  We introduce a new kind of spontaneous four wave mixing process for the
generation of photon pairs, in which the four waves involved counter-propagate
in a guided-wave \chi^{(3)} medium; we refer to this process as
counter-propagating spontaneous four wave mixing (CP-SFWM). We show that for
the simplest CP-SFWM source, in which all waves propagate in the same
polarization and transverse mode and in which self- and cross-phase modulation
effects are negligible, phasematching is attained automatically regardless of
dispersion in the fiber or waveguide. Furthermore, we show that in two distinct
versions of this source (both pumps pulsed, or one pump pulsed and the
remaining one monochromatic), the two-photon state is automatically factorable
provided that the length of the nonlinear medium exceeds a certain threshold,
easily achievable in practice since this threshold length tends to be in the
range of mm to cm. We also show that if one of the pumps approaches the
monochromatic limit, and for a sufficient nonlinear medium length, the
bandwidth of one of the two photons in a given pair may be reduced to the level
of MHz, compatible with electronic transitions for the implementation of
atom-photon interfaces, without the use of optical cavities.
