  Photon pairs generated by spontaneous parametric down-conversion are
essential for optical quantum information processing, in which the quality of
biphoton states is crucial for the performance. To engineer the biphoton
wavefunction (BWF) on-chip, the pump envelope function and the phase matching
function are commonly adjusted, while the modal field overlap has been
considered as a constant in the frequency range of interest. In this work, by
utilizing modal coupling in a system of coupled waveguides, we explore the
modal field overlap as a new degree of freedom for biphoton engineering. We
provide design examples for on-chip generations of polarization entangled
photons and heralded single photons, respectively. This strategy can be applied
to waveguides of different materials and structures, offering new possibilities
for photonic quantum state engineering.
