We study cross-slot waveguides for polarization diversity schemes that simultaneously offer strong confinement in the slot region for both TE and TM polarizations. A symmetric configuration is initially presented to demonstrate that the same strong confinement and propagation constants can be obtained for both polarizations and slot thicknesses down to $50\mathrm{nm}$ . To make easier further realization of these waveguides, an asymmetric waveguide configuration with a vertical slot height of up to $120\mathrm{nm}$ is proposed. The waveguide parameters are then optimized taking into account a $220\mathrm{nm}$ silicon thickness. Our simulation results show that no beating issues between TE and TM modes is observed for beating lengths under $6.68\mathrm{\mu m}$ , thus opening the way to efficient implementations of polarization diversity approaches.