Dynamics of Degenerate Optical Parametric Oscillators with Left-Handed Materials

In this contribution, we want to investigate the influence of left-handed materials on the spatiotemporal dynamics of degenerate optical parametric oscillators, which use a quadratic crystal to convert the energy of a pump laser to a signal field at half the pump frequency. It is well known that the coupling between diffraction and nonlinearity in such devices can induce a modulational instability in the homogeneous output beam, leading to the formation of dissipative structures. However, the inclusion of a left-handed material dramatically changes this dynamical behaviour.