PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Review on the structured light properties : rotational features and singularities

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The review exposes basic concepts and manifestations of the singular and structured light fields. The presentation is based on deep intrinsic relations between the singularities and the rotational phenomena in light; it involves essentially the dynamical aspects of light fields and their interactions with matter. Due to their topological nature, the singularities of each separate parameter (phase, polarization, energy flow, etc.) form coherent interrelated systems (singular networks), and the meaningful interconnections between the different singular networks are analysed. The main features of singular-light structures are introduced via generic examples of the optical vortex and circular vortex beams. The review describes approaches for generation and diagnostics of different singular networks and underlines the role of singularities in formation of optical field structures. The mechanical action of structured light fields on material objects is discussed on the base of the spin-orbital (canonical) decomposition of electromagnetic momentum, expressing the special roles of the spin (polarization) and spatial degrees of freedom. Experimental demonstrations spectacularly characterize the topological nature and the immanent rotational features of the light-field singularities. The review is based on the results obtained by its authors with a special attention to relevant works of other researchers.
Rocznik
Strony
art. no. e140860
Opis fizyczny
Bibliogr. 207 poz., rys., wykr., tab., fot.
Twórcy
  • Taizhou Research Institute of Zhejiang University, Taizhou, China
  • Chernivtsi National University, Chernivtsi, Ukraine
  • Physics Research Institute, Odessa I. I. Mechnikov National University, Odessa, Ukraine
  • Chernivtsi National University, Chernivtsi, Ukraine
  • Department of Optical Quantum Electronics, Institute of Physics of the NAS of Ukraine, Kyiv, Ukraine
  • Taizhou Research Institute of Zhejiang University, Taizhou, China
  • Chernivtsi National University, Chernivtsi, Ukraine
  • DTU Fotonik, Department of Photonics Engineering, DK-4000 Roskilde, Denmark
autor
  • Taizhou Research Institute of Zhejiang University, Taizhou, China
Bibliografia
  • [1] Descartes, R. Principia Phylosophiae. (Amsterdam, 1644); Dioptrique, Meteores. (Leyden, 1637).
  • [2] Descartes, R. [The World]. Le Monde, Ou Traité De La Lumière. (Abaris Books, 1979).
  • [3] Fresnel, A. OEuvres Complètes. (Imprimerie Imperiale, France, 1866–1870). (In French)
  • [4] Faraday, M. Experimental Researches in Chemistry and Physics. (Taylor & Francis, 1859). https://doi.org/10.5962/bhl.title.30054
  • [5] Maxwell, J. C. Treatise on Electricity and Magnetism. (Cambridge University Press, 1873). https://doi.org/10.1017/CBO9780511709333
  • [6] Sadowsky, A. Acta et Commentationes Imp. Universitatis Jurievensis (olim Dorpatensis) 7, 1–3 (1899). (In Russian)
  • [7] Poynting, J. H. The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proc. R. Soc. Lond. A 82, 560–567 (1909). https://doi.org/10.1098/rspa.1909.0060
  • [8] Beth, R. A. Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50, 115–125 (1939). https://doi.org/10.1103/PhysRev.50.115
  • [9] Ignatowski, W. S. Diffraction by a lens of arbitrary aperture. Trans. Opt. Inst. I, 1–36 (1919). https://doi.org/10.1017/9781108552264.019
  • [10] Boivin, A., Dow, J. & Wolf, E. Energy flow in the neighbourhood of the focus of a coherent beam. J. Opt. Soc. Am. 57, 1171–1176 (1967). https://doi.org/10.1364/JOSA.57.001171
  • [11] Baranova, N.B. et al. Wave-front dislocations: topological limitations for adaptive systems with phase conjugation. J. Opt. Soc. Am. 73, 525–528 (1983). https://doi.org/10.1364/JOSA.73.000525
  • [12] Angelsky, O. V., Maksimyak, P. P., Magun, I. I. & Perun, T. O. On spatial stochastiation of optical fields and feasibilities of optical diagnostics of objects with large phase inhomogeneities. Opt. Spectr. 71, 123–128 (1991).
  • [13] Coullet, P., Gil, L. & Rocca, F. Optical vortices. Opt. Commun. 73, 403–408 (1989). https://doi.org/10.1016/0030-4018(89)90180-6
  • [14] Gottfried, K. Quantum Mechanics. (Benjamin, 1966).
  • [15] Simmonds, J. W. & Guttmann, M. J. States, Waves and Photons. (Addison-Wesley, 1970).
  • [16] Berestetskii, V. B., Lifshits, E. M. & Pitaevskii, L. P. Quantum Electrodynamics. (Butterworth-Heinemann, 1982). https://doi.org/10.1016/C2009-0-24486-2
  • [17] Allen, L., Beijersbergen, M. V., Spreeuw, R. J. C. & Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992). https://doi.org/10.1103/PhysRevA.45.8185
  • [18] Bazhenov, V. Yu., Vasnetsov, M. V. & Soskin M. S. Laser beams with screw dislocations in their wavefronts. JETP Lett. 52, 429–431(1990).
  • [19] Soskin, M. S. & Vasnetsov, M. V. Nonlinear singular optics. Pure Appl. Opt. 7, 301–311 (1998). https://doi.org/10.1088/0963-9659/7/2/019
  • [20] Soskin, M. S. & Vasnetsov, M. V. Chapter 4–Singular optics. Prog. Opt. 42, 219–276 (2001). https://doi.org/10.1016/S0079-6638(01)80018-4
  • [21] Nye, J. F. & Berry, M. V. Dislocations in wave trains. Proc. R. Soc. Lond. 336, 165–190 (1974). https://doi.org/10.1098/rspa.1974.0012
  • [22] Berry, M. V. Singularities in Waves and Rays. in Physics of Defects. (eds. Balian, R., Klaeman, M. & Poirier, J. P.) 453–549 (North Holland Publishing Company, 1981).
  • [23] Nye, J. F. Natural Focusing and Fine Structure of Light. Caustics and Wave Dislocations. (Institute of Physics Publishing: Bristol and Philadelphia, 1999).
