Chinese Optics Letters, Volume. 20, Issue 6, 063701(2022)

Revisiting the relationship between composite multiscale entropy and THz optical parameters with exterior product

Haishun Liu1,*, Zhenwei Zhang1,**, Meiyan Liang2, and Cunlin Zhang1
Author Affiliations
  • 1Key Laboratory of Terahertz Optoelectronics, Ministry of Education, Department of Physics, Capital Normal University, Beijing 100048, China
  • 2Department of Electronics and Information Engineering, Shanxi University, Taiyuan 030006, China
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    With the framework of exterior product, we investigate the relationship between composite multiscale entropy (CMSE) and refractive index and absorption coefficient by reanalyzing six concentrations of bovine serum albumin aqueous solutions from the published work. Two bivectors are constructed by CMSE and its square by the refractive index and absorption coefficient under vectorization. The desirable linear behaviors can be captured, not only between the defined two bivectors in normalized magnitudes, but also between the normalized magnitude of bivectors pertinent to CMSE and the magnitude of a single vector on the refractive index or absorption coefficient, with the processing of optimum selection. Besides that, the relationship between the coefficients of two bivectors is also considered. The results reveal that plenty of sound linear behaviors can be found and also suggest the scale of 15, 16 and frequency of 0.2, 0.21 THz are prominent for those linear behaviors. This work provides a new insight into the correlation between terahertz (THz) time and frequency domain information.


    1. Introduction

    Terahertz (THz) spectroscopy has made great progress in numerous fields owing to its attractive and exclusive attributes[15]. 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.


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    Haishun Liu, Zhenwei Zhang, Meiyan Liang, Cunlin Zhang. Revisiting the relationship between composite multiscale entropy and THz optical parameters with exterior product[J]. Chinese Optics Letters, 2022, 20(6): 063701

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    Paper Information

    Category: Infrared and Terahertz Photonics

    Received: Jan. 25, 2022

    Accepted: Mar. 18, 2022

    Posted: Mar. 21, 2022

    Published Online: May. 6, 2022

    The Author Email: Haishun Liu (, Zhenwei Zhang (



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