How does the Kerr focusing effect leads modelocking? I read about the Kerr effect in a medium like a Ti:sapphire focuses the Gaussian beam by acting like a virtual lens.
That is fine. But here is my confusion. Inside the cavity when the laser beam is focused how does it lead to pulses or how does it locks the modes?
Someone wrote "In short, Kerr-lens modelocking is based on the difference in loss (or gain) for continuous-wave (CW) and pulsed operation."
But I still don't get the cause and effect relation here.
So there is a logical gap here in my thinking. I know what Kerr effect does to the intense Gaussian beam. I know(read) that this generates short pulses. But what is the relation between focusing and generating pulses here? Can this be explained intuitively using not much math?
 A: Simply put, you create a spatio-temporal window on which the laser has much less losses than for CW lasers.
Typically mode-locked lasers using Kerr lensing are not self-starting. You first need to create a perturbation of the field (in my laser I usually push a cavity mirror). Now this perturbation, lets call it a wavelet is enough to seed the process.
If containing enough energy, the Kerr effect shapes the spatial and temporal characteristics of the field. The temporal wings of the perturbation have low power so suffer more losses than the higher intensity of the main part of the wavelet. Now this wavelet with each roundtrip gets the wings chopped off and the center boosted, effectively shortening the pulse and creating new frequencies (needed for the pulse to be that short) as it goes. Because the wavelet seed then overpowers everything else, and "eats" all the gain of the medium, it resonates alone in the oscillator and all modes are locked. Often resulting in a solitonic type of wavelet where in the steady state there is a balance of nonlinear and linear phases as well as the gain/loss mechanism.
Then depending on the parameters of the lasers you can have more or less nonlinear spectral broadening, how short the pulses are, etc.