  • [24] Gbur, G., Tyson, R. K., Vortex beam propagation through atmospheric turbulence and topological charge conservation. J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 25, 225–230 (2008). https://doi.org/10.1364/JOSAA.25.000225
  • [25] Angelsky, O. V. et al. Structured light: ideas and concepts. Front. Phys. 8, 114 (2020). https://doi.org/10.3389/fphy.2020.00114
  • [26] Andrews, D. L. Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces. (Academic Press, 2011). https://doi.org/10.1016/B978-0-12-374027-4.X0001-1
  • [27] Bekshaev, A., Bliokh, K. & Soskin, M. Internal flows and energy circulation in light beams. J Opt. 13, 053001 (2011). https://doi.org/10.1088/2040-8978/13/5/053001
  • [28] Rubinsztein-Dunlop, H. et al. Roadmap on structured light. J. Opt. 19, 013001 (2017). https://doi.org/10.1088/2040-8978/19/1/013001
  • [29] Rotenberg, N. & Kuiper, L. Mapping nanoscale light fields. Nat. Photonics 8, 919–926 (2014). https://doi.org/10.1038/nphoton.2014.285
  • [30] Aiello, A. & Banzer, P. The ubiquitous photonic wheel. J. Opt. 18, 085605 (2016). http://dx.doi.org/10.1088/2040-8978/18/8/085605
  • [31] Aiello, A. et al. From transverse angular momentum to photonic wheels. Nat. Photonics 9, 789–795 (2015). https://doi.org/10.1038/nphoton.2015.203
  • [32] Bekshaev, A. Y. & Soskin, M. S. Transverse energy flows in vectorial fields of paraxial beams with singularities. Opt. Commun., 271, 332–348 (2007). https://doi.org/10.1016/j.optcom.2006.10.057
  • [33] Bliokh, K. Y. & Nori, F. Transverse and longitudinal angular momenta of light. Phys. Rep. 592, 1–38 (2015). https://doi.org/10.1016/j.physrep.2015.06.003
  • [34] Dennis, M. R., O’Holleran, K. & Padgett, M. J. Chapter 5 Singular optics: optical vortices and polarization singularities. Prog. opt. 53, 293–363 (2009). https://doi.org/10.1016/S0079-6638(08)00205-9
  • [35] Basisty, I. V., Soskin, M. S. & Vasnetsov, M. V. Optical wavefront dislocations and their properties. Opt. Comm. 119, 604–612 (1995). https://doi.org/10.1016/0030-4018(95)00267-C
  • [36] Soskin, M. S., Vasnetsov, M. V. & Basisty, I. V. Optical wavefront dislocations. Proc. SPIE 2647, 57–62 (1995). https://doi.org/10.1117/12.226741
  • [37] White, A. G. et al. Interferometric measurements of phase singulari-ties in the output of a visible laser. J. Mod. Opt. 38, 2531–2541 (1991). https://doi.org/10.1080/09500349114552651
  • [38] Heckenberg, N. R., McDuff, R., Smith, C. P. & White, A. G. Generation of optical singularities by computer-generated holograms. Opt. Lett. 17, 221–223 (1992). https://doi.org/10.1364/OL.17.000221
  • [39] Angelsky, O. Optical Correlation Techniques and Applications. (Bellingham: SPIE Press PM168, 2007). https://doi.org/10.1117/3.714999
  • [40] Allen, L., Padgett, M. J. & Babiker, M. IV The orbital angular momentum of light. Prog. Opt. 39, 291–372 (1999). https://doi.org/10.1016/S0079-6638(08)70391-3
  • [41] Bekshaev, A., Soskin, M. & Vasnetsov M. Paraxial Light Beams with Angular Momentum. (New York: Nova Science Publishers, 2008). https://arxiv.org/abs/0801.2309
  • [42] Gbur, G. J. Singular Optics. (CRC Press, 2016). https://doi.org/10.1201/9781315374260
  • [43] Senthilkumaran, P. Singularities in Physics and Engineering. (IOP Publishing, 2018). https://doi.org/10.1088/978-0-7503-1698-9
  • [44] Yao, A. M. & Padgett, M. J. Orbital angular momentum: origins, behavior and applications. Adv. Opt. Photonics 3, 161–204 (2011). https://doi.org/10.1364/AOP.3.000161
  • [45] Barnett, S. M., Babiker, M. & Padgett, M. J. Optical orbital angular momentum. Philos. Trans. R. Soc. A 375, 0444 (2017). http://doi.org/10.1098/rsta.2015.0444
  • [46] Habraken, S. J. M. Light with A Twist: Ray Aspects (Leiden University, Netherlands, 2010).
  • [47] Alexeyev, C. N. Propagation of optical vortices in periodically perturbed weakly guiding optical fibres. (Institute of Physical Optics of the Ministry of Education and Science of Ukraine, Lviv, 2010). (in Russian)
  • [48] Ruchi, Senthilkumaran P. & Pal, S. K. Phase singularities to polarization singularities. Int. J. Opt. 2020, 2812803 (2020). https://doi.org/10.1155/2020/2812803
  • [49] Born, M. & Wolf, E. Principles of Optics. (Pergamon, 1968).
  • [50] Landau, L. D. & Lifshitz, E. M. The classical theory of fields. Course of theoretical physics Vol. 2. (Pergamon, 1975). https://doi.org/10.1016/C2009-0-14608-1
  • [51] Berry, M. V. Optical currents. J. Opt. A: Pure Appl. Opt. 11, 11094001 (2009). https://doi.org/10.1088/1464-4258/11/9/094001
  • [52] Haus, H. A. Waves and Fields in Optoelectronics (Prentice-Hall, Inc., 1984).
  • [53] Bekshaev, A. Y. & Karamoch, A. I. Spatial characteristics of vortex light beams produced by diffraction gratings with embedded phase singularity. Opt. Commun. 281, 1366–1374 (2008). https://doi.org/10.1016/j.optcom.2007.11.032
  • [54] Bekshaev, A. Y., Karamoch, A. I., Khoroshun, G. M., Masajada, J. & Ryazantsev, O. I. Special features of a functional beam splitter: diffraction grating with groove bifurcation. in Advances in Engineering Research vol. 28. (ed. Petrova, V. M.) 1–86 (Nova Science Publishers New York, 2019).
