Enhanced Trace Amount Terahertz Fingerprint Spectroscopy Using Symmetrical Spoof Surface Plasmon Metasurfaces

Since the frequency range accords with the fingerprint characteristics of many biomacromolecular materials, terahertz (THz) waves are widely used in the detection of biomacromolecular materials. However, when it is used for real application, how to measure the spectral of trace amount analysis samples is a major challenge. By localizing electromagnetic fields in dielectric metagrating or metasurfaces is the most popular way to enhance the spectral signal. In this paper, we propose a design of THz structure that excites a series of spoof surface plasmon (SSP) sharp resonances on the geometry multiplexing metal metasurfaces in one layer to enhance the terahertz absorption spectrum of biomacromolecular materials. The structure can be manufactured and measured easily. The enhanced absorption spectrum can be built by linking a series of SSP sharp resonances. Numerical results show the absorption enhancement factor about 160 times for the 0.2-µm lactose film sample in the frequency range of 0.45–0.61 THz. This design will provide a better method for the detection of biomacromolecular materials.


Introduction
Terahertz waves, the electromagnetic wave with frequencies ranging from 0.1 to 10 THz (λ = 30 µm-3 mm), are in the middle of the electromagnetic spectrum between microwave and far-infrared waves. Terahertz waves have unique advantages, such as high transmission and low energy, and are suitable for biosensing applications [1,2]. Many biological macromolecules such as DNA molecules and protein molecules have rotational and vibrational levels in the terahertz band; therefore, terahertz waves have a very broad application in the detection of biological macromolecules [3][4][5]. However, conventional methods for detecting absorption spectra of samples usually require at least several hundred milligrams of material [6]. This is because only a sufficient thickness can match and interact with the incident terahertz waves. The volume of the sample is also limited by the power of the terahertz source, the absorption of moisture, and the sensitivity of the detector.
When the external electromagnetic wave is incident on the metal surface, the free electrons at the interface between the metal and the dielectric will respond collectively. This response will produce a collective oscillation, and the electron distribution will also change with the period of the electromagnetic wave. This will generate a surface wave known as surface plasmon polarization (SPP). However, in general, the SPP wave vector is larger than the wave vector of incident terahertz wave. Since the wave vector does not match, the incident terahertz wave cannot excite the SPP directly, and the incident terahertz wave needs to be compensated based on the special couplers, including prism, grating, waveguide, and optical fiber [7][8][9].
Recently, several studies have reported the use of local electric field of waveguides [6,9] and metasurfaces [10][11][12][13][14][15] to improve the sensitivity of terahertz absorption spectroscopy measurements. Terahertz dielectric waveguides have the advantages of small sample size, long interaction length, and good signal-to-noise ratio. However, dielectric waveguides can only operate in a narrow frequency band, and it 1 3 is difficult to effectively couple the terahertz waves into the dielectric waveguide [6]. Previously reported studies demonstrated that the dielectric meta-gratings [14] and metasurfaces [15] can enhance the broadband terahertz absorption spectra of thin film samples with multiple incidence angles or different size unit cell structures. Their principles are very different from those high sensitivity sensors whose singlefrequency resonance peak of the high Q resonant structure changes with the refractive index of the trace amount samples [16,17]. They can only enhance a single frequency interaction between the electromagnetic waves and the sample, which cannot identify the broad band characteristics.
In contrast, with multiplexing technique, the wide band absorption of trace amount analyte can be enhanced by linking a series of resonance peaks when changing the angle of incidence or the geometry of the metasurface or supercell units [7,8]. However, there are difficulties in scanning the incidence angle in very small steps or in the precision fabrication of thin terahertz dielectric metasurfaces with different unit cells at the scale of a few microns [13,18,19]. The use of grating couplers to excite SSPs and their use for enhancement of terahertz absorption spectra have been reported [20,21]. However, the enhancing mechanism and different structures with better performances should be further explored.
