Abstract

Multilevel phase-type diffractive lenses were fabricated by translating a filament of a femtosecond laser pulse into three-dimensional space inside synthesized silica. The profile of the lenses was designed by use of a multilevel approximation to a kinoform lens. Two-level diffractive lenses with multiple layers along the optical axis provided a maximum efficiency of 37.6% at a wavelength of 632.8 nm. A four-level diffractive lens provided a maximum efficiency of 56.9%. The lenses fabricated with filamentation were free from birefringence.

© 2004 Optical Society of America

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References

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    [CrossRef]
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2003 (4)

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, J. Appl. Phys. 93, 1889 (2003).
[CrossRef]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, Jpn. J. Appl. Phys. 42, 6916 (2003).
[CrossRef]

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, Opt. Lett. 28, 2491 (2003).
[CrossRef] [PubMed]

2002 (3)

W. Watanabe, D. Kuroda, K. Itoh, and J. Nishii, Opt. Express 10, 978 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200 (2002).
[CrossRef]

M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

2001 (2)

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, Opt. Lett. 26, 19 (2001).
[CrossRef]

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
[CrossRef]

1999 (1)

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[CrossRef]

1996 (1)

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

1989 (1)

D. A. Buralli, G. M. Morris, and J. R. Rogers, Appl. Opt. 28, 976 (1989).
[CrossRef] [PubMed]

1970 (1)

H. Dammann, Optik 31, 95 (1970).

Asano, T.

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, Opt. Lett. 28, 2491 (2003).
[CrossRef] [PubMed]

Baumberg, J. J.

E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200 (2002).
[CrossRef]

Bricchi, E.

E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200 (2002).
[CrossRef]

Brodeur, A.

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
[CrossRef]

Buralli, D. A.

D. A. Buralli, G. M. Morris, and J. R. Rogers, Appl. Opt. 28, 976 (1989).
[CrossRef] [PubMed]

Chichkov, B. N.

M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

Dammann, H.

H. Dammann, Optik 31, 95 (1970).

Davis, K. M.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

Franco, M.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[CrossRef]

Garcia, J. F.

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, Reading, Mass., 2002).

Hirao, K.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

Itoh, K.

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, J. Appl. Phys. 93, 1889 (2003).
[CrossRef]

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, Opt. Lett. 28, 2491 (2003).
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, Jpn. J. Appl. Phys. 42, 6916 (2003).
[CrossRef]

W. Watanabe, D. Kuroda, K. Itoh, and J. Nishii, Opt. Express 10, 978 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, Opt. Lett. 26, 19 (2001).
[CrossRef]

Kazansky, P. G.

E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200 (2002).
[CrossRef]

Klappauf, B. G.

E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200 (2002).
[CrossRef]

Kuroda, D.

W. Watanabe, D. Kuroda, K. Itoh, and J. Nishii, Opt. Express 10, 978 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Mazur, E.

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
[CrossRef]

Mills, J. D.

E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200 (2002).
[CrossRef]

Miura, K.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

Morris, G. M.

D. A. Buralli, G. M. Morris, and J. R. Rogers, Appl. Opt. 28, 976 (1989).
[CrossRef] [PubMed]

Mysyrowicz, A.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[CrossRef]

Nishii, J.

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, Jpn. J. Appl. Phys. 42, 6916 (2003).
[CrossRef]

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, Opt. Lett. 28, 2491 (2003).
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, J. Appl. Phys. 93, 1889 (2003).
[CrossRef]

W. Watanabe, D. Kuroda, K. Itoh, and J. Nishii, Opt. Express 10, 978 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, Opt. Lett. 26, 19 (2001).
[CrossRef]

Nolte, S.

M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

Prade, B.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[CrossRef]

Rogers, J. R.

D. A. Buralli, G. M. Morris, and J. R. Rogers, Appl. Opt. 28, 976 (1989).
[CrossRef] [PubMed]

Saito, M.

