Fig. 1. Generation of 6-order Fibonacci Lens. In the left side, set construction is presented, and in the right side, axial mapping function is shown.

Fig. 2. Schematic of photochemistry of photopolymerisation reaction. (a) The dye absorbs a photon from the incident light with wavelength $\lambda =533 \mathrm{nm}$. (b) Through a redox reaction the dye transfers its energy to the initiator, thereby activating it. (c) The photopolymerisation is initiated when the activated radical generator binds to a monomer. The generation of radicals is propagated along the chain to form a polymer chain [21]. (d) At $t_0$ the photopolymerisation reaction forms a dense mesh in the illuminated areas causing shrinkage. A monomer gradient forms. (e) After a certain exposure time, $t_0+\Delta t$, diffusion of monomers cause the illuminated areas to swell, as it is presented in [22]. An index matching liquid evens out the surface relief.

Fig. 3. Schematic of index-matching system. (a) after 24 hours of drying, paraffin and coverplate glass are put over the PVA/AA sample. (b) The final sample is ready to be placed into the experimental setup presented in Figure 4. (c) Fibonacci lens about 2000 $\mathrm{\mu }\mathrm{m}$ of radius is recorded into the sample.

Fig. 4. Set-up used to record FL and to analyze in real time the formation and the different focal points. Where D is a diaphragm, L denotes a lens, SF is a spatial filter, BS is a beam splitter, M is a mirror, LP is a linear polarizer, and RF is a red filter.

Fig. 5. In (a), the refractive index modulation due to the diffusion process during the recording of the FL phase into the photopolymer is represented. Therefore, in (b), a refractive index modulation slice is represented for the ideal lens and low-pass filtering. Red and blue curves represent the ideal refractive index modulation and low-pass effect, respectively.

Fig. 6. Evolution of the axial and transverse intensity distribution for a ${\mathrm{\Phi }}_9\left(\zeta \right)$ Fibonacci Lens with a radius of $a=1.75$ mm and the result obtained using the proposed diffusion model and the experimental results. Heat map plot corresponds to the intensity distribution of an ideal FL.

Fig. 7. Diffraction efficiency at each focal point for different values of exposure times and γ. Results obtained by the numerical diffusion model including low-pass filtering.

Fig. 8. Numerical simulation of the evolution of the axial and transverse numerical intensity distribution after 60 seconds of recording produced by a ${\mathrm{\Phi }}_9(a=1.75 \mathrm{mm})$ FL for different values of γ obtained by the diffusion model and the ideal result (represented in red dotted line). The heat-map above corresponds to the simulation for $\gamma =0.5$ for an ideal lens.

Fig. 9. Numerical simulation of the intensity distribution at each focal point produced by a FL for different exposure times and for different values of $D_m$ with low-pass filtering. The intensity pattern of the FL used was ${\mathrm{\Phi }}_9(a=1.75 \mathrm{mm})$.

Fig. 10. Evolution of the diffracted intensity at each focal point for a FL with ${\mathrm{\Phi }}_9(a=1.75 \mathrm{mm}$). Each curve corresponds to a different value of mean diffusivity, $D_m$, with low-pass filtering, and with or without coverplating. The label “no CP” in the green and blue dotted curves indicate the cases where coverplating technique was not used.