  Photonic computing is attracting increasing interest to accelerate
information processing in machine learning applications. The mode-competition
dynamics of multimode semiconductor lasers is useful for solving the
multi-armed bandit problem in reinforcement learning for computing
applications. In this study, we numerically evaluate the chaotic
mode-competition dynamics in a multimode semiconductor laser with optical
feedback and injection. We observe the chaotic mode-competition dynamics among
the longitudinal modes and control them by injecting an external optical signal
into one of the longitudinal modes. We define the dominant mode as the mode
with the maximum intensity; the dominant-mode ratio for the injected mode
increases as the optical injection strength increases. We find that the
characteristics of the dominant mode ratio in terms of the optical injection
strength are different among the modes owing to the different optical feedback
phases. We propose a control technique for the characteristics of the dominant
mode ratio by precisely tuning the initial optical frequency detuning between
the optical injection signal and injected mode. We also evaluate the
relationship between the region for the large dominant mode ratio and injection
locking range. The region for the large dominant mode ratio does not correspond
to the injection-locking range. This discrepancy results from the complex
mode-competition dynamics in multimode semiconductor lasers with both optical
feedback and injection. This control technique of chaotic mode-competition
dynamics in multimode lasers is promising for applications in reinforcement
learning and reservoir computing as photonic artificial intelligence.
