## 2 Description of the THID Tag and of the Measurement Setup  
The simplest form of the proposed THID tags is an 1D periodic stack of thin dielectric slabs, made of two different and transparent enough materials exhibiting high (\(H\)) and low (\(L\)) refractive index, respectively. On such a multilayer structure, an incident electromagnetic wave is either transmitted or reflected according to its frequency. The non-transmitted bandwidths are known as Photonic Band Gaps (PBGs) and appear periodically in the frequency domain. The spectral positions of these PBGs depend on the optical thicknesses of the quarter-wave equivalent layers, whereas their depth, also called rejection rate, depends on both the refractive index contrast between the successive layers \(H\) and \(L\), and their number. When the optical thickness (refractive index multiplied by thickness) of at least one layer of the structure is modified (creation of a structural defect), the period of the stack is broken, altering in turn the transmitted spectral response of the structure: peaks appear in the PBGs. Both the number and frequency positions of these peaks are directly related to the structural defect characteristics [25]. Thereby, a given structural defect configuration leads to a unique THz transmitted (respectively reflected) spectral response which can be used as a signature to reliably identify the corresponding tag. In order to obtain a high index contrast and, consequently, deep PBGs, we used pure Low-Density Polyethylene (LDPE) as \(L\) layer (\(n_{L}=1.51\)) and a mixture of TiO\({}_{2}\) (60%) --LDPE (40%), as \(H\) one (\(n_{H}=2.29\)). The thicknesses of these layers (\(e_{L}=240\) um for \(L\) and \(e_{H}=85\) um for \(H\) as shown in Figure 1) were chosen to centre the first PBG around 310 GHz, where the THz reading systems present a high dynamic range (see Figure 2-inset). The number of layers (19) has been practically optimized (i) to maximize the signal rejection in the PBG, (ii) to limit the overall losses due to the absorption, and (iii) to keep the structure thickness in the millimetre range (see Figure 1a). Note that the whole thickness of the above described device remains reasonable (few millimetres) when working in the THz frequency domain, compared to the same type of device in _RF_ (several tens of centimetres). The setup used to characterize the tag is a commercial THz Time Domain Spectrometer (THz-TDS) system from ADVANTEST(r) (model TAS7500 SP), which uses photoconductive antennas as the THz emitter and receiver. Contrarily to conventional THz-TDS systems based on mechanical delay lines [26], the pump/probe delay of the TAS/500 SP is achieved using an electrically controlled optical sampling (ECOPS) technique [27] that permits very high-speed measurements. This ECOPS-based system is then able to record a 132-ps long waveform in only 8 ms, with a time resolution of 2 fs. The spectral bandwidth spread typically from 0.1 to 4 THz (see Figure 2-inset) with a spectral resolution of about 7.6 GHz, whereas the signal to noise ratio and the dynamics depends, of course, directly on the number of waveforms averaged (from 1 to 4096). The signature of the tag i.e., its complex transmission coefficient \(\widetilde{T}(\omega)\) of the tag is obtained by dividing the Fast Fourier Transform (FFT) of two THz waveforms (see Figure 2), the first one measured with the tag in between the antennas \(S(t)\), and the second one without \(R(t)\). \(\widetilde{T}(\omega)\) can be then written:  
\[\widetilde{T}(\omega)=\frac{\widetilde{S}(\omega)}{\widetilde{R}(\omega)} \tag{1}\]  
Figure 1: (**a**) Picture of the realized multilayer tag; (**b**) microscope images of stacked layers made of pure LDPE and TiO\({}_{2}\) + LDPE mixture. © 2021 IEEE: this figure is plotted from [24]. Figure 2: THz pulse delivered by the THz-TDS setup TAS 7500 SP System from ADVANTEST (dashed line) and its associated spectrum (inset). Solid lines correspond to the THz pulse transmit-ted through the developed multilayer THID tag and its associated spectrum (inset).