  • [55] McGloin, D. & Dholakia, K. Bessel beams: diffraction in a new light. Contemp. Phys. 46, 15–28 (2005). https://doi.org/10.1080/0010751042000275259
  • [56] Karimi, E., Zito, G., Piccirillo, B., Marrucci, L. & Santamato, E. Hypergeometric-Gaussian modes. Opt. Lett. 32, 3053–3055 (2007). https://doi.org/10.1364/OL.32.003053
  • [57] Abramovitz, M. & Stegun, I. Handbook of Mathematical Functions (National Bureau of Standards, 1964)
  • [58] Berry, M. Paraxial beams of spinning light. Proc. SPIE 3487, 6–11 (1998). https://doi.org/10.1117/12.317704
  • [59] Roux, F. S. Distribution of angular momentum and vortex morphology in optical beams. Opt. Commun. 242, 45–55 (2004). https://doi.org/10.1016/j.optcom.2004.08.006
  • [60] Bekshaev, A., Orlinska, O. & Vasnetsov, M. Optical vortex generation with a “fork” hologram under conditions of high-angle diffraction. Opt. Commun. 283, 2006–2016 (2010). https://doi.org/10.1016/j.optcom.2010.01.012
  • [61] Baranova, N. B., Zel’dovich, B. Ya., Mamaev, A. V., Philipetskii, N. F. & Shkunov, V. V. Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment). JETP Lett. 33, 195–199 (1981).
  • [62] Beijersbergen, M. W., Allen, L., Van der Veen, H. E. L. O. & Woerdman, J. P. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun. 96, 123–132 (1993). https://doi.org/10.1016/0030-4018(93)90535-D
  • [63] Bekshaev, A. & Popov, A. Optical system for Laguerre-Gaussian / Hermite-Gaussian mode conversion. Proc. SPIE 4403, 296–301 (2001). https://doi.org/10.1117/12.428283
  • [64] Soroko, L. M. Holography and Coherent Optics. (Springer, Boston, 1980). https://doi.org/10.1007/978-1-4684-3420-0
  • [65] Petrov, D. V. Vortex–edge dislocation interaction in a linear medium. Opt. Commun., 188, 307–312 (2001). https://doi.org/10.1016/S0030-4018(01)00993-2
  • [66] Cheng, S. et al. Composite spiral zone plate. IEEE Photon. J. 11, 1–11 (2018). https://doi.org/10.1109/JPHOT.2018.2885004
  • [67] Sabatyan, A. & Behjat, Z. Radial phase modulated spiral zone plate for generation and manipulation of optical perfect vortex. Opt. Quantum Electron. 49, 371 (2017). https://doi.org/10.1007/s11082-017-1211-4
  • [68] Bekshaev, A. Y. & Karamoch, A. I. Displacements and deformations of a vortex light beam produced by the diffraction grating with embedded phase singularity. Opt. Commun. 281, 3597–3610 (2008). https://doi.org/10.1016/j.optcom.2008.03.070
  • [69] Anan'ev, Y. A. & Bekshaev, A. Y. Theory of intensity moments for arbitrary light beams. Opt. Spectrosc. 76, 558–568 (1994).
  • [70] Bekshaev, A. Y., Mohammed, K. A. & Kurka, I. A. Transverse energy circulation and the edge diffraction of an optical vortex beam. Appl. Opt. 53, B27–B37 (2014). https://doi.org/10.1364/AO.53.000B27
  • [71] Oemrawsingh, S. S. R. et al. Production and characterization of spiral phase plates for optical wavelengths. Appl. Opt. 43, 688–694 (2004). https://doi.org/10.1364/AO.43.000688
  • [72] Berry, M. V. Optical vortices evolving from helicoidal integer and fractional phase steps. J. Opt. A Pure Appl. Opt. 6, 259 (2004). https://doi.org/10.1088/1464-4258/6/2/018
  • [73] Kotlyar, V. V. et al. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate. J. Opt. Soc. Am. A: Opt. Image Sci. Vis. 22(5), 849–861 (2005). https://doi.org/10.1364/JOSAA.22.000849
  • [74] Bomzon, Z., Biener, G., Kleiner, V. & Hasman, E. Space-variant Pancharatnam–Berry phase optical elements with computer-generated subwavelength gratings. Opt. Lett. 27, 1141–1143 (2002). https://doi.org/10.1364/OL.27.001141
  • [75] Biener, G., Niv, A., Kleiner, V. & Hasman, E. Formation of helical beams by use of Pancharatnam–Berry phase optical elements. Opt. Let. 27, 1875–1877 (2002). https://doi.org/10.1364/OL.27.001875
  • [76] Niv, A., Biener, G., Kleiner, V. & Hasman, E. Manipulation of the Pancharatnam phase in vectorial vortices. Opt. Express 14, 4208–4220 (2006). https://doi.org/10.1364/OE.14.004208
  • [77] Marucci, L., Manzo, C. & Paparo, D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett. 96, 163905 (2006). https://doi.org/10.1103/PhysRevLett.96.163905
  • [78] Basistiy, I. V., Pas’ko, V. A., Slyusar, V. V., Soskin, M. S & Vasnetsov, M. V. Synthesis and analysis of optical vortices with fractional topological charges. J. Opt. A Pure Appl. Opt. 6, S166–S169 (2004). https://doi.org/10.1088/1464-4258/6/5/003
  • [79] Gbur, G. Fractional vortex Hilbert’s hotel. Optica 3, 222–225 (2016). https://doi.org/10.1364/OPTICA.3.000222
  • [80] Freund, I. & Shvartsman, N. Wave-field phase singularities: the sign principle. Phys. Rev. A 50, 5164 (1994). https://doi.org/10.1103/PhysRevA.50.5164
  • [81] Soskin, M. S., Gorshkov, V. N., Vasnetsov, M. V., Malos, J. T. & Heckenberg, N. R. Topological charge and angular momentum of light beams carrying optical vortices. Phys. Rev. A 56, 4064–4075 (1997). https://doi.org/10.1103/PhysRevA.56.4064
  • [82] Bialynicki-Birula, I. & Bialynicka-Birula, Z. Rotational frequency shift. Phys. Rev. Lett. 78, 2539–2542 (1997). https://doi.org/10.1103/PhysRevLett.78.2539
