Space-temporal behavior of a light pulse propagating in a nonlinear nondispersive medium

An analytical method for the calculation of the evolution of a spatially inhomogeneous light pulse in a nonlinear optical system is developed. The description of pulse modulation is derived by using a one-dimensional map with a quadratic maximum that shows regular and chaotic dynamics according to the Feigenbaum theory. This mechanism may dominate for a ring laser or a nonhomogeneous medium with alternating amplifying and nonlinear absorbing layers. The total length of the system should be sufficiently small so that dispersion and diffraction effects do not appear. In this paper, two-dimensional distributions of the wave field intensity are presented to illustrate regular and chaotic self-modulation of the light pulse. Quantitative estimates for such regimes of a ring laser with a saturable absorber, losses into the harmonics, and stimulated scattering are given. It is found that for period-doubling bifurcations to occur, there is no need for total conversion of the pulse into the harmonic or Stokes component.