## 2 Experimental Methodology
### Recording of Wave Evolution in Solid Waveguides
#### 2.2.2 Digital Holography  
In experiments with the digital recording of interference patterns, the initial shock wave was generated by a pulsed Nd:YAG laser Spitilight 600 (Innolas, Germany) with pulse energy up to 0.5 J at 532 nm and a pulse duration of 7 ns. For hologram recording, we used a CW laser module emitting at 532 nm and possessing high temporal coherence, which allowed for working with noticeably different pathlengths of the object and reference arms of the interferometer. To ensure sufficiently fast recording of interference patterns and to prevent blurring of interference fringes caused by fast propagation of elastic waves, a matrix photodetector with adjustable gain and exposure down to 20 ns, a Nanogate 24 (Nanoscan, Russia), with a resolution of 1392 \(\times\) 1040 pixels, was utilized. An accounting of the wave velocity and magnification of the optical system yielded the exposure within the range of 70-120 ns in our experiments that provided the required quality of digital holograms. To register elastic waves in the course of propagation in the waveguide for a long distance, a shutter of the digital camera and the laser pulse causing explosive evaporation of the metallic foil were synchronized using an AM300 Dual Arbitrary Generator (Rohde & Schwarz), allowing for fine adjustment of the delay time. Taking into account the pixel size of the utilized camera of about 30 \(\upmu\)m and horizontal angle between the object and reference waves of \(\approx\)0.35\({}^{\circ}\), the typical thickness of the interference fringes comprised 3-5 pixels. Signal amplification and exposure time were adjusted to provide detection of relatively fast strain wave (typical speed of about 1800-2000 m/s) and recording of high-contrast interference fringes. Note that, due to the distortion introduced to the probe wave by the waveguide itself, thickness of interference fringes was different in different areas of a digital hologram. Reconstruction of digital holograms was performed by separation of the first diffraction order in the Fourier domain. In further data processing Goldstein unwrapping algorithm [16] was used for elimination of phase image singularities. The optical layout of the experimental setup with digital recording is shown in Figure 1b. Several telescopic systems were used in the object arm of the Mach-Zehnder interferometer, providing a field of view in the object plane of about 60 mm in diameter. The telescopic system installed in the object beam after the object is used to image the enlarged field of view on the sample onto the camera matrix, so no wavefront propagation was needed to analyze the object in this schematic. However, being sufficient for reliable detection of already formed single solitons, such field of view was too small for the analysis of wave trains that were more than 100 mm long. In these experiments, a larger synthetic field of view was formed by stitching several profiles of elastic waves recorded at different delay times. To ensure robust stitching, recording of wave patterns was performed at slightly overlapped fields of view, namely at 0-60 mm, 50-110 mm and 100-160 mm from the waveguide input. An example of such numerical processing of several profiles of elastic waves is shown in Figure 2.  
In contrast with classical holographic interferometry, utilizing analogous data processing, digital holography allows for automatic processing of several digital holograms, corresponding to different pump-probe delays. In particular, stitching of several phase images has been proposed and implemented in this study. Since the strain wave propagation velocity was not, a priori, known exactly, for accurate stitching of two phase images they were iteratively overlapped onto each other and the best shift values were estimated by the minimization of misalignment errors. In contrast with typical image-stitching problem [45; 46], the holographic data processing is complicated by the reconstructed phase relativity.