  In this study, we employ density functional theory (DFT) based
first-principles calculations to investigate the spin-orbit effects in the
electronic structure of a polar-nonpolar sandwich heterostructure namely
LAO$_{2.5}$/STO$_{5.5}$/LAO$_{2.5}$. Our focus on the Ti-3d bands reveals an
inverted ordering of the STO-$\rm t_{2g}$ orbital near the n-type interface,
consistent with earlier experimental work. In contrast, toward the p-type
interface, the orbital ordering aligns with the natural ordering of STO
orbitals, influenced by crystal field splitting. Interestingly, we have found a
strong inter-orbital coupling between $t_{2g}$ and $e_g$ orbital, which has not
been reported earlier in $\rm SrTiO_3$ based 2D system. Additionally, our
observations highlight that the cubic Rashba splitting in this system surpasses
the linear Rashba splitting, contrary to experimental findings. This
comprehensive analysis contributes to a refined understanding of the role of
orbital mixing in Rashba splitting in the sandwich oxide heterostructures.
