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 4<br />
OAM transfer in<br />
noncollinear configurations<br />
The previous chapter describes the oam transfer from the pump to the signal<br />
and idler photons considering all the possible emission directions of those<br />
photons. However, in non collinear configurations, the photons detected are<br />
just a subset of the total emission cone; noncollinear configurations generate<br />
correlated photons, which are naturally spatially separated, which is exactly<br />
what makes noncollinear so important. The change in the geometry of the<br />
process, imposed by the detection system, has a strong effect on the oam of<br />
the detected photons. This chapter focuses on the description of the oam that<br />
is transferred to a small portion of the emitted photons in noncollinear configurations.<br />
To characterize the transfer, I study a particular spdc process in<br />
which the pump is a Gaussian beam and one of the photons is projected into a<br />
Gaussian mode. Therefore, the oam content of the other photon will indicate<br />
how close the configuration is to satisfying the oam selection rule. This chapter<br />
is divided in three sections. Section 4.1 shows a simple example in which the<br />
selection rule does not apply as just a small section of the cone is considered.<br />
In a more general scenario, section 4.2 shows that the violation of the selection<br />
rule is not only mediated by the emission angle, but also by the pump beam<br />
waist. Finally, section 4.3 shows the effect of the Poynting vector walk-off on<br />
the oam of the noncollinear photons. As a main result, this chapter explains<br />
how the pump beam waist and the Poynting vector walk-off affect the oam<br />
transfer, in the cases where the selection rule does not apply. By tailoring both<br />
parameters it is possible to generate photons with specific spatial shapes. For<br />
instance, it is possible to generate photons in Gaussian modes that are more<br />
efficiently coupled into single mode fibers.<br />
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