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.
1. General description of two-photon states<br />
virtual state<br />
pump<br />
ground state<br />
signal<br />
idler<br />
Figure 1.1: In spontaneous parametric down conversion the interaction of a molecule<br />
with the pump results in the annihilation of the pump photon and the creation of<br />
two new photons.<br />
1.1 Spontaneous parametric down-conversion<br />
Spontaneous parametric down-conversion is one of the possible resulting processes<br />
of the interaction of a pump photon and a molecule, in the presence of<br />
the vacuum field. In spdc, the pump-molecule interaction leads to the generation<br />
of a single physical system composed of two photons: signal and idler, as<br />
figure 1.1 shows.<br />
The name of the process reveals some of its characteristics. spdc is a<br />
parametric process since the incident energy totally transfers to the generated<br />
photons, and not to the molecule. And, it is a down-conversion process since<br />
each of the generated photons has a lower energy than the incident photon.<br />
The conservation of energy and momentum establish the relations between the<br />
frequencies (ωp,s,i) and wave vectors (kp,s,i) of the photons,<br />
ωp = ωs + ωi<br />
kp = ks + ki. (1.1)<br />
where the subscripts p, s, i stand for pump, signal and idler. Macroscopically,<br />
spdc results from the interaction of a field with a nonlinear medium. Commonly<br />
used mediums include uniaxial birefringent crystals. The conditions in<br />
equation 1.1 can be achieved for this kind of crystals, since their refractive index<br />
changes with the frequency and the polarization of an incident field [34, 35].<br />
This thesis considers type-i configurations in uniaxial birefringent crystals.<br />
In such configuration the pump beam polarization is extraordinary since it is<br />
contained in the principal plane, defined by the crystal axis and the wave vector<br />
of the incident field. The polarization of the generated photons is ordinary,<br />
which means that it is orthogonal to the principal plane.<br />
For a given material, the conditions imposed by equation 1.1 determine the<br />
characteristics of the generated pair. The second line in equation 1.1 defines the<br />
spdc geometrical configuration, and it is known as a phase matching condition.<br />
The generated photons are emitted in two cones coaxial to the pump, as shown<br />
in figure 1.2 (b). The apertures of the cone are given by the emission angles ϕs,i<br />
associated to the frequencies ωs,i. Once a single frequency or emission angle is<br />
selected, only one of all possible cones is considered. In degenerate spdc, both<br />
photons are emitted at the same angle ϕs = ϕi and the cones overlap, as in<br />
figure 1.2 (c). There are two kinds of degenerate spdc processes: noncollinear<br />
2