Broad Area Semiconductor edge-emitting lasers typically display self-focusing nonlinearity due to the refractive index dependence on the population inversion. It induces the homogeneous solution instability, multi-transverse mode operation and filamentation. This behavior strongly deteriorates the beam quality and drastically reduces their applicability. We suppress this instability for semiconductors with small enough linewidth enhancement factors, ¿H, by the introduction of a single spatial modulation in the transverse and longitudinal directions. For large ¿H values, optimized multi-frequency spatial modulations are needed. The proposed scheme becomes especially interesting for high nonlinearities that correspond to the normal laser operation.