Spatial Characterization Of Two-Photon States - GAP-Optique

CHAPTER 1
General description of
Two-photon states
Experimental implementations of spontaneous parametric down-conversion (spdc)
share three main components: A laser beam used as a pump, a nonlinear material
that induces the down-conversion, and a detection system that measures
the generated state. The properties of the resulting two-photon state depend
on the interaction, and on the individual properties of those components. This
chapter derives the two-photon mode function that characterizes the generated
state, using first order perturbation theory. The chapter is divided in four
sections. Section 1.1 describes the spdc process in general terms. Section 1.2
introduces a general expression for the mode function. Section 1.3 lists a series
of common approximations used to reduce the complexity of the mode function.
Finally, section 1.4 introduces a novel matrix notation for the simplified
mode function. One of the advantages of this new notation is that many characteristics
of the two-photon state can be analytically calculated by using it.
The following chapters will use the notation and results introduced here as a
starting point to describe the correlations between the generated photons, and
between their spatial states.
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