The spontaneous emergence of patterns beyond some critical value of an external stress parameter, is illustrated with three examples from nonlinear optics. Counterpropagating beam patterns in an extended optically transparent system pose a challenging nonlinear boundary value problem for which self-focusing hexagons and self-defocusing squares are the preferred planforms. Polarization-induced patterns in a passive ring cavity represents a more manageable problem and rolls turn out to be the preferred planforms. Finally, a single longitudinal mode, wide-aperture Raman laser is shown to select a transverse traveling wave mode, which appears in the far-field as an off-axis emission. Complex order parameter equations are derived for each situation, and are used to illustrate how intrinsic symmetries play a role in pattern selection.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics