Abstract
The spontaneous parametric down-conversion of photons has been widely applied for generating entangled photon pairs. We theoretically explore the entangled down-converted state of the photon pair, also known as biphoton state, for both degenerate and nondegenerate photon pairs. In particular, the spatial structure of the biphoton state has been expressed in Bessel modes to better understand the correlation with regard to the opening angle ${\ensuremath{\vartheta}}_{k}$ of Bessel modes. In fact, the opening angles of the down-converted photon pair are not independent of each other, but rather are correlated. Furthermore, we confirm the experimentally observed conditions concerning the optimization of generating high-degree spatial entanglement by controlling the beam waist of the pump beam. We also introduce a new experimental setup for efficient measurement of the spatial entanglement of the biphoton state using geometrical optics arguments.
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