The Fraunhofer diffraction pattern from a partially blocked spiral phase plate (SPP) produces a partial vortex output pattern that is rotated by 90 degrees compared with the input. The rotation direction depends on whether the angular phase pattern increases in the clockwise or counterclockwise direction. In this work, we present an explanation of this effect based on careful examination of classical diffraction theory and show new experimental results. This approach is very convenient for easily determining the sign of the vortex charge.

© 2011 OSA

1. P. A. M. Dirac, “Quantized singularities in the electromagnetic field,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 133(821), 60–72 (1931). [CrossRef]
2. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974). [CrossRef]
3. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994). [CrossRef]
4. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992). [CrossRef] [PubMed]
5. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39(5), 1147–1154 (1992). [CrossRef]
6. H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995). [CrossRef] [PubMed]
7. K. T. Gahagan and G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996). [CrossRef] [PubMed]
8. J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25(2), 99–101 (2000). [CrossRef] [PubMed]
9. J. A. Davis and J. B. Bentley, “Azimuthal prism effect with partially blocked vortex-producing lenses,” Opt. Lett. 30(23), 3204–3206 (2005). [CrossRef] [PubMed]
10. M. Born and E. Wolf, Principles of Optics (Macmillan, 1964), p. 395.
11. E. Hecht, Optics (Addison Wesley, 2002), p. 467. [PubMed]
12. J. Matthews and R. L. Walker, Mathematical Methods of Physics (Benjamin, 1964), p. 177.
13. Z. Jaroszewicz and A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102(5-6), 391–396 (1993). [CrossRef]
14. V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22(5), 849–861 (2005). [CrossRef] [PubMed]
15. C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates,” Opt. Commun. 268(2), 235–239 (2006). [CrossRef]
16. Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13(25), 10285–10291 (2005). [CrossRef] [PubMed]

J. Mod. Opt.

• S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39(5), 1147–1154 (1992). [CrossRef]

J. Opt. Soc. Am. A

• V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, “Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate,” J. Opt. Soc. Am. A 22(5), 849–861 (2005). [CrossRef] [PubMed]

Opt. Commun.

• C.-S. Guo, D.-M. Xue, Y.-J. Han, and J. Ding, “Optimal phase steps of multi-level spiral phase plates,” Opt. Commun. 268(2), 235–239 (2006). [CrossRef]
• Z. Jaroszewicz and A. Kolodziejczyk, “Zone plates performing generalized Hankel transforms and their metrological applications,” Opt. Commun. 102(5-6), 391–396 (1993). [CrossRef]
• M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112(5-6), 321–327 (1994). [CrossRef]

Opt. Express

• Q. Wang, X. W. Sun, P. Shum, and X. J. Yin, “Dynamic switching of optical vortices with dynamic gamma-correction liquid crystal spiral phase plate,” Opt. Express 13(25), 10285–10291 (2005). [CrossRef] [PubMed]

Opt. Lett.

• N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17(3), 221–223 (1992). [CrossRef] [PubMed]
• K. T. Gahagan and G. A. Swartzlander., “Optical vortex trapping of particles,” Opt. Lett. 21(11), 827–829 (1996). [CrossRef] [PubMed]
• J. A. Davis, D. E. McNamara, D. M. Cottrell, and J. Campos, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25(2), 99–101 (2000). [CrossRef] [PubMed]
• J. A. Davis and J. B. Bentley, “Azimuthal prism effect with partially blocked vortex-producing lenses,” Opt. Lett. 30(23), 3204–3206 (2005). [CrossRef] [PubMed]

Phys. Rev. Lett.

• H. He, M. E. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75(5), 826–829 (1995). [CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci.

• J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. Lond. A Math. Phys. Sci. 336(1605), 165–190 (1974). [CrossRef]

Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character

• P. A. M. Dirac, “Quantized singularities in the electromagnetic field,” Proc. R. Soc. Lond., A Contain. Pap. Math. Phys. Character 133(821), 60–72 (1931). [CrossRef]

Other

• M. Born and E. Wolf, Principles of Optics (Macmillan, 1964), p. 395.
• E. Hecht, Optics (Addison Wesley, 2002), p. 467. [PubMed]
• J. Matthews and R. L. Walker, Mathematical Methods of Physics (Benjamin, 1964), p. 177.

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