Subcycle Terahertz Nonlinear Optics

The nonlinear interaction of subcycle electromagnetic radiation with matter is the current frontier in ultrafast nonlinear optics and high-field physics. Here, we investigate nonlinear optical effects induced by intense, subcycle terahertz radiation in a doped semiconductor. We observe a truncation of the half-cycle terahertz pulse and an emission of high-frequency terahertz photons. We attribute our observations to the abrupt current drop caused by strong intervalley scattering effects. By adding an extra half-cycle terahertz pulse with opposite polarity, we monitor the evolution of the nonlinear carrier dynamics during a quasi-single-cycle pulse. Our results demonstrate the differences between nonlinear effects for subcycle and multicycle terahertz pulses. It also suggests a new approach to subcycle control of terahertz waveforms, and the generation of high-order terahertz harmonics could be realized by using multicycle pulses.

Figure 1

(a) Amplitude spectra of the transmitted terahertz pulses through the bare substrate ($E_{\mathrm{ref}}$) and the (In,Ga)As sample ($E_{\text{trans}}$) with the incident peak field of $190\mathrm{kV}/\mathrm{cm}$. Inset: corresponding terahertz waveforms, where the blue arrow indicates the propagation direction. (b) Measured field dependence of $E_{\text{trans}}$ and half-cycle duration (amplitude FWHM) as a function of the incident peak field $E_{\mathrm{in}}$ measured in air. (c) Measured transmission spectra at various incident fields. The gray area corresponds to the transmission lower than 1. (d) Calculated transmission spectra based on the described model.

Figure 2

(a) Incident terahertz waveform and the calculated current density with the field strength of $190\mathrm{kV}/\mathrm{cm}$. (b) Schematic of the experiment in momentum space: intense terahertz transient induces carrier intervalley scattering. The increased field strength leads to a damping of the subcycle current density and an increase in the total relaxation time. (c) Impact of current drop on the transmitted terahertz waveforms of three tested field strengths shown in Fig. 1. The transmitted waveforms are normalized by the corresponding peak values. (d) Normalized transmitted terahertz waves obtained from calculation.

Figure 3

Transmitted terahertz pulses (solid black curve) and the instantaneous terahertz intensity (broken green curve) at various incident fields of (a) $74\mathrm{kV}/\mathrm{cm}$, (b) $105\mathrm{kV}/\mathrm{cm}$, (c) $130\mathrm{kV}/\mathrm{cm}$, and (d) $177\mathrm{kV}/\mathrm{cm}$. (e) The transmitted fields of negative ($E_{\mathrm{neg}}$) and positive extremes ($E_{\mathrm{pos}}$) versus the incident field. Inset: $\mathrm{\Delta }{E}_{\text{trans}}/E_{\mathrm{pos}}$, where $\mathrm{\Delta }{E}_{\text{trans}}=E_{\mathrm{pos}}-E_{\mathrm{neg}}$. (f) field dependence of half-cycle durations (amplitude FWHM). Four field regions can be identified, representing: 1, the linear regime; 2, current truncation on the negative polarity; 3, current truncation on the positive polarity; and 4, pulse broadening of the negative polarity.