Programmable fractal zone plates (FraZPs) with foci finely tuned

We examined the focusing properties of fractal zone plates (FraZPs) in detail based on a liquid crystal on silicon (LCOS) spatial light modulator (SLM). It was shown that the focal length shifted linearly when the lacunarity of first order FraZPs experienced a linear displacement. From the theoretical analysis and the experimental results, we showed the potential to use the FraZPs as a focusing element whose focal length can be tuned finely. In addition, some side effects of this element were also discussed.