Terahertz Driven Amplification of Coherent Optical Phonons in GaAs Coupled to a Metasurface

We demonstrate amplification of longitudinal optical (LO) phonons by polar-optical interaction with an electron plasma in a GaAs structure coupled to a metallic metasurface using two-color two-dimensional spectroscopy. In a novel scheme, the metamaterial resonator enhances broadband terahertz fields, which generate coherent LO phonons and drive free electrons in the conduction band of GaAs. The time evolution of the LO phonon amplitude is monitored with midinfrared pulses via the LO-phonon-induced Kerr nonlinearity of the sample, showing an amplification of the LO phonon amplitude by up to a factor of 10, in agreement with a theoretical estimate.

Figure 1

(a),(b) The upper parts show the electron energy in the conduction band as a function of wave vector, the lower parts electron distribution functions. A phonon is absorbed when an electron is scattered from $\mathbf{k}-\mathbf{q}$ to $\mathbf{k}$ (the electron energy increases by $\hslash {\omega }_{\mathrm{LO}}$), a phonon is emitted when an electron is scattered from $\mathbf{k}$ to $\mathbf{k}-\mathbf{q}$ (the electron energy decreases by $\hslash {\omega }_{\mathrm{LO}}$). (a) Phonon absorption is more probable for $f_e(\mathbf{k}-\mathbf{q})>f_e(\mathbf{k})$, (b) phonon emission (gain) for $f_e(\mathbf{k}-\mathbf{q})<f_e(\mathbf{k})$. (c) Sample structure with the electric field distribution in the semiconductor layers underneath the MDRs. Right: strong electric fields create electron-hole pairs in GaAs. These electrons are accelerated into the thick GaAs layer thereby creating inversion for stimulated emission of coherent LO phonons. (d) Shape of the MDRs. (e) Black line: incident THz pump pulse $E_{\mathrm{THz}}^{\mathrm{in}}(t,\tau =0)$. The green curve shows a low-pass-filtered THz pump pulse without frequencies above 5 THz. (f) Spectrum of the THz pump pulse (red line) and of the MIR probe pulse (blue line). Black line: measured sample reflectivity $R(\nu )=|E_{\mathrm{re}}(\nu )/E_{\mathrm{in}}(\nu ){|}^2$.

Figure 2

Two-dimensional nonlinear terahertz spectroscopy performed on our sample. Measured reflected electric fields as a function of real time $t$ and delay time $\tau$: (a) the THz pump pulse $E_{\mathrm{THz}}(t,\tau )$, (b) the MIR probe pulse $E_{\mathrm{MIR}}(t,\tau )$, and (c) the nonlinearly emitted electric field $E_{\mathrm{NL}}(t,\tau )$. The values for $E_{\max }$ are (a) 33, (b) 150, and (c) $12\mathrm{kV}/\mathrm{cm}$. (d) Amplitude of the 2D Fourier transform $|{\widehat{E}}_{\mathrm{NL}}({\nu }_t,{\nu }_{\tau })|$ of the nonlinear signal. (e) Red curve: $E_{\mathrm{NL}}(t,\tau =437\mathrm{fs})$ [vertical dashed line in (a) to (c)] compared to the probe pulse $E_{\mathrm{MIR}}(t,\tau =437\mathrm{fs})$ (black line). The horizontal dashed lines in (a) to (c) and (e) illustrate the 90° phase shift between $E_{\mathrm{NL}}(t,\tau )$ and $E_{\mathrm{MIR}}(t,\tau )$.

Figure 3

(a) Time-dependent vector potential of the broadband THz pulses obtained from $E_{\mathrm{THz}}(t,\tau =0)$ in Fig. 2 [27]. The arrows indicate times for which the areas under the peaks [diamonds in panel (c)] show the steepest climbs. (b) (Linearly) emitted electric field by the GaAs TO phonons in the sample gained by a subtraction of the incident from the reflected THz field $E_{\mathrm{TO}}(\tau )=E_{\mathrm{THz}}^{\mathrm{re}}(t=0,\tau )-E_{\mathrm{THz}}^{\mathrm{in}}(t=0,\tau )$. (c) Nonlinearly emitted electric field $E_{\mathrm{NL}}(t=0,\tau )$ (black line) [horizontal dashed line at $t=0$ in Fig. 2]. The area under the individual peaks (diamonds) is proportional to the coherent LO phonon population.