## 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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### Equations (6)

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(1)
$$U\left(\rho \right)=2\pi {\int}_{0}^{\infty}u\left(r\right){J}_{0}\left(2\pi r\rho \right)r\mathrm{d}r,$$
(2)
$$u\left(r\right)=2\pi {\int}_{0}^{\infty}U\left(\rho \right){J}_{0}\left(2\pi r\rho \right)\rho \mathrm{d}\rho ,$$
(3)
$$U\left({P}_{0}\right)=\frac{1}{j\lambda}\underset{s}{\int \int}U\left({P}_{1}\right)\frac{\mathrm{exp}\left(jkr\right)}{r}\phantom{\rule{0.2em}{0ex}}\mathrm{cos}(\stackrel{\u20d7}{n},\stackrel{\u20d7}{r})\mathrm{d}s.$$
(4)
$$U\left(R\right)=\sum _{n=1}^{N}{U}_{n}\left(R\right),$$
(5)
$${U}_{n}\left(R\right)=\frac{1}{\lambda}\underset{{A}_{n}}{\int \int}\frac{f}{{\rho}^{2}}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}\left(jk\rho \right)r\mathrm{d}r\mathrm{d}\theta ,$$
(6)
$$\eta =\frac{{I}_{{\omega}_{0}}}{{I}_{\text{input}}}=\frac{{\int}_{0}^{{\omega}_{0}}I\mathrm{d}r}{{\int}_{0}^{\text{aperture}}I\mathrm{d}r}.$$