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Abstract
The multi-band metamaterial absorbers studied today offer optimal sensing performance by maximizing the absorption at resonance frequencies. A constrained multi-objective optimization problem (CMOP) model is proposed to intelligently obtain the optimized geometrical parameters of the designed MA for optimal multi-band absorption. The proposed multi-band terahertz metamaterial absorber is formed by a patterned metallic patches (symmetric snowflake-shaped resonators) layer and a continuous metallic layer separated by a dielectric layer. The simulation results show that there are three discrete narrow resonance peaks with the absorption of 99.1%, 90.0%, and 99.9% in the range of 0.5–2 THz after being optimized by the proposed CMOP model. The reflection loss of all resonance modes is improved significantly compared with the conventional brute-force approach. Specifically, reflection loss at the highest resonance frequency is suppressed from -6.76 dB to -28.17 dB. Consequently, the reported MA design can be used as a refractive index sensor with the highest sensitivity of 495 GHz/RIU and the figure of merit (FoM) of 8.9 RIU−1 through a refractive index ranging from 1.0 to 1.6 at the analyte thickness of 18.5 μm. It is worth noting that most of the liquid samples have a refractive index ranging from 1.0 to 1.6. Therefore, the reported sensor can be used for liquid detection with high sensitivity.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Nowadays, the trends toward liquid materials characterization in different applications, including environmental, industrial, and bio-medicine fields are rapidly increasing. For instance, monitoring the quality of water bodies and the causes of deterioration has been a priority for governments all over the world [1]. For another example, it is necessary for diabetics to monitor their blood glucose levels [2]. Hence, the discrimination of liquid samples in a fast detection approach has attracted great attention [3–5]. However, traditional detection techniques suffer from time-consuming and labor-intensive.
Various designs for point-of-care testing strategies have been demonstrated to overcome these limitations. The microwave absorbing technology, which can determine the refractive index of the analyte based on the absorption spectrum [6–8], is widely used for sensing applications due to its real-time measurement, quick response, high sensitivity, and ease of handling. In [9], a microwave absorber by means of a circular-ring monopole textile antenna was used for the determination of salinity and sugar concentration in water. Based on the microfluidic approach, a gauge proposed by Pandit et al. was used to measure the aqueous biological samples [10].
Terahertz (THz) sensing offers high spatial resolution [11,12]. Moreover, with no destruction to the molecular structure of analytes owning to the low photon energy of terahertz radiation, the applications of terahertz are considered potential solutions for label-free and non-invasive detection [13,14]. However, notorious as the THz gap, conventional and natural materials show negligible response to terahertz waves [15,16]. Applications of the microfluidic chip, metamaterials, nanowire arrays, and photonic crystal to improve the light-matter interaction between the terahertz waves and the analytes have attracted significant attention and developed rapidly in recent years [17–19]. Among them, metamaterials are widely used as sensors in a large range of applications due to their unusual properties not found in nature [8]. The terahertz metamaterial-based sensors can be classified by phase modulation and amplitude modulation [20–22]. For the case of phase modulation, a polarizer-analyzer mounting for the terahertz regime with metallic polarizers made of a periodic subwavelength pattern was proposed by Romain et al. allowing the detection of refractive index variations as small as 10−5 [23].
The terahertz metamaterial sensors based on amplitude modulation absorb the incident terahertz waves, and their absorption spectra shift with the change in the physical parameters [24]. The shift in the spectra can be used to detect the factors influencing the change, and thus, these structures can be used as sensors. Fang et al. [25] used a flexible terahertz metamaterial biosensor to detect serum tumor marker modified on a non-metal area, achieving a bulk refractive index sensitivity of 325 GHz/RIU (gigahertz per refractive index unit), and the limit of detection reaches 2.97 ng/mL for the concentration of the carcinoembryonic antigen (CEA) biomarkers. Weisenstein et al. [22] proposed an approach where the resonance feature of complementary asymmetric split ring resonators is maintained even for measurements in water, allowing highly sensitive detection of biomolecules in strongly absorbing liquids. Dao et al. [26] proposed a combined fabrication method of reactive ion etching and large-scale colloidal mask to fabricate mid-infrared metamaterial perfect absorbers using aluminum−aluminum oxide-aluminum tri-layers. The absorption of the fabricated samples reached as high as 98%. A novel spectroscopy technique utilizing accumulated spectral power and averaged group delay was proposed by Amlashi et al. [11] that analyzed the magnitude and phase of the reflection as a coherent technique for a graphene-based terahertz sensor. This enables the capability to distinguish between different analytes with high precision.
