The response of a nonlinear Bragg grating under bidirectional illumination is studied. By analytical and numerical techniques it is found that the threshold for bistability, pulsation development, and spatial transverse instability is strongly influenced by the phase difference between fields incident from opposite directions. Breakup of pulsations that are symmetrical for both directions into nonsymmetrical pulsations is demonstrated. Solutions for focusing and defocusing nonlinearities are found to be related by means of changes in phase of the incident wave. A change of phase of π may lead to the emergence of a regular spatiotemporal light structure or may cause a transverse static pattern to become turbulent.
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