Symmetry-Breaking Electron Dynamics Enable Ultrabroadband Optical-Field Sampling via Second-Harmonic Generation

Abstract

Optical-field sampling using second-harmonic generation (SHG) from strong-field ionization enables ultrabroadband terahertz detection, but the microscopic origin of the SHG signal and its ultrabroadband response have been unclear. Here we show that the target field lifts the half-cycle cancellation of photoelectron dipole emission, generating the SHG signal used for field sampling. Time-dependent Schrodinger-equation simulations, supported by classical-trajectory Monte Carlo analysis, demonstrate that the SHG yield directly encodes the instantaneous target electric field at the ionization time, enabling waveform retrieval by scanning the probe-target delay. Because the SHG response is gated by a subcycle ionization window rather than the probe envelope, the detection bandwidth can extend far beyond the probe duration. We further quantify practical constraints on retrieval, including intrinsic probe asymmetry and SHG back-action, providing a predictive framework to optimize sensitivity, temporal resolution, and fidelity through controlled electron dynamics.

Figures (5)

• Figure 1: (a) Sketch of the system: a strong probe pulse $\boldsymbol{E}_\mathrm{p}$ (orange) and a target field $\boldsymbol{E}_\mathrm{THz}$ (green and blue, for different time delay $\tau_1$ and $\tau_2$, respectively) interact with a hydrogen atom. The THz wave is accompanied by an optional DC bias to achieve the coherent detection in the SHG scheme dai2006detectionkarpowicz2008coherent, with peak field strength $\mathcal{E}_{\mathrm{THz}}=1.7\times10^{-5}$ a.u. (87 $\mathrm{kV / cm}$), $\mathcal{E}_\mathrm{DC}=2.0\times10^{-5}$ a.u. and central frequency $\omega_\mathrm{THz}=0.04\omega_{0}$ (15 THz). (b) Detectable SHG spectrum and (c) the reconstruction of the THz waveform by the SHG sampling process. The SHG signal form the TDSE simulation (blue dots) and the CTMC prediction (red crosses) are both normalized to the maximum of the THz field strength.
• Figure 2: (a) The dipole moment $\braket{\hat{\boldsymbol{d}}(t)}$ obtained by TDSE simulation. (b) Wavelet transform of $\braket{\hat{\boldsymbol{d}}(t)}$, denoted as $S(\chi, \mu)$ for the time delay $\tau_1$. Labels I and II denote two distinct classes of ionization events occurring in opposite half-cycles of $\boldsymbol{E}_\mathrm{p}$. The vertical dashed lines indicate the contributions from the two most probable trajectories within each respective class. (c) Section views of $|S(\chi, \mu)|$ for $\chi=2$ at time delays $\tau_1$ (red) and $\tau_2$ (blue), with the white-grey gradient background indicating the phase of $S(\chi=2, \mu)$ from 0 to $2\pi$. An obvious asymmetry between I and II appears for the time delay $\tau_2$. (d) and (e) show the contribution of the representative trajectories to the SHG signal in Eq.(\ref{['e3']}). The trajectories are around maximum ionization rate in I and II. The radius denotes the amplitude while the polar angle is the phase. The imbalance cancellation between I and II happens around $\tau_2$. The other parameters are the same as in Fig.\ref{['fig:2']}.
• Figure 3: Harmonic spectrum $\mathcal{G}_{x}(\omega)$ obtained from CTMC. Black dash dot: No factors are removed; Yellow line: Perturbation of ionization rate (factor A) is removed; Cyan line: Perturbation of the subsequent motions (factor B) is removed; and Blue line: Both factor A and B are removed. The other paramters are the same as in Fig.\ref{['fig:2']}.
• Figure 4: The change ratio $R$ as a function of the $2\omega_0$-field strength $\mathcal{E}_{2\omega_0}$. The dashed vertical line corresponds to the field strength reported in the experiment fujii2021electricgarriga2022observation. The other parameters are the same as in Fig.\ref{['fig:2']}.
• Figure 5: The signal contrast $C$ as a function of the pulse length $n_c$ for $\varphi_\mathrm{CEP}=\pi/2$ (a) and as a function of $\varphi_\mathrm{CEP}$ for $n_c=9$ (b). (c) The frequency response $|H(\omega^\prime)|$vs the pulse length $n_c$ at $\varphi_\mathrm{CEP}=\pi/2$, in units of dB. The maximum is normalized to 0 dB. The blue dashed line denotes the cutoff frequency $\omega^\prime_c$ where $|H(\omega^\prime)|$ declines to its half, and the green dashed line represents the traditional cutoff frequency given by the Fourier transform limit of the probe pulse (see in Supp).