  Quasi-phase-matching (QPM) has enriched the capacity of parametric
down-conversion (PDC) in generating biphotons for many fundamental tests and
advanced applications. However, it is not clear how the nonidealities and
randomness in the QPM grating of a parametric down-converter may affect the
quantum properties of the biphotons. This paper intends to provide insights
into the interplay between PDC and nonideal or random QPM structures. Using a
periodically poled nonlinear crystal with short periodicity, we conduct
experimental and theoretical studies of PDC subject to nonideal duty cycle and
random errors in domain lengths. We report the observation of biphotons
emerging through noncritical birefringent-phase-matching, which is impossible
to occur in PDC with an ideal QPM grating, and a biphoton spectrum determined
by the details of nonidealities and randomness. We also observed QPM biphotons
with a diminished strength. These features are both confirmed by our theory.
Our work provides new perspectives for biphoton engineering with QPM.