  • [83] Garetz, B. A. Angular Doppler effect. J. Opt. Soc. Am. 71, 609–611 (1981). https://doi.org/10.1364/JOSA.71.000609
  • [84] Garetz, B. A. & Arnold, S. Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave plate. Opt. Commun. 31, 1–3 (1979). https://doi.org/10.1016/0030-4018(79)90230-X
  • [85] Simon, R., Kimble, H. J. & Sudarshan, E. C. G. Evolving geometric phase and its dynamical manifestation as a frequency shift: An optical experiment. Phys. Rev. Lett. 61, 19–22 (1988). https://doi.org/10.1103/PhysRevLett.61.19
  • [86] Bretenaker, F.& Le Floch, A. Energy exchanges between a rotating retardation plate and a laser beam. Phys. Rev. Lett. 65, 2316 (1990). https://doi.org/10.1103/PhysRevLett.65.2316
  • [87] Courtial, J., Dholakia, K., Robertson, D. A., Allen, L. & Padgett, M. J. Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum. Phys. Rev. Lett. 80, 3217–3219 (1998). https://doi.org/10.1103/PhysRevLett.80.3217
  • [88] Courtial, J., Robertson, D. A., Dholakia, K., Allen, L. & Padgett, M. J. Rotational frequency shift of a light beam. Phys. Rev. Lett. 81, 4828–4830 (1998). https://doi.org/10.1103/PhysRevLett.81.4828
  • [89] Bekshaev, A. Ya. et al. Observation of rotational Doppler effect with an optical-vortex one-beam interferometer. Ukr. J. Phys. 47, 1035–1040 (2002). http://archive.ujp.bitp.kiev.ua/files/journals/47/11/471105p.pdf
  • [90] Basistiy, I.V., Bekshaev, A. Y., Vasnetsov, M. V., Slyusar, V. V. & Soskin, M. S. Observation of the rotational Doppler effect for optical beams with helical wave front using spiral zone plate. JETP Lett. 76, 486–489 (2002). https://doi.org/10.1134/1.1533771
  • [91] Basistiy, I. V., Slyusar, V. V., Soskin, M. S., Vasnetsov, M. V. & Bekshaev, A. Ya. Manifestation of the rotational Doppler effect by use of an off-axis optical vortex beam. Opt. Lett. 28, 1185–1187 (2003). https://doi.org/10.1364/OL.28.001185
  • [92] Bekshaev, A. & Popov, A. Non-collinear rotational Doppler effect. Proc. SPIE 5477, 55–66 (2004). https://doi.org/10.1117/12.558759
  • [93] Bekshaev, A. Ya. & Grimblatov, V. M. Energy method of analysis of optical resonators with mirror deformations. Opt. Spectrosc. 58, 707–709 (1985).
  • [94] Bekshaev, A. Ya., Grimblatov, V. M. & Kalugin, V. V. Misaligned Ring Resonator with A Lens-Like Medium. (Odessa University, 2016). https://doi.org/10.48550/arXiv.1612.01407
  • [95] Bekshaev, A. Y. Manifestation of mechanical properties of light waves in vortex beam optical systems. Opt. Spectrosc. 88, 904–910 (2000). https://doi.org/10.1134/1.626898
  • [96] Bekshaev, A. Ya. Mechanical properties of the light wave with phase singularity. Proc. SPIE 3904, 131–139 (1999). https://doi.org/10.1117/12.370396
  • [97] Bekshaev, A. Ya., Soskin, M. S. & Vasnetsov, M.V. Rotation of arbitrary optical image and the rotational Doppler effect. Ukr. J. Phys. 49, 490–495 (2004). http://archive.ujp.bitp.kiev.ua/files/journals/49/5/490512p.pdf
  • [98] Vinitskii, S. I., Derbov, V. L, Dubovik, V. M., Markovski, B. L. & Stepanovskii, Yu. P. Topological phases in quantum mechanics and polarization optics. Sov. Phys. Usp. 33, 403–429 (1990). https://doi.org/10.1070/PU1990v033n06ABEH002598
  • [99] Bekshaev, A. Ya., Soskin, M. S. & Vasnetsov, M. V. An optical vortex as a rotating body: mechanical features of a singular light beam. J. Opt. A Pure Appl. Opt. 6, S170–S174 (2004). https://doi.org/10.1088/1464-4258/6/5/004
  • [100] Allen, L. & Padgett, M. J. The Poynting vector in Laguerre-Gaussian beams and the interpretation of their angular momentum density. Opt. Commun. 184, 67–71 (2000). https://doi.org/10.1016/S0030-4018(00)00960-3
  • [101] Bekshaev, A. Ya. Transverse rotation of the instantaneous field distribution and the orbital angular momentum of a light beam. J. Opt. A Pure Appl. Opt. 11, 094004 (2009). https://doi.org/10.1088/1464-4258/11/9/094004
  • [102] Bekshaev, A. Ya. Internal energy flows and instantaneous field of a monochromatic paraxial light beam. Appl. Opt. 51, C13–C16 (2012). https://doi.org/10.1364/AO.51.000C13
  • [103] Lekner, J. TM, TE, and ‘TEM’ beam modes: exact solutions and their problems. J. Opt. A Pure Appl. Opt. 3, 407–412 (2001). https://doi.org/10.1088/1464-4258/3/5/314
  • [104] Lekner, J. Phase and transport velocities in particle and electromagnetic beams. J. Opt. A Pure Appl. Opt. 4, 491–499 (2002). https://doi.org/10.1088/1464-4258/4/5/301
  • [105] Lekner, J. Polarization of tightly focused laser beams. J. Opt. A Pure Appl. Opt. 5, 6–14 (2003). https://doi.org/10.1088/1464-4258/5/1/302
  • [106] He, H., Friese, M. E. J., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 75, 826–829 (1995). https://doi.org/10.1103/PhysRevLett.75.826
  • [107] Rubinsztein-Dunlop, H., Nieminen, T. A., Friese, M. E. J. & Heckenberg, N. R. Optical trapping of absorbing particles. Adv. Quantum Chem. 30, 469–492 (1998). https://doi.org/10.1016/S0065-3276(08)60523-7
  • [108] Gahagan, K. T. & Swartzlander, G. A. Optical vortex trapping of particles. Opt. Lett. 21, 827–829 (1996). https://doi.org/10.1364/OL.21.000827
