  The generalization of the area theorem is derived for the case of a pulse
circulating inside a ring laser cavity. In contrast to the standard area
theorem, which is valid for a single pass of a traveling pulse through a
resonant medium, the obtained generalized area theorem takes into account the
medium-assisted nonlinear self-action effects through the medium excitation
left by the pulse at the previous round-trip in the cavity. The generalized
area theorem was then applied to the theoretical description of the dynamics of
a single-section ring-cavity laser and the steady solutions for the pulse area
and for the medium parameters were found both in the limit of a lumped model
and for a spatially-extended system. The derived area theorem can be used for
the convenient analytical description of different coherent photonic devices,
like coherently mode-locked lasers or pulse compressors, as well as for the
analysis of the photon echo formation in cavity-based setups.
