An increasing demand for faster computers is rapidly growing to encounter the fast growing rate of Internet, space communication, and robotic industry. Unfortunately, the Very Large Scale Integration technology is approaching its fundamental limits beyond which the device will be unreliable. Optical interconnections and optical integrated circuits are strongly believed to provide the way out of the extreme limitations imposed on the growth of speed and complexity of nowadays computations by conventional electronics. This paper demonstrates two ultra-fast, all-optical logic gates and a high-density storage medium, which are essential components in building the future optical computer.