Abstract

Electrically switchable phase-type fractal zone plates and fractal photon sieves were fabricated using polymer-dispersed liquid crystal material based on a photomask. While both exhibited similar first-order diffraction behavior, the fractal photon sieves showed greatly suppressed diffraction at higher orders. Compared with current amplitude-type photomasks, our switchable, phase-type devices demonstrated higher diffraction efficiency, an important factor in the future development of adaptive optics.

©2009 Optical Society of America

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References

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  1. N. Bokor and N. Davidson, “Ideal collimation, concentration, and imaging with curved diffractive optical elements,” Rev. Sci. Instrum. 76(11), 111101 (2005).
    [Crossref]
  2. F. M. Dickey, “Laser beam shaping,” Opt. Photonics News 14, 30–35 (2003).
    [Crossref]
  3. M. A. Forastiere and G. C. Righini, “A new approach to the design of hybrid lenses for integrated optics,” Opt. Rev. 6(2), 124–130 (1999).
    [Crossref]
  4. Y. X. Wang, W. B. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
    [Crossref] [PubMed]
  5. G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
    [Crossref] [PubMed]
  6. W. D. Furlan, G. Saavedra, and J. A. Monsoriu, “White-light imaging with fractal zone plates,” Opt. Lett. 32(15), 2109–2111 (2007).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  22. Y. J. Liu, X. W. Sun, Q. Wang, and D. Luo, “Electrically switchable optical vortex generated by a computer-generated hologram recorded in polymer-dispersed liquid crystals,” Opt. Express 15(25), 16645–16650 (2007).
    [Crossref] [PubMed]
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    [Crossref]
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  25. H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
    [Crossref]

2008 (3)

H. T. Dai, J. H. Liu, X. C. Sun, and D. J. Yin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
[Crossref]

D. Wu, L.-G. Niu, Q.-D. Chen, R. Wang, and H.-B. Sun, “High efficiency multilevel phase-type fractal zone plates,” Opt. Lett. 33(24), 2913–2915 (2008).
[Crossref] [PubMed]

2007 (5)

2006 (3)

2005 (3)

2004 (2)

2003 (6)

F. M. Dickey, “Laser beam shaping,” Opt. Photonics News 14, 30–35 (2003).
[Crossref]

Y. X. Wang, W. B. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[Crossref] [PubMed]

G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28(12), 971–973 (2003).
[Crossref] [PubMed]

Q. Cao and J. Jahns, “Nonparaxial model for the focusing of high-numerical-aperture photon sieves,” J. Opt. Soc. Am. A 20(6), 1005–1012 (2003).
[Crossref]

L. Zunino and M. Garavaglia, “Fraunhofer diffraction by Cantor fractals with variable lacunarity,” J. Mod. Opt. 50(5), 717–727 (2003).
[Crossref]

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

2002 (1)

2001 (1)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

1999 (1)

M. A. Forastiere and G. C. Righini, “A new approach to the design of hybrid lenses for integrated optics,” Opt. Rev. 6(2), 124–130 (1999).
[Crossref]

Adelung, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Alieva, T.

Andersen, G.

Barbastathis, G.

Berndt, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Bokor, N.

N. Bokor and N. Davidson, “Ideal collimation, concentration, and imaging with curved diffractive optical elements,” Rev. Sci. Instrum. 76(11), 111101 (2005).
[Crossref]

Calvo, M. L.

Cao, Q.

Chen, Q.-D.

Dai, H. T.

H. T. Dai, J. H. Liu, X. C. Sun, and D. J. Yin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Davidson, N.

N. Bokor and N. Davidson, “Ideal collimation, concentration, and imaging with curved diffractive optical elements,” Rev. Sci. Instrum. 76(11), 111101 (2005).
[Crossref]

Davis, J. A.

Dickey, F. M.

F. M. Dickey, “Laser beam shaping,” Opt. Photonics News 14, 30–35 (2003).
[Crossref]

Elim, H. I.

Y. J. Liu, X. W. Sun, H. I. Elim, and W. Ji, “Gain narrowing and random lasing from dye-doped polymer-dispersed liquid crystals with nanoscale liquid crystal droplets,” Appl. Phys. Lett. 89(1), 011111 (2006).
[Crossref]

Fan, Y.-H.

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

Forastiere, M. A.