In this paper, we design and propose a new structure to enhance the terahertz absorption spectrum by scanning the geometrical parameters of a metallic metasurface with symmetrical metal grooves in the unit cell. The enhancing mechanism is investigated by multiples-decomposition in the first time. And the excellent performance in terahertz absorption spectrum enhancement can be realized based on the metasurface with a simple structure, small size, and easy fabrication process. The size-parameter scanning methods are treated to enhance the terahertz absorption spectra of trace amount samples by varying the SSP modes of the metasurface with different unit cell parameter sizes. The unit cells with different parameter sizes can provide a sharp resonance in the operation spectrum. The absorption spectra are simple to detect and easy to operate. The investigation results demonstrate that the scheme provides about 160 times absorption enhancement when 0.2 μm α-lactose is used as the substance to be measured. And the wide operating frequency band located in the range of 0.45 to 0.60 THz allows us to perform simple detection of trace amount samples, paving the way for compact and low-cost terahertz biosensors.

Structural Design and Multipole Decomposition Analysis
As shown in Fig. 1a, the designed terahertz broadband absorption spectrum enhancement scheme is a copper sheet with a conductivity of 5.998e7 S/m containing supercells with different unit cell sizes. The single-layer copper sheet contains 5 × 5 supercells, each supercell consists of multiple unit cells, and each unit cell consists of a rectangular copper frame and six metal strips located symmetrically on the top and bottom sides, respectively. The structure can be built by optical photolithography and reactive ion etching on the sheet. The unit cell structure diagram is shown in Fig. 1b. The designed parameter scanning scheme is realized by changing the length of the vertical metal strips in the SSP structure, only P y is gradually changed, and the rest of the parameters are kept constant. Figure 1c illustrates the 2D schematic of the overall metasurface, with different color lines indicating the positions of the corresponding supercell structures and connecting them to the corresponding resonance peaks. The specific dimensions of the unit cells are shown in Fig. 1d: P x = 450 μm, P y = 300 μm, p = 120 μm, a = 50 μm, b = 100 μm, c = 50 μm, d = 60 μm, w = 30 μm and t met = 50 μm. The performance of the proposed enhancing metasurface is simulated using the finite element method in COMSOL. The Floquet boundary conditions are used in the x and y directions. And the presented results may be validated with experiment in the future. When the TM-polarized terahertz waves incident on the metasurfaces vertically, each supercell will resonate sharply at a specific frequency related to the size parameter. Non-uniformity of the illuminating THz beam can be avoided by collimating and expanding beam and using an aperture in measurement. As the P y increases from 264 to 360 μm in a step of 4 μm, the corresponding transmission reflection peak will decrease from 0.6 to 0.44 THz as shown in Fig. 1e. Figure 1a, c and e indicates the position of the supercell on the copper sheet corresponding to a specific P y , and the position of the corresponding resonant peak by connecting lines of different colors.
The phase velocity of the polarization wave of the surface plasmonic excited in the low frequency band is close to the velocity of the electromagnetic wave propagating in the dielectric. And as the frequency increases, the polarization dispersion curve will be far away from the dispersion curve of the electromagnetic wave in free space, and finally the frequency will tend to a constant value. Due to the wave vector mismatch, free space terahertz wave cannot excite the SSP modes. In this scheme, an infinitely periodic rectangular metal array is used to compensate for the incident electromagnetic waves in order to excite the SSP mode. The rectangular metal array can be regarded as a two-dimensional grating, and the eigen mode of the structure can be modulated by changing its size in x and y directions. As shown in Fig. 1f, when the separation distance d keeps constant and the eigen mode frequencies of the two structures are adjusted by changing P y , the grating characteristic curve behaves as a straight line, and the slope of the line decreases as P y increases. The intersection frequency of the grating structure characteristic curve and the opposite open metal strip SSP structure characteristic curve are the frequency (0.45 to 0.61 THz) that can excite the SPP mode.
