  We analyze the process of photon-pair generation via spontaneous parametric
down-conversion in a quadratic nonlinear asymmetric waveguide coupler. The two
waveguides have different geometry, such that light coupling only occurs within
a narrow bandwidth of one of the generated (signal) photon modes, while the
other (idler) photon together with the pump stay localized in one (driven) arm
of the coupler. We demonstrate that such a setup represents a powerful and
flexible tool for engineering spectral properties of generated photon pairs.
Mode hybridization and dispersion of coupling can be utilized for shifting the
balance between group velocities of interacting pump, signal and idler fields,
subsequently leading to a significant increase of spectral factorisability
(purity) of photons. We also show that for interaction lengths shorter than one
beat length, generated pairs with signal photon being localized in the
auxiliary (not pumped) arm of the coupler appear to be spectrally localized in
both signal and idler components. The bandwidth of such intrinsic filtering of
generated photons can be controlled by several geometrical parameters.
