On-chip polarization control is in high demand for novel integrated photonic applications such as polarization division multiplexing and quantum communications. However, due to the sensitive scaling of the device dimension with wavelength and the visible-light absorption properties, traditional passive silicon photonic devices with asymmetric waveguide structures cannot achieve polarization control at visible wavelengths. In this paper, a new polarization-splitting mechanism based on energy distributions of the fundamental polarized modes in the r-TiO2ridge waveguide is investigated. The bending loss for different bending radii and the optical coupling properties of the fundamental modes in different r-TiO2ridge waveguide configurations are analyzed. In particular, a polarization splitter with a high extinction ratio operating at visible wavelengths based on directional couplers (DCs) in the r-TiO2ridge waveguide is proposed. Polarization-selective filters based on micro-ring resonators (MRRs) with resonances of only TE or TM polarizations are designed and operated. Our results show that polarization-splitters for visible wavelengths with a high extinction ratio in DC or MRR configurations can be achieved with a simple r-TiO2ridge waveguide structure.