Fig. 1. Same Fibonacci sequence with different seed elements: (a) E−1=A, E0=B; (b) E1=BA, E2=BAB; (c) E1=AA, E2=BAB.

Fig. 2. Generation of FiPS.

Fig. 3. (a) FiPS; (b) MFiPS; (c) TPS.

Fig. 4. Monochromatic plane wave incident on an MFiPS.

Fig. 5. Axial focusing properties of TPS, FiPS, and MFiPS: (a) normalized axial intensity produced by FiPS (solid line) and TPS (dashed line) against axial distance (d=1.53w in this case); (b) relationship of normalized axial intensity I and the value of dmn/wm at the two foci; (c) normalized axial intensity produced by FiPS against the axial distance z(dmn/wm=1.16); (d) normalized axial intensity produced by MFiPS against the axial distance z.

Fig. 6. (a) and (b) Normalized transverse intensity distribution on the prime focal spot of a TPS; (a) linear scale; (b) logarithmic scale; (c) and (d) normalized transverse intensity distribution on the focal spots of an unmodulated FiPS (solid line) and a modulated MFiPS (dashed line); (c) and (e) linear scale; (d) and (f) logarithmic scale; (c) and (d) first focal spot; (e) and (f) second focal spot; (g) WVm versus number of potentially transparent orbits.