  • [109] Gahagan, K. T. & Swartzlander, G. A. Trapping of low-index microparticles in an optical vortex. J. Opt. Soc. Am. B 15, 524–534 (1998). https://doi.org/10.1364/JOSAB.15.000524
  • [110] Simpson, N. B., McGloin, D., Dholakia, K., Allen, L. & Padgett, M. J. Optical tweezers with increased axial trapping efficiency. J. Mod. Opt. 45, 1943–1949 (1998). https://doi.org/10.1080/09500349808231712
  • [111] Simpson, N. B., Allen, L. & Padgett, M. J. Optical tweezers and optical spanners with Laguerre Gaussian modes. J. Mod. Opt. 43, 2485–2491 (1996). https://doi.org/10.1080/09500349608230675
  • [112] O’Neil, A. T. & Padgett, M. J. Three-dimensional optical confinement of micron-sized metal particles and the decoupling of the spin and orbital angular momentum within an optical spanner. Opt. Commun. 185, 139–143 (2000). https://doi.org/10.1016/S0030-4018(00)00989-5
  • [113] Higurashi, E., Sawada, R. & Ito, T. Optically induced angular alignment of trapped birefringent micro-objects by linearly polarized light. Phys. Rev. E 59, 3676–3681 (1999). https://doi.org/10.1103/PhysRevE.59.3676
  • [114] Friese, M. E. J., Rubinsztein-Dunlop, H., Gold, J., Hagberg, P. & Hanstorp, D. Optically driven micromachine elements. Appl. Phys. Lett. 78, 547–549 (2001). https://doi.org/10.1063/1.1339995
  • [115] Paterson, L. et al. Controlled rotation of optically trapped microscopic particles. Science 292, 912–914 (2001). https://doi.org/10.1126/science.1058591
  • [116] Grier, D. G. A revolution in optical manipulation. Nature 424, 810–816 (2003). https://doi.org/10.1038/nature01935
  • [117] Bowman, R. W.& Padgett, M. J. Optical trapping and binding. Rep. Prog. Phys. 76, 026401 (2013). https://doi.org/10.1088/0034-4885/76/2/026401
  • [118] Padgett, M. & Bowman, R. Tweezers with a twist. Nat. photonics 5, 343–348 (2011). https://doi.org/10.1038/nphoton.2011.81
  • [119] Jack, Ng., Lin, Zh. & Chan, C. T. Theory of optical trapping by an optical vortex beam. Phys. Rev. Lett. 104, 103601 (2010). https://doi.org/10.1103/PhysRevLett.104.103601
  • [120] Yuehan, T. et al. Multi-trap optical tweezers based on composite vortex beams. Opt. Commun. 485, 126712 (2021). https://doi.org/10.1016/j.optcom.2020.126712
  • [121] Chun-Fu, K. & Chu, S.-Ch. Numerical study of the properties of optical vortex array laser tweezers. Opt. Express 21, 26418–26431 (2013). https://doi.org/10.1364/OE.21.026418
  • [122] Mokhun, I. I. Introduction to Linear Singular Optics. in Optical Correlation Techniques and Applications (ed. Angelsky, O.) 1–132 (Bellingham, SPIE Press PM168, 2007). https://doi.org/10.1117/3.714999.ch1
  • [123] Mokhun, I .I. Introduction to Linear Singular Optics (Chernivtsi National University, 2012) (In Russian)
  • [124] Angelsky, O. V., Besaga, R. N. & Mokhun, I. I. Appearance of wave front dislocations under interference among beams with simple wave fronts. Proc. SPIE 3317, 97–100 (1997). https://doi.org/10.1117/12.295666
  • [125] O’Holleran, K., Padgett, M. J. & Dennis, M. R. Topology of optical vortex lines formed by the interference of three, four, and five plane waves. Opt. Express 14, 3039–3044 (2006). https://doi.org/10.1364/OE.14.003039
  • [126] Xavier, J., Vyas, S., Senthilkumaran, P. & Joseph, J. Tailored complex 3D vortex lattice structures by perturbed multiples of three-plane waves. Appl. Opt. 51, 1872–1878 (2012). https://doi.org/10.1364/AO.51.001872
  • [127] Kapoor, A., Kumar, M., Senthilkumaran, P. & Joseph, J. Optical vortex array in spatially varying lattice. Opt. Commun. 365, 99–102 (2016). https://doi.org/10.1016/j.optcom.2015.11.074
  • [128] Xavier, J., Vyas, S., Senthilkumaran, P. & Joseph, J. Complex 3D vortex lattice formation by phase-engineered multiple beam interference. Int. J. Opt. 2012, 863875 (2012). https://doi.org/10.1155/2012/863875
  • [129] Galvez, E. J., Rojec, B. L., Beach, K. & Cheng, X. C-point Singularities in Poincaré Beams (2014). http://citeseerx.ist.psu.edu/ viewdoc/download?doi=10.1.1.712.1192&rep=rep1&type=pdf
  • [130] Mokhun, A. I., Soskin, M. S. & Freund, I. Elliptic critical points in paraxial optical fields. Opt. Commun. 208, 223–253 (2002). https://doi.org/10.1016/S0030-4018(02)01585-7
  • [131] Mokhun, I., Galushko, Yu., Kharitonova, Ye., Viktorovskaya, Yu. & Khrobatin, R. Elementary heterogeneously polarized field modeling. Opt. Lett. 36, 2137–2139 (2011). https://doi.org/10.1364/OL.36.002137
  • [132] Angelsky, O. V., Dominikov, N. N., Maksimyak, P. P. & Tudor, T. Experimental revealing of polarization waves. Appl. Opt. 38, 3112–3117 (1999). https://doi.org/10.1364/AO.38.003112
  • [133] Angelsky, O. V., Hanson, S. G., Zenkova, C. Yu., Gorsky, M. P. & Gorodin’ska, N. V. On polarization metrology (estimation) of the degree of coherence of optical waves. Opt. Express, 17, 15623–15634 (2009). https://doi.org/10.1364/OE.17.015623
  • [134] Mokhun, I., Khrobatin, R. & Viktorovskaya, Ju. The behavior of the Poynting vector in the area of elementary polarization singularities. Opt. Appl. 37, 261–277 (2007).
