Biomedical Sensing with Free-Standing Complementary Supercell Terahertz Metasurfaces

: We present a free-standing terahertz metasurface supercell that consists of four complementary mirrored asymmetric split-rectangular resonators. The quality factor of the excited resonance of this supercell has been signiﬁcantly improved by 250% when compared to its counterpart nonmirrored supercell. The mirroring of the resonators leads to an enhanced out-of-phase oscillating current in each neighboring resonators of the supercell. In turn, this leads to a suppression of the dipole moments and its corresponding scattered ﬁelds. Moreover, this design can be realized by utilizing a simple laser machining technique. Furthermore, we numerically evaluate the performance of this design as a label-free biosensor for thin-ﬁlm analytes and biomolecules such as double-stranded DNA and single-stranded RNA viruses. A sensitivity level of 1.14 × 10 5 nm / refractive index unit (RIU) can be achieved using this design. Therefore, this design has the potential to be used as an e ﬀ ective label-free biomedical sensor for in-situ detection of various biomolecules.

At terahertz frequencies, metasurfaces consist of symmetric structures, typically featuring a wide band response that results in a low-quality (Q-) factor. At THz band, this low Q-factor results partially from ohmic losses and predominantly from radiation losses. Within the THz regime, the ohmic losses can be controlled and ultimately suppressed by selecting dielectric substrates and metals with a very low absorption coefficient within the frequency band of interest and very high conductivity, respectively. If such substrates and metals are used, the main channel of losses behind the broadband response is the radiation losses. Hence, a lot of efforts have been devoted to designing novel structures in order to reduce the in-phase dipole moments that lead to good coupling with free space and low radiation losses [7,20,21]. In order to minimize the in-phase dipole moment, out-of-phase Fano-type resonance has been proposed [22]. It is excited using asymmetric split-rectangular resonators (ASRs) in order to reduce the radiation losses and achieve quite high values of Q-factors in planar metamaterials or metasurfaces [23][24][25]. An ASR comprises two arms with slightly different lengths. A plethora of configurations has been designed by utilizing this idea to facilitate achieving high Q-factors, which consequently enhances the performance of the metamaterial designs [20]. However, the focus has been mostly limited to variations of the resonator geometries at the unit cell level [11,[26][27][28][29][30]. A few designs of supercells have been proposed that consist of multiple resonators that sustain a sharp resonance [31][32][33][34]. Conventionally, the metalized layer of such designs is patterned on the substrate using quite advanced and expensive photolithographic procedures. Additionally, these designs are fabricated on high resistivity silicon substrates that are quite expensive substrates and feature a large value of a refractive index of 3.42. Therefore, there is a significant reduction in the THz measured signal level due to this high refractive index.
Hence, in this article, we present a supercell composed of four complementary mirrored asymmetric split-rectangular resonators. In order to derive this design, we applied Babinet's principle [35] to the metamaterial configuration in [31]. Such complementary design can be fabricated in a timely fashion manner using a laser machining technique [36,37] using affordable aluminum foil. The amplitude spectra of transmission and reflection responses of both nonmirrored and mirrored supercells will be presented. Moreover, the spatial electric field will be shown in order to get an insight into the areas of high confinement. Next, the effect of sweeping the asymmetry distance of the resonators on the spectral sharpness will be investigated. The latter will offer a full view of the level of amplitude modulation versus the achievable sharpness, which is important to improve sensitivity for biosensing applications. As this design relies on a free-standing metasurface, there will be neither a need for a supportive substrate nor a necessity for complicated photolithographic techniques. Therefore, this configuration is a completely free-standing structure without a supportive substrate.

