The eigenstate spectrum of polarization self-modulated lasers is theor
etically and experimentally investigated. The polarizations and freque
ncies of the eigenstates of such lasers are theoretically derived in t
he framework of the Jones matrix formalism by assuming the self-consis
tency of the field after one round trip through the cavity. The result
ing predictions are successfully checked experimentally as well in the
case of a polarization self-modulated multimode gas laser as in the c
ase of st polarization self-modulated external-cavity semiconductor la
ser. In particular, it is shown experimentally that the pulses at a fr
equency equal to half the free spectral range observed in such lasers
can be interpreted as a beat between the two eigenstates that oscillat
e in a single round trip in the cavity. This behavior is shown to be i
n agreement with a one round trip operation of the laser. Then, the te
mporal properties of such lasers are suggested to be due to the self-m
ode-locking between the different eigenstates.