The satellite network is one of the key technology of future communications. However, traditional geostationary orbit (GEO) satellite systems have significant problems of a long latency and a heavy launch cost. Hence, low-earth orbit (LEO) satellites have emerged as an alternative system to mitigate the intrinsic problems of GEO satellites. Along with the development of LEO satellite technologies, the inter-satellite link (ISL) has been designed to provide improved system performance and more reliable service. In addition, the optical ISL has been highlighted due to its high data rate and small terminal size. In this study, we consider the mega-constellation architecture, time-varying satellite topology, and multiple visible satellites. The impacts of optical communications are investigated on the routing path discovery procedure. Then, we propose a routing algorithm and compare the system performances of RF and optical systems.