In order to study the electromagnetic properties as well as the scattering properties of the SSP metasurface, the Cartesian scattering power of the multipole moments is calculated to identify the electric, magnetic, and toloidal dipole moments whose contributions can be derived from the following equations [22][23][24]. where J is the induced volume current density, r is the position vector, c is the speed of light in vacuum, and α = x,y,z. The electric and magnetic quadrupole moments can be derived from the following equations: The multipole moment-dependent scattered power is given by The transmission spectra with P y = 193 μm ~ 199 μm are shown in Fig. 2a, and it can be seen that the curve each has a sharp resonant peak. To demonstrate the role of dipole moment excitation in resonance, the Cartesian scattering power of multipole moments is calculated according to the above equation as shown in Fig. 2b, where P x , M y , T x , QE, and QM are the electric dipole in the x-direction, the magnetic dipole in the y-direction, the x-direction of the toroidal dipole, electric quadrupole, and magnetic quadrupole, respectively. As shown in Fig. 2b, for the resonance peak at the frequency of 0.541 THz, the magnetic quadrupole is the main multipole contribution to the scattered power, which is about one order of magnitude stronger than the electric quadrupole. The same conclusion can be drawn from Fig. 3. The direction of the electric field shows that the main contribution is provided by the magnetic quadrupole.

Results and Discussions
When the P y value increases from 264 to 360 μm, the resonance peak corresponding to the structure decreases from 0.61 to 0.45 THz, and the absorption spectrum is established by connecting the structural resonance peak. It can Fig. 2 a Transmission spectra when the P y values are 293 μm, 295 μm, 297 μm, and 299 μm. b The scattered power of multiple multipoles of the provided metasurface P x , M y , T x , QE, and QM are the electric dipole in the x-direction, the magnetic dipole in the y-direction, the toroi-dal dipole in the x-direction, the electric quadrupole, and the magnetic quadrupole, respectively. y-axis is chosen as a logarithmic scale to show more clearly the contribution of each multipole be observed that the resonance peak gradually becomes sharper when the P y value increases linearly, while the Q-factor also gradually increases. The SSP resonance mode can enhance the interaction between the incident wave and the matter, producing a higher Q-factor (> 150), which is very suitable for application in biosensing.
To verify the sensing performance of this metasurface, α-lactose was used as the sample to be tested, and it was covered symmetrically on both sides of the metasurface, as shown in Fig. 4a. At present, powder or liquid samples cannot be directly applied on our structure only if they can form a film on it. The SPP waves generated by the metal microstructure will significantly enhance the absorption of electromagnetic waves by α-lactose. The dielectric constant of α-lactose can be described by the Lorentz model [25]: where ε ∞ = 2.08 is the lactose resonance background dielectric constant and ε p /2π = 0.53 THz and γ p /2π = 25.2 GHz are the angular frequency and damping rate of the first absorption oscillation, respectively. Δε p = 6.54 × 10 −3 is the oscillation strength factor. The real and imaginary parts corresponding to the dielectric constants in the frequency range of 0.4 ~ 0.6 THz are shown in Fig. 4b.
By analyzing the transmission and reflection peaks of the metasurface covered with 0.3 μm α-lactose, it can be found that the amplitude of the resonance peaks located around  Fig. 4c, and the change in amplitude becomes more obvious when the frequency is closer to 0.53 THz. This is caused by the absorption of incident terahertz waves by α-lactose. When the P y value changes from 264 to 360 μm in a step of 1 μm, the absorption peak (gray straight line) corresponding to each P y value moves between 0.61 and 0.45 THz by calculating the transmission and reflection spectra. In addition, the amplitude of the absorption peak varies with the characteristics of α-lactose. By connecting each absorption peak, the enhanced absorption spectrum of the metasurface (blue dashed line) can be derived, as shown in Fig. 4d. The largest enhancement factor of the α-lactose-coated metasurface can be realized at the frequency of 0.53 THz.
In order to further investigate the mechanism of SSPenhanced terahertz absorption spectrum, the electric field distribution of the metasurface uncovered with α-lactose and the metasurface covered with 0.3 μm α-lactose is discussed for comparison. As shown in Fig. 5a-d, the four cases of the metasurface uncovered with α-lactose are selected when the P y values are 293 μm, 295 μm, 297 μm, and 299 μm, respectively, and the positions of the resonance peaks corresponding to these four structures are located at the frequencies of 0.5515 THz, 0.5475 THz, 0.5440 THz, and 0.5405 THz. When the metasurface uncovered with α-lactose, the electric field intensity in the x-y plane only decreases slightly with the increase of P y value.
