  Sources of spectrally engineered photonic states are a key resource in
several quantum technologies. Of particular importance are the so-called
factorizable biphoton states which possess no spectral entanglement and hence,
are ideal for heralded generation of high-purity single photons. An essential
prerequisite for generating these states through nonlinear frequency conversion
is the control over the group indices of the photonic modes of the source.
Here, we show that thin-film lithium niobate on insulator (LNOI) is an
excellent platform for this purpose. We design and fabricate periodically poled
ridge waveguides in LNOI to demonstrate group index engineering of its guided
photonic modes and harness this control to experimentally realize on-chip group
index matched type-II sum-frequency generation (SFG) and photon-pair creation
through spontaneous parametric down-conversion (SPDC). Also, we numerically
study the role of the top cladding layer in tuning the dispersion properties of
the ridge waveguide structures and reveal a distinctive difference between the
air and silica-clad designs which are currently among the two most common
device cladding configurations in LNOI. We expect that these results will be
relevant for various classical and quantum applications where dispersion
control is crucial in tailoring the nonlinear response of the LNOI-based
devices.
