  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.
