  Heralded single-photon sources are a fundamental building block for optical
quantum technologies. These sources need to be unfiltered and integrated to
have good scalability and avoid unnecessary losses. To attain this goal, it is
necessary to control the effective nonlinearity seen by the fields as they mix
and propagate in a waveguide source. In this paper, we introduce a method to
design nonlinear waveguides with arbitrarily shaped effective nonlinearity
profiles. The method takes advantage of the fact that the second order
nonlinear response is a tensor quantity and thus the local effective
nonlinearity of a material depends on the propagation direction of the fields
participating in the interaction. Thus, by locally changing the propagation
direction of the fields we can modulate the wave-mixing process. Our methods
allows for the waveguide fabrication process to be significantly simplified:
The material structure of the waveguide is made by a single crystal, no longer
needing oriented patterning (OP) or periodic poling (PP). We use our method to
design waveguides with a nonlinearity profile that is Gaussian in the
propagation length, allowing to generate perfectly pure heralded single
photons.
