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We have developped a general method that allows the calculation
of the complete quantum fluctuation spatial distribution in the
transverse plane of a light beam, while it is propagation along
a non-linear medium. From this calculation, valid as long as we
can work in the small quantum fluctuations limit, it is possible
to compute the local noise properties and the correlation between
any two transverse areas of the field.
We first did apply this method to the spatial solition. In a
non-linear medium, either second or third order, it exists a range
of parameter where the non-linearity can compensate for the diffraction.
In such a case, a light beam can propagate along this medium without
any deformation. This system is very interesting as the quantum
properties can accumulate whereas the mean field do not change.
We have shown in this system how do the quantum fluctuations evolve
and that, whereas the mean field do not change, the diffration
is responsible for the dillution of the quantum properties that
shift from local squeezing to quantum correlations [1].
We are now applying this method to other systems, such as parametric
fluorescence and vectorial solitons. This recent work is lead
by Eric Lantz, from the Laboratoire
d'Optique P.M. Duffieux of the University of Franche-Comte,
with whom we have a strong collaboration.
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