Advances in optical technology have increased the interest for multiprocessor architectures based on lightwave networks because of the vast bandwidth available. In this paper we propose a passive star multi-hop lightwave network called stack-Kautz, based on the Kautz graph. We show that this architecture is very cost-effective with respect to its resources requirements. We also propose control protocols for accessing the optical passive star couplers, which improve on the bit complexity of the control sequence proposed in the literature for the Partitioned Optical Passive Star network. Finally, we show through simulation that these control protocols efficiently implement shortest path routing on the stack-Kautz network.