Abstract

When two vortex beams with unequal topological charges superpose coherently, orbital angular momentum (OAM) in the two beams would not be cancelled out completely in the interference. The residual OAMs contained by the superposed beam are located at different concentric rings and may have opposite orientations owing to the difference of the charges. The residual OAM can be confirmed by the rotation of microparticles when difference between the charges of two interfering beams is large.

© 2006 Optical Society of America

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References

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phy. Rev. A 45, 8185 (1992).
    [CrossRef]
  2. H. He, M. E. J. 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, 826 (1995).
    [CrossRef] [PubMed]
  3. A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phy. Rev. Lett. 88, 053601 (2002).
    [CrossRef]
  4. K. T. Gahagan, and G. A. Swartzlander Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827 (1996).
    [CrossRef] [PubMed]
  5. I. D. Maleev, and G. A. Swartzlander Jr., "Composite optical vortices," J. Opt. Soc. Am. B 20, 1169 (2003).
    [CrossRef]
  6. J. E. Curtis, and D. G. Grier, "Structure of optical vortices," Phy. Rev. Lett. 90, 133901 (2003).
    [CrossRef]
  7. J. Lin, X.-C.Yuan, S. H. Tao, X. Peng, and H. B. Niu, "Deterministic approach to the generation of modified helical beams for optical manipulation," Opt. Express 13, 3862 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3862.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3862.</a>
    [CrossRef] [PubMed]
  8. A. Vasara, J. Turunen, and A. Friberg, "Realization of general nondiffracting beams with computer-generated holograms," J. Opt. Soc. Am. A 6, 1748 (1989).
    [CrossRef] [PubMed]
  9. S. H. Tao, W. M. Lee and X.-C. Yuan, "Experimental study of holographic generation of fractional Bessel beams," Appl. Opt. 43, 122 (2004).
  10. S. H. Tao, X.-C. Yuan, and J. Lin, "Fractional optical vortex beam induced rotation of particles," Opt. Express 13, 7726 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7726.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7726.</a>
    [CrossRef] [PubMed]
  11. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Freespace information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5448.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5448.</a>
    [CrossRef] [PubMed]
  12. A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, "Size selective trapping with optical "cogwheel" tweezers," Opt. Express 12, 4129 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4129.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4129.</a>
    [CrossRef] [PubMed]
  13. J. W. Goodman, Introduction to Fourier Optics, 2nd ed (McGraw-Hill, New York, 1996).
  14. S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, "Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator," Rev. Sci. Instrum. 76, 056103 (2005).
    [CrossRef]

Appl. Opt. (1)

S. H. Tao, W. M. Lee and X.-C. Yuan, "Experimental study of holographic generation of fractional Bessel beams," Appl. Opt. 43, 122 (2004).

J. Opt. Soc. Am. A (1)

A. Vasara, J. Turunen, and A. Friberg, "Realization of general nondiffracting beams with computer-generated holograms," J. Opt. Soc. Am. A 6, 1748 (1989).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

I. D. Maleev, and G. A. Swartzlander Jr., "Composite optical vortices," J. Opt. Soc. Am. B 20, 1169 (2003).
[CrossRef]

Opt. Express (4)

J. Lin, X.-C.Yuan, S. H. Tao, X. Peng, and H. B. Niu, "Deterministic approach to the generation of modified helical beams for optical manipulation," Opt. Express 13, 3862 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3862.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-10-3862.</a>
[CrossRef] [PubMed]

S. H. Tao, X.-C. Yuan, and J. Lin, "Fractional optical vortex beam induced rotation of particles," Opt. Express 13, 7726 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7726.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-20-7726.</a>
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Freespace information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5448.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5448.</a>
[CrossRef] [PubMed]

A. Jesacher, S. Fürhapter, S. Bernet, and M. Ritsch-Marte, "Size selective trapping with optical "cogwheel" tweezers," Opt. Express 12, 4129 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4129.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-4129.</a>
[CrossRef] [PubMed]

Opt. Lett. (1)

K. T. Gahagan, and G. A. Swartzlander Jr., "Optical vortex trapping of particles," Opt. Lett. 21, 827 (1996).
[CrossRef] [PubMed]

Phy. Rev. A (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes," Phy. Rev. A 45, 8185 (1992).
[CrossRef]

Phy. Rev. Lett. (2)

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phy. Rev. Lett. 88, 053601 (2002).
[CrossRef]

J. E. Curtis, and D. G. Grier, "Structure of optical vortices," Phy. Rev. Lett. 90, 133901 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

H. He, M. E. J. 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, 826 (1995).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

S. H. Tao, X.-C. Yuan, H. B. Niu, and X. Peng, "Dynamic optical manipulation using intensity patterns directly projected by a reflective spatial light modulator," Rev. Sci. Instrum. 76, 056103 (2005).
[CrossRef]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed (McGraw-Hill, New York, 1996).

Supplementary Material (5)

» Media 1: AVI (1006 KB)     
» Media 2: AVI (956 KB)     
» Media 3: AVI (1322 KB)     
» Media 4: AVI (226 KB)     
» Media 5: MPG (1220 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

[1 MB, 1 MB, 1.3 MB, respective videos for phase evolutions of interferenced beams of (l 1=20, l 2=-3), (l 1=-20, l 2=3), and (l 1=20, l 2=-20)]. (a, b, c) Simulated intensities of interferenced beams of (l 1=20, l 2=-3), (l 1=-20, l 2=3), and (l 1=20, l 2=-20), respectively. (A1-3, B1-3, C1-3) Simulated phase distributions of the corresponding interferenced beams at distance of 166 mm+λ/3, 166 mm+λ/3, 166 mm+λ, respectively. [Media 1] [Media 2] [Media 3]

Fig. 2.
Fig. 2.

(a) Intensity profiles of vortex beams with charge of 20 (the dotted line) and -3 (the solid line), respectively, (b) intensity profile of the interferenced beam of (l 1=20, l 2=-3).

Fig. 3.
Fig. 3.

[226 KB, video for intensity evolution with varying charges of (l 1=20, l 2=-1 to -20)] The intensity percentages of the fringed ring (upper curve) and the innermost part (lower curve) of the interferenced beams of (l 1=20, l 2=-1 to -20). [Media 4]

Fig. 4.
Fig. 4.

Interferenced patterns recorded from the sample stage of a microscope. The beams are interfered by two vortex beams with (a) (l 1=20, l 2=-1), (b) (l 1=20, l 2=-3), (c) (l 1=20, l 2=-8), (d) (l 1=20, l 2=-12), (e) (l 1=20, l 2=-15), and (f) (l 1=20, l 2=-20), respectively.

Fig. 5.
Fig. 5.

(a) (1.2 MB, video for rotation) Sequent rotations induced by the residual OAM of the interferenced beams of (l 1=10, l 2=-2) and (l 1=-10, l 2=2) [Media 5]. (b) Rotation induced by the innermost ring and static trapping by the fringed ring of the interferenced beam of (l 1=10, l 2=-3).

Equations (3)

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E ( x , y ) = A 1 ( x , y ) exp [ il 1 θ ( x , y ) ] + A 2 ⋅exp [ il 2 θ ( x , y ) ] ,
u P l ( r , θ , z ) [ 2 r w ( z ) ] l L P l [ 2 r 2 w ( z ) 2 ] exp [ r 2 w ( z ) 2 ] exp [ ikr 2 2 R ( z ) ] exp [ i Ψ ( z ) ] exp ( ilθ ),
φ ( x , y ) = angle { exp [ il 1 θ ( x , y ) ] + exp [ il 2 θ ( x , y ) ] } + αx ,

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