Abstract

Light diffraction by volume Fresnel zone plates (VFZPs) is simulated by the Hankel transform beam propagation method (Hankel BPM). The method utilizes circularly symmetric geometry and small step propagation to calculate the diffracted wave fields by VFZP layers. It is shown that fast and accurate diffraction results can be obtained with the Hankel BPM. The results show an excellent agreement with the scalar diffraction theory and the experimental results. The numerical method allows more comprehensive studies of the VFZP parameters to achieve higher diffraction efficiency.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2007 (2)

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]

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]

2004 (2)

2002 (1)

1999 (2)

1994 (1)

1990 (1)

Cao, Q.

Chambers, D. M.

Ersoy, O. K.

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]

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]

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (Wiley-Interscience, 2006), pp. 21, 57-58, 190-191.

Guizar-Sicairos, M.

Gutiérrez-Vega, J.

Jahns, J.

Kurokhtin, A. N.

Nordin, G. P.

Piestun, R.

Popov, A. V.

Prather, D. W.

Shamir, J.

Shi, S.

Srisungsitthisunti, P.

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]

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]

Wyrowski, F.

Xu, X.

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]

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]

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 (6)

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

Opt. Lett. (1)

Other (1)

O. K. Ersoy, Diffraction, Fourier Optics and Imaging (Wiley-Interscience, 2006), pp. 21, 57-58, 190-191.

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Figures (10)

Fig. 1
Fig. 1

Example of a VFZP having four FZP layers.

Fig. 2
Fig. 2

Simulation model of a three-layer VFZP showing propagation steps used by the Hankel BPM calculation. The actual computational windows are twice the size of the maximum radius.

Fig. 3
Fig. 3

(a) Regular FZP, (b) central-ring FZP, and light diffraction computed by the RS integral (c) the axial diffractions, (d) the radial diffractions at the focal plane.

Fig. 4
Fig. 4

Diffraction results calculated by Hankel BPM for (a) the regular FZP and (b) the central-ring FZP. The gradient of the contour plots was reduced by plotting I ( 1 4 ) to clearly show the propagating pattern.

Fig. 5
Fig. 5

Light diffraction by VFZP consists of single diffractions (1,2) and multiple diffractions (3).

Fig. 6
Fig. 6

Comparison of (a) the regular FZP and (b) the two-layer regular VFZP to show the effect of double diffraction by the Hankel BPM. The phase modulation is 0.5 π for each FZP layer.

Fig. 7
Fig. 7

Simulation of regular VFZPs having up to 20 layers with phase modulations from 0.05 π to 0.4 π .

Fig. 8
Fig. 8

Simulation of central-ring VFZPs having up to 20 layers with phase modulations from 0.05 π to 0.4 π .

Fig. 9
Fig. 9

Simulation of central-ring VFZPs having up to 20 layers with different focal lengths and constant phase modulation of 0.23 π .

Fig. 10
Fig. 10

Comparison of the experimental results and the simulation results for the central-ring VFZP having 0.23 π phase modulation.

Equations (6)

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

U ( ρ ) = 2 π 0 u ( r ) J 0 ( 2 π r ρ ) r d r ,
u ( r ) = 2 π 0 U ( ρ ) J 0 ( 2 π r ρ ) ρ d ρ ,
U ( P 0 ) = 1 j λ s U ( P 1 ) exp ( j k r ) r cos ( n , r ) d s .
U ( R ) = n = 1 N U n ( R ) ,
U n ( R ) = 1 λ A n f ρ 2 exp ( j k ρ ) r d r d θ ,
η = I ω 0 I input = 0 ω 0 I d r 0 aperture I d r .

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