## Abstract

We report the experimental implementation of pseudo-nondiffracting
beams by use of diffractive phase elements (DPE’s). Based on
the conjugate-gradient method presented in J. Opt. Soc. Am. A **15**, 144–151 (1998), these DPE’s are designed and
fabricated on a flat quartz substrate. The experimental results
show that the performance of the fabricated DPE’s is in good agreement
with the theoretical prediction.

© 1998 Optical Society of America

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### Equations (3)

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(1)
$$E=\sum _{\mathrm{\alpha}=1}^{{N}_{z}}W\left(\mathrm{\alpha}\right)\left\{\sum _{m=1}^{{N}_{2\mathrm{\alpha}}}{\left[{\stackrel{\u02c6}{\mathrm{\rho}}}_{2m\mathrm{\alpha}}-\left|\sum _{n=1}^{{N}_{1}}{G}_{\mathit{mn}}\left({z}_{\mathrm{\alpha}}\right){\mathrm{\rho}}_{1n}exp\left(i{\mathrm{\varphi}}_{1n}\right)\right|\right]}^{2}\right\},$$
(2)
$${G}_{\mathit{mn}}\left({z}_{\mathrm{\alpha}}\right)=\frac{2\mathrm{\pi}}{i\mathrm{\lambda}{z}_{\mathrm{\alpha}}}exp\left(\frac{i2\mathrm{\pi}{z}_{\mathrm{\alpha}}}{\mathrm{\lambda}}\right)exp\left[\frac{i\mathrm{\pi}\left(r_{2m\mathrm{\alpha}}{}^{2}+r_{1n}{}^{2}\right)}{\mathrm{\lambda}{z}_{\mathrm{\alpha}}}\right]\times {J}_{0}\left(\frac{2\mathrm{\pi}{r}_{2m\mathrm{\alpha}}{r}_{1n}}{\mathrm{\lambda}{z}_{\mathrm{\alpha}}}\right){r}_{1n}.$$
(3)
$$W\left(\mathrm{\alpha}\right)=\left\{\begin{array}{ll}\frac{0.98}{{N}_{p}}& \mathrm{in}\mathrm{the}\mathrm{signal}\mathrm{region}\\ \frac{0.02}{{N}_{z}-{N}_{p}}& \mathrm{in}\mathrm{other}\mathrm{region}\end{array}\right.,$$