  • [135] Khrobatin, R. & Mokhun, I. Shift of application point of angular momentum in the area of elementary polarization singularity. J. Opt. A Pure Appl. Opt. 10, 064015 (2008). https:/doi.org/10.1088/1464-4258/10/6/064015
  • [136] Angelsky, O. V., Besaga, R. N., Mokhun, I. I., Soskin, M. S. & Vasnetsov, M. V. Singularities in vectoral fields. Proc. SPIE 3904, 40–55 (1999). https://doi.org/10.1117/12.370443
  • [137] Mokhun, I. I., Arkhelyuk, A., Galushko, Yu., Kharitonova, Ye., & Viktorovskaya, Ju. Experimental analysis of the Poynting vector characteristics. Appl. Opt. 51, C158–C162 (2012). https://doi.org/10.1364/AO.51.00C158
  • [138] Mokhun, I., Arkhelyuk, A. D., Galushko, Yu., Kharitonova, Ye. & Viktorovskaya, Yu. Angular momentum of an incoherent Gaussian beam. Appl. Opt. 53, B38–B42 (2014). https://doi.org/10.1364/AO.53.000B38
  • [139] Andronov, A. A., Vitt, A. A. & Khaikin, S. E. Theory of Oscillators (Pergamon Press, 1966).
  • [140] Bekshaev, A. Ya. Spin angular momentum of inhomogeneous and transversely limited light beams. Proc. SPIE 6254, 56–63 (2006). https://doi.org/10.1117/12.679902
  • [141] O’Neil, A. T., MacVicar, I., Allen, L. & Padgett, M. J. Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Phys. Rev. Lett. 88, 053601 (2002). https://doi.org/10.1103/PhysRevLett.88.053601
  • [142] Bekshaev, A. Ya., Soskin, M. S. & Vasnetsov, M. V. Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams. J. Opt. Soc. Amer. A 20, 1635–1643 (2003). https://doi.org/10.1364/JOSAA.20.001635
  • [143] Belinfante, F. J. On the current and the density of the electric charge, the energy, the linear momentum and the angular momentum of arbitrary fields. Physica 7, 449 (1940). https://doi.org/10.1016/S0031-8914(40)90091-X
  • [144] Bliokh, K. Y., Dressel, J. & Nori, F. Conservation of the spin and orbital angular momenta in electromagnetism. New J. Phys. 16, 093037 (2014). https://doi.org/10.1088/1367-2630/16/9/093037
  • [145] Angelsky, O. V. et al. Investigation of optical currents in coherent and partially coherent vector fields. Opt. Express 19, 660–672 (2011). https://doi.org/10.1364/OE.19.000660
  • [146] Zenkova, C. Yu., Gorsky, M. P., Maksimyak, P. P. & Maksimyak, A. P. Optical currents in vector fields. App. Opt. 50, 1105–1112 (2011) https://doi.org/10.1364/AO.50.001105
  • [147] Angelsky, O. V., Zenkova, C. Yu., Hanson, S. G. & Zheng, J. Extraordinary manifestation of evanescent wave in biomedical application. Front. Phys. 8, 159 (2020). https://doi.org/10.3389/fphy.2020.00159
  • [148] Angelsky, O., Bekshaev. A., Dragan, G., Maksimyak, P., Zenkova, C.Y. & Zheng, J., Structured light control and diagnostics using optical crystals. Front. Phys. 9, 368 (2021). https://doi.org/10.3389/fphy.2021.715045
  • [149] Angelsky, O. Introduction to Singular Correlation Optics. (SPIE Press, 2019).
  • [150] Allen, L. & Padgett, M. J. Response to question #79. Does a plane wave carry spin angular momentum? Am. J. Phys. 70, 567–568 (2002). https://doi.org/10.1119/1.1456075
  • [151] Pfeifer, R. N. C., Nieminen, T. A., Heckenberg, N. R. & Rubinsztein-Dunlop, H. Optical tweezers and paradoxes in electromagnetism. J. Opt. 13, 044017 (2011). https://doi.org/10.1088/2040-8978/13/4/044017
  • [152] Stewart, A. M. Angular momentum of the electromagnetic field: the plane wave paradox resolved. Eur. J. Phys. 26, 635–641 (2005). https://doi.org/10.1088/0143-0807/26/4/008
  • [153] Bekshaev, A. Ya. “Spin” and “Orbital” Flows in A Circularly Polarized Paraxial Beam: Orbital Rotation Without Orbital Angular Momentum. https://arxiv.org/ftp/arxiv/papers/0908/0908.2526.pdf (2009).
  • [154] Bekshaev, A. & Vasnetsov, M. Vortex Flow of Light: “Spin” and “Orbital” Flows in a Circularly Polarized Paraxial Beam. in Twisted Photons. Applications of Light with Orbital Angular Momentum (eds. Torres, J. P. & Torner, L.) chapter 2 (Weinheim: Wiley-VCH, 2011). https://doi.org/10.1002/9783527635368.ch2
  • [155] Bekshaev, A. & Soskin, M. Transverse energy flows in vectorial fields of paraxial light beams. Proc. SPIE 6729, 67290G (2007). https://doi.org/10.1117/12.751952
  • [156] Dienerowitz, M., Mazilu, M. & Dholakia, K. Optical manipulation of nanoparticles: a review. J. Nanophotonics 2, 021875 (2008). https://doi.org/10.1117/1.2992045
  • [157] Gouesbet, G. T-matrix methods for electromagnetic structured beams: a commented reference database for the period 2014–2018. J. Quant. Spectrosc. Radiat. Transf. 230, 247–281 (2019). https://doi.org/10.1016/j.jqsrt.2019.04.004
  • [158] Nieminen, T. A., Loke, V. L., Stilgoe, A. B., Heckenberg, N. R., & Rubinsztein-Dunlop, H. T-matrix method for modelling optical tweezers. J. Mod. Opt. 58, 528–544 (2011). https://doi.org/10.1080/09500340.2010.528565
  • [159] Bekshaev, A. Y., Bliokh, K. Y. & Nori, F. Mie scattering and optical forces from evanescent fields: A complex-angle approach. Opt. Express 21, 7082–7095 (2013). https://doi.org/10.1364/OE.21.007082
  • [160] Аngelsky, O., Bekshaev, A., Maksimyak, P., Maksimyak, A. & Hanson, S. Measurement of small light absorption in microparticles by means of optically induced rotation. Opt. Express 23, 7152–7163 (2015). https://doi.org/10.1364/OE.23.007152
  • [161] Bekshaev A. Ya., Angelsky O. V., Sviridova S. V. & Zenkova C. Yu. Mechanical action of inhomogeneously polarized optical fields and detection of the internal energy flows. Adv. Opt. Technol. 2011, 723901 (2011). https://doi.org/10.1155/2011/723901
  • [162] Bekshaev, A. Ya., Angelsky, O. V., Hanson, S. G. & Zenkova, C. Yu. Scattering of inhomogeneous circularly polarized optical field and mechanical manifestation of the internal energy flows. Phys. Rev. A 86, 023847-10 (2012). https://doi.org/10.1103/PhysRevA.86.023847
  • [163] Bohren, C. F. & Huffman, D. R. Absorption and Scattering of Light by Small Particles. (Wiley-VCH, 1983).
