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