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

Schaffer, C. B.

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
[CrossRef]

Sudrie, L.

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[CrossRef]

Sugimoto, N.

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

Takahashi, M.

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

Tokuda, Y.

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

Toma, T.

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, Opt. Lett. 26, 19 (2001).
[CrossRef]

Tunnermann, A.

M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

Watanabe, W.

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, J. Appl. Phys. 93, 1889 (2003).
[CrossRef]

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, Opt. Lett. 28, 2491 (2003).
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, Jpn. J. Appl. Phys. 42, 6916 (2003).
[CrossRef]

W. Watanabe, D. Kuroda, K. Itoh, and J. Nishii, Opt. Express 10, 978 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, Opt. Lett. 26, 19 (2001).
[CrossRef]

Will, M.

M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

Yamada, K.

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, J. Appl. Phys. 93, 1889 (2003).
[CrossRef]

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, Opt. Lett. 28, 2491 (2003).
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, Jpn. J. Appl. Phys. 42, 6916 (2003).
[CrossRef]

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, Opt. Lett. 26, 19 (2001).
[CrossRef]

Yoko, T.

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

Appl. Opt. (2)

M. Will, S. Nolte, B. N. Chichkov, and A. Tunnermann, Appl. Opt. 41, 4360 (2002).
[CrossRef] [PubMed]

D. A. Buralli, G. M. Morris, and J. R. Rogers, Appl. Opt. 28, 976 (1989).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, J. Appl. Phys. 93, 1889 (2003).
[CrossRef]

J. Non-Cryst. Solids (1)

Y. Tokuda, M. Saito, M. Takahashi, K. Yamada, W. Watanabe, K. Itoh, and T. Yoko, J. Non-Cryst. Solids 326&327, 472 (2003).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Yamada, W. Watanabe, J. Nishii, and K. Itoh, Jpn. J. Appl. Phys. 42, 6916 (2003).
[CrossRef]

Opt. Commun. (1)

L. Sudrie, M. Franco, B. Prade, and A. Mysyrowicz, Opt. Commun. 171, 279 (1999).
[CrossRef]

Opt. Express (1)

W. Watanabe, D. Kuroda, K. Itoh, and J. Nishii, Opt. Express 10, 978 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Opt. Lett. (5)

E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200 (2002).
[CrossRef]

W. Watanabe, T. Asano, K. Yamada, K. Itoh, and J. Nishii, Opt. Lett. 28, 2491 (2003).
[CrossRef] [PubMed]

K. M. Davis, K. Miura, N. Sugimoto, and K. Hirao, Opt. Lett. 21, 1729 (1996).
[CrossRef] [PubMed]

K. Yamada, W. Watanabe, T. Toma, K. Itoh, and J. Nishii, Opt. Lett. 26, 19 (2001).
[CrossRef]

C. B. Schaffer, A. Brodeur, J. F. Garcia, and E. Mazur, Opt. Lett. 26, 93 (2001).
[CrossRef]

Optik (1)

H. Dammann, Optik 31, 95 (1970).

Other (1)

E. Hecht, Optics, 4th ed. (Addison-Wesley, Reading, Mass., 2002).

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Figures (3)

Fig. 1
Fig. 1

Two- and four-level approximations of a phase-type diffractive lens.

Fig. 2
Fig. 2

Design of a two-level phase-type diffractive lens consisting of (a) two and (b) four layers. (c) Side view and (d) top view of the fabricated two-level phase-type diffractive lens, consisting of four layers with a changed refractive index.

Fig. 3
Fig. 3

(a) Design of a four-level phase-type diffractive lens. (b) Side view and (c) top view of a fabricated four-level phase-type diffractive lens. (d) Focal spot when a He–Ne laser beam (632.8 nm) was incident upon the lens.

Equations (2)

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ϕr=2πm-r22λ0f,    rmr<rm+1,
ηN=sin2π/Nπ/N=sinc21/N.

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