  • [164] Bekshaev, A. Y. Subwavelength particles in an inhomogeneous light field: Optical forces associated with the spin and orbital energy flows. J. Opt. 15, 044004 (2013). https://doi.org/10.1088/2040-8978/15/4/044004
  • [165] Bliokh, K. Y., Bekshaev, A.Y. & Nori, F. Extraordinary momentum and spin in evanescent waves. Nat. Commun. 5, 3300 (2014). https://doi.org/10.1038/ncomms4300
  • [166] Liberal, I., Ederra, I., Gonzalo, R. & Ziolkowski, R. W. Electromagnetic force density in electrically and magnetically polarizable media. Phys. Rev. A 88, 053808 (2013). https://doi.org/10.1103/PhysRevA.88.053808
  • [167] Nieto-Vesperinas, M., Saenz, J. J., Gomez-Medina, R. & Chantada, L. Optical forces on small magnetodielectric particles. Opt. Express 18, 11428–11443 (2010). https://doi.org/10.1364/OE.18.011428
  • [168] Canaguier-Durand, A., Cuche, A., Cyriaque, G. & Ebbesen, T.W. Force and torque on an electric dipole by spinning light fields. Phys. Rev. A 88, 033831 (2013). https://doi.org/10.1103/PhysRevA.88.033831
  • [169] Bliokh, K. Y., Bekshaev, A. Y. & Nori, F. Dual electromagnetism: helicity, spin, momentum and angular momentum. New J. Phy. 15, 033026 (2013). https://doi.org/10.1088/1367-2630/15/3/033026
  • [170] Xu, X. & Nieto-Vesperinas, M. Azimuthal imaginary Poynting momentum density. Phys. Rev. Lett. 123, 233902 (2019). https://doi.org/10.1103/PhysRevLett.123.233902
  • [171] Nieto-Vesperinas, M. & Xu, X. Reactive helicity and reactive power in nanoscale optics: Evanescent waves. Kerker conditions. Optical theorems and reactive dichroism. Phys. Rev. Res. 3, 043080 (2021). https://doi.org/10.1103/PhysRevResearch.3.043080
  • [172] Bekshaev, A., Kontush, S., Popov, A. & Van Grieken, R. Application of light beams with non-zero angular momentum in optical study of micrometer-size aerosol particles. Proc. SPIE 4403, 287–295 (2001). https://doi.org/10.1117/12.428282
  • [173] Bekshaev, A. Abraham-Based Momentum and Spin of Optical Fields Under Conditions of Total Reflection. https://arxiv.org/ftp/arxiv/papers/1710/1710.01561.pdf (2017).
  • [174] Angelsky, O. V. et al. Orbital rotation without orbital angular momentum: mechanical action of the spin part of the internal energy flow in light beams. Opt. Express 20, 3563–3571 (2012). https://doi.org/10.1364/OE.20.003563
  • [175] Angelsky, O.V. et al. Circular motion of particles suspended in a Gaussian beam with circular polarization validates the spin part of the internal energy flow. Opt. Express 20, 11351–11356 (2012). https://doi.org/10.1364/OE.20.011351
  • [176] Angelsky, O. V., Bekshaev, A. Ya., Maksimyak, P. P. & Polyanskii, P. V. Internal energy flows and optical trapping. Opt. Photonic News 25, 20–21 (2014).
  • [177] Bekshaev, A. Y., Bliokh, K. Y. & Nori, F. Transverse spin and momentum in two-wave interference. Phys. Rev. X 5, 011039 (2015). https://doi.org/10.1103/PhysRevX.5.011039
  • [178] Antognozzi, M. et al. Direct measurements of the extraordinary optical momentum and transverse spin-dependent force using a nano-cantilever. Nat. Phys. 12, 731–735 (2016). https//doi.org/10.1038/nphys3732
  • [179] Bekshaev, A. Y. Dynamical characteristics of an electromagnetic field under conditions of total reflection. J. Opt. 2, 045604 (2018). https://doi.org/10.1088/2040-8986/aab035
  • [180] Bliokh, K. Y. & Nori, F. Transverse spin of a surface polariton. Phys. Rev. A 85, 061801 (2012). https://doi.org/10.1103/PhysRevA.85.061801
  • [181] Bliokh, K. Y., Smirnova, D. & Nori, F. Quantum spin Hall effect of light. Science 348, 1448–1451 (2015). https://doi.org/10.1126/science.aaa9519
  • [182] Bliokh, K. Y. Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photonics 9, 796 (2015). https://doi.org/10.1038/nphoton.2015.201
  • [183] Skelton, S. E. et al. Evanescent wave optical trapping and transport of micro and nanoparticles on tapered optical fibers. J. Quant. Spectrosc. Radiat. Transf. 113, 2512–2520 (2012). https://doi.org/10.1016/j.jqsrt.2012.06.005
  • [184] Chang, S., Kim, J. T., Jo, J. H. & Lee, S. S. Optical force on a sphere caused by the evanescent field of a Gaussian beam; effects of multiple scattering. Opt. Commun. 139, 252–261 (1997). https://doi.org/10.1016/S0030-4018(97)00144-2
  • [185] Song, Y. G., Han, B. M. & Chang, S. Force of surface plasmon-coupled evanescent fields on Mie particles. Opt. Commun. 198, 7–19 (2001). https://doi.org/10.1016/S0030-4018(01)01484-5
  • [186] Angelsky, O. V. et al. Influence of evanescent wave on birefringent microplates. Opt. Express 25, 2299–2311 (2017). https://doi.org/10.1364/OE.25.002299
  • [187] Zenkova C. Yu., Ivanskyi, D. I. & Kiyashchuk, T. V. Optical torques and forces in birefringent microplate. Opt. Appl. 47, 1–11 (2017). https://doi.org/10.5277/oa170313
  • [188] Angelsky, O. V., Zenkova, C. Yu. & Ivansky, D. I. Mechanical action of the transverse spin momentum of an evanescent wave on gold nanoparticles in biological objects media. J. Optoelectron. Adv. Mater. 20, 217–226 (2018).
