  In this paper, we study the possible parametric down conversion processes in
a periodically poled customized Lithium Niobate (LiNbO3) ridge waveguide. Our
analysis of spontaneous parametric down-conversion (SPDC), first, with a
Gaussian pump beam mode and second, with an anti-symmetric Hermite-Gaussian HG
(1,0) pump beam mode predict the possible down conversion processes in each
case. From our JSA analysis, it is evident that the generated photons pairs in
all these cases are negatively correlated and have orthogonal polarizations. In
case of the former, degenerate photon pairs are emitted at 1550 nm with the
highest efficiency in the fundamental waveguide mode. While, in case of the
latter, non-degenerate photon pairs in different higher order spatial modes are
generated. Such photons, thus, have multiple degrees of freedom, like
polarization and spatial modes, which can be further harnessed towards
hyper-entangled photons for quantum information applications.
