The focusing property of the spiral Fibonacci zone plate

The concept of fractal, such as Cantor set, has been combined with the Fresnel zone plates (ZPs) to improve its imaging capability and introduce additional freedom for optimizing. In this letter, Fibonacci zone plates (FiZPs), which is generated by means of Fibonacci fractals, was proposed. The FiZPs can be constructed by the generating rules of the Fibonacci sequences similar with the Cantor set zone plate published. Numerical simulation based on Fresnel diffraction is performed to verify the on-axis intensity distribution of the FiZPs. According to the simulated results, the FiZPs can focus the incident beam as conventional zone plates as well but with fractal on-axis intensity profile. The theoretical results are also verified by the experiment by means of phase-only spatial light modulator (pSLM). Furthermore, the spiral Fibonacci zone plate (sFiZPs) was designed by overlapping the spiral phase on the FiZPs. Both numerical simulations and experiments are performed and the results are coincident well with each other.

[1]  Propagation properties of plasmonic micro-zone plates with and without fractals , 2008 .

[2]  Jiao Lin,et al.  Sequence of focused optical vortices generated by a spiral fractal zone plate , 2006 .

[3]  Jeffrey A. Davis,et al.  Focusing properties of fractal zone plates: experimental implementation with a liquid-crystal display. , 2004, Optics letters.

[4]  Y. Sakurada,et al.  Scaling properties of the Fresnel diffraction field produced by one-dimensional regular fractals , 1994 .

[5]  Chris Jacobsen,et al.  Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging , 2003, Nature.

[6]  B. C. Richards,et al.  Excitonic polaritons in Fibonacci quasicrystals. , 2008, Optics express.

[7]  M. Fernández-Alonso,et al.  Fractal generalized zone plates. , 2008, Journal of The Optical Society of America A-optics Image Science and Vision.

[8]  Genaro Saavedra,et al.  Fractal zone plates. , 2003, Optics letters.

[9]  Tatiana Alieva,et al.  Optical wave propagation of fractal fields , 1996 .

[10]  C. Sparrow.  The Fractal Geometry of Nature , 1984 .

[11]  Genaro Saavedra,et al.  White-light imaging with fractal zone plates. , 2007, Optics letters.

[12]  J. Gouyet.  Physics and Fractal Structures , 1996 .

[13]  Allain,et al.  Optical diffraction on fractals. , 1986, Physical review. B, Condensed matter.

[14]  L. Zunino,et al.  Fraunhofer diffraction by cantor fractals with variable lacunarity , 2003 .

[15]  J. P. Woerdman,et al.  Fractal structure of eigenmodes of unstable-cavity lasers. , 1998, Optics letters.

[16]  Dwight L. Jaggard,et al.  Scattering from fractally corrugated surfaces , 1990 .

[17]  A. Koshelev,et al.  Terahertz Technology: Terahertz TomographicImaging With a Fresnel Lens , 2002 .

[18]  Changqing Xie,et al.  Circular Fibonacci gratings. , 2011, Applied optics.

[19]  L. Lim,et al.  Near-field behavior of zone-plate-like plasmonic nanostructures. , 2008, Journal of the Optical Society of America. A, Optics, image science, and vision.

[20]  M. V. Berry,et al.  Integer, fractional and fractal Talbot effects , 1996 .

[21]  Jianhua Liu,et al.  Programmable fractal zone plates (FraZPs) with foci finely tuned , 2008 .

[22]  E. Akkermans,et al.  Thermodynamics of photons on fractals. , 2010, Physical review letters.