## 4 Model Simulations  
To have better understanding of the obtained results, we performed simulations of the colloidal crystal dynamics induced by an external IR pulse excitation. In our model colloidal crystals consist of isotropic homogeneous spheres. The characteristic frequencies of vibration of a colloidal particle were determined using the Lamb theory describing vibrations of an isotropic elastic sphere [29]. Theoretically, two families of Lamb modes, namely spheroidal and torsional ones, can be derived from the equations of motion. The spheroidal modes cause the change of the sphere volume, and the torsional modes leave the sphere volume unperturbed. During the IR pulse propagation through a sphere, the changes of the sphere volume are expected and, therefore, we used spheroidal modes in our simulations. We determined the frequencies of the first spheroidal mode for all three measured samples using reference [30]. Sphere diameter, longitudinal \(c_{L}\) and transverse \(c_{T}\) sound velocities of PS and silica were obtained from reference [31]. These parameters, as well as the frequencies of the first spheroidal mode for the colloidal crystals, are summarized in Table 1.  
Figure 8: Fourier spectra from the distance between the two opposite Bragg peaks \(\Delta q(\tau)/q\) (**a–c**) and Bragg peaks widths in radial \(\Delta w_{q}(\tau)/w_{q}\) (**d–f**) and azimuthal \(\Delta w_{\phi}(\tau)/w_{\phi}\) (**g–i**) directions for three selected samples. Fourier spectra calculated from the results of diffraction pattern analysis shown in Figure 7. Average value of all Fourier components is indicated by the red line. The dashed red line corresponds to the \(3\sigma\) level above the average value, where \(\sigma\) is the standard deviation and is determined from the distribution of Fourier components. The values of \(\Delta q(\tau)/q\) were obtained from the experimental data with the smallest error in comparison to other Bragg peak parameters for all investigated samples (see Figure 7a-c). Therefore, the parameter \(\Delta q(\tau)/q\) was considered for our simulations. Assuming an ideal close-packed crystal with the interparticle distances equal to the particles diameter, the unperturbed momentum transfer modulus of the 11.0 Bragg reflection can be described as \(q_{0}=2\pi/d_{11.0}=4\pi/d_{0}\), where \(d_{0}\) is the unperturbed particle diameter. We simulated vibrations of the colloidal spheres with the diameter \(d_{0}\) as a periodic sinusoidal signal:  
\[d(\tau)=d_{0}(1-S\cdot\sin(\omega\tau)) \tag{3}\]  
where \(S\) is the relative amplitude and \(\omega\) is the characteristic frequency of the vibration. The dynamics of the experimentally-observed 11.0 diffraction peak can be described as:  
\[q(\tau)=\frac{4\pi}{d(\tau)}\approx\frac{4\pi}{d_{0}}(1+S\cdot sin(\omega\tau)) \tag{4}\]  
where we used the Taylor series expansion of the momentum transfer vector \(q(\tau)\) due to the small values of the amplitude \(S<<1\). As a result, measured changes in the Bragg peak positions and \(\Delta q(\tau)/q\) can be simulated as a periodic sinusoidal signal. We should also take into account systematic errors of the measurement as an additional noise. Finally, simulations of the parameter \(\Delta q(\tau)/q\) in our model were described using the following expression:  
\[\frac{\Delta q(\tau)}{q_{0}}=\frac{q(\tau)-q_{0}}{q_{0}}=S\cdot sin(\omega\tau )+N\cdot\eta_{noise}(\tau) \tag{5}\]  
where \(N\) is the amplitude of a noise and \(\eta_{\mathrm{noise}}(\tau)\) is a random noise function with normal distribution and standard deviation value equal to one. The signal-to-noise ratio in this case is assumed to be equal to the ratio of the amplitudes \(S/N\). Next, we defined criterion when the periodic signal is detected by the algorithm in our simulations. Due to the random behavior of the noise function \(\eta_{\mathrm{noise}}(\tau)\), each realization of the signal \(\Delta q(\tau)/q_{0}\) (see Equation (5)) for a constant \(S/N\) is different.