  Dissipative solitons are fundamental wave-pulses that preserve their form in
the presence of periodic loss and gain. The canonical realization of
dissipative solitons is Kerr-lens mode locking in lasers, which delicately
balance nonlinear and linear propagation in both time and space to generate
ultrashort optical pulses. This linear-nonlinear balance dictates a unique
pulse energy, which cannot be increased (say by elevated pumping), indicating
that excess energy is expected to be radiated in the form of dispersive or
diffractive waves. Here we show that Kerr-lens mode-locked lasers can overcome
this expectation. Specifically, by breaking the spatial symmetry between the
forward and backward halves of the round-trip in a linear cavity, the laser can
modify the soliton in space to incorporate the excess energy. Increasing the
pump power leads therefore to a different soliton solution, rather than to
dispersive / diffractive loss. We predict this symmetry breaking by a complete
numerical simulation of the spatio-temporal dynamics in the cavity, and confirm
it experimentally in a Kerr-lens mode-locked Ti:Sapphire laser with
quantitative agreement to the simulation. The simulation opens a window to
directly observe the nonlinear space-time dynamics that molds the soliton
pulse, and possibly to optimize it.
