[1] [1] J. Kirz, “Phase zone plates for x rays and the extreme uv,” J. Opt. Soc. Am. 64, 301–309 (1974).

[2] [2] E. H. Anderson, V. Boegli, and L. P. Muray, “Electron beam lithography digital pattern generator and electronics for generalized curvilinear structures,” J. Vac. Sci. Technol. B 13, 2529–2534 (1995).

[3] [3] H. Kyuragi and T. Urisu, “Higher-order suppressed phase zone plates,” Appl. Opt. 24, 1139–1141 (1985).

[4] [4] J. A. Sun and A. Cai, “Archaic focusing properties of Fresnel zone plates,” J. Opt. Soc. Am. A 8, 33–35 (1991).

[5] [5] L. Kipp, M. Skibowski, R. L. Johnson, R. Berndt, R. Adelung, S. Harm, and R. Seemann, “Sharper images by focusing soft X-rays with photon sieves,” Nature 414, 184–188 (2001).

[6] [6] Q. Cao and J. Jahns, “Focusing analysis of the pinhole photon sieve: individual far field model,” J. Opt. Soc. Am. A 19, 2387–2393 (2002).

[7] [7] Q. Cao and J. Jahns, “Nonparaxial model for the focusing of highnumerical-aperture photon sieves,” J. Opt. Soc. Am. A 20, 1005–1012 (2003).

[8] [8] J. Zhang, Q. Cao, X. Lu, and Z. Lin, “Focusing contribution of individual pinholes of a photon sieve dependence on the order of local ring of underlying traditional Fresnel zone plate,” Chin. Opt. Lett. 8, 256–258 (2010).

[9] [9] C. Zhou, X. Dong, L. Shi, C. Wang, and C. Du, “Experimental study of a multiwavelength photon sieve designed by random- area-divided approach,” Appl. Opt. 48, 1619–1623 (2009).

[10] [10] J. M. Davila, “High-resolution solar imaging with a photon sieve,” Proc. SPIE 8148, 81480O (2011).

[11] [11] R. M. A. D. Gil, G. Barbastathis, and H. I. Smith, “Photon-sieve lithography,” J. Opt. Soc. Am. A 22, 342–345 (2005).

[12] [12] G. Andersen, “Large optical photon sieve,” Opt. Lett. 30, 2976–2978 (2005).

[13] [13] F. Giménez, J. A. Monsoriu, and W. D. F. A. A. Pons, “Fractal photon sieve,” Opt. Express 14, 11958–11963 (2006).

[14] [14] F. Gimenez, W. D. Furlan, and J. A. Monsoriu, “Lacunar fractal photon sieves,” Opt. Commun. 277, 1–4 (2007).

[15] [15] G. Cheng, C. Hu, P. Xu, and T. Xing, “Zernike apodized photon sieves for high-resolution phase-contrast X-ray microscopy,” Opt. Lett. 35, 3610–3612 (2010).

[16] [16] J. Jia and C. Xie, “Phase zone photon sieve,” Chin. Phys. B 18, 183–188 (2009).

[17] [17] C. Xie, X. Zhu, L. Shi, and M. Liu, “Spiral photon sieves apodized by digital prolate spheroidal window for the generation of hard-x-ray vortex,” Opt. Lett. 31, 1756–1766 (2010).

[18] [18] J. Zhang, Q. Cao, X. Lu, and Z. Lin, “Individual far-field model for photon sieves composed of square pinholes,” J. Opt. Soc. Am. A 27, 1342–1346 (2010).

[19] [19] M. Kallne, J. Buck, S. Harm, R. Seemann, K. Rossnagel, and L. Kipp, “Focusing light with a reflection photon sieve,” Opt. Lett. 36, 2405–2407 (2011).

[20] [20] N. Gao, Y. Zhang, and C. Xie, “Circular Fibonacci gratings,” Appl. Opt. 50, G142–G148 (2011).

[21] [21] R. Verma, V. Banerjee, and P. Senthilkumaran, “Fractal signatures in the aperiodic Fibonacci grating,” Opt. Lett. 39, 2557–2560 (2014).

[22] [22] R. Verma, M. K. Sharma, P. Senthilkumaran, and V. Banerjee, “Analysis of Fibonacci gratings and their diffraction patterns,” J. Opt. Soc. Am. A 31, 1473–1480 (2014).

[23] [23] A. Calatayud, V. Ferrando, L. Remon, W. D. Furlan, and J. A. Monsoriu, “Twin axial vortices generated by Fibonacci lenses,” Opt. Express 21, 10234–10239 (2013).

[24] [24] J. A. Monsoriu, A. Calatayud, L. Remon, W. D. Furlan, G. Saavedra, and P. Andres, “Bifocal Fibonacci diffractive lenses,” IEEE Photon. J. 5, 3400106 (2013).

[25] [25] V. Ferrando, A. Calatayud, P. Andres, R. Torroba, W. D. Furlan, and J. A. Monsoriu, “Imaging properties of Kinoform Fibonacci lenses,” IEEE Photon. J. 6, 6500106 (2014).

[26] [26] H. T. Dai, Y. J. Liu, and X. W. Sun, “The focusing property of the spiral Fibonacci zone plate,” Proc. SPIE 8257, 82570T (2012).

[27] [27] K. Kincade, “Photon sieves enhance weapons vision,” Laser Focus World 40, 34–37 (2004).

[28] [28] G. Saavedra, W. D. Furlan, and J. A. Monsoriu, “Fractal zone plates,” Opt. Lett. 28, 971–973 (2003).

[29] [29] J. Ke, J. Zhang, Y. Zhang, and M. Sun, “Focusing and Imaging properties of diffractive optical elements with star-ring topological structure,” Proc. SPIE, Paper No. 9624-5 [in press]