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