  We show that deliberately engineered dispersive metamaterial slab can enable
the co-existence and phase matching of contra-propagating ordinary fundamental
and extraordinary backward second harmonic surface electromagnetic modes.
Energy flux and phase velocity are contra-directed in the backward waves which
is the phenomenon that gives rise to unique nonlinear optical propagation
processes. We show that frequencies, phase, and group velocities, as well as
nanowaveguide losses inherent to the electromagnetic modes supported by such
metamaterial, can be tailored to maximize conversion of frequencies and to
reverse propagation direction of the generated wave. Such a possibility, which
is of paramount importance for nonlinear photonics, is proved with a numerical
model of the hyperbolic metamaterial made of carbon nanotubes standing on the
metal surface. Extraordinary properties of the backward-wave second harmonic
generation in the reflection direction and of the corresponding frequency
doubling metareflector in the THz are investigated with a focus on the pulsed
regime.
