Relativistic Doppler frequency upconversion of terahertz pulses reflecting from a photoinduced plasma front in silicon

We demonstrate experimentally the frequency upconversion of a terahertz (THz) pulse by the relativistic Doppler reflection from a counterpropagating charge-carrier plasma front in high-resistivity Si. The plasma front is generated via interband excitation with an ultrashort optical pump pulse. Spectral components extending to $\sim 28\mathrm{THz}$ are observed, using an input THz pulse with a bandwidth of $\sim 20\mathrm{THz}$ obtained from a two-color gas plasma emitter. We model the experiment using one-dimensional finite-difference time-domain simulations with realistic values of the Drude parameters for the plasma front, including effects due to excitation from a weak prepulse structure on the pump pulse.

Figure 1

Schematic of the experimental setup, including two-color plasma-THz generation of the probe, Doppler reflection at the Si sample, and sum-frequency detection of the reflected probe pulses.

Figure 2

Reference measurements of THz probe pulse (without pump). (a) Spectrally integrated SF signal as a function of detection delay time $t$, covering both the reflected signals from the front and back face (FF, BF) of the Si sample. Primary signals (direct path) and delayed signals due to Si-beamsplitter reflections, and subcomponents due to thick-crystal SF detection as indicated (see text). (b) SF spectrogram of the THz pulse reflected from the front face of the Si sample [black curve indicates the temporal first moment $\overline{t}\left(\nu \right)$]. (c) Corresponding frequency marginal $M\left(\nu \right)$.

Figure 3

(a) Experimental SF spectra $S(\nu ,t_0;\tau )$ vs pump-probe delay $\tau$, demonstrating the reflective Doppler upshift around $\tau =0$ (logarithmic color scale). (b) Corresponding differential SF spectra $\Delta S(\nu ,t_0;\tau )$ (obtained by subtracting the SF spectrum for sufficiently negative delay).

Figure 4

Detected spectrograms $S(\nu ,t;{\tau }_n)$ for selected pump-probe delays ${\tau }_n$: (a) $-1.0\mathrm{ps}$, (b) $-0.15\mathrm{ps}$, (c) $0\mathrm{ps}$, (d) $+0.05\mathrm{ps}$. Vertical dashed curves at $t=-0.2\mathrm{ps}$ added to aid comparison of the temporal rising edge of each spectrogram (see text). (e) Corresponding frequency marginals $M\left(\nu \right)$ and (f) relative temporal first-moment $\Delta \overline{t}\left(\nu \right)$.

Figure 5

Relative reflectivity spectra $R^{\prime }(\nu ,t_0;\tau )=R(\nu ,t_0;\tau )/R_0(\nu ,t_0)$ vs pump delay $\tau$ of GaAs sample in a front-face optical-pump THz-mid-ir-probe experiment. Drude plasma frequency ${\nu }_{\mathrm{p}}={\omega }_{\mathrm{p}}/2\pi$ from fitting each spectrum vs $\tau$ included as a dotted curve.

Figure 6

Predicted differential spectra $\Delta S(\nu ,t_0;\tau )$ vs pump delay $\tau$ from 1D-FDTD simulations: (a) without and (b) with additional prepulse at $t_{\mathrm{pp}}=-250\mathrm{fs}$ (see text for parameters). (c) Comparison of spectra $\Delta S(\nu ,t_0;\tau )$ for $\tau =25\mathrm{fs}$ (maximum Doppler upshift), including a reference spectrum (at sufficiently negative delay, $\tau =-1\mathrm{ps}$, i.e., corresponding to linear reflection from the Si-air interface).