## Abstract

The focal distribution produced by a zone plate under ultrashort pulsed laser illumination is investigated under the Fresnel approximation. A comparison of the diffraction patterns in the focal region between pulsed and continuous-wave illumination shows that the focal shape produced by a zone plate can be significantly altered when an ultrashort pulse is shorter than 100 fs. In particular, the focal width in the axial and the transverse directions is increased by approximately 5% and 85%, respectively, from continuous-wave illumination to 10-fs pulsed illumination.

© 2003 Optical Society of America

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### Equations (7)

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(1)
$$R_{m}{}^{2}=\mathit{mf}\mathrm{\lambda},$$
(2)
$$U\left(\mathrm{\rho},z,\mathrm{\omega}\right)=\frac{i2Nexp\left(-i2\mathrm{\pi}z/\mathrm{\lambda}\right)}{\mathrm{\lambda}z}\sum _{m=0}^{{M}_{0}}{\int}_{{\mathrm{\rho}}_{m}}^{{\mathrm{\rho}}_{m+1}}\times {U}_{0}\left({\mathrm{\rho}}_{1},\mathrm{\omega}\right){J}_{0}\left(2N\mathrm{\rho}{\mathrm{\rho}}_{1}\right)exp\left(-\mathit{iN}\mathrm{\rho}_{1}{}^{2}\right){\mathrm{\rho}}_{1}d{\mathrm{\rho}}_{1},$$
(3)
$$\mathrm{\rho}_{m}{}^{2}=\frac{R_{m}{}^{2}}{{a}^{2}}=\frac{\mathit{mf}\mathrm{\lambda}}{{a}^{2}}$$
(4)
$$N=\frac{\mathrm{\pi}{a}^{2}}{\mathrm{\lambda}z}.$$
(5)
$$I\left(\mathrm{\rho},{N}_{0}\right)=C{\int}_{0}^{+\infty}\frac{1}{{N}_{0}}{\left|exp\left[-\frac{{T}^{2}\mathrm{\omega}_{0}{}^{2}}{4}{\left(\frac{N}{{N}_{0}}-1\right)}^{2}\right]\times \sum _{m=0}^{{M}_{0}}{\int}_{{\mathrm{\rho}}_{m}}^{{\mathrm{\rho}}_{m+1}}{J}_{0}\left(2N\mathrm{\rho}{\mathrm{\rho}}_{1}\right)\times exp\left(-\mathit{iN}\mathrm{\rho}_{1}{}^{2}\right){\mathrm{\rho}}_{1}\mathrm{d}{\mathrm{\rho}}_{1}\right|}^{2}\mathrm{d}N,$$
(6)
$$I\left({N}_{0}\right)=\frac{{sin}^{2}\left(\frac{{m}_{0}\mathrm{\pi}{N}_{0}}{{N}_{f}}\right)}{{cos}^{2}\left(\frac{\mathrm{\pi}{N}_{0}}{2{N}_{f}}\right)}$$
(7)
$$I\left({N}_{0}\right)=C{\int}_{0}^{+\infty}\frac{1}{{N}_{0}}{\left|exp\left[-\frac{{T}^{2}\mathrm{\omega}_{0}{}^{2}}{4}{\left(\frac{N}{{N}_{0}}-1\right)}^{2}\right]\times \left[\frac{sin\left(\frac{{m}_{0}\mathrm{\pi}N}{{N}_{f}}\right)}{cos\left(\frac{\mathrm{\pi}N}{2{N}_{f}}\right)}\right]\right|}^{2}\mathrm{d}N$$