Spatial Characterization Of Two-Photon States - GAP-Optique

CHAPTER 3
Spatial correlations and
orbital angular momentum
transfer
The previous chapter describes the correlations between the signal and idler
photons considering space and frequency, as well as the correlations between
those degrees of freedom. This chapter focuses on the cases where the degrees
of freedom are not correlated, and the only relevant correlations are
those between the photons in the spatial degree of freedom. To characterize
those correlations I use the orbital angular momentum (oam) content of
the generated photons, which is directly associated to their spatial distribution.
The spatial correlations between the photons determine the mechanism
of oam transfer from the pump to the signal and idler. Most studies of the
oam correlations in spdc can be divided in two categories: those reporting a
full transference of the pump’s oam [7, 8, 22, 27, 28, 29], and those reporting
a partial transference [30, 31, 32, 33]. This chapter describes the oam transfer
mechanism, and shows the difference between both regimes. The chapter is
divided in three sections. Section 3.1 introduces the eigenstates of the oam
operator: the Laguerre-Gaussian modes. This section shows how to calculate
and measure the oam content of the photons. Section 3.2 describes how the
oam is transferred in spdc. As an example, section 3.3 shows how this transfer
happens in the collinear case, where all the emitted photons propagate in the
same direction. The main result of this chapter is a selection rule that summarizes
the oam transfer mechanism: the oam carried by the pump is completely
transferred to all the signal and idler photons emitted over the cone.
29