Recently, the metamaterial absorbers (MAs) displaying multi-band absorption characteristics have drawn great attention, because they are considered as paves to obtain more information related to the accuracy and stability of the sensors [13,27–29]. In [30], an ultrasensitive terahertz sensor consisting of a subwavelength graphene disk and an annular gold ring was proposed. The interference between the resonances arising from the graphene disk and the gold ring gives rise to double Fano resonances, exhibiting a figure of merit (FoM) of 6.5662 and 2.7812 at 9.046 THz and 11.23 THz, respectively. A terahertz triple-band MA was designed and characterized in [31], which has three distinctive absorption peaks at 0.5, 1.03, and 1.71 THz with absorption of 96.4%, 96.3%, and 96.7%, respectively. Lan et al. [13] presented a dual-band absorptive sensing platform in the terahertz range, and ultrahigh normalized sensitivities of 0.47/RIU and 0.51/RIU at 0.76 THz and 1.28 THz were produced, respectively. A tunable THz sensor based on a five-band perfect absorber with Dirac semimetal was presented by Luo et al. [17]. A wide-angle perfect absorber at infrared frequencies based on a perfectly impedance-matched sheet (PIMS) formed by plasmonic nanostructure was proposed in [32]. While multi-mode absorbers may yield rich and exotic scattering properties, designing MAs to achieve multi-band perfect absorption is difficult [33]. Besides, conventional brute-force approach for designing MAs involve large trial and error searches over candidate MA geometries. The designing process is labor-intensive, time-consuming and the final results of absorption performance are tentative and random [34]. Even worse, the conventional brute-force approach permits only a fraction of candidate geometrical parameters to be explored, which brings uncertainty to the optimization results. This is tolerable for simple meta-structures involving a limited set of geometric configurations. However, the problem is exacerbated for intricate meta-structure design, which is inevitable to deal with all kinds of practical application requirements.
There are several intelligent optimization algorithms available for metamaterials design, including particle swarm optimization (PSO), objective first, neural network topology, genetic algorithm, topology optimization, and so on [35,36]. Among them, PSO is widely used in various electromagnetic applications because of its simplified coding, fast convergence speed. Unlike the neural network algorithm, which can only be used to reproduce the simulation results of certain structures currently, the PSO algorithm is much more suitable for the optimization of the meta-structures, and can reduce the design time of a specialized surface as compared with the conventional brute-force approach [37,38]. PSO is initially proposed by Kenndey and Eberhart in 1995 [39], and in some instances outperforms its other counterparts [40]. Although the PSO algorithm has been developed maturely, research on the meta-structure design using the PSO algorithm was proposed recently. Thompson et al. [41] used PSO to discover different broadband reflector designs, each with different performance advantages including ultra-wide broadband reflectance and polarization independence. Hao et al. [37] designed a small-size broadband coding meta-surface for RCS reduction based on PSO which achieved over 10 dB of RCS reduction at 15–35 GHz. Hojjati et al. [34] designed a frequency-selective surface with a minimum resonance frequency and a linear-to-circular polarization converter with a maximum polarization conversion bandwidth employing PSO. Lalbakhsh et al. [38] designed a time-delay equalizer metasurface for an electromagnetic band-gap resonator antenna using the PSO algorithm. However, there is few report on multi-band MA designing with the PSO algorithm.
In this study, a CMOP model based on a multi-objective PSO algorithm is proposed to optimize the absorbing performance of multi-band terahertz MAs which are consisted of a metallic patterned layer, a dielectric layer, and a metallic reflector. The reflection loss of the MA in the highest absorption band is suppressed from -6.76 dB to -28.17 dB after optimized by the proposed PSO algorithm, and all three resonance modes exhibit high absorption of 99.1% at 0.583 THz, 90.0% at 1.356 THz, and 99.9% at 1.966 THz, respectively. The high quality factor of the MA indicates the potential application of sense. It is worth noting that a refractive index sensitivity of 495 GHz/RIU is observed in the highest absorption band. Hence, a novelty automated multi-band MA design method for time-saving and labor-saving is proposed. Compared with the conventional design methods, not only the absorbing and sensing performance is completely comparable to some outstanding previous works, but also the design efficiency is remarkably enhanced.
