Acoustic phonon generation and detection in $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum wells with picosecond laser pulses

Picosecond acoustic-phonon pulse generation and detection is investigated in a sample containing three $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum wells of different thickness with an interferometric optical pump and probe technique. The pump photon energy is tuned through the $hh1\text{−}e1$ transitions of each well and the probe photon energy is chosen to allow the detection of the phonon pulses at the sample surface. The phonon pulse shapes are explained with a model that relates the carrier wave functions to the acoustic strain, and the acoustic strain to the detected optical reflectance and phase changes.

Figure 1

(Color online) (a) Dimensions of the $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum well structure. (b) Experimental setup. AOM=acousto-optic-modulator, QWP=quarter wave plate, HWP=half wave plate, PBS=polarizing beam splitter, NPBS=nonpolarizing beam splitter, P=polarizer, and $\mathrm{BBO}=\beta \text{−}{\mathrm{BaB}}_2{\mathrm{O}}_4$ crystal. The region enclosed with a dotted line forms an interferometer.

Figure 2

(Color online) Calculated relation between the jitter $\Delta t$ and the output voltage $V_{\mathrm{out}}$ of the lock-in amplifier. The inset shows the cross correlation measurement setup that is used for the jitter correction system. $\mathrm{F}.\mathrm{G}.=\text{function generator}$. $\mathrm{BBO}=\beta \text{−}{\mathrm{BaB}}_2{\mathrm{O}}_4$ crystal.

Figure 3

(Color online) (a) Real and (b) imaginary parts of the complex relative reflectance change $\delta r∕r$ at pump photon energies from 1.44 to 1.68 eV in the order from top to bottom. Curves are shifted vertically for clarity.

Figure 4

(Color online) Magnified view of the (a) real and (b) imaginary parts of the complex relative reflectance change $\delta r∕r$ at a pump photon energy of 1.47, 1.50, and 1.64 eV. The experimental (expt.) curves and calculated (calc.) curves that are fitted to the data are shown together. The bottom 4 curves show the decomposed photoelastic contributions to the calculated curves for 1.64 eV; curves QW1, QW2, and QW3 correspond to acoustic phonon pulses generated in the respective quantum wells; the contribution from the surface displacement is shown separately (disp.). The horizontal arrows show the temporal regions associated with the contributions to the reflectance from each well. The vertical arrows in the $\delta \varphi$ plot denote the change in $\delta \varphi$ caused by the surface displacement due to the acoustic phonon pulses generated in the quantum wells for 1.64 eV.

Figure 5

(Color online) The value of ${\mid \varphi \mid }^2$ for the envelope function of (a) the $e1$ electronic state and (b) the $hh1$ heavy hole state for a $\mathrm{GaAs}∕{\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ quantum well of width 3 nm. The excitation of these states with an ultrashort light pulse generates the strain pulse (c) whose frequency spectrum is shown in (d). The dotted lines show the well width.

Figure 6

(Color online) Calculated and experimental curves for the real $\left(\rho \right)$ and imaginary $\left(\delta \varphi \right)$ parts of the complex relative reflectance change $\delta r∕r$ at pump photon energies 1.47 eV. The scales in each set of four curves are identical.

Figure 7

(Color online) Calculated and experimental curves for the real $\left(\rho \right)$ and imaginary $\left(\delta \varphi \right)$ parts of the complex relative reflectance change $\delta r∕r$ at pump photon energies 1.50 eV. The scales in each set of four curves are identical.

Figure 8

(Color online) Calculated and experimental curves for the real $\left(\rho \right)$ and imaginary $\left(\delta \varphi \right)$ parts of the complex relative reflectance change $\delta r∕r$ at pump photon energies 1.64 eV. The scales in each set of four curves are identical.

Figure 9

(Color online) Effective extinction coefficients $K$ for each quantum well deduced from the fitting. The order of the onset from lower to higher energy is QW2, QW1, and QW3 as expected. The lines are guides to the eye.

Figure 10

(Color online) Photoelastic constants for the cap GaAs and adjacent ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{As}$ layers obtained from the fitting for various pump photon energies. They show no apparent pump-photon energy dependence. The lines are guides to the eye.

Figure 11

(Color online) Surface displacement caused by the phonon pulses generated in each quantum well obtained from the fitting for various pump photon energies. The order of the onset from lower to higher energy is QW2, QW1, and QW3 as expected. The lines are guides to the eye.

Figure 12

(Color online) Temporal evolution of the surface displacement (referred to the left axis) and the surface velocity (right axis) both calculated for the pump photon energy of 1.64 eV for the thinnest well QW3. The features around 127 ps corresponds to the arrival at the surface of the acoustic phonon pulse generated in QW3. The inset shows the amplitude of the Fourier transform of the surface velocity.