Spectral purity of telecom photon pairs from on-chip LNOI waveguides: comparison between analytical and numerical calculations

The spectral correlation information of photon pairs generated from a quantum light source, based on nonlinear optical processes, is beneficial in determining the potential application of such sources. Here we outline an explicit procedure to perform the Schmidt decomposition in order to compute the spectral correlation between photon pairs generated in a spontaneous parametric down-conversion (SPDC) process. Hermite-Gaussian (HG) functions are used as the basis to decompose the biphoton state and simple analytical formulae for the Schmidt mode coefficients (eigenvalues) are derived. The accuracy of our analytical formulation is verified against two separate sets of published results. We also present an experimentally feasible lithium niobate on insulator (LNOI) ridge waveguide to generate spectrally pure telecom (1560 nm) photons (purity \(\sim \) $\sim$ 90 \(\%\) $\%$ without filtering) by utilizing degenerate type-II SPDC. Further, the waveguide can be used in either the Sagnac or single-pass configuration with post-selection to generate polarization entanglement along with spectral purity simultaneously. The comparison between our analytical expression of Schmidt decomposition and the exact numerical solution is carried out by extensively studying the effect of pump bandwidth and waveguide length on Schmidt number and spectral purity. The results highlight that, in general, the analytical formula slightly overestimates the purity, but the two methods converge if the contribution of side lobes arising from the phase-matching function is minimized. Finally, we study the effect of scattering losses (resulting from the fabrication imperfections) on the spectral purity of the biphoton state. Our proposed on-chip source can have applications in quantum communication, photonic quantum computing, quantum information processing, and quantum metrology.