## Abstract

In this paper, periodic peaks in a terahertz absorption spectrum are confirmed to be induced from interference effects. Theoretically, we explained the periodic peaks and calculated the locations of them. Accordingly, a technique was suggested, with which the interference peaks in a terahertz spectrum can be eliminated and therefore a real terahertz absorption spectrum can be obtained. Experimentally, a sample, Methamphetamine, was investigated and its terahertz fingerprint was successfully extracted from its interference destruction spectrum. This technique is useful in getting samples’ terahertz fingerprint spectra, and furthermore provides a fast nondestructive testing method using a large size terahertz beam to identify materials.

© 2010 OSA

## 1. Introduction

The newly developed technique of Terahertz time-domain spectroscopy (THz-TDS) has been demonstrated to be a powerful tool for characterization and identification of chemicals and biological materials which have spectral features within the terahertz region. In most of the work reported so far, THz-TDS were performed on sample in the form of tablet by neglecting the scattering and diffraction [1–3].

However, effects such as scattering, diffraction, and interference induce mutation of the spectral features. It’s essential to investigate the mechanism of the mutation and then to get reliable terahertz spectra for the identification purpose. In a recent study, Y. C. Shen [4] measured terahertz scattering of granular materials for both absorbing and non-absorbing particles in different size and eliminated scattering effect by summing and averaging over a mapped area. Moreover, a discrepancy of absorption spectra of non-uniform medium has recently been reported by F. Theberge [5,6]. They presented a model in order to predict the distortion of spatial coherence when a terahertz pulse passing through a non-uniform medium and indicated that this distortion can result into the generation of artificial absorption peaks in the medium’s absorption spectrum. Unfortunately, in the case that the sample’s thickness or refractive index is randomly distributed, there is no way to get rid off the artificial absorption peaks since there is no analytic solution in their model.

In the studies of materials identification by THz fingerprint spectra we find the similar interference case. When a terahertz pulse illuminating on the edge of a sample, it splits into two parts, with and without illuminating the sample, we called it partial-through measurement, and then the artificial absorption peaks emerged in the measured THz transmitted spectrum. Fortunately, this relatively simple case can be solved analytically on the basis of electromagnetic wave interference theory.

In this work, we report on the theoretical analysis and experimental demonstration of the artificial absorption peaks in the partial-through measurement. An absorptive material and its measured THz spectrum have been investigated and its real absorption peaks have been successfully extracted from the interference destruction spectrum. Correspondingly, a fast nondestructive identification method using a large size terahertz beam to detect concealed materials and identify them is suggested.

## 2. Analysis

Typical THz-TDS is performed in two steps. First, a reference signal ${E}_{ref}(t)$is detected in the absence of a sample. Second, a signal in the presence of the sample,${E}_{sam}(t)$, is detected. ${E}_{ref}(t)$and${E}_{sam}(t)$ are shown as black and blue line in Fig. 1 , respectively. After Fourier transform the transmission function and absorption coefficient are given by

In the study of terahertz pulse imaging [7], which performed by scanning imaged object point-by-point, a discrepancies phenomenon was observed. Spectral features presents anomalous as terahertz pulse illuminate on the edge of the object. In this measurement, the incident terahertz pulse passively split into two parts, with and without illuminating on the sample. In this case we called partial-through measurement. For thick samples the measured THz electric field intensity in time domain exhibits well separated peaks, which basically consists of time windowing of two terahertz pulses caused by with and without illuminating the sample. The temporal waveform is detected and displayed as sum of this two terahertz pulse and shown as red line in Fig. 1. In frequency domain it is easy to express the complex amplitudes ${\tilde{E}}_{o}(\omega )$as

*p*is the proportion of leak THz pulse from the edge of the sample to the entire input pulse, or the reference pulse.

Transmission function of the THz-TDS in this model is given by

Interference destruction spectrum was then calculated as

*d*is the thickness of the sample. In the last expression, ${p}^{2}$is a constant, $T(\omega )$is the transmission coefficient of the sample which we interested in, $F(\omega )$is the interference factor. Obviously, ${\alpha}^{\prime}$is no longer the absorption coefficient of the sample but including three factors. Except the first term which is a constant, the third term will make the calculated absorption spectrum appear periodic peaks or interference peaks. When $\u25b3\varphi (\omega )=(2k+1)\pi $(k is an integer), the periodic interference maximum is observed in the interference destruction spectrum at the frequency ofwhere $n(\omega )$ is the refractive index of the sample. The interference peaks would be observed at regular intervals$\Delta f=c/[(n(\omega )-1)d]$, and the first peak locates at the frequency of$\frac{1}{2}\Delta f$.

## 3. Observation and Extraction Results

We performed an experiment to validate the above analysis by using a polytetrafluoroethylen (Teflon) plate (5cm*5cm) as a sample. The incident THz pulse was a parallel beam in the frequency range of 0.1–2.6 THz, which totally (typical) or partially (partial-through) illuminates the sample. The typical and partial-through measurement results are presented in Fig. 2 . The partial-through spectrum is obtained in the condition of 50% THz pulse portion propagating through the sample of a uniform thickness of 3.00mm.

