Abstract

Cylindrical dielectric diffractive microlenses are designed by the use of rigorous electromagnetic diffraction theory, and their performances are compared with microlenses based on a conventional scalar design concept. Microlenses with a relief of four depth levels are considered as well as binary microlenses with subwavelength structures. We show that the density of energy in the focus of high-numerical-aperture microlenses can be significantly increased if the phase distribution of the transmitted electrical field is optimized.

© 1997 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  13. J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
    [CrossRef]
  14. J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f/1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
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  24. P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
    [CrossRef]

1996 (1)

1995 (4)

1994 (4)

E. Pawlowski, H. Engel, M. Ferstl, W. Fürst, B. Kuhlow, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

H. Zarschizky, A. Stemmer, F. Mayerhofer, G. Lefranc, W. Gramann, “Binary and multilevel diffractive lenses with submicrometer feature sizes,” Opt. Eng. 33, 3527–3536 (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]

F. Pincemin, A. Sentenac, J. J. Greffet, “Near field scattered by a dielectric rod below a metallic surface,” J. Opt. Soc. Am. A 11, 1117–1127 (1994).
[CrossRef]

1993 (4)

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

E. Noponen, J. Turunen, A. Vasara, “Electromagnetic theory and design of diffractive-lens arrays,” J. Opt. Soc. Am. A 10, 434–443 (1993).
[CrossRef]

W. H. Welch, J. E. Morris, M. R. Feldman, “Iterative discrete on-axis encoding of radially symmetric computer-generated holograms,” J. Opt. Soc. Am. A 10, 1729–1738 (1993).
[CrossRef]

S. Haselbeck, H. Schreiber, J. Schwider, N. Streibl, “Microlenses fabricated by melting a photoresist on a base layer,” Opt. Eng. 32, 1322–1324 (1993).
[CrossRef]

1992 (1)

1991 (2)

1990 (3)

1989 (1)

J. J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2d obstacle near an interface,” Opt. Commun. 72, 274–278 (1989).
[CrossRef]

1988 (1)

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

1986 (1)

Asahara, Y.

Baer, T. M.

Bojko, R. J.

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f/1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

Brenner, K.-H.

Chen, F. T.

Chou, S. Y.

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

Craighead, H. G.

Engel, H.

E. Pawlowski, H. Engel, M. Ferstl, W. Fürst, B. Kuhlow, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Feldman, M. R.

Ferstl, M.

E. Pawlowski, H. Engel, M. Ferstl, W. Fürst, B. Kuhlow, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Finlan, J. M.

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f/1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

Fischer, P. B.

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

Flood, K. M.

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f/1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

Fürst, W.

E. Pawlowski, H. Engel, M. Ferstl, W. Fürst, B. Kuhlow, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Goering, R.

Goodman, J. W.

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

Gramann, W.

H. Zarschizky, A. Stemmer, F. Mayerhofer, G. Lefranc, W. Gramann, “Binary and multilevel diffractive lenses with submicrometer feature sizes,” Opt. Eng. 33, 3527–3536 (1994).
[CrossRef]

Grann, E. B.

Greffet, J. J.

Haidner, H.

Hamanaka, K.

Haselbeck, S.

S. Haselbeck, H. Schreiber, J. Schwider, N. Streibl, “Microlenses fabricated by melting a photoresist on a base layer,” Opt. Eng. 32, 1322–1324 (1993).
[CrossRef]

Herzig, H. P.

Hosokawa, H.

Izumitani, T.

Jahns, J.

Kipfer, P.

Kuhlow, B.

E. Pawlowski, H. Engel, M. Ferstl, W. Fürst, B. Kuhlow, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Kuittinen, M.

Lefranc, G.

H. Zarschizky, A. Stemmer, F. Mayerhofer, G. Lefranc, W. Gramann, “Binary and multilevel diffractive lenses with submicrometer feature sizes,” Opt. Eng. 33, 3527–3536 (1994).
[CrossRef]

Leger, J. R.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Mayerhofer, F.

H. Zarschizky, A. Stemmer, F. Mayerhofer, G. Lefranc, W. Gramann, “Binary and multilevel diffractive lenses with submicrometer feature sizes,” Opt. Eng. 33, 3527–3536 (1994).
[CrossRef]

Messerschmidt, B.

Moharam, M. G.

Moisel, J.

Morris, J. E.

Nakayama, S.

Nemeto, H.

Nishihara, H.

H. Nishihara, T. Suhara, “Micro fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, Chap. 1, pp. 3–37.

Noponen, E.

Ohmi, S.

Oikawa, M.

Okuda, E.

Pawlowski, E.

E. Pawlowski, H. Engel, M. Ferstl, W. Fürst, B. Kuhlow, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

Pincemin, F.

Pommet, D. A.

Possner, T.

Reichert, P.

Sakai, H.

Schreiber, H.

S. Haselbeck, H. Schreiber, J. Schwider, N. Streibl, “Microlenses fabricated by melting a photoresist on a base layer,” Opt. Eng. 32, 1322–1324 (1993).
[CrossRef]

Schwider, J.

S. Haselbeck, H. Schreiber, J. Schwider, N. Streibl, “Microlenses fabricated by melting a photoresist on a base layer,” Opt. Eng. 32, 1322–1324 (1993).
[CrossRef]

Scott, M. L.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Sentenac, A.

Sinzinger, S.

Snyder, J. J.

Spick, T.

Stemmer, A.

