Optimized multilayer structure for sensitive THz characterization of thin-film glucose solutions

: Terahertz time-domain spectroscopy (THz-TDS) has shown promise in biomedical sample characterization and high characterization sensitivity is in demand due to the thin-film (TF) feature of the sample. This paper proposes an optimized multilayer structure for sensitive characterization of TF aqueous solutions in reflection THz-TDS. Theoretical simulations are conducted for structural optimization and the 75 µm window-sample-mirror structure displays the best sensitivity compared to other sandwich structures and traditional THz measurement geometries. 0-20% TF glucose solutions are then measured; and a spectral peak introduced by the proposed structure is observed to result in the high sensitivity. Our work provides a new way of customizing multilayer structure for THz thin-film characterization.


Introduction
Terahertz time-domain spectroscopy (THz-TDS) is a cutting-edge characterization technique that has many potential areas of application [1]. Due to its high water-sensitivity and non-ionizing photon energies, THz-TDS has been widely used in biomedical research [2]. Biomedical samples, including biological solutions and paraffin-embedded tissues, are often small in volume or thickness leading to high requirements on the characterization sensitivity. This is further compounded by the long THz wavelengths [3 mm -300 µm], when compared to visible light, because what is an optically thick sample is likely to be considered a thin-film (TF) sample for THz frequencies. In TF samples the sample thickness is comparable or smaller than the wavelength which results in very short interaction length between the sample and electromagnetic wave. For time-domain pulsed measurements there is an overlap between pulses during sample measurement resulting in reduced characterization sensitivity. This problem can be alleviated by either reducing system noise or improving the signal contrast induced by the TF sample [3].
Transmission THz-TDS is normally used to measure solid TF samples, however conductive samples can be difficult to characterize accurately because of the significant absorption of THz signal amplitude and the negligible phase shift [4,5]. Attenuated total reflection (ATR) spectroscopy is an efficient way to measure liquid samples, but it requires the sample thickness to be larger than the THz penetration depth which can be hundreds of microns [6,7]. Metamaterial sensing can be used to trace little concentration changes in liquid TF samples, however the fabrication process is often complex and uneconomical [8,9]. Some researchers have been trying to utilize microfluidic techniques for TF liquid measurements [10][11][12][13], where the liquid flows through a micro-sized channel whilst being measured by THz waves; and others like Soltani et al. have been researching on manufacturing small-volume liquid sensor based on electromagnetic resonance [14]. Finally, Sun et al. proposed a multilayer structure to enhance the THz characterization sensitivity of aqueous solutions and also paraffin-embedded tissues [15].
Glucose is an essential monosaccharide in the human body and using THz-TDS to study aqueous glucose solutions has aroused researchers' interest [16][17][18]. Furthermore, with the increasing number of diabetics, methods for blood glucose monitoring have been developed, including vibrational spectroscopic techniques like Raman spectroscopy, mid-infrared and nearinfrared spectroscopy [19,20]. In recent years, THz-TDS has been demonstrated to be a powerful tool in measuring diabetic blood plasma ex vivo, and correlations have been seen between the optical properties and blood glucose concentration [21][22][23]. The aforementioned research has been conducted in bulk reflection geometry or transmission geometry; the former geometry requires large amount of liquid sample and the latter geometry can hardly detect any subtle concentration changes in TF solutions. To measure blood plasma more sensitively without strong THz absorption from water, Lykina et al. pretreated the human blood plasma samples by lyophilization and pressing the powder into pellets before measuring with transmission THz-TDS, however the pretreatment process can be time-consuming and solid-state plasma pellets may have different features compared with real liquid plasma [24].
To overcome the problems outlined above, this paper proposes an optimized multilayer structure to improve the sensitivity of THz characterization of TF glucose solutions with a reflection measurement geometry. In the multilayer structure, the TF liquid sample is sandwiched between a top substrate and an imaging window with a fixed slot thickness. Theoretical simulations are carried out for structural optimization, and we find the most sensitive multilayer structure customized for our samples. TF glucose solutions with different concentrations are then measured, and we show that the signal contrast between different glucose concentrations is enhanced with the proposed structure compared to an ordinary transmission geometry. Our work provides a new method for characterizing TF samples, and results presented here can be used as a reference for future research on THz sensing of blood glucose.

