PATTERN SELECTION IN PASSIVE AND ACTIVE NONLINEAR-OPTICAL SYSTEMS

The spontaneous emergence of patterns beyond some critical value of an external stress parameter, is illustrated with three examples from no nlinear optics. Counterpropagating beam patterns in an extended optica lly transparent system pose a challenging nonlinear boundary value pro blem for which self-focusing hexagons and self-defocusing squares are the preferred planforms. Polarization-induced patterns in a passive ri ng cavity represents a more manageable problem and rolls turn out to b e the preferred planforms. Finally, a single longitudinal mode, wide-a perture Raman laser is shown to select a transverse traveling wave mod e, which appears in the far-field as an off-axis emission. Complex ord er parameter equations are derived for each situation, and are used to illustrate how intrinsic symmetries play a role in pattern selection.