Free electron cascaded third-harmonic generation

We study free electron nonlinearities in heavily doped semiconductors, which have recently emerged as low-loss and tunable materials for plasmonics at mid-infrared frequencies. We develop a hydrodynamic description that takes into account contributions up to the third order, usually negligible for noble metals. Our model predicts that nonlinear optical phenomena caused by free electron dynamics could overcome intrinsic semiconductor nonlinearities by two orders of magnitude. In this context, we demonstrate that, despite showing zero second-harmonic generation efficiency, a semiconductor slab can generate a cascaded third-harmonic signal (due to second-harmonic filed interactions) comparable to direct third-harmonic generation. Moreover, we suggest a possible experiment to observe such effect.