1. Introduction

Terahertz radiations have been intensively used for sensing and biomedical applications due to their transparency in most dielectrics and the low photon energy of them (4meV for 1 THz), which will not cause harmful photoionization in biological tissues [1,2]. Furthermore, many chemicals and molecules have some characteristic absorption frequencies located in terahertz regime due to the rotation, vibration and collective vibration of their chemical bonds, which can be utilized for the identification of them. These kinds of fingerprint detection have found broad applications in e.g. security sensing [3] and medical diagnosis [4]. However, due to the extremely small absorption cross sections of molecules compared to the terahertz wavelengths (a few hundred microns), the interactions between molecules and THz radiations are quite weak and a large volume of chemicals are usually required to have an observable absorption for identification. For example, in the traditional fingerprint detection using THz time-domain spectroscopy (TDS) systems, the powder of the samples is usually compressed into a pellet with the scale of thickness and diameter about few millimeters [3]. This restricts the applications of THz sensing where the amount of chemicals is small or in some cases it is required to use the smallest possible volume of samples, e.g. in medical applications. In order to obtain pronounced characteristic absorption effect with a small amount of samples, people proposed using artificial microstructures or nanostructures to achieve the localized field enhancement for improving detection sensitivity, e.g. using InSb-metallic gratings structure to detect ɑ-lactose monohydrate on the bottom surface of the InSb layer in transmission mode [5], using nano-antenna array deposited on the Si substrate to identify glucose molecule and measure the changes in concentration [6]. However, although the above cases can identify different substances in transmission mode, the sensitivity is poor. Even using a composite structure consisting of a metamaterial and a dielectric based on hybridization induced transparency (HIT) to observe the intermediate transmission peak due to the appearance of lactose layer, a thickness of the lactose around a few tens of microns is still required [7]. Waveguides are especially advantageous in this respect because the THz waves can propagate along the waveguide within a small cross section [8,9]. For the same volume of sample, using waveguides thus provides a much longer interaction length between THz radiations with matters compared to the case when THz waves transmit through the matter, and then more pronounced absorption feature of the chemicals can be observed. In this respect, subwavelength waveguides with tight mode confinement and long propagation length are more appealing [10, 11].

In this paper we propose to use a coupled comb-shaped waveguide for biosensing using lactose as the chemical representative for fingerprint detection. We demonstrate that a well pronounced transmission dip at the frequency of 0.529THz is observed in the transmission spectrum of the straight waveguide onto which a very thin layer of lactose with the thickness of 2.3μm deposited. This spectral feature is an intrinsic characteristic of lactose and this can never be seen using THz transmission through a layer of lactose of the same thickness. It is known that the coupled comb-shaped waveguide supports the propagation of CSSP mode. The relation between the absorption frequency and the cutoff frequency of the waveguide, the sensitivity affected by the waveguide-gap and the length of the straight waveguides are further discussed.

2. Theory and configuration

The schematic of the investigated coupled comb-shaped waveguide structure is illustrated in Fig. 1. The structure consists of two parallel metal stripes of the same thickness t and overall width H, each of which is corrugated with periodic groove array with groove period d, width a and depth h. The two corrugated stripes are separated with a gap g and aligned to each other so that the grooves from the two stripes are center-to-center. All the metallic structures are placed on the top of a quartz crystal substrate (the refractive index being 2). In this paper the geometrical relations are fixed as t = 250 nm, a = 0.5d, h = d and H = 1.2d while the period d varies to adjust the transmission spectrum. The value of d is chosen to be a few tens of microns so that the characteristic frequencies are in the THz regime. The dispersion of the investigated structure is first analyzed to demonstrate its waveguiding property. Using a finite element method (FEM), the eigen values for the mode propagating along the x-direction are numerically calculated at different propagation constants of k_x. For simplicity, the metal is assumed to be perfect electric conductor (PEC), which is valid at THz frequencies since most metals have conductivity at the order of 10⁷ S/m. The calculated dispersion relations for different gaps g = 0.1d and g = 0.2d are plotted in Fig. 2(a), in which the period d is assumed to be 25μm. It is also plotted in the same figure the dispersion of a single corrugated metal stripe (as the bold purple solid line), i.e. half of the structure investigated in this paper. The waveguiding properties of spoof surface plasmon (SSP) modes propagating along this kind of one-dimensional rectangular groove arrays have been investigated [12,13]. It is clear that for a specific value of g two lines are present resulting from the splitting of the original dispersion line, which is a signature of the waveguide mode coupling. One can also see in Fig. 2(a) that a closer layout of the two stripes leads to a further stronger splitting, due to the increased coupling strength as the gap decreases. The results in Fig. 2(b) show that the position of both the two lines can be tuned by changing the array period d to fit into different frequencies, demonstrating that the CSSP structure can be oriented for chemicals with different characteristic frequencies by changing the geometrical parameters.

