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Applied Optics

Applied 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)

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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

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

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)

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