Abstract

We analyze the focusing properties of Fresnel zone plates fabricated over steel tapes using laser ablation. Our intention is to implement the use of micro-optical elements when the use of conventional chrome–glass elements is not indicated. Because of the manufacture process, the surface presents a certain anisotropic roughness, which reduces the focusing properties. First, we develop numerical simulations by means of the Rayleigh–Sommerfeld approach, showing how roughness in both levels of the Fresnel zone plate affects the focalization of the lens. We also manufacture Fresnel zone plates over steel tape, and perform experimental verification that corroborates the numerical results.

© 2010 Optical Society of America

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References

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  1. J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, 1998).
  2. H. P. Herzig, Micro-Optics. Elements, Systems and Applications (Taylor & Francis, 1997).
  3. F. J. González, J. Alda, B. Illic, and G. Boreman, “Infrared antennas coupled to lithographic Fresnel zone plate lenses,” Appl. Opt. 43, 6067-6073 (2004).
    [CrossRef]
  4. J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
    [CrossRef]
  5. X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
    [CrossRef]
  6. M. F. Modest, “Transient elastic and viscoelastic thermal stresses during laser drilling of ceramics,” J. Heat Transfer 120, 892-898 (1998).
    [CrossRef]
  7. J. Krüger and W. Kautek, “Femtosecond-pulse visible laser processing of transparent materials,” Appl. Surf. Sci. 96-98, 430-438 (1996).
  8. J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35, 1156-1167 (1999).
    [CrossRef]
  9. F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Talbot effect in rough reflection gratings,” Appl. Opt. 46, 3668-3673 (2007).
    [CrossRef]
  10. L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278, 23-27 (2007).
    [CrossRef]
  11. F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Double grating systems with one steel tape grating,” Opt. Commun. 281, 5647-5652 (2008).
    [CrossRef]
  12. F. Shen and A. Wang, “Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula,” Appl. Opt. 45, 1102-1110 (2006).
    [CrossRef]
  13. R. W. Wood, “Phase-reversal zone plates, and diffraction-telescopes,” Philos. Mag. 45, 511-522 (1898).
  14. A. V. Baez, “Fresnel zone plate for optical image formation using extreme ultraviolet and soft x radiation,” J. Opt. Soc. Am. 51, 405-412 (1961).
    [CrossRef]
  15. J. Kirz, “Phase zone plates for x rays and the extreme uv,” J. Opt. Soc. Am. 64, 301-309 (1974).
    [CrossRef]
  16. J. A. Ogilvy, Theory of Wave Scattering From Random Rough Surfaces (Taylor & Francis, 1991).
  17. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves form Rough Surfaces (Artech House, 1987), Chap. 5.

2008

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Double grating systems with one steel tape grating,” Opt. Commun. 281, 5647-5652 (2008).
[CrossRef]

2007

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Talbot effect in rough reflection gratings,” Appl. Opt. 46, 3668-3673 (2007).
[CrossRef]

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278, 23-27 (2007).
[CrossRef]

2006

J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
[CrossRef]

F. Shen and A. Wang, “Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula,” Appl. Opt. 45, 1102-1110 (2006).
[CrossRef]

2004

1999

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35, 1156-1167 (1999).
[CrossRef]

X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
[CrossRef]

1998

M. F. Modest, “Transient elastic and viscoelastic thermal stresses during laser drilling of ceramics,” J. Heat Transfer 120, 892-898 (1998).
[CrossRef]

1996

J. Krüger and W. Kautek, “Femtosecond-pulse visible laser processing of transparent materials,” Appl. Surf. Sci. 96-98, 430-438 (1996).

1974

1961

1898

R. W. Wood, “Phase-reversal zone plates, and diffraction-telescopes,” Philos. Mag. 45, 511-522 (1898).

Alda, J.

J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
[CrossRef]

F. J. González, J. Alda, B. Illic, and G. Boreman, “Infrared antennas coupled to lithographic Fresnel zone plate lenses,” Appl. Opt. 43, 6067-6073 (2004).
[CrossRef]

Baez, A. V.

Beckmann, P.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves form Rough Surfaces (Artech House, 1987), Chap. 5.

Bernabeu, E.

