Frequency pushing and pulling in semiconductor lasers subject to optical frequency comb injection

We theoretically investigate the frequency shift of a free-running semiconductor laser when optically injected by an optical frequency comb. By numerical integration of the laser rate equations, we have identified two types of frequency shifts, frequency pulling, and frequency pushing. The free-running slave laser seems to switch between pulling and pushing in a regular manner. We have systematically determined the dependence of these shifts on comb parameters, including comb spacing and number of lines. We have found that the occurring frequency pushing seems to be almost independent of comb signals and comb spacing, while in contrast, the frequency pulling shows weak dependence on comb signals but largely affected by comb spacing. We have also shown that carrier density dynamic is the origine of these phenomena.