Sensor Design and Simulation Methods
The three metasurface supercells studied in this paper are depicted in Figure 1. We start with a supercell shown in Figure 1a that consists of completely identical four complementary symmetric split-rectangular resonators (CS-SRRs) with the following dimensions: a side length of l = 50 µm, a width of w = 3 µm, and a gap of g = 3 µm of each CSRR, with a period of p = 120 µm of the supercell. The metallic sheet thickness of aluminum is 200 nm. The nonmirrored supercell is shown in Figure 1b, where the microstrip gap is moved by an asymmetry distance (d) of 20.5 µm for all four CS-SRRs. Next, the top two resonators in Figure 1b are mirrored vertically around their axis. Then, the two resonators on the right-hand side are mirrored horizontally around their axis. The final mirrored supercell depicted in Figure 1c represents a supercell composed of four complementary mirrored asymmetric split-rectangular resonators (CM-ASRs).
Crystals 2020, 10, x FOR PEER REVIEW 2 of 8 lengths. A plethora of configurations has been designed by utilizing this idea to facilitate achieving high Q-factors, which consequently enhances the performance of the metamaterial designs [20]. However, the focus has been mostly limited to variations of the resonator geometries at the unit cell level [11,[26][27][28][29][30]. A few designs of supercells have been proposed that consist of multiple resonators that sustain a sharp resonance [31][32][33][34]. Conventionally, the metalized layer of such designs is patterned on the substrate using quite advanced and expensive photolithographic procedures. Additionally, these designs are fabricated on high resistivity silicon substrates that are quite expensive substrates and feature a large value of a refractive index of 3.42. Therefore, there is a significant reduction in the THz measured signal level due to this high refractive index. Hence, in this article, we present a supercell composed of four complementary mirrored asymmetric split-rectangular resonators. In order to derive this design, we applied Babinet's principle [35] to the metamaterial configuration in [31]. Such complementary design can be fabricated in a timely fashion manner using a laser machining technique [36,37] using affordable aluminum foil. The amplitude spectra of transmission and reflection responses of both nonmirrored and mirrored supercells will be presented. Moreover, the spatial electric field will be shown in order to get an insight into the areas of high confinement. Next, the effect of sweeping the asymmetry distance of the resonators on the spectral sharpness will be investigated. The latter will offer a full view of the level of amplitude modulation versus the achievable sharpness, which is important to improve sensitivity for biosensing applications. As this design relies on a free-standing metasurface, there will be neither a need for a supportive substrate nor a necessity for complicated photolithographic techniques. Therefore, this configuration is a completely free-standing structure without a supportive substrate.

Sensor Design and Simulation Methods
The three metasurface supercells studied in this paper are depicted in Figure 1. We start with a supercell shown in Figure 1a that consists of completely identical four complementary symmetric split-rectangular resonators (CS-SRRs) with the following dimensions: a side length of l = 50 m, a width of w = 3 m, and a gap of g = 3 m of each CSRR, with a period of p = 120 m of the supercell. The metallic sheet thickness of aluminum is 200 nm. The nonmirrored supercell is shown in Figure  1b, where the microstrip gap is moved by an asymmetry distance (d) of 20.5 m for all four CS-SRRs. Next, the top two resonators in Figure 1b are mirrored vertically around their axis. Then, the two resonators on the right-hand side are mirrored horizontally around their axis. The final mirrored supercell depicted in Figure 1c represents a supercell composed of four complementary mirrored asymmetric split-rectangular resonators (CM-ASRs).  The numerical simulations have been carried out using the commercial software package Computer Simulation Technology (CST) Microwave Studio [38]. As the amplitude response of the proposed designs is expected to feature somewhat sharp resonances with high Q-factor, it was important to choose the frequency-domain solver of this package as it is recommended in such a situation. As the final device will be a two-dimensional array of the proposed supercells, unit-cell periodic boundary conditions have been used to mimic the actual scenario. The number of Floquet modes for both transmitting and receiving ports of the simulation setup was set to 20. Moreover, a tetrahedral mesh scheme with adaptive wavelength refinement was utilized and the number of result data samples was set to 5001. The yellow color in Figure 1 represents aluminum, and the white color is basically air. The electric field orientation has been chosen to be horizontally polarized with normal incidence excitation, as designated in the inset of Figure 1b. Thus, the inductive-capacitive (LC) resonance can only be excited when asymmetry distance (d) is greater than 0. The question is: What will happen when we mirror the resonators as in Figure 1c? Figure 2 shows the simulated transmission (green, solid-curve in the left-scale) and reflection (red, dashed-curve in the right-scale) amplitude results for the three structures depicted in Figure 1. The supercell of each structure is depicted as an inset in each part of Figure 2 for clarity. Figure 1a presents the results of the symmetric structure. Due to the fact that the electric field is horizontally polarized, we expect the excitation of the dipole mode to only be shown at higher frequencies (not shown here). Indeed, no resonance feature is noticed in this configuration as expected. The results of the nonmirrored design are shown in Figure 1b, where the gap has been moved by 20.5 µm.

