Abstract

Optical phase singularities, also called optical vortices, are known to have applications in various branches of optics. Here the role played by optical vortices in collimation testing is explained. Interference and a diffractive experimental setup in which the presence of an optical vortex permits collimation testing are presented. It is shown that the moire fringes that aid in collimation detection are due solely to the presence of vortices and not to the accompanying phase factors that are involved in producing a grating structure.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1999), Vol. XXXIX, pp. 291–372.
    [CrossRef]
  2. C. T. Law, X. Zhang, G. A. Swartzlander, “Waveguiding properties of optical vortex solitons,” Opt. Lett. 25, 55–57 (2000).
    [CrossRef]
  3. F. S. Roux, “Diffractive optical implementation of rotation transform performed by using phase singularities,” Appl. Opt. 32, 3715–3719 (1993).
    [CrossRef] [PubMed]
  4. G. A. Swartzlander, “Peering into darkness with a vortex spatial filter,” Opt. Lett. 26, 497–499 (2001).
    [CrossRef]
  5. M. V. R. K. Murty, “The use of a single plane parallel plate as a lateral shear interferometer with a visible gas laser source,” Appl. Opt. 3, 531–534 (1964).
    [CrossRef]
  6. R. S. Sirohi, M. P. Kothiyal, “Double wedge plate shearing interferometer for collimation test,” Appl. Opt. 26, 4054–4056 (1987).
    [CrossRef] [PubMed]
  7. M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
    [CrossRef]
  8. K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1992).
    [CrossRef]
  9. K. V. Sriram, P. Senthilkumaran, M. P. Kothiyal, R. S. Sirohi, “Double wedge plate interferometer for collimation testing: new configurations,” Appl. Opt. 32, 4199–4203 (1993).
    [CrossRef] [PubMed]
  10. D. E. Silva, “A simple interferometric method of beam collimation,” Appl. Opt. 10, 1980–1982 (1971).
    [CrossRef]
  11. M. P. Kothiyal, R. S. Sirohi, “Improved collimation testing using Talbot interferometry,” Appl. Opt. 26, 4056–4057 (1987).
    [CrossRef] [PubMed]
  12. C. W. Chang, D. C. Su, “Collimation method that uses spiral gratings and Talbot interferometry,” Opt. Lett. 16, 1783–1784 (1991).
    [CrossRef] [PubMed]
  13. J. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
    [CrossRef]
  14. I. V. Basistry, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
    [CrossRef]
  15. I. V. Basistry, V. Yu. Bazhennov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
    [CrossRef]
  16. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef]
  17. V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
    [CrossRef]
  18. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
    [CrossRef]

2001 (1)

2000 (1)

1995 (1)

I. V. Basistry, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

1993 (3)

1992 (4)

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1992).
[CrossRef]

1991 (1)

1988 (1)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

1987 (2)

1974 (1)

J. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

1971 (1)

1964 (1)

Allen, L.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1999), Vol. XXXIX, pp. 291–372.
[CrossRef]

Babiker, M.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1999), Vol. XXXIX, pp. 291–372.
[CrossRef]

Basistry, I. V.

I. V. Basistry, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

I. V. Basistry, V. Yu. Bazhennov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Bazhennov, V. Yu.

I. V. Basistry, V. Yu. Bazhennov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Berry, M. V.

J. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Chang, C. W.

Heckenberg, N. R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

Kothiyal, M. P.

Law, C. T.

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Murty, M. V. R. K.

Nye, J.

J. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Padgett, M. J.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1999), Vol. XXXIX, pp. 291–372.
[CrossRef]

Rosenbruch, K. J.

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Roux, F. S.

Rubinsztein Dunlop, H.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Senthilkumaran, P.

Silva, D. E.

Sirohi, R. S.

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef]

Soskin, M. S.

I. V. Basistry, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

I. V. Basistry, V. Yu. Bazhennov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Sriram, K. V.

Su, D. C.

Swartzlander, G. A.

Vasnetsov, M. V.

I. V. Basistry, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

I. V. Basistry, V. Yu. Bazhennov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

White, A. G.

Zhang, X.

Appl. Opt. (6)

J. Mod. Opt. (1)

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Opt. Commun. (2)

I. V. Basistry, M. S. Soskin, M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995).
[CrossRef]

I. V. Basistry, V. Yu. Bazhennov, M. S. Soskin, M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993).
[CrossRef]

Opt. Eng. (1)

K. V. Sriram, M. P. Kothiyal, R. S. Sirohi, “Self referencing collimation testing techniques,” Opt. Eng. 32, 94–100 (1992).
[CrossRef]

Opt. Laser Technol. (1)

M. P. Kothiyal, R. S. Sirohi, K. J. Rosenbruch, “Improved techniques of collimation testing,” Opt. Laser Technol. 20, 139–144 (1988).
[CrossRef]

Opt. Lett. (4)

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein Dunlop, M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

J. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Other (1)

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed. (Elsevier Science, Amsterdam, 1999), Vol. XXXIX, pp. 291–372.
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) Negatively charged optical vortex phase (m = -1). (b) Positively charged optical vortex phase (m = 2).

Fig. 2
Fig. 2

Interference between a plane wave and a vortex-infested wave when (a) β ≠ 0 (m = 2) and (b) β = 0 (m = 2).

Fig. 3
Fig. 3

Fringes in Fig. 2(b) spiral when collimation is disturbed (m = 2).

Fig. 4
Fig. 4

Interferometric setup for collimation testing: M1, M2, mirrors; BS, beam splitter; P, spiral phase plate.

Fig. 5
Fig. 5

Interference between beams of Eq. (15) and a vortex-free beam when (a) D < 0, (b) D = 0, and (c) D > 0.

Fig. 6
Fig. 6

Talbot interferometric setup for collimation testing: G1, G2, spiral gratings; dotted lines, self-image planes.

Fig. 7
Fig. 7

Grating structures when a vortex phase and (a) a quadratic phase and (b) a linear phase are involved.

Fig. 8
Fig. 8

Moire fringes when (a) quadratic gratings and (b) linear gratings of different periods are superimposed.

Fig. 9
Fig. 9

The number of arms in the fringes indicates the number of optical vortices that are present in the two elements put together. An odd number of fringes is shown when (a) D = 0 and (b) D ≠ 0.

Equations (23)

Equations on this page are rendered with MathJax. Learn more.

Wx, y=Dx2+y2,
D=Δf/2f2.
ΔW=Dx2+y2=nλ,
ΔW=Wx Δx=2DxΔx=nλ.
ΔW=Wx Δx±yβ=nλ.
tx, y=rectxa* p=- δx-2parectxLrectyL,
ZN=N/λμ2.
|Δμ|=N/λμR,
U=x±iymE0 exp-ikz,
Θx, y=argx±iym-kz.
m=12πC Θ · dl.
ΔW=1k Θx, y.
1k Θx, y+yβ=nλ.
ΔW=1k Θx, y+Dx2+y2=nλ.
2k Θx, y+l1-l21+x2+y22l1l2=nλ,
t1x, y=12+12cosΘx, y+kRx2+y2.
t1Sx, y12+12cosΘx, y+kRSx2+y2.
t2x, y=12+12cosΘx, y-kRx2+y2
ax, y=t1Sx, yt2x, y.
Ix, y=I0x, y+αI1x, y =I0x, y+αcosΘx, y+kRx2+y2cosΘx, y-kRSx2+y2,
I1x, y=12cos2Θx, y+kx2+y21R-1RS+coskx2+y21R-1RS.
l1-l21+x2+y22l1l2
kx2+y21R-1RS

Metrics