An analytical theory is developed for parametric interactions in metamaterialmultilayer structures with simultaneous nonlinear electronic and magneticresponses and with near-zero refractive-index. We demonstrate theoreticallythat electromagnetic fields of certain frequencies can be parametricallyshielded by a nonlinear left-handed material slab, where the permittivity andpermeability are both negative. The skin depth is tunable, and even in theabsence of material absorption, can be much less than the wavelength of theelectromagnetic field being shielded. This exotic behavior is a consequence ofthe intricate nonlinear response in the left-handed materials and vanishingoptical refractive-index at the pump frequency.
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