We study theoretically the effect of transverse boundary conditions on the traveling waves found in infinitely extended and positively detuned laser systems. We find that for large-aspect-ratio systems, well above threshold and away from the boundaries, the traveling waves persist. Source and sink defects are observed on the boundaries, and in very-large-aspect-ratio systems these defects can also exist away from the boundaries. The transverse size of the sink defect, relative to the size of the transverse domain, is important in determining the final pattern observed, and so, close to threshold, standing waves are always observed.
Pattern formation is analyzed and simulated in a nonlinear optical system involving all three space dimensions as well as time in an essential way. This system, counterpropagation in a Kerr medium, is shown to lose stability, for sufficient pump intensity, to a nonuniform spatial pattern. We observe hexagonal patterns in a self-focusing medium, and squares in a self-defocusing one, in good agreement with analysis based on symmetry and asymptotic expansions.