H. Zarschizky, A. Stemmer, F. Mayerhofer, G. Lefranc, W. Gramann, “Binary and multilevel diffractive lenses with submicrometer feature sizes,” Opt. Eng. 33, 3527–3536 (1994).
[CrossRef]

Stork, W.

Streibl, N.

S. Haselbeck, H. Schreiber, J. Schwider, N. Streibl, “Microlenses fabricated by melting a photoresist on a base layer,” Opt. Eng. 32, 1322–1324 (1993).
[CrossRef]

W. Stork, N. Streibl, H. Haidner, P. Kipfer, “Artificial distributed-index media fabricated by zero-order gratings,” Opt. Lett. 16, 1921–1923 (1991).
[CrossRef] [PubMed]

Suhara, T.

H. Nishihara, T. Suhara, “Micro fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, Chap. 1, pp. 3–37.

Testorf, M.

Turunen, J.

Vasara, A.

Veldkamp, W. B.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Walker, S. J.

Welch, W. H.

Yamashita, T.

Yoneda, Y.

Zarschizky, H.

H. Zarschizky, A. Stemmer, F. Mayerhofer, G. Lefranc, W. Gramann, “Binary and multilevel diffractive lenses with submicrometer feature sizes,” Opt. Eng. 33, 3527–3536 (1994).
[CrossRef]

Appl. Opt. (7)

Appl. Phys. Lett. (2)

P. B. Fischer, S. Y. Chou, “Sub-50 nm high aspect-ratio silicon pillars, ridges, and trenches fabricated using ultrahigh resolution electron beam lithography and reactive ion etching,” Appl. Phys. Lett. 62, 1414–1416 (1993).
[CrossRef]

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

J. Opt. Soc. Am. A (5)

Opt. Commun. (1)

J. J. Greffet, “Scattering of s-polarized electromagnetic waves by a 2d obstacle near an interface,” Opt. Commun. 72, 274–278 (1989).
[CrossRef]

Opt. Eng. (4)

J. M. Finlan, K. M. Flood, R. J. Bojko, “Efficient f/1 binary-optics microlenses in fused silica designed using vector diffraction theory,” Opt. Eng. 34, 3560–3564 (1995).
[CrossRef]

S. Haselbeck, H. Schreiber, J. Schwider, N. Streibl, “Microlenses fabricated by melting a photoresist on a base layer,” Opt. Eng. 32, 1322–1324 (1993).
[CrossRef]

E. Pawlowski, H. Engel, M. Ferstl, W. Fürst, B. Kuhlow, “Diffractive microlenses with antireflection coatings fabricated by thin film deposition,” Opt. Eng. 33, 647–652 (1994).
[CrossRef]

H. Zarschizky, A. Stemmer, F. Mayerhofer, G. Lefranc, W. Gramann, “Binary and multilevel diffractive lenses with submicrometer feature sizes,” Opt. Eng. 33, 3527–3536 (1994).
[CrossRef]

Opt. Lett. (3)

Other (2)

H. Nishihara, T. Suhara, “Micro fresnel lenses,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1987), Vol. 24, Chap. 1, pp. 3–37.

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

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Figures (7)

Fig. 1
Fig. 1

Incident plane wave transformed into a converging cylindrical wave by the cylinder lens.

Fig. 2
Fig. 2

(a) Desired phase distribution of the transmitted electrical field (solid curves) approximated with four discrete phase values (dashed curves). Geometries of different F/0.5 diffractive cylindrical microlenses: Four-level microlenses determined with (b) the scalar and (c) the rigorous design concept; (d) binary microlens with a minimum feature size δ=0.1λ.

Fig. 3
Fig. 3

Desired (dotted curves) and real (dashed, dotted–dashed, and solid curves) phase distributions of the transmitted electrical fields of different F/0.5 diffractive microlenses: Four-level microlenses determined with (a) the scalar and (b) the rigorous design concept, and binary microlenses with minimum feature sizes of (c) δ=0.1λ and (d) δ=0.05λ.

Fig. 4
Fig. 4

Scalar (dotted lines) and real (dashed, dotted–dashed, and solid curves) amplitude distributions of the transmitted electrical fields of different F/0.5 diffractive microlenses: Four-level microlenses determined with (a) the scalar and (b) the rigorous design concept; and binary microlenses with minimum feature sizes of (c) δ=0.1λ and (d) δ=0.05λ.

Fig. 5
Fig. 5

Densities of electrical energy of different F/0.5 diffractive microlenses (a) in the focal plane and (b) along the optical axis. The markings of the curves correspond to those of Figs. 3 and 4.

Fig. 6
Fig. 6

Desired (dotted curves) and real (dashed, dotted–dashed, and solid curves) phase distributions of the transmitted electrical fields of different F/1 diffractive microlenses: Four-level microlenses determined with (a) the scalar and (b) the rigorous design concept, and binary microlenses with minimum feature sizes of (c) δ=0.1λ and (d) δ=0.05λ.

Fig. 7
Fig. 7

Densities of electrical energy of different F/1 diffractive microlenses (a) in the focal plane and (b) along the optical axis. The markings of the curves correspond to those of Fig. 6.

Equations (9)

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ϕ(x)=2πλ(F-F2+x2),
NA=11+4(F/#)2.
φ(x)=[ϕ(x)]mod2π.
φK(x)=2πKm(x),
Einc(x, z)=yˆ exp[-iknz],
h(x)=λ2π(n-1)[2π-φK(x)].
neff=fn2+(1-f),
E(x, z)=yˆE(x, z)=yˆ|E(x, z)|exp[iφ(x, z)].
we(x, z)=we(x, z)totwe(x, z)inc=|E(x, z)|2n2,

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