Extracting the dielectric properties of thin-film samples
When a TF sample is measured in reflection THz-TDS, the sample is placed on an imaging window, and an additional top substrate could be put on top of the sample and thus form a sandwich structure. In this case, unlike the reflection geometry for bulk sample measurements, the multiple internal reflections inside the TF sample must be considered. As illustrated in Fig. 1, when the THz light is directed onto a TF (Medium 2) there are reflections from both interfaces between the sample and the substrates, therefore the measured reflected and transmitted responses from the structure contain all the reflections from within the TF layer (Fabry-Perot reflections) [25,26].
Thus, the reflection coefficient of such a tri-layer TF geometry is acquired through the summation of the internal reflections. The theoretical sample-reference ratio of geometries commonly used in THz characterization of TF liquid samples are given [27][28][29]: where M trans is the ratio of the TF liquid measured in transmission geometry, and the sample is sandwiched between two substrates. T sam and T ref are the transmitted signals from the sample and reference, respectively, where the reference is taken with air as "Medium 2" in the middle layer. d sam and d air are the thicknesses of the middle layer for sample and reference. The written form of t 1−2−3 and r 1−2−3 represent the transmission and reflection coefficient of a tri-layer TF geometry formed by "Medium 1", "Medium 2" and "Medium 3" sequentially; t 1−2 and r 1−2 represent the transmission and reflection coefficients from "Medium 1" to "Medium 2".
is the phase propagation and amplitude attenuation in "Medium 2" for a distance of d 2 , andñ 2 = n 2 − ik 2 is the complex refractive index. The subscripts "sub1", "sub2", "sam" and "air" stand for substrate 1, substrate 2, sample and air respectively. Similarly, M TF is the ratio of the TF liquid measured in a tri-layer reflection geometry, where the sample is sandwiched by an imaging window (subscript "win") on the bottom and a top substrate (subscript "top"). R sam and R ref represent the sample and reference signal, and reference would be the reflected signal from this tri-layer system with air as "Medium 2". θ sam and θ air are the refractive angles in the middle layer of the sample and air respectively. Finally, M br is the ratio of bulk sample measured in reflection geometry, where sample would be placed on an imaging window; the reference signal is taken using the bare window.

THz characterization sensitivity
In THz material characterization, the optical properties of a sample can be extracted by fitting the experimentally measured sample-reference ratio to the theoretically calculated ratio M (Eqs. (1-3)). When measuring a group of samples with similar optical properties, the values of M are often close for every sample, leading to systematic errors in the classification of those samples. Therefore, measurement geometries that can produce larger differences between the sample-reference ratios have higher sensitivities in measuring such samples. Thus the characterization sensitivity of a geometry can be defined by the relative change rate (RC) of M where M 0% is the base value by definition (i.e., when measuring aqueous solution samples with different concentrations, it can be the theoretical ratio of pure water).

Optimization of the multilayer structure
Sun et al. proposed a prism-sample-quartz tri-layer sandwich structure and utilized it to characterize aqueous ethanol solutions [15]. We further investigate into this idea by considering the top substrate refractive index and the slot thickness of the sandwich structure as two variables and optimize them to find out the most sensitive structure, in other words it has the largest relative change in M for the samples to be measured. Here, the samples are aqueous glucose solutions (Glu-Sols) with different mass fractions. Simulations are conducted in MATLAB by calculating Eq. (1), and the theoretical complex refractive indices of the mixtures are estimated by Landau-Liftshitz-Looyenga Effective Medium Theory [30]. The top substrates are categorized into four types according to their refractive index (n) relative to that of the imaging window (made of quartz, n win = 2.1), and the ratio is defined as N = n/n win . The slot thickness is varied in the range of 25-75 µm which is below the wavelength of 1 THz. As shown in Fig. 2(a-b), when the top substrate has a smaller (N<1) or similar (N ≈ 1) refractive index to the window, the curve of relative change in abs(M) has a steeper rise as the slot thickness d decreases, and thus the structure is most sensitive when d = 25µm. The high sensitivity comes from the matching the impedance of the top and bottom layer, therefore a thinner sample layer produces higher sensitivity. While in Fig. 2 (c-d), when the top substrate has a larger (N>1) or far larger (N ≫ 1) refractive index, there is an opposite trend as the RC abs(M) curve grows steeper when the slot thickness increases, and then reaches the highest slope at d = 75µm. Here we suppose the high sensitivity is related to the addition of pulses reflected from the lower and upper interface of sample, and when the slot thickness increases to a certain value, the overlapping between pulses introduces high contrast in M. Altogether, Fig. 2 shows that the sandwich structure with mirror as the top substrate and 75 µm slot thickness displays the most significant contrast in THz responsivity as the Glu-Sol concentration changes. The new 75 µm window-sample-mirror (win-sam-mirr) structure is then compared with the 25 µm prism-sample-quartz (psm-sam-qz) structure proposed in [15]. Figure 3 displays the RC abs(M) for different THz measurement geometries at 0.5, 0.6, 0.7 THz, including sandwich structures in reflection geometry: 75 µm window-sample-mirror (refle, win-sam-mirr), 75 µm prism-sample-mirror (refle, psm-sam-mirr), 25 µm window-sample-quartz (refle, win-sam-qz), 25 µm prism-sample-quartz (refle, psm-sam-qz); and ordinary bulk reflection geometry (bulk refle) and transmission geometry with 75 µm thickness (trans). The figure indicates that the 75 µm win-sam-mirr structure has the largest variation in RC abs(M) with gradient approximately 3 times of other geometries at 0.5 THz and 10 times of others at 0.6 and 0.7 THz. Simulations have also been conducted at other frequency points and the 75 µm win-sam-mirr structure gives better sensitivity in the range of 0.4-0.8 THz.

