The spatiotemporal dynamics of two counterpropagating beams in a photorefractive crystal with nonlocal and sluggish response is investigated in the longitudinal and one transverse dimension. A static external electric field is applied to the crystal to control the coupling strength of the two-wave mixing process. A nonautonomous linear stability analysis is performed that takes a nonconstant modulation depth into account. The onset of pattern formation for arbitrary coupling constants and pump ratios and the influence of linear absorption are discussed. Above the threshold predicted by stability analysis, running transverse waves appear in the optical near field and wandering spots appear in the corresponding far field. A nonlinear eigenmode analysis reveals the running transverse waves as secondary instabilities.
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