How can the repetition rate of mode-locked lasers be tuned? In my job there is a femtosecond mode locked laser. It is able to operate at a range of repetition rates. I understand the principle behind mode locking of a laser, but I do not know how it would be possible to change the repetition rate of the laser without changing the cavity length. How is that achieved in real applications?
 A: Changing the cavity length is exactly how it is done. I have a (mode-locked) Ti:sapphire oscillator in my lab with a repetition-rate stabilization system, which works by using a mirror on a piezo stage to tune the cavity length.
On the other hand, if you need a large change in rep rate, you could always use a pulse-picker, which essentially blocks some fraction of pulses to reduce the duty cycle of the laser.  The ones I’ve seen of this use an electro-optic crystal and a polarizer to controllably reject pulses.  This wouldn’t change the rep rate of the laser itself, but you could ultimately get a slower rep rate rate this way if that’s what you want. 
A: The cavity length (and therefore the mode-locked pulse repetition rate) of a laser can be changed in any of several different ways.  The easiest is to move one of the cavity mirrors using a piezoelectric stack.  Another is to insert a pair of optical wedges into the cavity and move them to vary the thickness of glass the beam must traverse.  The piezo stack is, of course, faster but has a shorter range.  
The range of repetition rate adjustment depends on the total cavity length and the range of length adjustment.  It would be possible to put a "trombone" section into a cavity and obtain a very large repetition rate adjustment range.
