We study the spatiotemporal dynamics of optical cavities containing both a traditional Kerr type material and a layer of left-handed material. We show that the insertion of such a metamaterial allows for controlling the strength and the sign of the diffraction
experienced by the field in the cavity. We show that negative diffraction induces a new modulational instability and we study the formation of dissipative structures in the case of one, two and three transverse dimensions. In the case of small positive diffraction, we investigate how the nonlocal response of the metamaterial alters the size and stability of localized structures.
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