Nonstationary parametric processes in negative refraction media

The article gives theoretical analysis of propagation of the fundamental wave and the second harmonic wave in quadratic nonlinear metamedia. The linear properties of metamaterial are characterised by a negative refraction index at the fundamental frequency and a positive refraction index at the second harmonic frequency. The analytical solutions in the form of periodic cnoidal waves and the coupled pump and harmonic waves – simultons, are obtained. The complete model, which includes the factors of dispersion of the second order group velocities and the pulse walk-off effect, is numerically investigated. A relation similar to the Manley–Rowe law is obtained for parametric processes in metamaterials.