  We present a detailed theoretical study of transverse exciton-polariton
patterns in semiconductor quantum-well microcavities. These patterns are
initiated by directional instabilities in the uniform pump-generated polariton
field and are measured as optical patterns in a transverse plane in the far
field. Based on a microscopic many-particle theory, we investigate the
spatio-temporal dynamics of the formation, selection, and optical control of
these patterns. An emphasis is placed on a previously proposed low-intensity,
all-optical switching scheme designed to exploit these instability-driven
patterns. Simulations and detailed analyses of simplified and more physically
transparent models are used. Two aspects are studied in detail. First we study
the dependencies of the stability behaviors of various patterns, as well as
transition time scales, on parameters relevant to the switching action(the
degree of built-in azimuthal anisotropy in the system and the switching beam
intensity). It is found that if the parameters are varied, the pattern system
undergoes abrupt transitions at threshold parameter values which are
accompanied by multiple-stability and hysteresis behaviors. Moreover, during a
real-time switching action, the transient dynamics of the system may depend
significantly on the proximity of unstable patterns. The second aspect is a
classification and detailed analysis of the polariton scattering processes
contributing to the pattern dynamics, giving us an understanding of the
selection and control of patterns as results of these processes' intricate
interplay. The crucial role played by the relative phases of the polariton
field in determining the gains or losses of polariton densities in various
momentum modes is highlighted, and interpretation of the actions of the various
processes in terms of concepts commonly used in classical pattern-forming
systems is given.