2. Sensor design and analysis
Inspired by the shape of a snowflake which possesses branches with different sizes and distributions, the snowflake-shaped meta-structure will lead to multi-band and discrete resonant modes which is suitable for sensing application. A schematic of the proposed multi-band MA over the terahertz band is depicted in Fig. 1, in which a sandwiched structure is employed. The top layer consists of periodic defective metallic patches (snowflake-shaped resonators with four main branches), which are coated on a dielectric layer, and backed by a continuous metallic layer. Both the top and bottom metallic layers are modeled as lossy copper with a conductivity σ = 5.7 × 107 S/m, while the dielectric substrate is modeled as polytetrafluoroethylene (PTEE) with a relative permittivity ε = 2.1.
2.1 Optimization procedure by CMOP model for multi-band terahertz MA
Three resonance modes can be found in the frequency range of 0.2–2.1 THz for the initial design of the MA based on snowflake-shaped resonators as shown in Fig. 1. For convenience, the three resonance frequency peaks are respectively named f1, f2, and f3. The optimal design of such intricate meta-structures has always been the research hotspot and challenge. In order to find the optimal meta-structure design with multi-band strong absorption near resonance frequencies f1, f2, and f3, we use a multi-objective PSO algorithm to remarkably strengthen the absorbing performance of the proposed terahertz MA. The absorption (A) can be calculated by
where T and R are the transmission and reflection, respectively. S11 and S21 are the reflection coefficient and transmission coefficient, respectively. In this case, T = 0, and A = 1 – R. It is worth noting that among three resonance modes, achieving effective absorption (absorption of 90%, corresponding to S11 < -10 dB) or even nearly perfect absorption (absorption of 99%, corresponding to S11< -20 dB) is relatively easier for the resonance modes near f1 and f3 compared with the resonance mode near f2, according to abundant absorption spectra of the proposed MAs with different geometrical parameters. In order to significantly enhance and balance the absorption near all resonance frequencies, we set S11 less than -15 dB at resonance frequencies f1 and f3 as a restricted condition. Thus, the fitness function F(x) of the proposed CMOP model can be defined asSuch multi-dimensional fitness makes a reasonable compromise between the absorption of all three resonance modes based on the complexity of achieving strong absorption for each resonance mode. The PSO algorithm used for optimal design is illustrated by a flowchart in Fig. 2. The maximum iteration number is set as Niter = 20 based on the number of variables being optimized, and by tracking the behavior of the algorithm in early iterations [38]. During the algorithm iterations, each particle’s position xij is adjusted according to the velocity vij given by [34,37]
As shown in Fig. 2, a swarm containing 15 particles is initialized, along with the initial velocity and initial position of each particle are randomly generated. Each particle, which represents a group of candidate geometrical parameters of the snowflake-shaped meta-structure, is transformed from the MATLAB environment to a unit cell in the commercial electromagnetic solver (CST Studio Suite 2019). A plane beam is vertically incident on the MA, as shown in Fig. 1(a). Then, by applying periodic boundary conditions in the x and y directions, this snowflake-shaped unit cell is analyzed using the full-wave frequency-domain solver of CST, and the results are returned to MATLAB in order to calculate the fitness function according to Eq. (4). The calculated fitness function is then delivered to the optimization algorithm to update $x_{ij}^\textrm{P}(\textrm{t})$ and $x_{ij}^\textrm{G}(\textrm{t})$ for the next iteration till reaching the termination criteria and the optimization process stops. The convergence of the fitness values for terahertz MA is shown in Fig. 3. The final result of the geometrical parameters is listed in Table 1.
Table 1. The Geometrical Parameters of the Proposed MAs Designed by the CMOP Model
2.2 Absorption characteristics of the multi-band terahertz MA designed by CMOP Model
Figure 4(a) shows the reflection loss (RL) of the proposed terahertz MA via full-wave simulations using the commercial electromagnetic solver (CST Studio Suite 2019). The relationship between reflection loss and reflection can be written as
The reflection loss spectra of the MA designed by the proposed CMOP mode are signed as a solid blue line; as a reference, the spectra of the MA designed by the conventional brute-force approach [42], which was trialed for a few months, are shown as a dotted red line in Fig. 4(a). While the CMOP model proposed here is an automated design method for great time-saving and labor-saving. It can be seen that the MA designed by CMOP model outperforms for all three resonance modes in terms of the reflection loss. The reflection loss of the MA designed by the proposed CMOP model at three resonance frequencies f1 = 0.583 THz, f2 = 1.356 THz and f3 = 1.966 THz is -19.28 dB, -11.27 dB and -28.17 dB, respectively, showing excellent multichannel band-stop characteristics. Compared with our previous work in [42], the absorption at all three resonant frequencies is improved significantly. Specifically, the reflection loss of the MA designed by the CMOP model at resonance frequency f3 decreases by 21.41 dB from -6.76 dB to -28.17 dB compared with the MA designed by the conventional brute-force approach.