  • [189] Angelsky, O.V. et al. Controllying and manipulation of red blood cells by evanescent waves. Opt. Appl. 49, 597–611 (2019). https://doi.org/10.37190/oa190406
  • [190] Angelsky, O. V. et al. Peculiarities of control of erythrocytes moving in an evanescent field. J. Biomed. Opt. 24, 055002 (2019). https://doi.org/10.1117/1.JBO.24.5.055002
  • [191] Angelsky, O.V. et al. Peculiarities of energy circulation in evanescent field. Application for red blood cells. Opt. Mem. Neural Netw. (Inf. Opt.) 28, 11–20 (2019). https://doi.org/10.3103/S1060992X19010028
  • [192] Berry, M. V. & Dennis, M. R. The optical singularities of birefringent dichroic chiral crystals. Proc. R. Soc. Lond. 459, 1261 (2003). https://doi.org/10.1098/rspa.2003.1155
  • [193] Bliokh, K. Y. & Nori, F. Characterizing optical chirality. Phys. Rev. A 83, 021803(R) (2011). https://doi.org/10.1103/PhysRevA.83.021803
  • [194] Desyatnikov, A. S., Sukhorukov, A. A. & Kivshar, Y. S. Azimuthons: spatially modulated vortex solitons. Phys. Rev. Lett. 95: 20, 203904 (2005). https://doi.org/10.1103/PhysRevLett.95.203904
  • [195] Kivshar, Y. S. Vortex solitons and rotating azimuthons in nonlinear media. Topologica 2, 005 (2009). https://doi.org/10.3731/topologica.2.005
  • [196] Bekshaev, A., Angelsky, O. & Hanson, S.G. Transformations and Evolution of Phase Singularities in Diffracted Optical Vortices. in Advances in Optics: Reviews, Book Series Vol. 1 (ed. Yurish, S. Y.) 345–385 (International Frequency Sensor Association (IFSA), Spain, 2018). http://www.sensorsportal.com/HTML/BOOKSTO-RE/Advances_in_Optics_Vol_1.pdf
  • [197] Bekshaev, A., Chernykh, A., Khoroshun, A. & Mikhaylovskaya, L. Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams. Opt. Commun. 397, 72–83 (2017). https://doi.org/10.1016/j.optcom.2017.03.062
  • [198] Bekshaev, A., Chernykh, A., Khoroshun, A. & Mikhaylovskaya, L. Localization and migration of phase singularities in the edge-diffracted optical-vortex beams. J. Opt. 18 024011 (2016). https://doi.org/10.1088/2040-8978/18/2/024011
  • [199] Bekshaev, A., Khoroshun, A. & Mikhaylovskaya, L. Transformation of the singular skeleton in optical-vortex beams diffracted by a rectilinear phase step. J. Opt. 21, 084003 (2019). https://doi.org/10.1088/2040-8986/ab2c5b
  • [200] Bekshaev, A. Spin-orbit interaction of light and diffraction of polarized beams. J. Opt. 19, 085602 (2017). https://doi.org/10.1088/2040-8986/aa746a
  • [201] Fedoseyev, V. G. Spin-independent transverse shift of the centre of gravity of a reflected and of a refracted light beam. Opt. Commun. 193, 9–18 (2001). https://doi.org/10.1016/S0030-4018(01)01262-7
  • [202] Okuda, H. & Sasada, H. Significant deformations and propagation variations of Laguerre-Gaussian beams reflected and transmitted at a dielectric interface. J. Opt. Am. A: Opt. Image Sci. Vis. 25, 881–890 (2008). https://doi.org/10.1364/JOSAA.25.000881
  • [203] Bekshaev, A. Ya. & Popov, A. Yu. Method of light beam orbital angular momentum evaluation by means of space-angle intensity moments. Ukr. J. Phys. Opt. 3, 249–257 (2002). https://doi.org/10.3116/16091833/3/4/249/2002
  • [204] Bekshaev, A. Ya. Oblique section of a paraxial light beam: criteria for azimuthal energy flow and orbital angular momentum. J. Opt. A Pure Appl. Opt. 11, 094003 (2009). https://doi.org/10.1088/1464-4258/11/9/094003
  • [205] Bekshaev, A. Ya. Improved theory for the polarization-dependent transverse shift of a paraxial light beam in free space. Ukr. J. Phys. Opt. 12, 10–18 (2011). https://doi.org/10.3116/16091833/12/1/10/2011
  • [206] Bekshaev, A. Ya. Polarization-dependent transformation of a paraxial beam upon reflection and refraction: A real-space approach. Phys. Rev. A 85, 023842 (2012). https://doi.org/10.1103/PhysRevA.85.023842
  • [207] Bliokh, K. Y. & Aiello, A. Goos–Hänchen and Imbert–Fedorov beam shifts: an overview. J. Opt. 15, 014001 (2013). https://doi.org/10.1088/2040-8978/15/1/014001
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b3120b5d-8b69-4a72-9e52-3b273fda1ba9
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.