## 5 Conclusions  
In this work, we have experimentally demonstrated the ability to identify an 8-bit coding capacity (coding density \(\sim\)40 bits/cm\({}^{2}\)) THID tag only made of dielectric materials and by using a commercial THz-TDS spectrometer. The tag signature is read with a reliability rate bigger than 99 percent in only a few tens of milliseconds. Such a performance has been obtained by comparing the binary words encoded in the frequency domain by the spectral position of two defect modes appearing in the first photonic band gap of a few-mm thick tag, constituted of 19 layers of LDPE and of LDPE-TiO\({}_{2}\) mixture (40/60 volume ratio), alternately stacked. To ensure such success rate, we define a decision threshold (\(\sim\)11 dB) as an absolute criterion to reliably, find the frequency position of the peaks, and therefore, the binary code of the tag. Consequently, it implies that a THz reading system must exhibit a sufficiently large SNR to perform both video-rate and reliable reading of a tag (\(>\)18 dB). Let noticed that the SNR of course depends on the averaging rate but also on the intrinsic noise sources in THz-TDS systems [29]. The performance limits, in terms of coding capacity, have been also explored both versus the material permittivity (dielectric losses) and the angular acceptance. On the other hand, the recent developments of ultrafast high-resolution ASOPS-based THz-TDS systems [30] or in the longer term, THz-CW systems [22], associated with denoising extraction techniques [31; 32], would provide a powerful THz reader, perfectly suited for the video-rate identification of tags exhibiting large storage capacities. Indeed, a better performance would be obtained by improving the frequency resolution of the reader, leading to a larger number of channels, and by increasing the number of peaks in the PBG from the tag side [33]. Based on these results, we showed that such a multilayer tag family is able, with the realistic improvements suggested previously on both the tag and the reader, to exhibit coding capacity up to 60 bits, corresponding to a coding density of about 300 bits/cm\({}^{2}\), i.e., more than 6 times bigger than the one reported by [PERSON] et al. [14]. Moreover, the structures proposed in [14; 18] are made of a 2D arrangement of several \"unitary cells\", whose size of each of them is very close to that of our entire tag. The surface of these devices  
Figure 9: Maximum incident angle \(\theta\) of the THz reading beam for the previous considered THID tag versus the coding capacity \(\rho\). Insert: calculations (continuous lines) and measurements (dots) of the frequency shift of the PBG and defect peaks versus the incident angle of measurement. then increases with the coding capacity, while it remains constant in our case. Indeed, the surface of our tag is only limited by the THz beam diameter, itself limited by the diffraction phenomenon (in case of far field reading); it will then be smaller the higher the frequency. Finally, the optimization of the technique used to encode the binary information, for example by taking into account either the Q-factor and/or the magnitude of each defect peaks, would also considerably increase the performances of the whole system. Conceptualization, methodology, F.B., M.B., F.G., E.P., N.B., R.S., D.H.; software, F.B. ; measurements and data analysis, F.B., M.B., F.G., E.K. ; writing--original draft preparation, F.B. ; writing--review and editing, M.B., F.G.; supervision, M.B., F.G.; project administration, F.G.; funding acquisition, M.B., E.P., F.G. All authors have read and agreed to the published version of the manuscript. This research was funded by the French Agence Nationale de la Recherche, grant number ANR-18-CE39-0002 and the Region AURA, grant number. C2019-086. Not applicable. The authors want to thank [PERSON] and [PERSON] from Clairet Scientific Ltd. (Northampton, UK) for having graciously put at our disposal the spectrometer TAS7500 SP, without which it would not have been possible to experimentally validate our study.