The purpose of this tutorial paper is to present a broad overview of photon-pair generation through the spontaneous four wave mixing (SFWM) process in optical fibers. Progress in optical fiber technology means that today we have at our disposal a wide variety of types of fiber, which together with the fact that SFWM uses two pump fields, implies a truly remarkable versatility in the resulting possible photon-pair properties. We discuss how the interplay of the frequency, transverse mode, and polarization degrees of freedom, the first linked to the latter two through fiber dispersion, leads to interesting entanglement properties both in individual degrees of freedom and also permitting hybrid and hyper entanglement in combinations of degrees of freedom. This tutorial covers methods for photon pair factorability, frequency tunability, and SFWM bandwidth control, the effect of frequency non-degenerate and counter-propagating pumps, as well methods for characterizing photon pairs generated in optical fibers.
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