Abstract

We generate double-charge white-light optical vortices by sending a circularly polarized partially incoherent light through an uniaxial crystal. We show that the generated polichromatic vortices are structurally stable, and their correlation properties can be altered by the beam focusing, resulting in changes of the vortex core visibility.

© 2005 Optical Society of America

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References

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    [CrossRef]
  2. G. A. Swartzlander, Jr., �??Optical vortex filaments,�?? in Optical Vortices, eds. M. Vasnetsov and K. Staliunas Vol. 228 of Horizons in World Physics (Nova Science, Huntington, N.Y., 1999).
  3. See, e.g., a comprehensive review paper, M. S. Soskin and M. V. Vasnetsov, �??Singular optics,�?? in Progress in Optics, Vol. 42, Ed. E. Wolf (Elsevier, Amstredam, 2001).
  4. See an extensive list of references on optical vortices in G. A. Swartzlander, Jr., Singular Optics/Optical Vortex References, <a href="http://www.u.arizona.edu/~grovers/SO/so.html."> http://www.u.arizona.edu/~grovers/SO/so.html</a>
  5. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, �??Optical vortices and vortex solitons,�?? in Progress in Optics, Vol. 47, Ed. E.Wolf (Elsevier, Amstredam, 2005).
    [CrossRef]
  6. M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, 1999).
  7. G. Gbur, T. D. Visser, and E.Wolf, �??Anomalous behaviour of spectra near phase singularities of focused waves,�?? Phys. Rev. Lett. 88, 013901(4) (2002).
    [CrossRef] [PubMed]
  8. M. Berry, �??Coloured phase singularities,�?? New J. Phys. 4, 66.1�??66.14 (2002).
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  9. M. Berry, �??Exploring the colours of dark light,�?? New J. Phys. 4, 74.1�??74.14 (2002).
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  10. J. Leach and M. J. Padgett, �??Observation of chromatic effects near a while-light vortex,�?? New J. Phys. 5, 154.1�??154.7 (2003).
    [CrossRef]
  11. A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, �??Fine structure of white optical vortices in crystals,�?? Tech. Phys. Lett. 30, 701�??704 (2004).
    [CrossRef]
  12. M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, �??Computer-synthesized hologram-based rainbow optical vortices,�??New J. Phys. 6, 196 (2004
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  13. O. V. Angelsky, S. G. Hanson, A. P. Maksimyak, and P. P. Maksimyak, �??On the feasibility for determining the amplitude zeroes in polychromatic fields,�?? Opt. Express 13, 4396�??4405 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4396."> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4396</a>
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    [CrossRef]
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  18. D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., �??Spatial correlation singularity of a vortex field,�?? Phys. Rev. Lett. 92, 143905 (2004).
    [CrossRef] [PubMed]
  19. I. D. Maleev, D. M. Palacios, A. S. Marathay, and G. A. Swartzlander, Jr., �??Spatial correlation vortices in partially coherent light: theory,�?? J. Opt. Soc. Am. B 21, 1895�??1900 (2004).
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    [CrossRef]
  23. See also a review paper A. V. Volyar, �??Singular beams in unixial crystals,�?? Ukr. J. Phys. 4, 400�??408 (2004).
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  25. G. A. Swartzlander, Jr. and J.Schmit, �??Temporal Correlation Vortices and Topological Dispersion,�?? Phys. Rev. Lett. 93, 093901(4) (2004).
    [CrossRef] [PubMed]
  26. S. A. Ponomarenko and E. Wolf, �??Spectral anomalies in a Fraunhofer diffraction pattern,�?? Opt. Lett. 27, 1211�??1213 (2002).
    [CrossRef]
  27. G. Popescu, A. Dogariu, �??Spectral Anomalies at Wave-Front Dislocations,�?? Phys. Rev. Lett. 88, 183902(4) (2002).
    [CrossRef] [PubMed]
  28. G. Gbur, T. D. Visser and E. Wolf, �??Hidden singularities in partially coherent and polychromatic wavefields,�?? J. Opt. A 6, S239-S242 (2004).
    [CrossRef]
  29. D. G. Fischer and T. D. Visser, �??Spatial correlation properties of focused partially coherent fields,�?? J. Opt. Soc. Am. A 21, 2097�??2102 (2004).
    [CrossRef]

J. Opt. A

G. Gbur, T. D. Visser and E. Wolf, �??Hidden singularities in partially coherent and polychromatic wavefields,�?? J. Opt. A 6, S239-S242 (2004).
[CrossRef]

J. Opt. Soc. Am. A

D. G. Fischer and T. D. Visser, �??Spatial correlation properties of focused partially coherent fields,�?? J. Opt. Soc. Am. A 21, 2097�??2102 (2004).
[CrossRef]

S. A. Ponomarenko, �??A class of partially coherent vortex beams carrying optical vortices,�?? J. Opt. Soc. Am. A 18, 150�??156 (2001).
[CrossRef]

J. Opt. Soc. Am. B

New J. Phys.

