With the development of 5G, mobile communication, and optical communication technologies, semiconductor optical amplifiers (SOAs) have become an important research topic. However, most SOA-related studies have focused on a technical discussion or market research but have failed to indicate the critical SOA technologies and the SOA technology development trends. Therefore, this study analyzes SOA patents and constructs a technology network for SOA patents. The results indicate that the critical SOA technologies are mainly used in lasers, semiconductor lasers, light guides, electromagnetic wave transmission communication other than radio-wave communication, and devices controlling light sources. Among the five critical SOA technologies, lasers (H01S3) account for the highest percentage at 22.21%. Consequently, the critical technologies do not focus on specific technology fields but have characteristics of multiple technology fields. In addition, considerable development has occurred in semiconductor lasers in recent years. Finally, patentee analysis indicates that for SOA technologies, the public sector and academia play relatively weak roles in early technology development or following technology development. However, with the rapid development of mobile communication and optical communication, the government of each country can consider investing additional R&D funds and resources in the future. This study constructs a network model for patent technologies to explore the development tendencies for SOA technologies. This model can be used as a reference for R&D resource management and the promotion of new technologies.