Spatial Characterization Of Two-Photon States - GAP-Optique
Spatial Characterization Of Two-Photon States - GAP-Optique
Spatial Characterization Of Two-Photon States - GAP-Optique
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Phase front<br />
3.3. OAM transfer in collinear configurations<br />
OAM respect to z<br />
direction<br />
Figure 3.3: The direction of rotation of the phase shift defines the sign of the mode’s<br />
oam content. For a Laguerre-Gaussian mode corresponding to positive oam content,<br />
the phase shift rotates clockwise with respect to the propagation direction. If the<br />
same mode propagates backwards, the phase shift rotates anticlockwise with respect<br />
to the original propagation direction, and the mode has a negative oam content.<br />
can be generalized to<br />
lp = dsls + d1li<br />
+2<br />
-2<br />
-2<br />
(3.19)<br />
where ds,i = ±1 corresponds to forward and backward propagation of the<br />
corresponding photon.<br />
Conclusion<br />
The oam content of the pump is completely transferred to the signal and idler<br />
photons, emitted all over a cone. This makes it possible to introduce a selection<br />
rule that always holds if all possible emission directions are considered, but not<br />
necessarily if only a small part is detected. This result clarifies the apparent<br />
contradiction between several works that support the selection rule [7, 28, 56],<br />
and those that report that it is not valid [32, 31, 57].<br />
When only a portion of all generated photons are considered there is no<br />
simple relationship between lp, ls and li. The next chapter studies the oam<br />
transfer in those cases, describing the effect of different spdc parameters on<br />
the amount of oam that is transferred to the subset of the photons considered.<br />
35