Third-order harmonic radiation from gapped graphene: from Landau-Zener tunneling to far-field propagation

We theoretically investigate harmonic generation from gapped graphene and focus on the third-order harmonic to study the influence of the minimum band gap 2 Δ and macroscopic propagation processes on harmonic radiation. When macroscopic propagation processes during harmonic generation are neglected, the intensities of third-order harmonic components depend nonmonotonically on the minimum band gap, first increasing and then decreasing as the band gap increases. Such behavior is primarily governed by the Landau–Zener tunneling probability through the harmonic emission weight, which combines the tunneling-excitation probability with the surviving valence-band population.Moreover, the far-field harmonic radiation of monolayer graphene can be obtained from the corresponding near-field distribution via a Hankel transformation of the Huygens-type propagation integral, and the resulting far-field characteristics of the third-order harmonic can be interpreted qualitatively in terms of the spatial profile of the near-field radiation. In the small-band-gap regime ( Δ ≤ 0.4 eV), integrating the near-field harmonic intensity over a finite spatial region ( r ≤ 30 μ m) provides a potential route for determining the minimum band gap of gapped graphene.