Fig. 4. (a) Reflection loss of the terahertz MA, (b) Absorption of the microwave MA designed by the CMOP model.
In order to provide the application of the CMOP model in various cases, a microwave MA based on snowflake-shaped meta-structure with varying geometrical parameters (listed in Table 1) is designed by the CMOP model. Figure 4(b) shows the simulated absorption spectra of the microwave MA designed by the CMOP model indicating that multi-band absorption is achieved. Among several discrete peaks, there are four resonance modes with absorption over 90%, which is the absorption of 94% at 15.3 GHz, 90% at 19.1 GHz, 98% at 35.9 GHz, and 96% at 39.4 GHz in the frequency range of 12–40 GHz as shown in Fig. 4(b).
In order to get an insight into the absorption mechanism, the simulated electromagnetic field distributions and surface currents on the top of the unit cell are illustrated at resonance frequencies at normal incidence of linearly TE-polarized wave (Fig. 5). Due to the symmetry of the unit cell, the electromagnetic field and induced surface currents at the surface will have the same distributions as a result for both TE and TM waves. It can be observed from Fig. 5 that these modes are highly localized modes; the electric field is mainly concentrated at the apex of the sub-branches and the main branches, while the magnetic field is mainly gathered around the edge of the main branches in the x-direction at resonance frequency f1 = 0.583 THz. The resonance modes at frequency f2 = 1.356 THz and f3 = 1.966 THz are observed to behave similarly to the absorption mode at f1 with the electromagnetic fields concentrated at different positions of the branches’ edges, indicating that the absorption modes are dominated by different parts of the unit cell and each part of the snowflake-shaped meta-structure is essential. Such multi-band absorption is benefited from the specific snowflake-shaped meta-structure, due to the electromagnetic fields gathered at different parts of the snowflake-shaped meta-structure, including the apexes of the branches and the edge of the center square. The multi-band absorption is induced by the localized surface plasmon resonance (LSPR). Both the electric field distributions and magnetic field distributions shown in Fig. 5 indicate that the LSPR for the resonance modes near f1 and f3 is much stronger than the LSPR for the resonance modes near f2. Figure 5(g)–5(i) show that an induction current is produced in the snowflake-shaped unit cell. It is clear that the electromagnetic power can be dramatically dissipated at places where the currents accumulate at three resonance frequencies since the currents will lead to significant ohmic loss at the meta-surface with Ploss = I2Rsur, where Rsur is the surface resistance. This means that the reported design can absorb the incident wave effectively and will play an important role in the sensing operation for any small change in the surrounding refractive index.
Fig. 5. Electric field distributions (a)–(c), magnetic field distributions (d)–(f) and surface currents (g)–(i) of the proposed terahertz MA designed by CMOP model at three resonance frequencies f1 = 0.583 THz, f2 = 1.356 THz and f3 = 1.966 THz.
Figure 6 shows the simulated absorption spectra of the terahertz MA designed by the CMOP model at normal and oblique incidence for a TEM wave with TE polarization and TM polarization, which shows that this work has identical responses to the incident waves with TE and TM polarizations because of the four-fold symmetrical of the unit cell. As expected, there are three discrete peaks with the absorption of 99.1% at 0.583 THz, 90.0% at 1.356 THz, and 99.9% at 1.966 THz at normal incidence. The full-width at half-maximum (FWHM) which is also defined as the resonance linewidth is 22 GHz, 75 GHz, and 56 GHz, respectively for three resonance modes. The quality factor Q can be derived from the ratio of resonance frequency to the FWHM, such that Q = f/FWHM, where f is the resonance frequency of the absorption peak. The quality factors Q are approximately 29, 18, and 35 for these three resonance modes, respectively. The quality factor Q reflects the spectral resolution and leads to a strong frequency selectivity due to the narrow absorption bandwidth. The performance of high quality factors and narrow linewidth is highly desirable for achieving superior sensing performance.
Fig. 6. Terahertz absorption for the case of TEM waves incident at different angles from 0° to 60° for (a) TE polarization and (b) TM polarization.
The angular dependence of the absorption performance was investigated, as shown in Fig. 6. Based on the interaction between the incident terahertz waves and absorber, the as-designed MA can still maintain an excellent terahertz absorption performance at an oblique angle of TEM wave incidence. It is worth noting that the absorption ability at resonance frequency f2 tends to be even stronger at oblique incident angles compared with normal incidence for TM polarization, as illustrated in Fig. 6(b). The FWHM of the absorption spectra is nearly independent of the incident angle below 60°. Meanwhile, the MA exhibits a high quality factor for all resonance modes even when the incident angle is increased to 60° for both TE and TM polarization.
