A re-configurable optical waveguide includes an electro-optic substrate and plurality of electrodes above substrate. Electrodes are forming photonic crystal waveguide with photonic crystal periodic structure which has a slab optical waveguide on the top surface of a substrate and also has refractive index variation areas due to electro-optical effect with a different refractive index from that of the core layer of the slab optical waveguide arranged in a lattice array shape at part of the slab optical waveguide. In this case, the refractive index variation areas are formed of the same material as the material constituting the core layer of the slab optical waveguide. The refractive index variation areas are arranged in the lattice array shape on both the sides of an optical waveguide area, where light is propagated. The refractive index of the core layers of the refractive index variation areas is larger than that of the core layer of an area of the refractive index variation area. A plurality of electrodes are placed a field emission array with structure density possibly being higher than 10+8 per square centimeter. Groups of the structures are united in pixels with size a equal to the waveguide's width. Different arrays of pixels form variable shapes and, appropriately, variable waveguides. Thus light propagates in the different directions according the waveguide which is formed. Such a waveguide allows implementation of different optical functions simply by changing the arrangement of the patterns. Arrangement of the patterns is controlled with integrated transistor structure, and with a coupled control circuit.