Rare ultrahigh pulses, classified as rogue waves (RWs), are inevitable and catastrophic in many different systems. Considering the damage they may produce, it is meaningful to understand the formation mechanism of these pulses and, if possible, control them. However, the rarity of RW and the difficulty in implementing the experiment are major limitations to understanding their formation. In 2007, Solli et al. (Solli D R, Ropers C, Koonath P, Jalali B 2007 Nature 450 1054) introduced the concept of optical RW, i.e. extreme event (EE) by comparing the appearance of oceanic RWs with the propagation of light fields in optical fibers. After that, the research of EEs entered into a flourishing period and different optical systems were proposed to analyze the generation and origin of EEs. Linear system is one of the most widely studied EE systems, such as linear light propagation in glass fibers, random media, and linear interference models. In addition to the linear systems mentioned above, efforts have also been made to produce nonlinear systems of EEs, such as microstructure fibers and tapered gradient exponential nonlinear fibers. In these nonlinear systems, the formation mechanism of EE is studied by using the nonlinear Schrödinger equation. Recently, the EEs in semiconductor laser systems have received a great deal of attention. On the one hand, semiconductor lasers with rich dynamic properties provide a cheap and controllable platform for understanding and predicting EE. The behavior of EE, on the other hand, is a powerful tool for understanding the fundamental mechanism of different laser systems.

In this work, based on the EEs generated in a semiconductor laser with phase-conjugate optical feedback (the master laser, ML), we inject its output into another free-running semiconductor laser (the slave laser, SL) and discuss the evolution of EEs in the system by numerical simulation. Herein, we analyze the influence of injection parameters on EEs through the two-dimensional maps of the relative number of EEs in the injection-parameter space. It can be concluded that in an area of high correlation, the relative number of EEs in SL tends to be a stationary value close to that in ML, while it may be enhanced in some weakly correlated regions. The results demonstrate the possibility of controlling EEs by optical injection, which is beneficial to optimizing the performance of chaotic laser systems or expanding their application scope.