Mirrored vs. Nonmirrored Supercells Results and Discussion
Crystals 2020, 10, x FOR PEER REVIEW 3 of 8 The numerical simulations have been carried out using the commercial software package Computer Simulation Technology (CST) Microwave Studio [38]. As the amplitude response of the proposed designs is expected to feature somewhat sharp resonances with high Q-factor, it was important to choose the frequency-domain solver of this package as it is recommended in such a situation. As the final device will be a two-dimensional array of the proposed supercells, unit-cell periodic boundary conditions have been used to mimic the actual scenario. The number of Floquet modes for both transmitting and receiving ports of the simulation setup was set to 20. Moreover, a tetrahedral mesh scheme with adaptive wavelength refinement was utilized and the number of result data samples was set to 5001. The yellow color in Figure 1 represents aluminum, and the white color is basically air. The electric field orientation has been chosen to be horizontally polarized with normal incidence excitation, as designated in the inset of Figure 1b. Thus, the inductive-capacitive (LC) resonance can only be excited when asymmetry distance (d) is greater than 0. The question is: What will happen when we mirror the resonators as in Figure 1c?  Figure 1a presents the results of the symmetric structure. Due to the fact that the electric field is horizontally polarized, we expect the excitation of the dipole mode to only be shown at higher frequencies (not shown here). Indeed, no resonance feature is noticed in this configuration as expected. The results of the nonmirrored design are shown in Figure 1b, where the gap has been moved by 20.5 m.   In this case, we notice the excitation of a weak LC resonance. The sharpness of the resonance can be assessed by evaluating its Q-factor. It is defined as the ratio between full-width half-maximum (FWHM) bandwidth and the resonance frequency (f r ). As a result, we observe the excitation of a broad spectral response with FWHM of 231 GHz at the resonance frequency (f r ) of 0.78 THz. Hence, the Q-factor (f r /FWHM) is 3.4. Remarkably, a much sharper spectral response is revealed when the mirrored design depicted as an inset in Figure 2c is used. It features FWHM of 90 GHz at a resonance frequency of 0.76 THz and hence a Q-factor of 8.44. Therefore, comparing the Q-factor of the mirrored supercell to the nonmirrored supercell, the improvement factor is two and a half times larger. This is a direct result of enhanced out-of-phase dipole moments that resulted from mirroring the resonators [31]. The resonance of the mirrored structure in part (c) of the figure is slightly red-shifted and can be interpreted to the increased coupling in the mirrored resonators. In order to get an insight into the electric field distribution of both nonmirrored supercell shown in Figure 1b and mirrored supercell shown in Figure 1c, the electric field spatial distribution at the surface of both metasurfaces at the resonance frequency is demonstrated in Figure 3. It is evident that once the resonators are mirrored as depicted in Figure 3b of the figure, a much larger electric field can be confined within the complementary resonators, i.e., in the area where there is no metal. This not only helps in understanding why the Q-factor has been improved but also visualizes the areas where the analyte can be placed. In this case, it is not needed or useful to cover the whole device, except in areas with high field confinement. It is worth mentioning that this issue was a topic of a recent paper [14]. So, if we coat two sides of the resonators where the E-field is highly confined, we will need to coat only {[(w = 3) × (l = 50) × (2 sides of each resonator) × (4 resonators)]/[total area = p 2 = 120 × 120] = 1/12} of the whole area. This means only 