OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 41, Iss. 24 — Aug. 20, 2002
  • pp: 5096–5104

Implementing Torsional-Mode Doppler ladar

David U. Fluckiger  »View Author Affiliations

Applied Optics, Vol. 41, Issue 24, pp. 5096-5104 (2002)

View Full Text Article

Acrobat PDF (161 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Laguerre–Gaussian laser modes carry orbital angular momentum as a consequence of their helical-phase front screw dislocation. This torsional beam structure interacts with rotating targets, changing the orbital angular momentum (azimuthal Doppler) of the scattered beam because angular momentum is a conserved quantity. I show how to measure this change independently from the usual longitudinal momentum (normal Doppler shift) and derive the apropos coherent mixing efficiencies for monostatic, truncated Laguerre and Gaussian-mode ladar antenna patterns.

© 2002 Optical Society of America

OCIS Codes
(120.0280) Instrumentation, measurement, and metrology : Remote sensing and sensors
(120.7250) Instrumentation, measurement, and metrology : Velocimetry
(120.7280) Instrumentation, measurement, and metrology : Vibration analysis
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(280.3340) Remote sensing and sensors : Laser Doppler velocimetry
(280.3640) Remote sensing and sensors : Lidar

David U. Fluckiger, "Implementing Torsional-Mode Doppler ladar," Appl. Opt. 41, 5096-5104 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset


  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,” Phys. Rev. A 45, 8185–8189 (1992).
  2. V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
  3. W. Beijersbergen, L. Allen, H. E. L. O. van der Ween, and J. P. Woerdman, “Astigmatic laser mode converter and transfer of angular momentum,” Opt. Commun. 96, 123–132 (1993).
  4. M. S. Soskin, V. N. Vasnetsov, J. T. Malow, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1998).
  5. M. Harris, C. A. Hill, and J. M. R. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
  6. G. Indebetauw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
  7. S. A. Ponomarenko, “A class of partially coherent beams carrying optical vortices,” J. Opt. Soc. Am. A 18, 150–156 (2001).
  8. S. Ramee and R. Simon, “Effect of holes and vortices on beam quality,” J. Opt. Soc. Am. A 17, 84–93 (2000).
  9. M. S. Soskin, ed., International Conference on Singular Optics, Proc. SPIE 3487 (1998).
  10. J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998).
  11. L. Allen, M. Babiker, and W. L. Power, “Azimuthal Doppler shift in light beams with orbital angular momentum,” Opt. Commun. 112, 141–144 (1994).
  12. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997).
  13. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986).
  14. R. L. Phillips and L. C. Andrew, “Spot size and divergence for Laguerre Gaussian beams of any order,” Appl. Opt. 22, 643–644 (1983).
  15. The actual circulation of energy is determined by the Gouy phase term (2p + m + 1)ψ(z), as well as the mθ term, hence there is a z dependence on the rate of rotation of the field energy. However, in the far field, ψ(z) → π/2, a constant, where the phase advance is then determined by the mθ term alone.
  16. M. W. Beijersbergen, M. Kristensen, and J. P. Woerdman, “Spiral phase-plate used to produce helical wavefront laser beams,” in Conference on Lasers and Electro-Optics, 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper CFA5.
  17. G. F. Brand, “Phase singularities in beams,” Am. J. Phys. 67 (1), 55–60 (1999).
  18. R. J. Hull, D. G. Biron, S. Marcus, and J. H. Shapiro, “Coherent laser radar remote sensing,” Final Rep. MIT Lincoln Laboratory ESD-TR-83–238/ESD-TR-83–72 (Lincoln Laboratory, Lexington, Mass., 1983).
  19. D. U. Fluckiger, S. Marcus, R. J. Hull, and J. H. Shapiro, “Coherent laser radar remote sensing,” Final Rep. MIT Lincoln Laboratory ESD-TR-84–306/ESE-TR-85–03 (Lincoln Laboratory, Lexington, Mass., 1984).
  20. J. H. Shapiro, B. A. Capron, and R. C. Harney, “Imaging and target detection with a heterodyne-reception optical radar,” Appl. Opt. 20, 3292–3313 (1981).
  21. J. F. Corum, “Relativistic rotation and the anholonomic object,” J. Math. Phys. 18, 770–776 (1977).
  22. J. F. Corum, “Relativistic covariance and rotational electrodynamics,” J. Math. Phys. 21, 2360–2364 (1980).
  23. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), Chaps. 3 and 4.
  24. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972), formula entry 9.1.80.
  25. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited