  Kerr lens-mode-locked Ti:Sapphire lasers are known to display three
coexistent modes of operation, that can be described as: continuous wave (CW),
transform limited pulses (P1) and positive chirped pulses (P2). Optical rogue
waves, in the form of pulses of high energy appearing much often than expected
in a Gaussian distribution, are observed in the chaotic regime of the mode P2,
but not of P1. These high energy pulses appear in an unpredictable way, but it
is observed that their separation (if measured in number of round trips) can
take only some definite values, which received the name of "magic numbers". The
existence of optical rogue waves in P2 and not in P1, and also of the magic
numbers, are correctly reproduced by a numerical simulation based on a
five-variables iterative map. But, a successful numerical simulation provides
limited insight on the physical causes of the observed phenomena. We present
evidence that optical rogue waves in this laser follow a modulational
instability, and that an initial condition in P1 rapidly evolves into P2 if the
parameters' values are beyond that instability's threshold. The magic numbers
are residuals of the periodic orbits of the "cold" cavity when it is perturbed
by the opposite effects of a dissipative term, due to the presence of
transversal apertures, and an expansive term, due to the Kerr effect.