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Double grating systems with one steel tape grating,” Opt. Commun. 281, 5647-5652 (2008).
[CrossRef]

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278, 23-27 (2007).
[CrossRef]

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Talbot effect in rough reflection gratings,” Appl. Opt. 46, 3668-3673 (2007).
[CrossRef]

Boreman, G.

J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
[CrossRef]

F. J. González, J. Alda, B. Illic, and G. Boreman, “Infrared antennas coupled to lithographic Fresnel zone plate lenses,” Appl. Opt. 43, 6067-6073 (2004).
[CrossRef]

Corkum, P. B.

X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
[CrossRef]

González, F. J.

Herzig, H. P.

H. P. Herzig, Micro-Optics. Elements, Systems and Applications (Taylor & Francis, 1997).

Illic, B.

Kautek, W.

J. Krüger and W. Kautek, “Femtosecond-pulse visible laser processing of transparent materials,” Appl. Surf. Sci. 96-98, 430-438 (1996).

Kirz, J.

Krüger, J.

J. Krüger and W. Kautek, “Femtosecond-pulse visible laser processing of transparent materials,” Appl. Surf. Sci. 96-98, 430-438 (1996).

Lail, B.

J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
[CrossRef]

López-Alonso, J. M.

J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
[CrossRef]

Modest, M. F.

M. F. Modest, “Transient elastic and viscoelastic thermal stresses during laser drilling of ceramics,” J. Heat Transfer 120, 892-898 (1998).
[CrossRef]

Naumov, A. Yu.

X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
[CrossRef]

Nikumb, S.

X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
[CrossRef]

Noack, J.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35, 1156-1167 (1999).
[CrossRef]

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering From Random Rough Surfaces (Taylor & Francis, 1991).

Rico-García, J. M.

J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
[CrossRef]

Sanchez-Brea, L. M.

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Double grating systems with one steel tape grating,” Opt. Commun. 281, 5647-5652 (2008).
[CrossRef]

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Talbot effect in rough reflection gratings,” Appl. Opt. 46, 3668-3673 (2007).
[CrossRef]

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278, 23-27 (2007).
[CrossRef]

Shen, F.

Spizzichino, A.

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves form Rough Surfaces (Artech House, 1987), Chap. 5.

Torcal-Milla, F. J.

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Double grating systems with one steel tape grating,” Opt. Commun. 281, 5647-5652 (2008).
[CrossRef]

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278, 23-27 (2007).
[CrossRef]

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Talbot effect in rough reflection gratings,” Appl. Opt. 46, 3668-3673 (2007).
[CrossRef]

Turunen, J.

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, 1998).

Villeneuve, D. M.

X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
[CrossRef]

Vogel, A.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35, 1156-1167 (1999).
[CrossRef]

Wang, A.

Wood, R. W.

R. W. Wood, “Phase-reversal zone plates, and diffraction-telescopes,” Philos. Mag. 45, 511-522 (1898).

Wyrowski, F.

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, 1998).

Zhu, X.

X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
[CrossRef]

Appl. Opt.

Appl. Surf. Sci.

X. Zhu, D. M. Villeneuve, A. Yu. Naumov, S. Nikumb, and P. B. Corkum, “Experimental study of drilling sub-10 μm holes in thin metal foils with femtosecond laser pulses,” Appl. Surf. Sci. 152, 138-148 (1999).
[CrossRef]

J. Krüger and W. Kautek, “Femtosecond-pulse visible laser processing of transparent materials,” Appl. Surf. Sci. 96-98, 430-438 (1996).

IEEE J. Quantum Electron.

J. Noack and A. Vogel, “Laser-induced plasma formation in water at nanosecond to femtosecond time scales: calculation of thresholds, absorption coefficients, and energy density,” IEEE J. Quantum Electron. 35, 1156-1167 (1999).
[CrossRef]

J. Heat Transfer

M. F. Modest, “Transient elastic and viscoelastic thermal stresses during laser drilling of ceramics,” J. Heat Transfer 120, 892-898 (1998).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

L. M. Sanchez-Brea, F. J. Torcal-Milla, and E. Bernabeu, “Talbot effect in metallic gratings under Gaussian illumination,” Opt. Commun. 278, 23-27 (2007).
[CrossRef]

F. J. Torcal-Milla, L. M. Sanchez-Brea, and E. Bernabeu, “Double grating systems with one steel tape grating,” Opt. Commun. 281, 5647-5652 (2008).
[CrossRef]

J. Alda, J. M. Rico-García, J. M. López-Alonso, B. Lail, and G. Boreman,·“Design of Fresnel lenses and binary-staircase kinoforms of low value of the aperture number,” Opt. Commun. 260, 454-461 (2006).
[CrossRef]

Philos. Mag.

