Chaotic optical communication at high bit rates has attracted great attention because of its potential application in high-speed optical spread spectrum communications. Among several proposed setups, all-optical systems, such as the optical injection system and the optical feedback system, can achieve chaotic synchronization on the amplitude, the slowly-varying phase of the chaotic envelope, and the fast-varying phase of the optical field. However, all of the experimental work reported so far demonstrated only the synchronization of the intensity waveform or, equivalently, the amplitude waveform of the laser field. This report experimentally demonstrates chaotic synchronization on the fast-varying and the slowly-varying optical phases of the bandwidth-broadened semiconductor lasers subject to the optical injection. The result shows a good synchronization quality.