We simulate and discuss novel spatio-temporal propagation effects that relate specifically to pulsed, phase-mismatched second harmonic generation in a negative index material having finite length. Using a generic Drude model for the dielectric permittivity and magnetic permeability, the fundamental and second harmonic frequencies are tuned so that the respective indices of refraction are negative for the pump and positive for the second harmonic signal. A phase-locking mechanism causes part of the second harmonic signal generated at the entry surface to become trapped and dragged along by the pump and to refract negatively, even though the index of refraction at the second harmonic frequency is positive. These circumstances culminate in the creation of an anomalous state consisting of a forward-moving second harmonic wave packet that has negative wave vector and momentum density, which in turn leads to non-specular reflections at intervening material interfaces. The forward-generated second harmonic signal trapped under the pump pulse propagates forward, but has all the attributes of a reflected pulse, similar to its twin counterpart generated at the surface and freely propagating backward away from the interface. This describes a new state of negative refraction, associated with nonlinear frequency conversion and parametric processes, whereby a beam generated at the interface can refract negatively even though the index of refraction at that wavelength is positive.
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