gaylord, T. K.

Glytsis, E. N.

Gu, B.-Y.

Hayashi, Y.

Herzig, H. P.

P. Blattner and H. P. Herzig, "Rigorous diffraction theory applied to microlenses," J. Mod. Opt. 45, 1395-1403 (1998).
[CrossRef]

M. Rossi. R. E. Kunz, and H. P. Herzig, "Refractive and diffractive properties of planar micro-optical elements," Appl. Opt. 34, 5996-6007 (1995).
[CrossRef] [PubMed]

Hirayama, K.

Igarashi, K.

Jin, G.

Kunz, R. E.

Liu, S.-T.

Mait, J. N.

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, "Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements," J. Opt. Soc. Am. A 15, 1599-1607 (1998).
[CrossRef]

D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 8, 34-43 (1997).
[CrossRef]

Mirotznik, M. S.

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, "Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements," J. Opt. Soc. Am. A 15, 1599-1607 (1998).
[CrossRef]

D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 8, 34-43 (1997).
[CrossRef]

Moreno, V.

V. Moreno. J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Morris, G. M.

Prather, D. W.

Rogers, J. R.

Roman, J. F.

V. Moreno. J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Rossi, M.

Salgueiro, J. R.

V. Moreno. J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Shi, S.

Van Stryland, E. M.

M. Bass, E. M. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Vol. II, Devices, Measurements and Properties (McGraw-Hill, 1995).

Williams, D. R.

M. Bass, E. M. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Vol. II, Devices, Measurements and Properties (McGraw-Hill, 1995).

Wilson, D. W.

Wolfe, W. L.

M. Bass, E. M. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Vol. II, Devices, Measurements and Properties (McGraw-Hill, 1995).

Yan, Y. B.

Yang, G.-Z.

Ye, J.-S.

Zhuang, J. Y.

Am. J. Phys. (1)

V. Moreno. J. F. Roman, and J. R. Salgueiro, "High efficiency diffractive lenses: deduction of kinoform profile," Am. J. Phys. 65, 556-562 (1997).
[CrossRef]

Appl. Opt. (5)

J. Mod. Opt. (1)

P. Blattner and H. P. Herzig, "Rigorous diffraction theory applied to microlenses," J. Mod. Opt. 45, 1395-1403 (1998).
[CrossRef]

J. Opt. Soc. Am. A (7)

D. W. Prather, M. S. Mirotznik, and J. N. Mait, "Boundary integral methods applied to the analysis of diffractive optical elements," J. Opt. Soc. Am. A 8, 34-43 (1997).
[CrossRef]

J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Metallic surface-relief on-axis and off-axis focusing diffractive cylindrical mirrors," J. Opt. Soc. Am. A 16, 113-130 (1999).
[CrossRef]

K. Hirayama, K. Igarashi, Y. Hayashi, E. N. Glytsis, and T. K. Gaylord, "Finite-substrate-thickness cylindrical diffractive lenses: exact and approximate boundary-element methods," J. Opt. Soc. Am. A 16, 1294-1302 (1999).
[CrossRef]

D. W. Prather, J. N. Mait, M. S. Mirotznik, and J. P. Collins, "Vector-based synthesis of finite aperiodic subwavelength diffractive optical elements," J. Opt. Soc. Am. A 15, 1599-1607 (1998).
[CrossRef]

J. M. Bendickson. E. N. Glytsis, and 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]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, and D. W. Wilson, "Rigorous electromagnetic analysis of diffractive cylindrical lenses," J. Opt. Soc. Am. A 13, 2219-2231 (1996).
[CrossRef]

J.-S. Ye, B.-Y. Gu, B.-Z. Dong, and S.-T. Liu, "Applications of improved first Rayleigh-Sommerfeld method to analyze the performance of cylindrical microlenses with different f-numbers," J. Opt. Soc. Am. A 22, 862-869 (2005).
[CrossRef]

Opt. Lett. (2)

Optik (Stuttgart) (1)

J.-S. Ye and S.-T. Liu, "Applying the finite-thickness model to designs of cylindrical microlenses with small f-numbers," Optik (Stuttgart) 117, 225-230 (2005).
[CrossRef]

Other (1)

M. Bass, E. M. Van Stryland, D. R. Williams, and W. L. Wolfe, Handbook of Optics, Vol. II, Devices, Measurements and Properties (McGraw-Hill, 1995).

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Figures (4)

Fig. 1
Fig. 1

Geometry of a cylindrical microlens. In this case, the optical element is diffractive.

Fig. 2
Fig. 2

Flow chart of the modified Yang–Gu algorithm used in the present iterative design method.

Fig. 3
Fig. 3

Transverse-intensity distributions in the focal plane calculated with the rigorous BEM for TE-polarized incident light; (a) f 0.333 microlenses and (b) f 0.5 microlenses. Each figure shows four intensity distributions, two kinds of microlenses—diffractive and nondiffractive—each designed with two different iterative methods. The curves with triangles correspond to diffractive microlenses, while the curves with circles correspond to nondiffractive microlenses. All the solid curves correspond to microlenses designed with the proposed FTM; while all the dashed curves correspond to microlenses designed by the ZTM.

Fig. 4
Fig. 4

Appraisal of the two design methods of microlenses by using the rigorous BEM: (a) dependence of the diffraction efficiency on the f-number and (b) variation of the focal-spot size as a function of the f-number. All the solid curves correspond to an evaluation of the performance of microlenses designed by the presented FTM, while all the dashed curves correspond to the microlenses designed by the ZTM. All the curves with triangles correspond to the case of diffractive microlenses; while all the curves with circles correspond to the case of nondiffractive microlenses.

Equations (6)

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ψ ( r 2 ) = Γ [ ψ 1 inc ( r Γ ) G 2 RS 1 ( r 2 , r Γ ) y ̂ ] d l ,
ψ ( r 2 ) = G ̂ ( r Γ , r 2 ) ψ 1 inc ( r Γ ) ,
ϕ 2 ( n ) ( x 2 ) = arg { G ̂ ρ 1 ( n ) exp [ i ϕ 1 ( n ) ] } ,
ϕ 1 ( n , m + 1 ) ( x 1 ) = arg ( A ̂ D 1 { G ̂ ρ 2 exp ( i ϕ 2 ) A ̂ N D ρ 1 exp [ i ϕ 1 ( n , m ) ] } ) .
Δ y = ϕ 1 ( x ) k 0 ( n 1 n 2 ) .
ρ 2 ( n ) ( x 2 ) = w ( x 2 ) G ̂ ρ 1 exp ( i ϕ 1 ( n ) ) .

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