Classical and quantum photonic sources based upon a nonlinear GaP/Si-superlattice micro-ring resonator

We present a theoretical investigation, based on the tight-binding Hamiltonian, of efficient second- and third-order nonlinear optical processes in the lattice-matched undoped ${\left(\text{GaP}\right)}_N/{\left(S{i}_2\right)}_M$ short-period superlattice that is waveguide-integrated in a microring resonator on an opto-electronic chip. The nonlinear superlattice structures are situated on the optically pumped input area of a heterogeneous “XOI” chip based on silicon. The spectra of ${\chi }_{zzz}^{\left(2\right)}\left(2\omega ,\omega ,\omega \right)$, ${\chi }_{xzx}^{\left(2\right)}\left(2\omega ,\omega ,\omega \right)$, ${\chi }_{xxxx}^{\left(3\right)}\left(3\omega ,\omega ,\omega ,\omega \right)$ and the Kerr refractive index ($n_2$), have been simulated as a function of the number of the atomic monolayers for “non-relaxed” heterointerfaces; These nonlinearities are induced by transitions between valence and conduction bands. The large obtained values make the ${\left(\text{GaP}\right)}_N/{\left(S{i}_2\right)}_M$ short-period superlattice a good candidate for future high-performance XOI photonic integrated chips that may include Si₃N₄ or SiC or AlGaAs or Si. Near or at the 810-nm and 1550-nm wavelengths, we have made detailed calculations of the efficiency of second- and third-harmonic generation as well as the performances of entangled photon-pair quantum sources that are based upon spontaneous parametric down conversion and spontaneous four-wave mixing. The results indicate that the ${\left(\text{GaP}\right)}_N/{\left(S{i}_2\right)}_M$ short-period superlattice is competitive with present technologies and is practical for classical and quantum applications.