Twin axial vortices generated by Fibonacci lenses - DiOG

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Fig. 5. Experimental and numerical transverse irradiance at the focal planes provided bytheS8 based on FVL withm= 6 anda= 1.1mm. The intensity profiles along the white,dotted lines are plotted (bottom) together with the numerical results for comparison.

Figure 5 shows the experimental and the numerically simulated transverse irradiance at thefocal planes for the same FVL. Interestingly, the diameter of the focal rings,∆, which alsodepends on the topological charge of the FVL, satisfies a similar rule i.e.∆1/∆2 ≈ ϕ (seeFig. 5). Thus, FVLs are capable of generating twin axial vortices with different, but perfectlyestablished, diameter of the central core.

5. Conclusions

Sumarizing, a new type of bifocal vortex lenses has been introduced, whose design is based onthe Fiboonacci sequence. It was found that a FVL produces a twin optical vortices along theaxial coordinate. The positions of both foci depend on the two incommensurable periods of theFibonacci sequence in which the FVL is based on. The radii of these twin vortices increase withthe topological charge of the vortex lens, but always their ratio approaches the golden mean.The 3D distribution of the diffracted field provided by FVLs has been tested experimentallyusing a SLM. An excellent agreement between the experimental results and the theoreticalpredictions has been demonstrated.

Acknowledgments

We acknowledge the financial support from Ministerio de Economıa y Competitividad(grant FIS2011-23175), Generalitat Valenciana (grant PROMETEO2009-077), and UniversitatPolitecnica de Valencia (SP20120569), Spain. L.R. acknowledges a fellowship of “FundacionCajaMurcia”, Spain.

(C) 2013 OSA 22 April 2013 | Vol. 21, No. 8 | DOI:10.1364/OE.21.010234 | OPTICS EXPRESS 10239