Transmission Phase Holography: Spatial-Mode Filter Design for Quantum Information Applications

Photon spatial modes offer access to promising new applications in quantum information because they provide a higher-dimensional basis set than the usual two-dimensional one associated with polarization. Downconversion experiments have demonstrated spatial-mode entanglement [1], and even hyperentanglement in polarization and spatial mode [2]. However optical elements currently lack the refinement necessary to perform efficient, high-fidelity operations using spatial modes. Holographic filters for Laguerre-Gaussian and Hermite-Gaussian laser modes can act as modes converters, and have long been studied (under the terms ``modans'' and ``kinoforms'') for use in electrical engineering applications [3,4]. Her we present analytical refinements and optimizations of these techniques, with predicted mode fidelities over 95{\%} and diffraction efficiencies up to 98{\%}. Results of our experimental implementions of these solutions are presented. \newline [1] Walborn, S.P, et al, ``Entanglement and conservation of orbital angular momentum in spontaneous parametric down-conversion,'' Phys. Rev. A \textbf{69}, 023811 (2004); [2] Barreiro, J.T. et al, ``Generation of Hyperentangled Photon Pairs,'' Phys. Rev. Lett. \textbf{95}, 260501 (2005); [3] Soifer, V.A., ``Methods of Computer Design of Diffractive Optical Elements,'' John Wiley \& Sons, Inc., 2002; [4] Golub, M. and Soifer, V., ``Laser Beam Mode Selection by Computer Generated Holograms,'' CRC Press, Inc., 1994.