
\begin{thebibliography}{99}
\Latin
%Ch 1
\bibitem{beh1}M. Born, E. Wolf, ''Principles of optics'', (pergamon, Oxford 1975).
\bibitem{beh2}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 \textbf{414} (6860), 184-188, (2001) .
\bibitem{beh3} J E Curtis and D G Grier, "Structure of optical vortices." Phys. Rev. Lett.\textbf {90} 133901 (2003).
\bibitem{beh4} آ ثباتیان،ز بهجت،" ایجاد آرایه هایی دلخواه از پرتو های گردابه کامل".مجله پزوهش فیزیک ایران4،19(1398)793.
\bibitem{beh5} A.T. O’Neil, I. MacVicar, L. Allen, M.J. Padgett,'' Intrinsic and extrinsic nature of the orbital angular momentum of a light beam'', Phys. Rev. lett.\textbf {88}  053601(2002).
\bibitem{beh6}  A. Vaziri, G. Weihs, A. Zeilinger,'' Experimental two-photon, three-dimensional entanglement for quantum communication'', Phys. Rev. lett. \textbf{89} , 240401(2002).
\bibitem{beh7} J.P. Torres, Y. Deyanova, L. Torner, G. Molina-Terriza,'' Preparation of engineered two-photon entangled states for multidimensional quantum information'', Phys. Rev. \textbf {67} , 052313(2003).
\bibitem{beh8}F. Tamburini, G. Anzolin, G. Umbriaco, A. Bianchini, C. Barbieri, ''Overcoming the Rayleigh criterion limit with optical vortices'', Phys. Rev. lett. \textbf{97}, 163903 (2006).
\bibitem{beh9} S.W. Hell,'' Far-field optical nanoscopy'', Science \textbf{316}, 1153–1158 (2007).
\bibitem{beh10}A. Sakdinawat, Y. Liu,'' Soft-x-ray microscopy using spiral zone plates'', Opt. Lett.\textbf {32}, 2635–2637 (2007).
\bibitem{beh11} S. Fürhapter, A. Jesacher, S. Bernet, M. ''Ritsch-Marte, Spiral interferometry'', Opt. Lett. \textbf{30} ,1953–1955(2005).
\bibitem{beh12}N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, ''Terabit-scale orbital angular momentum mode division multiplexing in fibers'', Science \textbf{340}, 1545–1548 (2013).
\bibitem{beh13}J. Wang, J. Y. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. E. Willner, ''Terabit free-space data transmission employing orbital angular momentum multiplexing'', Nat. Photonics\textbf{6}, 488–496 (2012).
\bibitem{beh14} D.G.A. Grier,"A revolution in optical manipulation." , Nature (London) \textbf{424} , 810(2003).
\bibitem{beh15}Huang, Nanshun, and Haixiao Deng. "Generating X-rays with orbital angular momentum in free-electron laser oscillator." arXiv preprint arXiv.2007.08773 (2020).
\bibitem{beh16} Matthew N. Julian, David G. MacDonnell, Mool C. Gupta, ''High-efficiency flexible multilevel photon sieves by single-step laser-based fabrication and optical analysis'', Appl. Opt.\textbf{58},  109–114 (2019).
\bibitem{beh17}Hickmann, J. M., E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda. "Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum." Phys. Rev. lett. \textbf{105} 053904 (2010).
\bibitem{beh18}de Araujo, Luís EE, and Matthew E. Anderson. "Measuring vortex charge with a triangular aperture." Opt. lett. \textbf{36}, 787-789  (2011).
\bibitem{beh19} Amiri, Pouria, Ali Mardan Dezfouli, and Saifollah Rasouli. "Efficient characterization of optical vortices via diffraction from parabolic-line linear gratings." J Opt Soc Am B\textbf{37}, 2668-2677 (2020).
\bibitem{beh20}Prabhakar, Shashi, Ashok Kumar, J. Banerji, and R. P. Singh. "Revealing the order of a vortex through its intensity record." Opt. lett. \textbf{36},4398-4400 (2011).
\bibitem{beh21} Vaity, Pravin, and R. P. Singh. "Topological charge dependent propagation of optical vortices under quadratic phase transformation." Opt.  lett.\textbf {37}, 1301-1303 (2012).
\bibitem{beh22}A. P. Prudnikov, Y. A. Brychkov, and O. I. Marichev,'' Integrals and Series, Elementary Functions'' (Gordon and Breach, 1986).
\bibitem{beh23}A. P. Prudnikov, Y. A. Brychkov, and O. I.'' Marichev, Integrals and Series, Special Functions'' (Gordon and Breach, 1981).
\bibitem{beh24}Gao, N., Xie, C., Li, C., Jin, C. and Liu, M.,  Square optical vortices generated by binary spiral zone plates. Appl. Phys. Lett., \textbf{98}, p.151106 (2011).
\bibitem{beh25}Rafighdoost, J. and Sabatyan, A. " Remarkable ability of spiral orthogonal zone plate in generating various focused optical vortices". Opt Lasers Eng,\textbf{86},275-280 (2016).
\end{thebibliography}