 

Fig. 1 Simulation model of the coupled comb-shaped waveguide. The upper is metallic waveguide and the lower is quartz crystal substrate with d = 25um; a = 0.5d; h = d; H = 1.2d; t = 250 nm.

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Fig. 2 Dispersion relation of the coupled comb-shaped waveguide with different values of the air gap g and the period d. The other geometric parameters with a = 0.5d; h = d; H = 1.2d. (a) d = 25 um; g = 0.1d and g = 0.2d. The bold purple solid line represents the dispersion relation of a single corrugated metallic stripe structure. (b) d = 25um and d = 50um; g = 0.2d.

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In Fig. 3 it demonstrates the field distribution of H_z within one period for the two dispersion lines at the same k_x of 0.9π/d when g equals to 0.2d, and the results show that the two lines correspond to the mode with symmetric and antisymmetric distributions respectively, confirming the origin of the two lines. We note that the mode with symmetric field distribution at the frequency of 1.310THz has the enhanced field located in the gap between two corrugated stripes while the antisymmetric mode at 1.518THz for the same k_x has minima at the same place. The symmetric mode associated with the lower dispersion line can be interpreted with the charge distributions shown in Fig. 3 (note that the symmetry property of H_z and E_x are opposite). Due to the opposite charge polarity distributions between the two corrugated stripes, they will appeal each other and result in a lower energy state of the coupling system, which is reflected by the lower eigen frequency at a fixed k_x. For the antisymmetric mode the situation is the opposite and the two stripes will push each other, leading to a higher energy state. Due to the difficulty in the antisymmetric mode excitation using a focused THz beam or another waveguide, which usually exhibits symmetric mode distribution as well, we are only interested in the symmetric mode which corresponds to the solid lines in Fig. 2(a). The maximum mode distribution between the two stripes is also beneficial for sensing application because a large proportion of the chemicals will be accommodated in the gap area where they can feel the propagation of the guided THz mode.

 

Fig. 3 The magnetic field component H_z distribution with the period d = 25um and air gap g = 0.2d. (left) Symmetric mode with k_xd/π = 0.9 and f = 1.310THz. (right) Antisymmetric mode with k_xd/π = 0.9 and f = 1.518THz.

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3. Results and discussion

In this section, we will demonstrate how this waveguide can be used to enhance the sensing for fingerprint detection in THz regime. The detection will still rely on finding the absorption at the characteristic frequencies for a specific chemical. Here we use the transmission spectrum through the straight CSSP waveguide with lactose as an example for the chemical to be detected. The transmission spectrum is numerically calculated using the finite-difference time domain (FDTD) algorithm. In the simulations, a magnetic dipole is used at the beginning of the waveguide to excite the mode propagating along the x direction. The simulated structure is terminated all around with perfectly matching layers. Two power monitors at a distance of L are used across the cross section of the waveguides to probe the power flow and the transmission spectrum is calculated using the power spectrum through the second monitor normalized to that through the first one closer to the excitation. Copper is used as the metal material with a conductivity of 5.8 × 10⁷ S/m and the permittivity of lactose is modelled using a series of Lorentzian oscillators [14] to demonstrate its characteristic absorption frequencies as follows:

