Fig. 1: Propagation-induced limits on HHG in 3D Dirac semimetals (DSMs).

a An x-polarized laser pulse centered at angular frequency 1 THz impinges on a 3D DSM thin film at normal incidence, resulting in the radiation of higher harmonics. In momentum space \({{{{{{{\mathbf{p}}}}}}}} = ({{{{{{{\mathbf{p}}}}}}}}_ \bot ,p_x)\) (inset), the driving field induces intraband carrier oscillations (solid purple arrows) within and interband carrier transitions (dotted purple arrow) between the valence and conduction bands of the Dirac cone, resulting in the emission of light peaked at odd-integer multiples of the input angular frequency ω₀. b shows orders-of-magnitude enhancements in output intensity with increasing film thickness up to an optimal value of about 1500 nm, beyond which the harmonic output drastically falls. The existence of an optimal thickness arises due to the propagation-induced phase shift of the harmonic current (normalized 3rd harmonic current plotted in c, d) for 1 μm and 5 μm) across the film thickness. In thinner films c the phase shift in the current as a function of propagation distance z is insignificant. Thus, the emitted waves from different z are in-phase and add constructively. For films much thicker than the optimal thickness d a π-phase-flip occurs in the current density. The emitted radiation from opposite sides of this phase flip destructively interfere, resulting in the drastic decrease in HHG output with increasing film thickness seen in (b).