Experimental setup and protocol
In this study, a TeraView TPS spectra 3000 spectrometer was used for measurements; for reflection geometry, the incident angle is 45°, and the incident THz wave is s-polarized. Figure 4 shows the design of the 75 µm win-sam-mirr structure, where the top substrate is a silver-plated reflecting mirror, the bottom substrate is the quartz imaging window from the THz system, and they are spaced by two 75 µm thick Teflon spacers. Glu-Sol samples with mass fraction in the range of 0-20% at 5% intervals (∆ = 5%) were made from dehydrated D-glucose powder (Fisher Chemical) and distilled water; Glu-Sol concentrations up to 20% were chosen for experiments due to the practicality of sample preparation and storage. Higher glucose concentrations could be used but they are more difficult to prepare. The technique could also be extended to measure other solutions including protein solutions.
For the experimental procedure of the win-sam-mirr structure, we started with the acquisition of the slot thickness, which is a crucial step for the subsequent properties extraction process. First we measured the window-air interface (win-air) of the bare imaging window as a reference signal (ref1); then we placed spacers, quartz and a weight sequentially to form a window-air-quartz structure (win-air-qz) and acquired the reflected signal from the middle layer as a sample signal (sam1); and eventually by fitting the experimental ratio R sam1 /R ref 1 to the theoretical ratio, we could get the slot thickness. We use win-air-qz instead of win-air-mirr for thickness acquisition is because the former structure is more sensitive to the change in slot thickness. Here the combination of the spacers and weight is for thickness control, so that we would not expect any change in the slot thickness during the measurements of different samples. In the sample measurement process, we replaced the top substrate quartz with a mirror and used the reflected signal from the window-air-mirror structure (win-air-mirr) as reference (ref2). Then after taking away the weight and mirror, we dropped an appropriate amount of the aqueous sample on the imaging window, placed the mirror and weight on again, and then finally measured the window-sample-mirror layer (win-sam-mirr) as our sample signal (sam2). Optical properties of the sample are then extracted by fitting the experimental ratio R sam2 /R ref 2 to the theoretical ratio as given in Eq. (2).
Measurements are also conducted in bulk reflection and transmission geometries: for the former geometry, bulk liquid is held within a 2.5 mm-thick polymer ring placed on the imaging window; for the latter geometry, a liquid sample cell with two polymer wafers (n = 1.454) and a 75 µm Teflon spacer is used to hold the liquid.

Validation of the proposed geometry
We first measured TF water in the proposed win-sam-mirr structure in order to validate the results, the extracted optical properties were compared with those measured in bulk reflection and transmission geometries and also the results from references [34,35]. As shown in Fig. 5, the refractive index and absorption coefficient match well with the results from other geometries and references. Some variation between the literature values comes from differences in the experimental environment and system, while results from win-sam-mirr and transmission agree within 2%. The error bars on the win-sam-mirr results are the standard deviation from 3 repeat measurements and the narrow span shows good robustness and repeatability.

