In this work, we focus on optimizing waveguides based on Lithium Niobate on Insulator (LNOI) for the generation of cross-polarized spectrally pure photons at telecommunication wavelength using type II spontaneous Parametric Down-Conversion (SPDC) process. Our optimization process is based on avoiding lateral leakage losses for all the modes involved in considered SPDC process by choosing waveguide parameters appropriately. In addition, we also ensure single mode operation for all the interacting wavelengths. We further engineer the waveguide such that it satisfies group index matching for generating spectrally pure single photons with high purity (⪆95 %). Such single-mode and loss-free waveguides are poised to have broad applications in both classical and quantum optical fields.
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