More theory of modelocking

Another way to understand how the loss (or gain) modulation leads to modelocking is to consider that modulating the loss (or gain) at some frequency introduces sidebands into the frequency spectrum of a mode, just as modulation always introduces frequency sidebands.  Because the modulation frequency equals the frequency separation between modes, the sidebands of the mode happen to exactly match the frequencies of the ‘neighbor’ modes (the next-higher-frequency mode and the next-lower-frequency mode).  Thus, we are coupling energy from one mode into its neighbors.  This has the effect of locking their relative phases.