The two-frequency problem of synchronization of the pulse train of a
passively mode locked soliton laser to an externally injected pulse train is
solved in the weak injection regime. The source and target frequency combs are
distinguished by the spacing and offset frequency mismatches. Locking diagrams
map the domain in the mismatch parameter space where stable locking of the
combs is possible. We analyze the dependence of the locking behavior on the
relative frequency and chirp of the source and target pulses, and the
conditions where the relative offset frequency has to be actively stabilized.
Locked steady states are characterized by a fixed source-target time and phase
shifts that map the locking domain.Comment: 7 pages, 2 figure