M. A. Forastiere and G. C. Righini, “A new approach to the design of hybrid lenses for integrated optics,” Opt. Rev. 6(2), 124–130 (1999).
[Crossref]

Furlan, W. D.

Garavaglia, M.

L. Zunino and M. Garavaglia, “Fraunhofer diffraction by Cantor fractals with variable lacunarity,” J. Mod. Opt. 50(5), 717–727 (2003).
[Crossref]

Gil, D.

Gimenez, F.

F. Gimenez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277(1), 1–4 (2007).
[Crossref]

Giménez, F.

Harm, S.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Jacobsen, C.

Y. X. Wang, W. B. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[Crossref] [PubMed]

Jahns, J.

Ji, W.

Y. J. Liu, X. W. Sun, H. I. Elim, and W. Ji, “Gain narrowing and random lasing from dye-doped polymer-dispersed liquid crystals with nanoscale liquid crystal droplets,” Appl. Phys. Lett. 89(1), 011111 (2006).
[Crossref]

Jia, J.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
[Crossref]

Jiang, J.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
[Crossref]

Johnson, R. L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Kipp, L.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Liu, J. H.

H. T. Dai, J. H. Liu, X. C. Sun, and D. J. Yin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Liu, M.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
[Crossref]

Liu, Y. J.

Y. J. Liu and X. W. Sun, “Electrically switchable computer-generated hologram recorded in polymer-dispersed liquid crystal,” Appl. Phys. Lett. 90(19), 191118 (2007).
[Crossref]

Y. J. Liu, X. W. Sun, Q. Wang, and D. Luo, “Electrically switchable optical vortex generated by a computer-generated hologram recorded in polymer-dispersed liquid crystals,” Opt. Express 15(25), 16645–16650 (2007).
[Crossref] [PubMed]

Y. J. Liu, X. W. Sun, P. Shum, and X. J. Yin, “Tunable fly’s-eye lens made of patterned polymer-dispersed liquid crystal,” Opt. Express 14(12), 5634–5640 (2006).
[Crossref] [PubMed]

Y. J. Liu, X. W. Sun, H. I. Elim, and W. Ji, “Gain narrowing and random lasing from dye-doped polymer-dispersed liquid crystals with nanoscale liquid crystal droplets,” Appl. Phys. Lett. 89(1), 011111 (2006).
[Crossref]

Luo, D.

Martín-Romo, J. A. R.

Menon, R.

Monsoriu, J. A.

Niu, L.-G.

Pons, A.

Ramirez, L.

Ren, H.

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

Righini, G. C.

M. A. Forastiere and G. C. Righini, “A new approach to the design of hybrid lenses for integrated optics,” Opt. Rev. 6(2), 124–130 (1999).
[Crossref]

Saavedra, G.

Seemann, R.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Shum, P.

Skibowski, M.

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Smith, H.

Sun, H.-B.

Sun, X. C.

H. T. Dai, J. H. Liu, X. C. Sun, and D. J. Yin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Sun, X. W.

Y. J. Liu and X. W. Sun, “Electrically switchable computer-generated hologram recorded in polymer-dispersed liquid crystal,” Appl. Phys. Lett. 90(19), 191118 (2007).
[Crossref]

Y. J. Liu, X. W. Sun, Q. Wang, and D. Luo, “Electrically switchable optical vortex generated by a computer-generated hologram recorded in polymer-dispersed liquid crystals,” Opt. Express 15(25), 16645–16650 (2007).
[Crossref] [PubMed]

Y. J. Liu, X. W. Sun, P. Shum, and X. J. Yin, “Tunable fly’s-eye lens made of patterned polymer-dispersed liquid crystal,” Opt. Express 14(12), 5634–5640 (2006).
[Crossref] [PubMed]

Y. J. Liu, X. W. Sun, H. I. Elim, and W. Ji, “Gain narrowing and random lasing from dye-doped polymer-dispersed liquid crystals with nanoscale liquid crystal droplets,” Appl. Phys. Lett. 89(1), 011111 (2006).
[Crossref]

Tullson, D.

Wang, Q.

Wang, R.

Wang, Y. X.

Y. X. Wang, W. B. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[Crossref] [PubMed]

Wu, D.

Wu, S.-T.

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

Xie, C.

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
[Crossref]

Yin, D. J.

H. T. Dai, J. H. Liu, X. C. Sun, and D. J. Yin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

Yin, X. J.