8% of the whole device is required to be covered with the analyte. Therefore, the required analyte volume is reduced by 92%. It is also worth mentioning that the same results would be achieved if the gaps were moved to the opposite sides or placed on the outer corner of the structure. The final overall structure would feature the exact same frequency response. In this case, we notice the excitation of a weak LC resonance. The sharpness of the resonance can be assessed by evaluating its Q-factor. It is defined as the ratio between full-width half-maximum (FWHM) bandwidth and the resonance frequency (fr). As a result, we observe the excitation of a broad spectral response with FWHM of 231 GHz at the resonance frequency (fr) of 0.78 THz. Hence, the Qfactor (fr/FWHM) is 3.4. Remarkably, a much sharper spectral response is revealed when the mirrored design depicted as an inset in Figure 2c is used. It features FWHM of 90 GHz at a resonance frequency of 0.76 THz and hence a Q-factor of 8.44. Therefore, comparing the Q-factor of the mirrored supercell to the nonmirrored supercell, the improvement factor is two and a half times larger. This is a direct result of enhanced out-of-phase dipole moments that resulted from mirroring the resonators [31]. The resonance of the mirrored structure in part (c) of the figure is slightly red-shifted and can be interpreted to the increased coupling in the mirrored resonators. In order to get an insight into the electric field distribution of both nonmirrored supercell shown in Figure 1b and mirrored supercell shown in Figure 1c, the electric field spatial distribution at the surface of both metasurfaces at the resonance frequency is demonstrated in Figure 3. It is evident that once the resonators are mirrored as depicted in Figure 3b of the figure, a much larger electric field can be confined within the complementary resonators, i.e., in the area where there is no metal. This not only helps in understanding why the Q-factor has been improved but also visualizes the areas where the analyte can be placed. In this case, it is not needed or useful to cover the whole device, except in areas with high field confinement. It is worth mentioning that this issue was a topic of a recent paper [14]. So, if we coat two sides of the resonators where the E-field is highly confined, we will need to coat only {[(w = 3) × (l = 50) × (2 sides of each resonator) × (4 resonators)] / [total area = p 2 = 120 × 120] = 1/12} of the whole area. This means only 8% of the whole device is required to be covered with the analyte. Therefore, the required analyte volume is reduced by 92%. It is also worth mentioning that the same results would be achieved if the gaps were moved to the opposite sides or placed on the outer corner of the structure. The final overall structure would feature the exact same frequency response.

Mirrored Supercell Sensor Evaluation
In order to evaluate the effect of the gap position, a parametric study of the mirrored structure was performed. This was done to reveal the influence of the asymmetry of the mirrored supercell design on the radiative properties. Figure 4 shows the transmission and reflection amplitude spectra for a sweep of values of d = 0, 5.5, 10.5, 15.5, and 20.5 m. The resonance broadens, and hence the Qfactor decreases as the asymmetry distance increases while the modulation depth, defined here by the depth of the resonance of the reflection response, increases. By increasing the asymmetry distance from 5.5 m to 20.5 m, the Q-factor decreases from 20.4 to 8.4 and the modulation depth increases from 15.6% to 66.7%, respectively. These results reveal a clear trade-off between the modulation depth and the Q-factor of the resonance. In fact, a modulation depth of 15.6%, where we get a Qfactor of 20.4, can be easily measured using commercially available terahertz spectrometers [39].

