Generation, amplification, frequency conversion, and reversal of propagation of THz photons in nonlinear hyperbolic metamaterial

We propose metamaterial (MM) that supports a mixture of three or more normal and backward electromagnetic modes with equal co-directed phase velocities and mutually contra-directed energy fluxes. This enables extraordinary three-wave mixing, greatly enhanced optical parametric amplification, and frequency-changing generation of entangled photons in the reflection direction. Proof-of-principle numerical simulation of such processes is presented based on the particular example of the wave-guided terahertz waves contra-propagating in the MM made of carbon nanotubes.