## 3 Results  
Figure 3a shows the Bragg diffraction peaks arising from the film and the substrate layers of the sample. The angular separation between the two peaks implies the lattice mismatch less than (0.1%) between the layers. The oscillatory intensity signatures between the Bragg peaks is due to interference between X-rays diffracted from the side bands of the film and substrate peaks. We are able to estimate the film thickness of 500 nm from the oscillation period that is found consistent with the sample design. Figure 3b,c show symmetric (0 0 4) Bragg diffraction curves from the heterostructure sample at selected time-points relative to the optical excitation at an absorbed fluence of 3 mJ/cm\({}^{2}\). The vertical axis is the relative time-delay between the X-ray and the laser pulses and the horizontal axis represents  
Figure 2: Experimental configuration. Monochromatic synchrotron X-ray pulses (green) are focused horizontally by a dynamically-bent mirror, while the vertical dimension is slit to preserve angular resolution. The synchronized amplified laser pulse is focused and then frequency doubled in a BBO crystal to 400 nm before overlapping the X-ray beam on the sample. A gated Avalanche Photodiode in proportional detection mode and digital oscilloscope [15] are used to record high dynamic-range rocking curves over several hundred X-ray pulses at the laser’s 1 kHz repetition rate. Rocking curves are repeated as the laser-to-X-ray delay is scanned by introducing electronic delays via a phase shifter in the phase locked loop that maintains synchronization. The centroid of the peak is used to determine average strain and after several ns following electron recombination, the average temperature of the layer. the X-ray incidence angle. Under the kinematical diffraction approximation, the resulting average lattice displacements can be extracted by converting the angular diffraction shifts, \(\Delta\theta_{B}\), to changes in the lattice parameter, \(\Delta d\), using Bragg's law, \(\lambda=2(d\pm\Delta d(\Delta t))\sin(\theta_{B}\pm\Delta\theta_{B}(\Delta t))\), where \(\lambda\) is the X-ray wavelength and \(d(\Delta t)\) and \(\theta_{B}(\Delta t)\) are the temporally evolving crystal lattice spacing and Bragg diffraction angle, respectively. Such transient deviation in the diffraction condition represent the aggregate lattice conditions over the finite X-ray extinction depth of 1.5 \(\upmu\)m, and thus provides averaged changes in the lattice spacing for both the film and the substrate layers. Here, we discuss the information that can be directly inferred from the measured transient strains in both layers. Initially, the AlGaAs layer shows marginal compression followed by rapid expansion after the photoexcitation, of which behavior is expected from a bipolar wave propagating away from the surface. The rise of the initial tensile response reaching its maximum within 100 ps corresponds to the transit time of the longitudinal acoustic wave propagating out of the film thickness of 500 nm. In meantime, the GaAs layer gets compressed and then expanded reaching the peak lattice displacement at about \(\Delta t=\) 500 ps. The disparities between the lattice behaviors between the two layers within 1-ns time-scale can be explained in terms of an elastic response consisting of two counter-propagating compression waves that are generated by instantaneous expansion of the AlGaAs surface due to electron-hole plasma [17]. Since the timescale of the charge carrier diffusion across the film layer is comparable to that of the acoustic-transit time, it is reasonable to assume that the tensile effect in the film layer is caused by sum of electronic strain driven by deformation potential, thermalized lattice (heat) and sound wave propagation. Within the acoustic and electronic timescales (\(<\)5 ns) in the substrate, we only observe the impulsive lattice response generated by the sound wave propagation, or transient compression followed by expansion.