Intrinsic temporal and spectral mixing in time-resolved terahertz spectroscopy

TL;DR

The study addresses how pump–probe overlap in time-resolved terahertz spectroscopy can induce non-stationary, nonlinear current responses that distort extracted conductivities, potentially mimicking coherent dynamics. By combining finite-difference time-domain (FDTD) simulations with an extended non-equilibrium framework characterized by a two-dimensional response $\Sigma(t,t')$ and a Lorentzian variant $\Sigma_L(\omega;t_{ps})$, the authors predict and validate intrinsic time–frequency artifacts in 2D TRTS maps. Experiments on photoexcited SnSe show time–frequency features near a narrow TO phonon resonance (around 3.9 THz) that are qualitatively captured by $\Sigma_L$, supporting an artifact origin rather than genuine coherent processes. The work highlights the necessity of accounting for non-equilibrium current dynamics when interpreting ultrafast THz measurements, especially in systems with fast photoconductivity changes and long momentum relaxation times, such as photoinduced phase transitions.

Abstract

In an ultrafast optical-pump terahertz-probe measurement, the photoinduced material response can be modulated on a timescale shorter than the extent of the THz pulse. In this situation, the measured time-frequency response deviates from a simple time-dependent linear response. When full two-dimensional time-frequency maps are measured, this yields complex features that can be incorrectly assigned to a photoexcited coherent response. We investigate this experimentally via the measured response of photoexcited SnSe, whereby photoinduced phase change dynamics lead to ultrafast changes of the charge carrier and lattice optical conductivity response. Two-dimensional time-frequency THz transmission maps subsequently show unexpected time-frequency features at early pump-probe delay times. These features are reproduced in both finite-difference time-domain simulations of the THz experiment and in an extension of non-equilibrium response function theory, demonstrating their systematic origin. This work improves the understanding of systematic effects in high time resolution optical-pump THz-probe spectroscopy, and explores the conditions in which they are likely to appear.

Figures (5)

• Figure 1: (a) Pulse diagram showing the absolute ($\tau_{pump}$, $\tau_{probe}$, $\tau_{samp}$) and relative ($t$, $t_{ps}$, $t_{pp}$) time axes for a TRTS experiment involving pump (top), probe (middle), and sampling (bottom) pulses. (b) Pulse delay representation showing the 'unprojected' delay scheme where $t_{ps}$ is varied to collect THz waveform data. (c) Similar representation showing the 'projected' case where $t_{ps}$ is fixed and $t_{pp}$ is varied. The SnSe experiments discussed in this work use the delay scheme shown in (c), where each part of the sampled THz probe experiences the same pump delay, whereas the simulation results model the scheme shown in (b).
• Figure 2: (a) Experimental time-domain photoinduced change in THz field $\Delta E (t,t_{ps}) = E_p(t,t_{ps}) - E_r(t)$ with guide line showing an additional feature along $t = t_{ps}$. (b) Unprojected FDTD simulation of a THz experiment showing a long-lived response at $t_{pp} = 0$, where the pump arrival crosses the main peak of the THz pulse. (c) Projection of the data in (b) from $(t,t_{pp})$ to $(t,t_{ps})$ showing how the projected $t_{pp} = 0$ feature now follows the $t = t_{ps}$ line, matching that seen for the measured data in (a). All color scales are reduced to 10% of the full signal range.
• Figure 3: (a) Nonlinear current response as given by Eqn. \ref{['eqn1']} for various pump-sampling delays $t_{ps}$ and $\gamma$ = 0.3 ps$^{-1}$. Note the extension of the current response to later times as the pump-sampling delay is increased. (b) Normalized comparison between typical Drude response in the THz regime $\sigma$ and the nonlinear current model given by Equation \ref{['eqn2']}$\Sigma$. At early sampling times ($t_{ps} \approx 1$ ps) the extended nonlinear current response leads to additional time-frequency oscillations that are visible in spectroscopy results. Here $\gamma$ has been set equal to 2 to better display the modulations.
• Figure 4: FDTD simulations of a THz transmission experiment on a material with phonon dispersion, showing time-frequency structure appearing in $\Delta E (\omega,t_{ps})$. Spectral oscillations appear centered around the simulated phonon frequency, shown for values of $\omega_0 =$ 1.4 THz (a) and 6.0 THz (b). Modifying the momentum scattering time of the photoexcited carriers shows that these features are less severe for short momentum scattering times (c) and are enhanced as the momentum relaxation time becomes long (d), as expected from the form of Equation 5.
• Figure 5: Comparison between the measured SnSe (a) Re[$\Delta \sigma(\omega, t_{ps})$] and (c) Im[$\Delta \sigma(\omega, t_{ps})$] versus the real (b) and imaginary (d) components of the derived nonlinear Lorentzian response $\Sigma_L(\omega;t_{ps})$. $\Sigma_L(\omega;t_{ps})$ reproduces both the dynamic time-frequency features and the Im[$\Delta \sigma(\omega, t_{ps})$] sign change seen in the SnSe TRTS data. The $\Sigma_L(\omega;t_{ps})$ shown here was calculated using $\omega_0$ = 4 THz, $\Gamma$ = 0.1 ps$^{-1}$, and $\gamma$ = 0.1 ps$^{-1}$.