Abstract

Fractal zone plates (FZPs), i.e., zone plates with fractal structure, have been recently introduced in optics. These zone plates are distinguished by the fractal focusing structure they provide along the optical axis. In this paper we study the effects on this axial response of an important descriptor of fractals: the lacunarity. It is shown that this parameter drastically affects the profile of the irradiance response along the optical axis. In spite of this fact, the axial behavior always has the self-similarity characteristics of the FZP itself.

© 2004 Optical Society of America

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References

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J. Mod. Opt. (1)

L. Zunino and M. Garavaglia, �??Fraunhofer diffraction by Cantor fractals with variable lacunarity,�?? J. Mod. Opt. 50, 717-727 (2003).

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

Nature (2)

Y Wang, W. Yun, and C. Jacobsen, �??Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging,�?? Nature 424, 50-53 (2003).
[CrossRef]

L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, �??Sharper images by focusing soft x-rays with photon sieves,�?? Nature 414, 184-188 (2001).
[CrossRef]

Opt. Commun. (1)

A.D. Jaggard and D.L. Jaggard, �??Cantor ring diffractals,�?? Opt. Commun. 158, 141�??148 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Photon. News (1)

S. Wang, X. Zhang, �??Terahertz tomographic imaging with a Fresnel lens,�?? Opt. Photon. News 13, 59 (2002).

Opt.& Photon. News (1)

W.D. Furlan, G. Saavedra, and J.A. Monsoriu, �??Fractal zone plates produce axial irradiance with fractal profile,�?? Opt.& Photon. News 28, 971-973 (2003).

Pure Appl. Opt. (1)

Y. Sakurada, J. Uozumi, and T Asakura, �??Fresnel diffraction by 1-D regular fractals,�?? Pure Appl. Opt. 1, 29�??40 (1992).
[CrossRef]

Other (2)

B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).

J. Ojeda-Castañeda and C. Gómez-Reino, Eds., Selected papers on zone plates (SPIE Optical Engineering Press, Washington, 1996).

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