2.3 Sensing characteristics of the multi-band terahertz MA designed by the CMOP model
The investigation of the reported design as a refractive index sensor will be studied. Therefore, an analyte layer is placed on the defective top copper layer. The thickness of the analyte layer is set as 18.5 μm. Besides, the refractive index of the analyte layer can be changed from 1.0 to 1.6, considering most of the liquid samples have a refractive index in the range of 1.0–1.6. In order to check the sensing performance of the designed terahertz MA by the CMOP Model, Fig. 7 shows the absorption as a function of the frequency at different analyte refractive indices. It can be seen from Fig. 7(a)–7(c) that all the resonance frequencies are obviously shifted according to the change in the refractive index of the analyte layer. As the refractive index of the analytes increases from 1 to 1.6, the resonance modes at frequencies f1, f2, and f3 can achieve large frequency shifts from 0.585 to 0.510 THz, 1.356 to 1.172 THz, and 1.966 to 1.668 THz, respectively. The perturbations in resonance amplitudes of the frequencies f1, f2 and f3 are 1.6%, 16.7%, and 16.8%, respectively, when the refractive index increases from 1 to 1.6. Thus, it is preferable to probe analyte properties by monitoring frequency shifts rather than resonance amplitudes.
Fig. 7. Absorption spectra of the terahertz MA when the refractive indexes of the analytes n change from 1 to 1.6 for three resonance modes at frequencies (a) f1, (b) f2, and (c) f3.
Two key parameters of sensitivity and the figure of merit are emphasized for sensing evaluation. The sensitivity S is measured as
where Δn is the refractive index variation of the analyte and air (n = 1). Δf is the resonance frequency shift of the initial and shifted resonance frequencies, due to the change in the refractive index. Figure 8 shows the frequency shifts of resonance modes versus refractive indices. It is worth noting that the resonance frequencies shift linearly with changes in the refractive index. In order to show the linearity of the sensor performance, the linear fittings of the calculated data are shown in Fig. 8, and the sensitivity S can be indicated by the slope of the fitting line. The sensitivity of the MA sensor for three resonance modes over the analyte refractive index n range from 1 to 1.6 is S(f1) = 123 GHz/RIU, S(f2) = 307 GHz/RIU and S(f3) = 495 GHz/RIU, respectively. Except for sensitivity S, the figure of merit FoM is another coefficient to demonstrate the sensing performance of the proposed terahertz MA, which is defined as the ratio of sensitivity to FWHM according to the following formulaThe FoM for three resonance modes is 5.6 RIU−1, 3.9 RIU−1, and 8.9 RIU−1 respectively as shown in Table 2. More absorption bands can offer more information volume during detection. Hence, it is reasonable to consider the number of absorption bands as an important indicator to evaluate the sensing performance. Thus, the terahertz MA designed by the CMOP model is outstanding compared with single-band absorbers in terms of the resonant modes number. Besides, both the absorption and the sensing performance of the terahertz MA designed by the CMOP model is outperforms or matches the terahertz MAs shown in Table 2.
Fig. 8. Resonance frequency shift as a function of the analyte refractive index for three resonance modes.
Table 2. Resonance frequency, absorption, sensitivity, quality factor, and FoM of the resonance modes in the present study and in previous works.
3. Conclusion
In this study, a generalized approach for designing and optimizing the multi-band MAs based on CMOP Model is proposed. The terahertz MA optimized by the proposed CMOP model produces a 21.41 dB suppression in reflection loss at the highest resonance mode, along with a nearly perfect absorption of 99.9%. The simulated results reveal the existence of three resonance peaks with absorption over 90% and high quality factors. Additionally, the suggested design possesses high sensitivity of 123 GHz/RIU, 307 GHz/RIU, and 495 GHz/RIU respectively for three resonance modes for the detection of the analyte refractive index ranging from 1.0 to 1.6. The proposed intelligent design method of MAs with these superior performances would significantly improve the optimization efficiency of the multi-band MAs, and pave the way to the applications of label-free sensing and non-contacting detecting.
Funding
China Postdoctoral Science Foundation (2020TQ0152); Natural Science Foundation of Jiangsu Province (BK20190405); National Natural Science Foundation of China (61905112, 61905114); Fundamental Research Funds for the Central Universities (NT2021013).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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