Silicon photonic integrated devices and circuits have offered a promising means to revolutionalize information processing and computing technologies. In this talk we present our recent efforts of design, fabrication, and characterization of ultracompact, linear, passive on-chip optical diodes, isolators and logic gates based on silicon two-dimensional photonic crystal slabs. Both simulation and experiment results show high performance of these novel designed devices. The success of these devices would help to construct nanophotonic on-chip processor architectures for future optical computers.