Angular momentum decomposition of entangled photons with an arbitrary pump

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We calculate the biphoton state generated by spontaneous parametric down-conversion in a thin crystal and under collinear phase matching conditions using a pump consisting of any superposition of Laguerre-Gauss modes. The result has no restrictions on the angular or radial momenta or, in particular, on the width of the pump, signal and idler modes. We demonstrate the strong effect of the ratio of the pump width to the signal/idler widths on the composition of the down-converted entangled fields. The knowledge of this ratio is shown to be essential for calculating the maximally entangled states that can be produced using pumps with a complex spatial profile.

Original languageEnglish
Article number053048
Number of pages12
JournalNew Journal of Physics
Publication statusPublished - 24 May 2011


  • photons
  • parametric down-conversion
  • crystals
  • spontaneous parametric down-conversion
  • Laguerre–Gauss modes
  • spatial profile


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