Terahertz (THz) spectroscopy has made great progress in numerous fields owing to its attractive and exclusive attributes^[1–5]. The coherent detection of THz radiation enables the amplitude and phase of temporal signal to be precisely measured in order to conveniently obtain the refractive index and absorption coefficient dependent on frequency. The optical properties of the measured sample are integrated into the THz waveform in the coupling between THz temporal signal and sample, which can be roughly observed by the shape alteration for the sample signal relative to the reference one. This also changes the complexity of the reference waveform, which leads to the introduction of composite multiscale entropy (CMSE)^[6,7], sample entropies at different scales, to measure the THz temporal signal. In the case of similar samples with weak variation of signals complexities where it is hard to detect the disparities using CMSE, the variational mode decomposition (VMD) technique is taken into account to decompose the signal into several mode functions with different frequency components because THz signal can be seen as a synthesis composed of sub-signals with different frequency components^[8,9]. So, the selected mode functions dependent on the intervals of frequency components can be described by CMSE. From our previous work^[9], sample entropy at scale 16 extracted from the selected mode function showed strong pertinence to the refractive index or absorption coefficient at different frequencies as expected, which reveals that the characteristic of sample entropy describing THz mode functions is relevant to optical properties. Nevertheless, the in-depth association needs to be investigated because more valuable information could be captured by a combination of refractive index with absorption coefficients, and the purely numerical information from the refractive index or absorption coefficient sometimes may not fully exhibit the further relationship with sample entropy. Besides that, it is sensible to describe the complexity of signal at multiple scales, thereby considering the sample entropies integration of several scales.