Measurements of Glu-Sols with different concentrations
Glu-Sol samples with concentrations in the range of 0-20% at 5% intervals were measured with the 75 µm win-sam-mirr structure; and samples with 0, 10% and 20% concentrations were measured with transmission geometry for comparison. Figure 6(a-b) show the THz time-domain signals measured with the win-sam-mirr and transmission geometries respectively; where the reference pulses have been multiplied by a factor of 0.3 and 0.5 respectively. In the results from the win-sam-mirr structure, there is an overlap of multiple reflected THz pulses which creates a notable peak distinguishing different Glu-Sols as shown in Fig. 6(a). Figure 6(c) shows the frequency-domain signals of both geometries, which are obtained by performing the Fast Fourier Transform (FFT) on the time domain signals. A peak is also visible in the win-sam-mirr signals at 0.6-0.7 THz, leading to high contrast in the experimental sample over reference ratios of different Glu-Sols as shown in Fig. 6(e). The shape of each resonance is related to the refractive index of the liquid sample. In particular, the depth of the resonance is related to the Fresnel coefficients, and the frequency position is related to the relative delay between the echoes. Figure 6(d) illustrates the relative change in FFT integral as glucose concentration increases from 0% to 20%; due to the introduced peak, the change in the FFT integral of the win-sam-mirr signals is much larger compared to the transmission signals, with the gradient approximately 5 times of the latter. Compared to the results acquired by transmission geometry, the win-sam-mirr structure has a better capability for enhancing the contrast between different concentrations of Glu-Sol samples by introducing a notable peak in both the time-and frequency-domain signals. The relative change in the experimental ratio of Glu-Sols measured by win-sam-mirr is also enlarged around the peak, which agrees with the large variation in RC abs (M) in the previous simulation results.
Using the slot thickness acquired in the previous process, the optical properties of the Glu-Sol samples measured with the win-sam-mirr structure were extracted and compared to those extracted from measurements performed in the transmission geometry. As illustrated in Fig. 7, the refractive indices and absorption coefficients measured by both geometries match well for Glu-Sols with 10% concentration difference. Furthermore, the proposed win-sam-mirr structure can reliably detect samples with 5% concentration difference: this is below the sensitivity that can be reliably detected using transmission geometry. In Fig. 7(a), refractive indices of Glu-Sols with 5% concentration difference are close to each other, yet they can still be clearly distinguished in the range of 0.3-0.5 THz without the error bars overlapping (as shown in the inset figure). In Fig. 7(b), the absorption coefficients of different Glu-Sols measured using the sandwich structure are distinguishable throughout the measured frequency range with no overlapping of error bars for most frequencies. However, in transmission geometry, the error bars are much larger and as seen in the inset of Fig. 7(b), they already start to overlap in the range 0.3-0.5 THz even when the change in concentration is 10%. This highlights the lower sensitivity achievable in transmission geometry.  Figure 8 plots the correlation between the optical properties and glucose concentration. The refractive index and absorption coefficient of Glu-Sols are reported to have a linear relationship with the concentration of the solute, so a first order polynomial is fitted to each of the experimental data curves [35,36]. The fitted polynomials and the Pearson correlation coefficients r are annotated in the figures. In general, a decreasing trend can be seen in both the refractive index and absorption coefficient, and according to the correlation coefficients, both properties show very strong linear correlation with the mass fraction of glucose with |r|>0.98 for all the three frequencies. For refractive index, the slope of the fitted lines decreases as the frequency increases from 0.3 THz to 0.5 THz, and the change rate of the refractive index is 30%, 47% and 73% per percentage concentration for 0.3, 0.4 and 0.5 THz; whereas for absorption coefficient the slope increases with frequency, and the change rate is between 174%, 177% and 190% per percentage concentration for 0.3, 0.4 and 0.5 THz. The correlation between the optical properties and the solute concentration shows potential in estimating the concentration of an unknown Glu-Sol by measuring its refractive index and/or absorption coefficient. Glu-Sols with mass fraction of 0∼20% contain a high proportion of water, and the 5% concentration difference leads to small differences in the refractive indices; hence, limited by the experimental system, sensitive characterization of Glu-Sols could be difficult, while absorption coefficients are more acquirable than refractive indices. The peak in THz time-and frequency-domain signals introduced by our geometry could be used in the application of THz sensing of Glu-Sols with little concentration differences, and the linear correlation between the optical properties and the glucose concentration could be used in mapping Glu-Sol concentration to our THz-TDS technique.

Summary
In this work, we propose an optimized sandwich structure (75 µm win-sam-mirr) for sensitive THz characterization of thin-film aqueous glucose solutions. We conduct theoretical simulations to quantify the characterization sensitivity of the sandwich structure with different top substrates and slot thicknesses, and compare the sensitivity of our proposed structure with other THz geometries to show its advantage in thin-film characterization. We then utilize the proposed win-sam-mirr structure to measure thin-film liquids; thin-film water is measured for validation, and thin-film Glu-Sols with mass fractions between 0% and 20% are measured. The results are compared to those acquired by the ordinary transmission geometry. A notable peak is observed in both time-and frequency-domain signals, which is introduced by the use of our proposed geometry and enhances the contrast between the sample-reference ratios of different Glu-Sols. Experimental results are in line with the theoretical simulations and indicate that the high sensitivity comes from the overlapping effect of multiple reflected THz signals. Optical properties of 0∼20% Glu-Sols are also extracted and linear correlation is found between the refractive index, absorption coefficient and glucose concentration. Our work provides a new train of thought for THz thin-film characterization: with the proposed approach of utilizing theoretical simulation to optimize multilayer structures, such a structure could be customized for sensitive measurements of specific thin-film samples. The observed spectral feature at 0.6-0.7 THz introduced by our structure shows potential in THz sensing of Glu-Sols.