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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 47, Iss. 4 — Feb. 1, 2008
  • pp: A32–A42

Holographic generation of complex fields with spatial light modulators: application to quantum key distribution

Mark T. Gruneisen, Warner A. Miller, Raymond C. Dymale, and Ayman M. Sweiti  »View Author Affiliations


Applied Optics, Vol. 47, Issue 4, pp. A32-A42 (2008)
http://dx.doi.org/10.1364/AO.47.000A32


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Abstract

There has been considerable interest recently in the generation of azimuthal phase functions associated with photon orbital angular momentum (OAM) for high-dimensional quantum key distribution. The generation of secure quantum keys requires not only this pure phase basis but also additional bases comprised of orthonormal superposition states formed from the pure states. These bases are also known as mutually unbiased bases (MUBs) and include quantum states whose wave functions are modulated in both phase and amplitude. Although modulo 2 π optical path control with high-resolution spatial light modulators (SLMs) is well suited to creating the azimuthal phases associated with the pure states, it does not introduce the amplitude modulation associated with the MUB superposition states. Using computer-generated holography (CGH) with the Leith–Upatnieks approach to hologram recording, however, both phase and amplitude modulation can be achieved. We present a description of the OAM states of a three-dimensional MUB system and analyze the construction of these states via CGH with a phase-modulating SLM. The effects of phase holography artifacts on quantum-state generation are quantified and a prescription for avoiding these artifacts by preconditioning the hologram function is presented. Practical effects associated with spatially isolating the first-order diffracted field are also quantified, and a demonstration utilizing a liquid-crystal SLM is presented.

© 2008 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(090.1970) Holography : Diffractive optics
(090.2890) Holography : Holographic optical elements
(230.6120) Optical devices : Spatial light modulators
(270.0270) Quantum optics : Quantum optics

History
Original Manuscript: May 16, 2007
Manuscript Accepted: June 9, 2007
Published: October 10, 2007

Citation
Mark T. Gruneisen, Warner A. Miller, Raymond C. Dymale, and Ayman M. Sweiti, "Holographic generation of complex fields with spatial light modulators: application to quantum key distribution," Appl. Opt. 47, A32-A42 (2008)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-47-4-A32


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References

  1. P. Hariharan, Optical Holography--Principles, Techniques and Applications (Cambridge U. Press, 1991).
  2. J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967). [CrossRef]
  3. J. Turunen and F. Wyrowski, Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, 1997), Chap. 1.4, pp. 38-45.
  4. T. C. Poon, T. Yatagai, and W. Juptner, "Digital holography-coherent optics of the 21st century: introduction" and collected papers, Appl. Opt. 45, special issue on Digital Holography, 821-983 (2006). [CrossRef]
  5. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP, 2003).
  6. C. H. Bennett and G. Brassard, "Quantum cryptography: public key distribution and coin tossing," in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE, 1984), pp. 175-179. [PubMed]
  7. N. J. Cerf, A. Karlsson, and N. Gisin, "Security of quantum key distribution using d-level systems," Phys. Rev. Lett. 88, 127902 (2002). [CrossRef] [PubMed]
  8. J. Schwinger, "Unitary operator bases," Proc. Natl. Acad. Sci. U.S.A. 46, 570-579 (1960). [CrossRef] [PubMed]
  9. W. K. Wootters and B. D. Fields, "Optimal state-determination by mutually unbiased measurements," Ann. Phys. (N. Y.) 191, 363-381 (1989). [CrossRef]
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  11. D. A. Buralli, G. M. Morris, and J. R. Rogers, "Optical performance of holographic kinoforms," Appl. Opt. 28, 976-983 (1989). [CrossRef] [PubMed]
  12. G. J. Swanson, "Binary optics technology: the theory and design of multi-level diffractive optical elements," MIT Lincoln Laboratory Tech. Rep. 854 (MIT, 1989), pp. 1-47.
  13. M. T. Gruneisen, R. C. Dymale, J. R. Rotge, L. F. DeSandre, and D. L. Lubin, "Wavelength-dependent characteristics of a telescope system with diffractive wavefront control," Opt. Eng. 44, 068002 (2005). [CrossRef]
  14. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, "Synthesis of digital holograms by direct binary search," Appl. Opt. 26, 2788-2798 (1987). [CrossRef] [PubMed]
  15. E. N. Leith and J. Upatnieks, "Reconstructed wavefronts and communication theory," J. Opt. Soc. Am. 52, 1123-1130 (1962). [CrossRef]
  16. E. N. Leith and J. Upatnieks, "Wavefront reconstruction with continuous-tone objects," J. Opt. Soc. Am. 53, 1377-1381 (1963). [CrossRef]
  17. E. N. Leith and J. Upatnieks, "Wavefront reconstruction with diffused illumination and three-dimensional objects," J. Opt. Soc. Am. 54, 1295-1301 (1964). [CrossRef]
  18. J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, 1994).
  19. A. Gehner, M. Wildenhain, H. Neumann, J. Knobbe, and O. Komenda, "MEMS analog light processing--an enabling technology for adaptive optical phase control," Proc. SPIE 6113, 61130K 1-15 (2006).
  20. X. Wang, B. Wang, J. Pouch, F. Miranda, M. Fisch, J. E. Anderson, V. Sergan, and P. Bos, "Liquid crystal on silicon (LCOS) wavefront corrector and beam steerer," Proc. SPIE 5162, 139-146 (2003). [CrossRef]
  21. M. T. Gruneisen, L. F. DeSandre, J. R. Rotge, R. C. Dymale, and D. L. Lubin, "Programmable diffractive optics for wide-dynamic-range wavefront control using liquid-crystal spatial light modulators," Opt. Eng. 43, 1387-1393 (2004). [CrossRef]
  22. Y. Igasaki, F. Li, N. Yoshida, H. Toyoda, T. Inoue, N. Mukohzaka, Y. Kobayashi, and T. Hara, "High efficiency electrically-addressable phase-only spatial light modulator," Opt. Rev. 6, 339-344 (1999). [CrossRef]
  23. K. Bauchert, S. Serati, and A. Furman, "Advances in liquid crystal spatial light modulators," Proc. SPIE 4734, 35-43 (2002). [CrossRef]
  24. http://www.holoeye.com/phase_only_modulator_heo1080p.html.
  25. A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, "Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays based on a simple physical model," Opt. Eng. 40, 2558-2564 (2001). [CrossRef]
  26. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Dover Publications, 2000), Chap. 21.8.
  27. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 1966).
  28. C. Paterson, "Atmospheric turbulence and orbital angular momentum of single photons for optical communication," Phys. Rev. Lett. 94, 153901 (2005). [CrossRef] [PubMed]

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