Abstract

We demonstrate the transfer of information encoded as orbital angular momentum (OAM) states of a light beam. The transmitter and receiver units are based on spatial light modulators, which prepare or measure a laser beam in one of eight pure OAM states. We show that the information encoded in this way is resistant to eavesdropping in the sense that any attempt to sample the beam away from its axis will be subject to an angular restriction and a lateral offset, both of which result in inherent uncertainty in the measurement. This gives an experimental insight into the effects of aperturing and misalignment of the beam on the OAMmeasurement and demonstrates the uncertainty relationship for OAM.

© 2004 Optical Society of America

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References

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Appl. Opt.

Appl. Phys. Lett.

A. J. Shields, M. P. O�??Sullivan, I. Farrer, D. A. Ritchie, R. A. Hogg, M. L. Leadbeater, C. E. Norman, M. Pepper, �??Detection of single photons using a field-effect transistor gated by a layer of quantum dots,�?? Appl. Phys. Lett. 76, 3673 (2000).
[CrossRef]

IEEE Microwave and Wireless Comp Letters

M. D�??Amico, A. Leva, B.Micheli, �??Free-space optics communication systems: First results from a pilot field-trial in the surrounding area of Milan, Italy,�?? IEEE Microwave and Wireless Components Lett. 13, 305 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Nature

D. Bouwmeester, J. V. Pan, K. Mattle, M. Eible, H. Weinfurter, A. Zeilinger, �??Experimental quantum teleportation,�?? Nature 390, 575 (1997).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, A. Zeilinger, �??Entanglement of the orbital angular momentum states of photons,�?? Nature 412, 313 (2001).
[CrossRef] [PubMed]

New J. Phys.

R. J. Hughes, J. E. Nordholt, D. Derkacs, C. G. Peterson, �??Practical free-space quantum key distribution over 10 km in daylight and at night,�?? New J. Phys. 4, 43.1 (2002).
[CrossRef]

S. Franke-Arnold, S. Barnett, E. Yao, J. Leach, J. Courtial,M. Padgett, �??Uncertainty principle for angular position and angular momentum,�?? New J. Phys. 6, 103 (2004).
[CrossRef]

Opt. Commun.

J. Courtial, M. J. Padgett, �??Performance of a cylindrical lens mode converter for producing Laguerre-Gaussian laser modes,�?? Opt. Commun. 159, 13, (1999).
[CrossRef]

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. Lett.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, J. Courtial, �??Measuring the orbital angular momentum of a single photon,�?? Phys. Rev. Lett. 88, 257901 (2002).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, L. Torner, �??Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,�?? Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef] [PubMed]

A. Aspect, P. Grangier, G. Roger, �??Experimental tests of realistic local theories via Bell�??s theorem,�?? Phys. Rev. Lett. 47, 460 (1981).
[CrossRef]

A. T. O�??Neil, I.MacVicar, L. Allen,M. J. Padgett, �??Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,�?? Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

Proc. SPIE

G. Gibson, J. Courtial, M. Vasnetsov, S. Barnett, S. Franke-Arnold, M. Padgett, �??Increasing the data density of free-space optical communications using orbital angular momentum,�?? Proc. SPIE 5550, In Press.

Progress in Optics

L. Allen, M. J. Padgett, M. Babiker, �??The orbital angular momentum of light,�?? in Progress in Optics XXXIX, edited by E. Wolf (Elsevier Science B. V., New York, 1999), pp. 291�??372.
[CrossRef]

Quant. Electron.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soifer, G. V. Usplen�??ev, �??Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,�?? Quant. Electron. 26, 184 (1996).
[CrossRef]

Other

M. V. Vasnetsov, V. A. Pas�??ko, M. S. Soskin, Analysis of orbital angular momentum of a misaligned optical beam, submitted for publication (2004).

L. Allen, S. M. Barnett, M. J. Padgett, Optical Angular Momentum (Institute of Physics Publishing, London, 2003).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Optical configuration of the free-space optics (FSO) demonstration system. Shown here is the case of a beam with l=8.

Fig. 2.
Fig. 2.

Some examples of phase-hologram designs (top) and schematic representation of the corresponding far-field diffraction patterns under plane wave illumination (bottom). The phase-hologram patterns are represented in grey-scale. (a) Horizontally shifted l=1 beam. (b) Setting the phase at each point in the hologram pattern for the horizontally shifted l=1 beam to either 0 or π (whichever is closest) gives three horizontally separated beams with l=-1, 0 and +1. (c) Similarly, we can obtain three vertically separated beams with l=-3, 0 and +3. (d) The sum of the two phase patterns that create the horizontally and vertically separated beams gives a 3×3 array of beams with l=-4, -3, …, +3, +4.

Fig. 3.
Fig. 3.

A subset of results from transmitting a data set using OAM. We have used a data transmission set corresponding to the azimuthal indices -16,-12,-8,-4,0,+4,+8,+12,+16. We have defined a matrix of detectors by measuring the intensity at specific points on the CCD image.

Fig. 4.
Fig. 4.

Spread – or uncertainty – in the measured values P(l) for various apertures inserted into the path of an l=1 beam. The beam immediately after the aperture is shown in the left column. The measured spread in l-values (dark bars) compares well with the power spectrum of the aperture function P(ϕ) (light bars).

Fig. 5.
Fig. 5.

Spread in the values of l for various angular misalignments of an l=1 beam. Θ is the angular misalignment as a fraction of the beam divergence. The measured results (dark bars) are compared to those predicted by a decomposition of the detected beams in terms of cylindrical harmonics (light bars).

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