Spatial Characterization Of Two-Photon States - GAP-Optique

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