Abstract

Modified volume Fresnel zone plates (MVFZPs) fabricated with laser direct writing were optimized for higher diffraction efficiencies. The Fresnel radii in each layer of a volume zone plate were iteratively adjusted by a simulation-based direct search optimization. The results show that optimization is effective but depends strongly on the starting diffraction efficiencies determined by the MVFZP parameters. The simulations indicate that the optimized MVFZP can achieve 93% diffraction efficiency.

© 2009 Optical Society of America

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References

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  1. P. Srisungsitthisunti, O. K. Ersoy, and X. Xu, “Volume Fresnel zone plates fabricated by femtosecond laser direct writing,” Appl. Phys. Lett. 90, 011104 (2007).
    [CrossRef]
  2. P. Srisungsitthisunti, O. K. Ersoy, and X. Xu, “Laser direct writing of volume modified Fresnel zone plates,” J. Opt. Soc. Am. B 24, 2090-2096 (2007).
    [CrossRef]
  3. P. Srisungsitthisunti, O. K. Ersoy, and X. Xu, “Beam propagation modeling of modified volume Fresnel zone plates fabricated by femtosecond laser direct writing,” J. Opt. Soc. Am. A 26, 188-194 (2009).
    [CrossRef]
  4. B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).
  5. T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45, 385-482 (2004).
    [CrossRef]
  6. Q. Cao and J. Jahns, “Modified Fresnel zone plates that produce sharp Gaussian focal spots,” J. Opt. Soc. Am. A 20, 1576-1581 (2003).
    [CrossRef]
  7. R. G. Mote, S. F. Yu, B. K. Ng, W. Zhou, and S. P. Lau, “Near-field focusing properties of zone plates in visible regime--New insights,” Opt. Express 16, 9554-9564 (2008).
    [CrossRef] [PubMed]
  8. N. Huot, R. Stoian, A. Mermillod-Blondin, C. Mauclair, and E. Audouard, “Analysis of the effects of spherical aberration on ultrafast laser-induced refractive index variation in glass,” Opt. Express 15, 12395-12408 (2007).
    [CrossRef] [PubMed]

2009 (1)

2008 (1)

2007 (3)

2004 (1)

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45, 385-482 (2004).
[CrossRef]

2003 (1)

Audouard, E.

Cao, Q.

Ersoy, O. K.

Huot, N.

Jahns, J.

Kolda, T. G.

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45, 385-482 (2004).
[CrossRef]

Kress, B.

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

Lau, S. P.

Lewis, R. M.

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45, 385-482 (2004).
[CrossRef]

Mauclair, C.

Mermillod-Blondin, A.

Meyrueis, P.

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

Mote, R. G.

Ng, B. K.

Srisungsitthisunti, P.

Stoian, R.

Torczon, V.

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45, 385-482 (2004).
[CrossRef]

Xu, X.

Yu, S. F.

Zhou, W.

Appl. Phys. Lett. (1)

P. Srisungsitthisunti, O. K. Ersoy, and X. Xu, “Volume Fresnel zone plates fabricated by femtosecond laser direct writing,” Appl. Phys. Lett. 90, 011104 (2007).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (1)

Opt. Express (2)

SIAM Rev. (1)

T. G. Kolda, R. M. Lewis, and V. Torczon, “Optimization by direct search: new perspectives on some classical and modern methods,” SIAM Rev. 45, 385-482 (2004).
[CrossRef]

Other (1)

B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (Wiley, 2000).

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Figures (13)

Fig. 1
Fig. 1

Comparing the geometry of (a) regular FZP and (b) central-ring FZP. The central-ring FZP has a uniform-linewidth rings located on the middle of the Fresnel zones.

Fig. 2
Fig. 2

Direct search algorithm for diffraction efficiency optimization. This is a single iteration including both directions of radius adjustment.

Fig. 3
Fig. 3

(a) Peak intensities and (b) their corresponding diffraction efficiencies of low NA MVFZP optimizations during the first 1000 iterations. Three low NA MVFZP were simulated: f = 10 mm ( NA = 0.037 ) , f = 20 mm ( NA = 0.026 ) , and f = 30 mm ( NA = 0.021 ) .

Fig. 4
Fig. 4

Optimized result of a low NA MVFZP with a focal length of 20 mm ( NA = 0.026 ) .

Fig. 5
Fig. 5

(a) Peak intensities and (b) their corresponding diffraction efficiencies with high NA MVFZP optimizations during the first 1000 iterations. Three high NA MVFZP were simulated: f = 10 μ m ( NA = 0.82 ) , f = 20 μ m ( NA = 0.67 ) , and f = 30 μ m ( NA = 0.58 ) .

Fig. 6
Fig. 6

Optimized result of a high NA MVFZP with a focal length of 20 μ m (NA0.67).

Fig. 7
Fig. 7

Optimization of MVFZP having 20 mm focal length with different linewidth ranging from 2 μ m to 20 μ m .

Fig. 8
Fig. 8

Diffraction efficiencies before optimization with various focal lengths and linewidths for low NA MVFZP.

Fig. 9
Fig. 9

Diffraction efficiencies before optimization with various focal lengths and linewidths for high NA MVFZP.

Fig. 10
Fig. 10

Optimization of two linewidth and focal length combinations that have similar starting efficiency.

Fig. 11
Fig. 11

Fabrication error simulations of low NA MVFZP ( NA = 0.026 ) .

Fig. 12
Fig. 12

Fabrication error simulations of high NA MVFZP ( NA = 0.67 ) .

Fig. 13
Fig. 13

Phase error simulations of low and high NA MVFZPs.

Equations (1)

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r n = ( 2 n + 1 ) λ f 2 + ( ( 2 n + 1 ) λ 4 ) 2 ; n = 1 , 2 , 3 , ,

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