Yun, W. B.

Y. X. Wang, W. B. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[Crossref] [PubMed]

Zunino, L.

L. Zunino and M. Garavaglia, “Fraunhofer diffraction by Cantor fractals with variable lacunarity,” J. Mod. Opt. 50(5), 717–727 (2003).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

Y. J. Liu, X. W. Sun, H. I. Elim, and W. Ji, “Gain narrowing and random lasing from dye-doped polymer-dispersed liquid crystals with nanoscale liquid crystal droplets,” Appl. Phys. Lett. 89(1), 011111 (2006).
[Crossref]

Y. J. Liu and X. W. Sun, “Electrically switchable computer-generated hologram recorded in polymer-dispersed liquid crystal,” Appl. Phys. Lett. 90(19), 191118 (2007).
[Crossref]

H. Ren, Y.-H. Fan, and S.-T. Wu, “Tunable Fresnel lens using nanoscale polymer-dispersed liquid crystals,” Appl. Phys. Lett. 83(8), 1515–1517 (2003).
[Crossref]

J. Mod. Opt. (1)

L. Zunino and M. Garavaglia, “Fraunhofer diffraction by Cantor fractals with variable lacunarity,” J. Mod. Opt. 50(5), 717–727 (2003).
[Crossref]

J. Opt. Soc. Am. A (3)

Nature (2)

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414(6860), 184–188 (2001).
[Crossref] [PubMed]

Y. X. Wang, W. B. Yun, and C. Jacobsen, “Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,” Nature 424(6944), 50–53 (2003).
[Crossref] [PubMed]

Opt. Commun. (3)

H. T. Dai, J. H. Liu, X. C. Sun, and D. J. Yin, “Programmable fractal zone plates (FraZPs) with foci finely tuned,” Opt. Commun. 281(22), 5515–5519 (2008).
[Crossref]

J. Jia, J. Jiang, C. Xie, and M. Liu, “Photon sieve for reduction of the far-field diffraction spot size in the laser free-space communication system,” Opt. Commun. 281(17), 4536–4539 (2008).
[Crossref]

F. Gimenez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277(1), 1–4 (2007).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Opt. Photonics News (1)

F. M. Dickey, “Laser beam shaping,” Opt. Photonics News 14, 30–35 (2003).
[Crossref]

Opt. Rev. (1)

M. A. Forastiere and G. C. Righini, “A new approach to the design of hybrid lenses for integrated optics,” Opt. Rev. 6(2), 124–130 (1999).
[Crossref]

Rev. Sci. Instrum. (1)

N. Bokor and N. Davidson, “Ideal collimation, concentration, and imaging with curved diffractive optical elements,” Rev. Sci. Instrum. 76(11), 111101 (2005).
[Crossref]

Supplementary Material (2)

» Media 1: AVI (4055 KB)     
» Media 2: AVI (3928 KB)     

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Figures (5)

Fig. 1
Fig. 1 Computer-generated (a) FraZP and (b) FraPS, and (c, d) their corresponding simulated diffraction patterns at the focal plane. The parameters used were S = 2, N = 4, γ = 1/7, and ε = 1/7.

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Fig. 2
Fig. 2 Normalized irradiance distributions along the optical axis produced by a (a) FraZP and (b) FraPS, respectively.

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Fig. 3
Fig. 3 The experimental setup to characterize the focusing properties of the FraZP and FraPS.

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Fig. 4
Fig. 4 CCD captured images of the (a) primary and (b) secondary focal points, and (c, d) their corresponding normalized intensity distribution for the FraZP. CCD captured images of the (e) primary and (f) secondary focal points, and (g, h) their corresponding normalized intensity distribution for the FraPS.

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Fig. 5
Fig. 5 Intensity changes of the primary focus for (a−d) FraZP (Media 1) and (e−h) FraPS (Media 2).

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I(z)=(2πλz)2|∫0a∫02πp(r,φ)exp(iπλzr2)rdrdφ|2.
I(z)=42S+1sin2(πγSa22λz){∏i=1Scos2[πa22λzγi(1−εγ−2)]cos2[πa22λzγi(εγ+1)]}.
I(z)=∑n=1Nh|2NfAnexp[jk(Ln+R'22z)]Jinc(2πanλzρ)|2,
Δδ=2π(neven−nodd)d/λ,

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