Abstract
Generalized spiraling Bessel beams (GSBB) of arbitrary order are created by illuminating a curved fork-shaped hologram (CFH) by Laguerre–Gaussian beam (LGB). The analytical expressions of the diffracted wave field amplitudes and intensities are calculated and analyzed using the stationary phase method. The numerical results are given to understand the features of the GSBB by using CFH. Our finding provides the study of the LGB with null mode number n and azimuthal mode index l and the fundamental Gaussian beam through the considered optical system, which are as particular cases of the present investigation.
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Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1970)
Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P.: Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser mode. Phys. Rev. A 45, 8185–8189 (1992)
Arlt, J., Dholakia, K.: Generation of high-order Bessel beams by use of an axicon. Opt. Commun. 177, 297–301 (2000)
Arlt, J., Graces-Chavez, V., Sibbett, W., Dholakia, K.: Optical micromanipulation using a Bessel light beam. Opt. Commun. 197, 239–245 (2001)
Bazhenov, V.Y., Vasnetsov, M.V., Soskin, M.S.: Laser beams with screw dislocations in their wavefronts. Pisma Zh. Eksp. Teor. Fiz. 52, 1037–1039 (1900)
Born, M., Wolf, E.: Principles of optics. U. Press, Cambridge (1999)
Cai, Y., He, S.: Propagation of a Laguerre–Gaussian beam through a slightly misaligned paraxial optical system. Appl. Phys. B. 84, 493–500 (2006)
Gradshteyn, I.S., Ryzhik, I.M.: Tables of Integrals Series, and Products, 5th edn. Academic Press, New York (1994)
Heckenberg, N.R., McDuff, R., Smith, C.P., Rubinsztein-Dunlop, H., Wegener, M.J.: Laser beams with phase singularities. Opt. Quant. Electron. 24, S951–S962 (1992)
Janicijevic, L., Topuzoski, S.: Fresnel and Fraunhofer diffraction of a Gaussian laser beam by fork- shaped grating. J. Opt. Am. A. 25, 2659–2669 (2008)
Jarutis, V., Paskauskas, R., Stabinis, A.: Focusing of Laguerre–Gaussian beam by axicon. Opt. Commun. 184, 105–112 (2000)
Khonina, S.N., Kotlyer, V.V., Shinkaryer, M.V., Soifer, V.A., Uspleniev, G.V.: The phase rotor filter. J. Mod. Opt. 39, 1147–1154 (1992)
Kotlyer, V.V., Kovalev, A.A., Skidanov, R.V., Moiseev, OYu., Soifer, V.A.: Diffraction of a finte-raduis plane wave and a Gaussian beam by a helical axicon and a spiral phase plate. J. Opt. Soc. Am. A 24, 1955–1964 (2007)
Ruffato, G., Massari, M., Romanato, F.: Generation of high-order Laguerre–Gaussian modes by means of spiral phase plates. Opt. Lett. 39, 5094–5097 (2014)
Stoyanov, L., Topuzoski, S., Stefanov, I., Janicijevic, L.: Far field diffraction of an optical vortex beam by a fork-shaped grating. Opt. Commun. 350, 301–308 (2015)
Sun, Q., Zhon, K., Fang, G., Liu, Z., Liu, S.: Generation of spiraling high-order Bessel beam. Apple. Phys. B. 104, 215–221 (2011)
Sun, Q., Zhon, K., Fang, G., Liu, Z., Liu, S.: Generalization and propagation of spiraling Bessel beams with a helical axicon. Chin. Phys. B 21(1), 014208 (2012)
Topuzoski, S.: Generation of optical vortices with curved fork-shaped holograms. Opt. Quant. Electron. 48, 138–144 (2016)
Topuzoski, S., Janicijevic, L.J.: Conversion of high-order Laguerre-Gaussian beams into Bessel beams of increased, reduced or zeroth order by use of a helical axicon. Opt. Commun. 282, 3426–3432 (2009a)
Topuzoski, S., Janicijevic, L.J.: Diffraction of Laguerre–Gaussian beam by a helical axicon. Acta Phys. Pol. A 116, 557–559 (2009b)
Vijayakumar, A., Bhattacharya, S.: Design of multifunctional diffractive optical elements. Opt. Eng. 54(2), 024104 (2015)
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The first author was supported by the Ministry of higher Education and Scientific Research and the Ministry of Education of Yemen.
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Saad, F., El Halba, E.M. & Belafhal, A. Generation of generalized spiraling Bessel beams of arbitrary order by curved fork-shaped holograms. Opt Quant Electron 48, 454 (2016). https://doi.org/10.1007/s11082-016-0723-7
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DOI: https://doi.org/10.1007/s11082-016-0723-7