We show that a deliberately engineered dispersive metamaterial slab can enable the coexistence and phase matching of ordinary fundamental and contra-propagating backward second harmonic electromagnetic waves. Energy flux and phase velocity are contra-directed in the backward waves, which is the extraordinary phenomenon that gives rise to unique nonlinear optical propagation processes. We demonstrate that frequencies, phase, and group velocities, as well as the losses inherent to the guided electromagnetic modes supported by such metamaterial, can be tailored to maximize the conversion of frequencies and to reverse the propagation direction of the generated second harmonic wave. Such a possibility, which is of paramount importance for nonlinear photonics, is proven using a numerical model describing 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.
Popov, A., Nefedov, I., & Myslivets, S. (2017). Hyperbolic carbon nanoforest for phase matching of ordinary and backward electromagnetic waves: Second Harmonic Generation. ACS Photonics, 4(5), 1240-1244. https://doi.org/10.1021/acsphotonics.7b00146