We based on integrated silicon-on-insulator platforms design the key components of an on-chip interferometer, beam splitter and directional coupler included, valid in high-visibility interference at telecommunication wavelengths. Special attention is given to the equal-proportion beam splitting and directional coupling, which is achieved by carefully designing the geometric dimension of multi-mode interferometer structure. The proposed interferometer facilitates low loss, broad operating bandwidth, anticipated large tolerance on size variation induced in fabrication procedures, based on a particular wafer with silicon layer thickness of 320 nm. The most highlight property of polarization-insensitive, enables the path-selective qubits generation for bi-polarization that further makes possible quantum key distribution using high dimensional protocols. We numerically demonstrate interference at 1550 nm with visibilities of 99.50% and 93.99% for transverse-electric and transverse-magnetic polarization, respectively, revealing that the proposed interferometer structure is well capable of on-chip optical control especially in quantum optics regime.

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We derive full-vectorial nonlinear propagation equations of dual-pumped four-wave mixing in straight waveguides, which are valid in characterizing the one-to-six wavelength multicasting. Special attention is paid to the resulting idler wavelengths and their conversion efficiency, which enables the optimization of the experimental designs, including the incident wavelength and the power of pumps and signal. We validate the model by comparing the numerical simulation to the experimental measurement in a silicon-on-insulator waveguide, for the first time to our best knowledge, and achieve a good agreement. We further derive the general form of the proposed model for the case of using multiple,pumps, which holds a potential to numerically predict the performance of complex wavelength multicasting, and essentially guide the waveguide designs.