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We show that deliberately engineered spatially dispersive metamaterial slabcan enable co-existence and phase matching of contra-propagating ordinaryfundamental and backward second harmonic electromagnetic modes. Energy flux andphase velocity are contra-directed in backward waves which determinesextraordinary nonlinear-optical propagation processes. Frequencies, phase andgroup velocities, as well as nanowavequide losses inherent to theelectromagnetic modes supported by the metamaterial can be tailored to optimizenonlinear-optical conversion of frequencies and propagation directions of thecoupled waves. Such a possibility, which is of paramount importance fornonlinear photonics, is proved with numerical model of the hyperbolicmetamaterial made of carbon nanotubes standing on metal surface. Extraordinaryproperties of backward-wave second harmonic in the THz and IR propagating inthe reflection direction are investigated with focus on pulsed regime.

Phase matched backward-wave second harmonic generation in a hyperbolic carbon nanoforest