Then as shown in Fig. 5e-h, we discuss the x-y plane electric field distribution when 0.3 μm α-lactose is coated, and the resonant frequencies are 0.5460 THz, 0.5425 THz, 0.5388 THz, and 0.5350 THz, corresponding to the metasurface P y values of 293 μm, 29 5 μm, 297 μm, and 299 μm, respectively. It can be found that the resonant frequency gradually decreases with the increase of P y value, and the electric field intensity decreases more obviously when the frequency is close to 0.53 THz. Comparing Fig. 5e-h with Fig. 5a-d, it can be found that α-lactose can strongly absorb the electric field near the frequency of 0.53 THz, and the weakening is particularly obvious. Based on the above analysis, the SSP electric field plays a key role in the sensing of trace biomolecular materials.
When performing sensing probes, the amount of the material to be measured also greatly affects the absorption, and thus the performance of the proposed sensing scheme. As shown in Fig. 6, the absorption spectra of metasurface covered with α-lactose film with different thicknesses of 0.2-0.5 μm are discussed separately. The gray curves in Fig. 6a-d illustrate the absorption peaks of the metasurface covered with 0.2-0.5 μm α-lactose as the P y increasing from 264 to 360 μm. The blue line is the absorption spectrum established by connecting the absorption peaks, and the magenta line is the unenhanced absorption peak multiplied by an enhancing factor of about 95. The enhancement factor is defined as the peak value ratio of the enhanced lactose absorption by the metasurface to the original lactose absorption with the same thickness. Because the SSP wave decays rapidly in the direction perpendicular to the metal surface, the closer to the metal surface, the more energy the field has. For this reason, the thinner sample has a higher absorptivity on average thickness. As the lactose thickness decreases, the enhancement factor gradually increases. When the thicknesses of lactose are 0.5 μm, 0.4 μm, 0.3 μm, and 0.2 μm, the corresponding enhancement factors are 95, 110, 128, and 160. We also have added the absorption enhancement comparison with other similar techniques in Table 1. Our SSP-enhancing schemes with varying lengths and widths of bars in the unit cell have good performances with more than 100 times absorption spectrum compared with original analyte film.
According to the design results, our structure is easily built by traditional photolithography and etching technology. The normal incident coupling mode also will make the experiment accurate and convenient. Though the above results are simulations, we will try to experimentally validate them in the very near future.
The absorption enhancement performances compared with other similar techniques are listed in Table 1. Our SSPenhancing schemes with varying lengths and widths of

Conclusions
In summary, a metasurface structure integrated with multiple sizes of supercells on a single copper plate is proposed and investigated. Each supercell contains the same size of the unit cell which can generate sharp resonance peaks under the vertical incidence of terahertz waves. This scheme is more suitable for detecting trace amount materials, and the absorption enhancement of more than 160 times can be obtained when 0.2 μm α-lactose is selected as the material to be measured. Numerical results show that the SSP metasurface can significantly enhance the fingerprint spectra of biomolecular materials, presenting a new option for biosensing applications in the terahertz band. By adjusting the structure size, it is possible to achieve the recognition of more frequency band absorption spectra, which has a very broad research prospect.  [11] Dielectric grating cBN Angle of incident Mid-infrared < 10 times [14] Dielectric grating ɑ-Lactose Angle of incident THz < 20 times [26] Inverted dielectric metagrating ɑ-Lactose Angle of incident THz~308/ ~330 times [20] One side metal bars in mesh (varying widths) ɑ-Lactose Geometry THz~200 times [21] One side metal bars in mesh (varying lengths) ɑ-Lactose Geometry THz < 100 times This work Symmetric metal bars in mesh (varying lengths) ɑ-Lactose Geometry THz > 160 times