GHz control of THz QCL band structure and gain by standing acoustic strain

Abstract

Active frequency comb generation and waveform control are central challenges in the terahertz (THz) domain. In THz quantum cascade lasers (QCLs), these functions have typically been achieved through active bias modulation, which alters the operating point of the device and imposes severe limitations on its flexibility. To address these challenges, we propose an approach based on the direct modulation of the QCL bandstructure using GHz-frequency standing bulk acoustic waves (BAWs), promising direct and localized control of the optical gain and chromatic dispersion. To this end, we fabricated a bulk acoustic transducer on top of a THz QCL in order to excite GHz standing BAWs within its active region. We demonstrate that radio-frequency driving of the transducer leads to the tunable generation of standing BAWs in 5-12 GHz frequency range with wavelengths commensurate to the QCL period length. The effect of the BAW on the QCL bandstructure is revealed by measuring photoluminescence (PL) of the active region, where the BAW strain leads to a considerable modulation of the PL energy up to a few meV around its non-modulated value. We also develop a model and perform bandstructure simulations to predict the effect of the BAW on the QCL subband structure and gain. These results mark the first demonstration of dynamic bandstructure modulation in a THz QCL using GHz acoustic strain, introducing a fundamentally new paradigm that establishes a powerful synergy between QCLs and BAWs towards coherent control and frequency comb engineering in the THz domain.

Figures (10)

• Figure 1: Structure of the investigated device.a Sketch of a quantum cascade laser (QCL) active region modulated by a standing bulk acoustic wave (BAW) generated using a radio-frequency (RF) driven bulk acoustic resonator (BAR). The active region is excited using a non-resonant laser through a small aperture in the BAR and the photoluminescence (PL) is collected and analyzed. b Conduction band edge profile of the QCL layer structure over three QCL periods ($w_\mathrm{QCL}$), including interface grading. The color-shaded regions identify the longitudinal-optical phonon transition (green), injector well (purple), lasing well (red) and electron transfer miniband (blue). The strain of a standing BAW with wavelength $\lambda_\mathrm{BAW}$ is indicated with the green curve.
• Figure 2: BAR response on a QCL.a Schematic side-view of a BAR on a QCL (not-to-scale). The BAR consists of a top (TC) and a bottom (BC) metal contacts and a thin film of piezoelectric ZnO. The active region of the BAR is defined by the overlap between TC and BC. The vertical red arrows indicate two possible propagation paths for the acoustic wave: (i) through the whole structure, and (ii) localized in the QCL. b Measured time-domain $s_{11}^{\text{TD}}$ RF reflection coefficient of a BAR on a QCL. The red and blue rectangles depict time-gate regions. c Time-gated $s_{11}^{\text{TG}}$ curves of the first BAW (red line) and first three (dark blue line) echoes in b indicated by the red and blue rectangular areas, respectively. The inset shows a close-up of low-periodicity oscillations. d A zoom of the high-periodicity oscillations in $s_{11}^{\text{TG}}$ in c.
• Figure 3: BAW modulation of a QCL active region.a Schematic top-view of the QCL waveguide with a BAR with an aperture for PL measurements. b A camera image of the actual QCL-BAR device. The RF excitation is provided by the probes (dark shape). The bright spot on the aperture is the focused laser beam. The curving of the lines of the BAR and the waveguide is an artifact. c PL spectrum of the QCL active region with RF off. d Central section, PL spectrum as a function of RF frequency ($F_{\text{RF}}$) applied to the BAR for a fixed RF power of $P_{\text{RF}} = 29$ dBm ($0.89 \sqrt{\text{W}}$). The right inset shows two spectra for the out-of-phase condition (black curve) and in-phase one for $F_{\text{RF}} = 7.91$ GHz (red curve) resonance cases. The upper inset compares the PL intensity profile around 1513 meV (red curve) and the time-gated s-parameter (green curve). e Comparison of the intensity profile at 1513 meV extracted from d (red curve) with the time-gated s-parameter (green curve) over the 6.5--10.5 GHz range from Fig. \ref{['Fig2']}c. The black curves superimposed on the PL and $s_{11}$ show smoothed-by-averaging PL intensity profile and first echo $s_{11}$, respectively. f Normalized PL spectrum as a function of the acoustic amplitude ($A_{\text{M}} \propto \sqrt{P_{\text{RF}}}$) applied to the BAR for $F_\text{RF} = 7.91$ GHz.
• Figure 4: Theory: QCL gain under the BAW modulation.a Simulated potential profile and subband structure (moduli squared of the envelope functions) for a 4.75 THz QCL active region at a field strength of -4.6 kV/cm and without any BAW modulation. The lasing levels are in blue, the injection level in green, and the LO-phonon transition levels are in violet. The levels of the miniband are in dashed red. b Spatial profile assumed for the BAW potential ($V_\text{BAW}$) with the amplitude $M_{0} = 10$ meV. The spatial phase ($\phi = \pi$) has been set to show a maximum at the extractor barrier, which leads to a strong energy mismatch between the injector level and the upper laser level. c The same simulated subband structure as in (a), with a applied BAW potential in (b). d Gain maps at three BAW amplitudes and $\phi$ = 0. One can notice the switch from gain to losses for all field strengths at higher BAW modulations. e Exemplary gain profiles for -4.6 kV/cm bias for BAW amplitudes from 0 meV to 10 meV and $\phi$ = $0.50 \pi$. f Exemplary gain profiles for -4.6 kV/cm bias for various BAW phases and a modulation amplitude $M_\mathrm{0}$ = 5 meV.
• Figure 5: QCL PL spectrum. Comparison of the PL of the GaAs substrate (blue curve) and the QCL region excited from the top (green curve). Note that the blue curve was multiplied by a factor of ten.