M. Berry, �??Coloured phase singularities,�?? New J. Phys. 4, 66.1�??66.14 (2002).
[CrossRef]

M. Berry, �??Exploring the colours of dark light,�?? New J. Phys. 4, 74.1�??74.14 (2002).
[CrossRef]

J. Leach and M. J. Padgett, �??Observation of chromatic effects near a while-light vortex,�?? New J. Phys. 5, 154.1�??154.7 (2003).
[CrossRef]

M. S. Soskin, P. V. Polyanskii, and O. O. Arkhelyuk, �??Computer-synthesized hologram-based rainbow optical vortices,�??New J. Phys. 6, 196 (2004
[CrossRef]

Opt. Commun.

G. Gbur and T. D. Visser, �??Coherence vortices in partially coherent beams,�?? Opt. Commun. 222, 117�??125 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

A. V. Volyar and T. A. Fadeeva, �??Generation of singular beams in uniaxial crystals,�?? Opt. Spectrosc. 94, 235�??244 (2003).
[CrossRef]

A. V. Volyar and T. A. Fadeeva, �??Decay and fusion of polarization umbilics in a singular beam passed though a crystal,�?? Opt. Spectrosc. 95, 792�??799 (2003).
[CrossRef]

Phys. Rev. Lett.

D. M. Palacios, I. D. Maleev, A. S. Marathay, and G. A. Swartzlander, Jr., �??Spatial correlation singularity of a vortex field,�?? Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef] [PubMed]

G. Popescu, A. Dogariu, �??Spectral Anomalies at Wave-Front Dislocations,�?? Phys. Rev. Lett. 88, 183902(4) (2002).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and J.Schmit, �??Temporal Correlation Vortices and Topological Dispersion,�?? Phys. Rev. Lett. 93, 093901(4) (2004).
[CrossRef] [PubMed]

G. Gbur, T. D. Visser, and E.Wolf, �??Anomalous behaviour of spectra near phase singularities of focused waves,�?? Phys. Rev. Lett. 88, 013901(4) (2002).
[CrossRef] [PubMed]

Tech. Phys. Lett.

A. V. Volyar, Yu. A. Egorov, A. F. Rubass, and T. A. Fadeeva, �??Fine structure of white optical vortices in crystals,�?? Tech. Phys. Lett. 30, 701�??704 (2004).
[CrossRef]

Ukr. J. Phys.

See also a review paper A. V. Volyar, �??Singular beams in unixial crystals,�?? Ukr. J. Phys. 4, 400�??408 (2004).

Other

J. F. Nye and M. V. Berry, �??Dislocations in wave trains,�?? Proc. R. Soc. London A 336, 165�??190 (1974).
[CrossRef]

G. A. Swartzlander, Jr., �??Optical vortex filaments,�?? in Optical Vortices, eds. M. Vasnetsov and K. Staliunas Vol. 228 of Horizons in World Physics (Nova Science, Huntington, N.Y., 1999).

See, e.g., a comprehensive review paper, M. S. Soskin and M. V. Vasnetsov, �??Singular optics,�?? in Progress in Optics, Vol. 42, Ed. E. Wolf (Elsevier, Amstredam, 2001).

See an extensive list of references on optical vortices in G. A. Swartzlander, Jr., Singular Optics/Optical Vortex References, <a href="http://www.u.arizona.edu/~grovers/SO/so.html."> http://www.u.arizona.edu/~grovers/SO/so.html</a>

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, �??Optical vortices and vortex solitons,�?? in Progress in Optics, Vol. 47, Ed. E.Wolf (Elsevier, Amstredam, 2005).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th (expanded) ed. (Cambridge U. Press, Cambridge, 1999).

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Figures (4)

Fig. 1.
Fig. 1.

Experimental setup for the generation of partially incoherent double-charge vortices; HL - halogen white-light source (50 W), L - lenses, D - diffuser, A - aperture, P - polarizers, λ/4 - quarter-wave plate (532 nm), MO - microscope objectives, UaC- uniaxial crystal.

Fig. 2.
Fig. 2.

(a) Color images of the vortex beam at different distances after the crystal for two different apertures: D = 1 mm (upper row) and D = 13 mm (lower row). (b) Visibility length as a function of aperture size D. Solid line is ~ 1/D fit to the experimental points. Inset: transverse beam profiles for the case of low coherence.

Fig. 3.
Fig. 3.

Focusing of the polychromatic vortex beam: f = 60 mm, D = 1 mm. Left - beam before the lens; right - intensity distribution after the lens for different positions relative to the focal point.

Fig. 4.
Fig. 4.

The same as in Fig. 3 for f = 35 mm and D = 13 mm. Left - beam before the lens; right - intensity distribution for different distances behind the focal point.

Equations (1)

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Γ ( r 1 , r 2 ; z ) = E * ( r 2 , z , t ) E ( r 1 , z , t ) ,

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