From Fig. 2 we can see that the real absorption spectrum (the typical measurement) of the Teflon sample is flat and there is no absorption peaks [8], while 11 peaks were observed in the partial-through measurement in the range of 0.1-2.6 THz, the effective frequency range of our THz-TDS system. It indicates that the peaks in the partial-through measurement do not present the spectral features but maybe from the interference or something else. To confirm the interference guess we plotted both the frequency locations of the measured peaks and the theoretically predicted frequencies using Eq. (5) and $\Delta f=c/[(n(\omega )-1)d]=0.244THz$, with a frequency free refractive index of the Teflon plate of 1.41, as shown in Fig. 3 . It can be seen from Fig. 3 that the theoretical and experimental results agree very well. Since in the theoretical analysis we did not take into account the scattering and diffraction at the edge of the Teflon plate, it indicates that the observed peaks are really due to the interference instead of absorption coefficient of Teflon or coming from scattering and diffraction.

As discussed above, the interference induced frequency destruction prevents us to get a real absorption spectrum. However, in practical applications, the real absorption spectra or fingerprints of samples are used to identify materials. In the condition of THz pulse partially transmitted through the sample, interference would induce artifacts on the measured absorption spectrum that makes identification error. Therefore, it is necessary to find a way to remove the interference peaks and extract fingerprints of materials from the destructive spectra.

Here we firstly proposed a method to obtain the absorption spectrum by subtracting signal which without propagating through the sample from the detected signal in time domain. However, the interference peaks cannot be well removed if the partial through THz pulse portion is not correctly determined and then the interference factor not completely subtracted. To make the result better, we presently estimate the portion by the ratio of amplitude maximum of these two beams. Another method we proposed is so-called amplitude vector method as shown in Fig. 4 , which deals with the THz electric field in frequency domain. In partial-through measurement, ${\tilde{E}}_{o}(\omega )$ is the detected terahertz electric field intensity, $p{\tilde{E}}_{ref}(\omega )$and $(1-p){\tilde{E}}_{sam}(\omega )$ presents the electric field intensity that the THz pulse without and with propagating through the sample, respectively. $\u25b3\varphi (\omega )={\varphi}_{o}(\omega )-{\varphi}_{r}(\omega )$ is the phase retardation of ${\tilde{E}}_{o}(\omega )$and$p{\tilde{E}}_{ref}(\omega )$which we can get after Fourier transform of${E}_{o}(t)$ and ${E}_{ref}(t)$. These three electric field intensities follow the amplitude vector relation as shown in Fig. 4. As${\tilde{E}}_{o}(\omega )$and $p{\tilde{E}}_{ref}(\omega )$ can be acquired from the partial-through measurement, we, therefore, obtain the analytic solution of ${\tilde{E}}_{sam}(\omega )$ using cosine law.

Figure 1 shows the temporal waveform for both typical and partial-through measurements of the 1.08 mm thick plate of methamphetamine (MA), respectively. The experimental system is purged with nitrogen gas to eliminate absorption lines of water vapor. It is obvious that five equidistance peaks were observed in partial-through measurement shown in Fig. 5(a) , while the four not equidistance peaks in typical measurement [9,10] can be found in Fig. 5(b). The existence of attenuation maximum which does not exist in the absorption spectrum expose that the periodic attenuation maximum is caused by the interference instead of the material absorption. Figure 5(c) and 5(d) show the absorption spectrum extracted from the Fig. 5(a), the extracted absorption spectrum agreed very well with the real fingerprint in Fig. 5(b). The results indicate that the suggested methods of both in time domain and in frequency domain are effective for extracting the real fingerprint from the destroyed spectrum caused by interference factor.

## 4. Conclusion and discussion

We explained periodicity peaks in THz spectrum with interference theory and calculated the location of the interference peaks. Fingerprint was successfully extracted from interference destruction spectrum. This method could be a complementary to the traditional optical property measurement of material. Using this new method, one can employ a large size parallel THz beam illuminate a package conceal one material, as the THz beam partial-through this material, the absorption spectrum can be obtained. It’s especially useful when both the exact position and size of a material in a package are unknown. In this case one should scan the package to get a partial-through spectrum. The scan times is not big since the beam size is large and is determined by the size of package and THz beam. Additionally, the system providing a large size THz beam needs only 2 parabolic mirrors instead 4 in a traditional THz-TDS system, obviously is easier and cheaper for the future application. In practical materials detection applications, the main challenge here is that if there more than one sample in a package, the situation becomes more complicate to extract the fingerprint of each of them. This technique provides a fast nondestructive testing and identification method to identify materials. It has the potential to become a complementary method in a real-time detection and identification system.

## Acknowledgments

This work was funded by the Science and Technology Program of Beijing Educational Committee under Grant No. KM200910028005, and the Nature Science Foundation of Beijing under Grant No. 4102016. This work was also funded by the National Keystone Basic Research Program (973 Program) under Grant Nos. 2007CB310408 and 2006CB302901.

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