An investigation is made of the resonant amplification of two counterpropagating monochromatic beams having pseudorandom spatial modulation. A system of equations describing the change in the average intensities of the beams in the direction of propagation is derived and solved.
The dynamical behavior of counterpropagating light beams interacting with a nonlinear medium is studied numerically. When the incident intensities are increased, this system becomes unstable and exhibits oscillations undergoing complex behavior, including quasiperiodic motion and chaos. We analyze the output fields by using Fourier spectra, phase portraits, and autocorrelation functions. In the chaotic regime, the Lyapunov exponents and dimensions are calculated. A physical interpretation of the quasiperiodic motion is also given by an exact calculation of the absorption spectrum of a two-level atom.