Spatial Characterization Of Two-Photon States - GAP-Optique

Weight
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0
4.3. Effect of the Poynting vector walk-off on the OAM transfer
0º 90º Azimuthal angle 360º
other
modes
Gaussian
mode
0º 90º Azimuthal angle 360º
Gaussian
mode
other
modes
Figure 4.7: The probability of generating a Gaussian signal photon varies with the
azimuthal angle, and has a maximum at α = 90 ◦ where the noncollinearity effect
compensates the Poynting vector walk-off. At other angles, like α = 360 ◦ the probability
of generating a Gaussian signal decreases and other modes become important
in the distribution. Those non-Gaussian modes are more numerous for more focused
beams, as seen by comparing the left part of the figure, where wp = 100 µm, to the
right part, where wp = 600 µm.
Signal
purity
0.3
0.1
0.0
without
walk-off
with
walk-off
azimuthal
0º 90º 180º 270º 360º angle
Figure 4.8: Like the signal oam content, the correlations between the photons change
with the azimuthal angle. The walk-off not only introduces an azimuthal variation
but increases the correlations.
translated into a change in the oam content of the generated pair with respect
to the z axis.
Additionally, because of the walk-off the generated photons are not symmetric
with respect to the displaced pump beam, and their azimuthal position
α becomes relevant. Figure 4.7 shows the weight of the mode ls = 0, and the
weight of all other oam modes, as a function of the angle α for two different
pump beam widths. In the left part, the pump beam waist is 100 µm, while
in the right part it is 600 µm. The oam correlations of the two-photon state
change over the down-conversion cone due to the azimuthal symmetry break-
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