Frequency combs: comb line spectra from periodic pulse train? Stabilized frequency combs can be generated using femtosecond mode-locked lasers after $f_{CEO}$ and $f_{rep}$ stabilization. 
Numerous sources have also pointed out that the periodic pulse train from the femtosecond laser generates the unique comb line spectra where $f_{rep}$ is equal to $1/T$ where $T$ is the period of the femtosecond pulses. However, this relationship between independent (that pulses are apart from each other), femtosecond pulses and the comb line spectrum is not intuitive to me.
My question: How does a coherent periodic pulse train generate such a unique comb line spectra (a frequency comb)?
 A: If you sum random frequency sinusoids with random phase you get cancellation from destructive interference.  If, however, the random sinusoids have a fixed phase, then they sum constructively to a band limited delta function amplitude.  You can easily demonstrate this as well by adding a train of Gaussians that have a fixed phase relation.  Because the Fourier transform of a Gaussian (not centered at t=0) has a complex phase term in front, you get constructive and destructive interference.  So the envelope of the spectrum is still a gaussian, but you'll see the comb of interference fringes under this envelope.  This is sometimes called spectral interferometry since you see the interference in the spectral domain.  This is exploited, for instance in earthquake seismology to get a comb spectrum from surface waves going round and round the earth.  They are phase locked since they all originated at the same time.
A: Physically such phenomena happen because of the oscillations inside the laser cavity; a Fabry-Perot cavity, which imposes the criterion that the spacing between the frequencies that are allowed to oscillate inside the cavity has to be 1/T. This is a consequence of Electromagnetic theory and interference of EM waves inside the cavity.
On the other hand if you need to control the $f_{rep}$ then it needs an APD that can integrate over several pulses and then the frequency counter takes the Fourier transform and gives you the $f_{rep}$.