The black line in Fig. 4(a) gives the calculated transmission spectrum through a bare CSSP waveguide (air-cladded) which has a period d of 25 μm and gap g = 0.2d. The transmission is through the two monitors with a distance L = 20d. The drop in the transmission when the frequency is above approaching to 1.3THz is a signature of cut-off, consistent with the results in Fig. 2(a). One may note in Fig. 4(a) that the transmittance is about 90% even at frequencies far below cut-off. This loss is mainly attributed to the radiation losses associated with the transverse electromagnetic (TEM) mode propagating within each groove, and partly from the Ohmic loss of copper in the CSSP waveguide. When a thin layer (2.3 μm) of lactose is deposited onto the waveguide, the transmission drops pronouncedly appear by an absolute value of 0.14 at the frequency of 0.529THz. This shows that the absorption by the thin layer of lactose can be well observed. The slight decrease in the overall transmission and a red-shift of the cut-off frequency are due to the presence of lactose, which increases the propagation loss and pushes the dispersion line downward (in Fig. 2). For comparison, we also plot the transmission through the thin layer of lactose of the same thickness as the inset in Fig. 4(b). One can see that at resonance the drop in transmission is only 0.1% and this number only increases to 0.8% and 1.6% even when the lactose thickness is 10 μm and 20 μm respectively. We can claim that for the same thickness of lactose, using the waveguide of CSSP can enhance the sensitivity by two orders of magnitude.

 

Fig. 4 (a) Transmission rate of the coupled comb-shaped waveguide and after lactose layer deposited on the waveguide surface with d = 25 um; a = 0.5d; h = d; H = 1.2d and the air gap g = 0.2d or g = 0.1d. The thickness of the lactose being 2.3 um and the length of the waveguide set as 20d (the period of air grooves array being d). (b) The transmittance of lactose with different thickness when the incident wave is normal to the lactose layer.

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One can further increase the absorption at resonance in consideration that the absorptivity A is determined by:

To have a larger integration volume or in other words a larger distance between the two monitors is tricky when the propagation loss of the straight waveguide must be considered. However, within the limit of the propagation length, one can still try using a longer waveguide. In Fig. 5, it is shown the transmission spectrum when the distance between the two monitors changes and the gap value is fixed as 0.05d. It is evident that with a longer waveguide, the transmission drop is more pronounced, from 0.13 when L = 10d to 0.3 for L = 40d. We note that even at the longest case (L = 40d) shown in Fig. 5, the overall transmission is still above the level of 60% thanks to the relatively low propagation loss in the SSP waveguides composed of rectangular grooves.

 

Fig. 5 Transmission rate of lactose film deposited on the surface of the coupled comb-shaped waveguide with different values of waveguide length. Geometric parameters with d = 25 um; a = 0.5d; g = 0.05d; h = d; H = 1.2d. The thickness of the lactose film being 2.3 um.

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4. Conclusion

In conclusion, we have investigated the use of CSSP waveguides for the enhanced identification of lactose using the fingerprint detection in the THz regime. Thanks to the tight mode confinement provided by CSSP waveguides and the relatively long interaction length between the THz radiations and chemicals along the waveguide, a pronounced absorption dip in the transmission spectrum can be observed which is impossible using a thin layer of lactose of the same thickness. How to further enhance the sensitivity is further discussed. We note that the design can be easily transferred to other frequencies and different substances can be detected using our proposed waveguide structure by simply adjusting the periodicity of the groove array so that the working frequency range can be adjusted to match the absorption frequencies of new chemicals. Combining with the fact that the excitation of the investigated CSSP mode has already investigated in the millimeter wave regime using other waveguides [15], we believe that our results provide a simple while versatile way for enhanced fingerprint detection in the THz regime.