Ukrainian Journal of Physical Optics

Number 4, Volume 3, 2002

Method of Light Beam Orbital Angular Momentum Evaluation by Means of Space-Angle Intensity Moments
¹Bekshaev A.Ya., ²Popov A.Yu.

¹I.I. Mechnikov Odessa National University, Dvoryanska 2, 65026, Odessa, Ukraine
²Research Institute of Physics, I.I. Mechnikov Odessa National University, Pastera, 27, 65026, Odessa, Ukraine

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Value of the orbital angular momentum (OAM) of an optical beam can be determined through the structure of matrix of its space-angle intensity moments. Considering the properties of these moments and their transformations, a conclusion has been made that any light beam with the OAM experiences a characteristic transverse shift during its interaction with a plane refracting boundary or a diffraction grating. On this base, a method for the immediate measurement of the beam OAM is proposed. The simple experimental arrangement for such a measurement includes a self-collimating diffraction grating, a position-sensitive quadrant photodetector and a device for the beam rotation around its longitudinal axis.

Key words: optical vortex, angular momentum, intensity moments, dispersion elements, beam shift, diffraction grating.

PACS: 41.85.-p, 42.25.Gy, 42.60.Jf

doi 10.3116/16091833/3/4/249/2002

References
1. Allen L, Beijersbergen MW, Spreeuw RJC and Woerdman JP, 1992. Phys. Rev. A 45: 8185-8189.
        doi:10.1103/PhysRevA.45.8185 http://dx.doi.org/10.1103/PhysRevA.45.8185
2. Bekshaev AYa, 1999. Proc. SPIE 3904: 131-139.
        doi:10.1117/12.370396 http://dx.doi.org/10.1117/12.370396
3. He H, Friese MEJ, Heckenberg NR, and Rubinsztein-Dunlop H, 1995. Phys. Rev. Lett. 75: 826-829.
doi:10.1103/PhysRevLett.75.826
http://dx.doi.org/10.1103/PhysRevLett.75.826
4. Simpson NB, Dholakia K, Allen L and Padgett MJ, 1997. Opt. Lett. 22: 52-54.
5. Anan'ev YuA and Bekshaev AYa, 1994. Optics and Spectroscopy 76: 558-568.
6. Anan'ev YuA and Bekshaev AYa, 1995. Optics and Spectroscopy 78: 729-736.
7. Anan'ev YuA and Bekshaev AYa, 1996. Optics and Spectroscopy 80: 445-452.
8. Marcuse D, 1972. Light Transmission Optics. Van Nostrand Reinhold.
9. Bastiaans MJ, 1979. J. Opt. Soc. Amer. 69: 1710-1716.
10. Bekshaev AYa, Vasnetsov MV, Denisenko VG and Soskin MS, 2002. JETP Letters 75: 127-130.
        doi:10.1134/1.1469497 http://dx.doi.org/10.1134/1.1469497
11. Anan’ev YuA and Bekshaev AYa, 1998. Proc. SPIE 3267: 317-328.
        doi:10.1117/12.308123 http://dx.doi.org/10.1117/12.308123
12. Gerrard A and Birch JM, 1978. Introduction to Matrix Method in Optics. John Wiley & Sons, London.
13. Anan'ev YuA and Bekshaev AYa, 1989. Optics and Spectroscopy 66: 411-414.
14. Solimeno S, Crosignani B and Di Porto P Guiding, 1986. Diffraction, and Confinement of Optical Radiation. Academic Press, Orlando (Fla.).
15. Fedoseyev VG, 2001. Proc.SPIE 4403: 91-97
16. Fedoseyev VG, 2001. Optics Comm. 193: 9-18.
        doi:10.1016/S0030-4018(01)01262-7 http://dx.doi.org/10.1016/S0030-4018(01)01262-7
17. Diffraction Grating Handbook. Palmer C, Loewen E, 2000. Eds. Richardson Grating Laboratory, Rochester, N.Y.
18. Bekshaev A and Popov A, 2001. Proc. SPIE 4403: 296-301.
19. Bekshaev AYa, 2000. Optics and Spectroscopy 88: 904-910.
        doi:10.1134/1.626898 http://dx.doi.org/10.1134/1.626898
20. Bekshaev AYa, Grimblatov VM and Okunishnikov ON, 1988. Measurement Techniques 31: 444-446.
        doi:10.1007/BF00864468 http://dx.doi.org/10.1007/BF00864468
21. Eppich B, 1996. Proc. SPIE 2870: 31-39.
22. Beijersbergen MW, Allen L, van der Veen HELO and Woerdman JP, 1993. Optics Comm. 96: 123-132.
        doi:10.1016/0030-4018(93)90535-D http://dx.doi.org/10.1016/0030-4018(93)90535-D
23. Siegman AE, 1993. Proc. SPIE 1868: 2-12.
        doi:10.1117/12.150601 http://dx.doi.org/10.1117/12.150601
24. Third International Workshop on Laser Beam and Optics Characterization. Giesen A, Morin M, 1996. Eds. Proc. SPIE 2870.
25. Fedorov FI, 1955. Dokl. Akad. Nauk SSSR 105: 465-468.
26. Imbert C, 1972. Phys. Rev. D 5: 787-797.
        doi:10.1103/PhysRevD.5.787 http://dx.doi.org/10.1103/PhysRevD.5.787
27. Fedorov FI, 1977. J. Priklad. Spektrosk. 27: 580-588.
28. Fedoseev VG, 1991. Opt. Spektrosk. 71: 992-997.

ev VG, 1991. Opt. Spektrosk. 71: 829-834.

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