Abstract
The study of Fraunhofer diffraction of a Gaussian laser beam by a computer-generated, binary four-sector grating (FSG) is presented. In the four equal angular sectors of the FSG, parts of a binary rectilinear grating are embedded in such a way that, two neighboring parts are shifted by a half spatial rectilinear grating period. Analytical expressions, describing the diffracted wave field amplitude and intensity distributions in the focal plane of a converging lens, are derived. The zeroth-diffraction-order beam is a Gaussian beam whose transverse cross section has a reduced Gaussian radius. The higher-diffraction-order beam transverse intensity profiles have four bright spots divided by dark crossed lines and a central dark, non-vortex core. They can be described as cosine-Laguerre–Gaussian Kummer beams. The numerically calculated diffraction patterns, as well as the interference patterns of the diffracted beam with a slightly inclined plane wave, are supported by experimentally obtained ones. In both investigations (theoretical and experimental) the interferograms confirm the non-vortex nature of the diffraction spots.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramochkin, E., Volostnikov, V.: Spiral-type beams. Opt. Commun. 102, 336–350 (1993)
Abramochkin, E.G., Volostnikov, V.G.: Generalized Gaussian beams. J. Opt. A Pure Appl. Opt. 6, S157–S161 (2004)
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1964)
Allen, L., Barnett, S.M., Padgett, M.J.: Optical Angular Momentum. Institute of Physics Publishing, Bristol (2003)
Arlt, J., Padgett, M.J.: Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam. Opt. Lett. 25, 191–193 (2000)
Bandres, M.A., Gutiérrez-Vega, J.C.: Ince–Gaussian beams. Opt. Lett. 29, 144–146 (2004)
Basistiy, I.V., Soskin, M.S., Vasnetsov, M.V.: Optical wavefront dislocations and their properties. Opt. Commun. 119, 604–612 (1995)
Brown, B.R., Lohmann, A.W.: Complex spatial filtering with binary masks. Appl. Opt. 5, 967–969 (1966)
Brown, B.R., Lohmann, A.W.: Computer-generated binary holograms. IBM J. Res. Dev. 13, 160–168 (1969)
Janicijevic, Lj, Topuzoski, S., Stoyanov, L., Dreischuh, A.: Diffraction of a Gaussian beam by a four-sector binary grating with a shift between adjacent sectors. Opt. Commun. 389, 203–211 (2017)
Jaroszewicz, Z., Kotodziejczyk, A.: Zone plates performing generalized Hankel transforms and their metrological applications. Opt. Commun. 102, 391–396 (1993)
Jaroszewicz, Z., Kolodziejczyk, A., Mouriz, D., Gomez-Reino, C.: Spiral zone plates with arbitrary diameter of the dark spot in the center of their focal point. Opt. Commun. 114, 1–8 (1995)
Karimi, E., Zito, G., Piccirillo, B., Marrucci, L., Santamato, E.: Hypergeometric-Gaussian modes. Opt. Lett. 32, 3053–3055 (2007)
Kotlyar, V.V., Skidanov, R.V., Khonina, S.N., Soifer, V.A.: Hypergeometric modes. Opt. Lett. 32, 742–744 (2007)
Lohmann, A.W., Paris, D.P.: Computer generated spatial filters for coherent optical data processing. Appl. Opt. 7, 651–656 (1968)
Ojeda-Castañeda, J., Ramírez, G.: Zone plates for zero axial irradiance. Opt. Lett. 18, 87–89 (1993)
Siviloglou, G.A., Christodoulides, D.N.: Accelerating finite energy Airy beams. Opt. Lett. 32, 979–981 (2007)
Supp, S., Jahns, J.: Coaxial superposition of Bessel beams by discretized spiral axicons. J. Eur. Opt. Soc. 14, 1–9 (2018)
Swartzlander Jr., G.A.: Peering into darkness with a vortex spatial filter. Opt. Lett. 26, 497–499 (2001)
Vias, S.B., Jaroszewicz, Z., Kolodziejczyk, A., Sypek, M.: Zone plates with black focal spots. Appl. Opt. 31, 192–198 (1992)
Acknowledgements
L.S. and A.D. gratefully acknowledge funding by National Science Fund (Bulgaria) within the framework of project DFNI T-02/10-2014.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Janicijevic, L., Topuzoski, S., Stoyanov, L. et al. Fraunhofer diffraction of a Gaussian beam by a four-sector binary grating with a half period fringes shift between adjacent sectors. Opt Quant Electron 51, 71 (2019). https://doi.org/10.1007/s11082-019-1783-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-019-1783-2