R. W. Wood, “Phase-reversal zone plates, and diffraction-telescopes,” Philos. Mag. 45, 511-522 (1898).

Other

J. A. Ogilvy, Theory of Wave Scattering From Random Rough Surfaces (Taylor & Francis, 1991).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves form Rough Surfaces (Artech House, 1987), Chap. 5.

J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Wiley-VCH, 1998).

H. P. Herzig, Micro-Optics. Elements, Systems and Applications (Taylor & Francis, 1997).

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Figures (6)

Fig. 1
Fig. 1

Images of the Fresnel zone plate used in the simulations. The FZP presents a focal length of f = 450 mm . (a) Ideal FZP. (b) Simulation of a RFZP engraved by laser ablation (data from Table 1: σ 2 = 0.27 μm , T 2 x = 4.2 μm , T 2 y = 4.8 μm ) over a flat surface, σ 1 = 0 μm . (c) Simulation of a RFZP engraved by laser ablation over a real surface with low roughness level (data from Table 1: σ 1 = 0.05 μm , T 1 x = 50.23 μm , T 1 y = 164.38 μm ) but with σ 2 = 0 μm .

Fig. 2
Fig. 2

(a) Simulation of a RFZP engraved by laser ablation over a real surface with low roughness level (data from Table 1: σ 1 = 0.05 μm , T 1 x = 50.23 μm , T 1 y = 164.38 μm ). (b) Simulation of a RFZP engraved by laser ablation over a real surface with high roughness level (data from Table 1: σ 1 = 0.15 μm , T 1 x = 11.60 μm , T 1 y = 119.20 μm ).

Fig. 3
Fig. 3

Dependence of the focusing capability with roughness. (a) Maximum of intensity at the focal plane for different values of σ 1 , with σ 2 = 4.5 μm . (b) Irradiance profiles along the z axis for different values of σ 1 : 0 (highest), 0.01, 0.03, 0.05, and 0.07 μm and the same value for σ 2 = 4.5 μm , normalized to the maximum. (c) Maximum of intensity at the focal plane for different values of σ 2 , with σ 2 = 0.05 μm . (d) Irradiance profiles along the z axis for different values of σ 2 : 0 (lowest), 0.03, 0.06, and 0.1, and the same value for σ 1 = 0.05 μm , normalized to the maximum.

Fig. 4
Fig. 4

(a) and (b) Optical microscopy image of a RFZP for low and high roughness steel substrates respectively. (c) and (d) Confocal microscopy image of a RFZP for low and high roughness steel substrates, respectively.

Fig. 5
Fig. 5

Experimental setup. FPLD is a fiber pigtailed laser diode, CL is a collimation lens, BS is a beam splitter, and f is the focal length of the RFZP.

Fig. 6
Fig. 6

(a) and (b) Transversal view of the propagation of light with RFZP from Figs. 4a, 4b, respectively (experimental data). (c) and (d) Simulations with the Rayleigh–Sommerfeld approach of propagation of light from Figs. 4a, 4b respectively. All the intensities are normalized to the unit.

Tables (1)

Tables Icon

Table 1 Roughness Values Obtained by Confocal Microscopy from the Two Manufactured Rough Fresnel Zone Plates

Equations (5)

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L ( x , y ) = { 1 if     m λ f x 2 + y 2 < ( m + 1 ) λ f 0 if     ( m 1 ) λ f x 2 + y 2 < m λ f ,
σ = h 2 s .
C ( R ) = exp ( R 2 T 2 ) ,
r ( x , y ) = L ( x , y ) exp [ 2 i k h 1 ( x , y ) ] + [ 1 L ( x , y ) ] exp [ 2 i k h 2 ( x , y ) ] .
U ( x , y , z ) = A 0 e i k z i λ z r ( ξ , η ) e i k 2 z [ ( x ξ ) 2 + ( y η ) 2 ] d ξ d η ,

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