Mirrored Supercell Sensor Evaluation
In order to evaluate the effect of the gap position, a parametric study of the mirrored structure was performed. This was done to reveal the influence of the asymmetry of the mirrored supercell design on the radiative properties. Figure 4 shows the transmission and reflection amplitude spectra for a sweep of values of d = 0, 5.5, 10.5, 15.5, and 20.5 µm. The resonance broadens, and hence the Q-factor decreases as the asymmetry distance increases while the modulation depth, defined here by the depth of the resonance of the reflection response, increases. By increasing the asymmetry distance from 5.5 µm to 20.5 µm, the Q-factor decreases from 20.4 to 8.4 and the modulation depth increases from 15.6% to 66.7%, respectively. These results reveal a clear trade-off between the modulation depth and the Q-factor of the resonance. In fact, a modulation depth of 15.6%, where we get a Q-factor of 20.4, can be easily measured using commercially available terahertz spectrometers [39]. Next, we investigate the sensitivity of the mirrored design by sweeping the analyte thickness. As the range of biomolecules refractive index (n) ranges between 1.4 and 2.0 [40], we choose an average value of 1.6 to carry out this investigation. Multiple simulations have been performed by sweeping the analyte thickness between 2 m and 16 m. This procedure is essential in order to evaluate the performance of the sensors and their effectiveness. Figure 5 presents the transmission amplitude spectra, where the asymmetric resonance reveals a clear redshift of 114.5, 140.8, 166.6, and 186.5 GHz for analyte thickness of 2, 4, 8, and 16 m, respectively. A significant redshift is achieved with quite a small change of only 2 m thickness. Hence, changing the dielectric environment by even a minute amount by applying a 2 m thickness of analyte onto the sensor results in a large redshift of [(resonance shift = 114.5GHz)/(fr = 750 GHz) = 15.3%]. The shift is increased by a small amount only to reach 24.9% when the analyte thickness is increased to 16 m. This is due to the limited interaction between the THz field and the metasurface sensor when the analyte thickness is larger than 8 m. It is important to note that this kind of sensor is meant to sense thin-film analytes, i.e., a thickness of 4 m or less.  Next, we investigate the sensitivity of the mirrored design by sweeping the analyte thickness. As the range of biomolecules refractive index (n) ranges between 1.4 and 2.0 [40], we choose an average value of 1.6 to carry out this investigation. Multiple simulations have been performed by sweeping the analyte thickness between 2 µm and 16 µm. This procedure is essential in order to evaluate the performance of the sensors and their effectiveness. Figure 5 presents the transmission amplitude spectra, where the asymmetric resonance reveals a clear redshift of 114.5, 140.8, 166.6, and 186.5 GHz for analyte thickness of 2, 4, 8, and 16 µm, respectively. A significant redshift is achieved with quite a small change of only 2 µm thickness. Hence, changing the dielectric environment by even a minute amount by applying a 2 µm thickness of analyte onto the sensor results in a large redshift of [(resonance shift = 114.5 GHz)/(f r = 750 GHz) = 15.3%]. The shift is increased by a small amount only to reach 24.9% when the analyte thickness is increased to 16 µm. This is due to the limited interaction between the THz field and the metasurface sensor when the analyte thickness is larger than 8 µm. It is important to note that this kind of sensor is meant to sense thin-film analytes, i.e., a thickness of 4 µm or less. Next, we investigate the sensitivity of the mirrored design by sweeping the analyte thickness. As the range of biomolecules refractive index (n) ranges between 1.4 and 2.0 [40], we choose an average value of 1.6 to carry out this investigation. Multiple simulations have been performed by sweeping the analyte thickness between 2 m and 16 m. This procedure is essential in order to evaluate the performance of the sensors and their effectiveness. Figure 5 presents the transmission amplitude spectra, where the asymmetric resonance reveals a clear redshift of 114.5, 140.8, 166.6, and 186.5 GHz for analyte thickness of 2, 4, 8, and 16 m, respectively. A significant redshift is achieved with quite a small change of only 2 m thickness. Hence, changing the dielectric environment by even a minute amount by applying a 2 m thickness of analyte onto the sensor results in a large redshift of [(resonance shift = 114.5GHz)/(fr = 750 GHz) = 15.3%]. The shift is increased by a small amount only to reach 24.9% when the analyte thickness is increased to 16 m. This is due to the limited interaction between the THz field and the metasurface sensor when the analyte thickness is larger than 8 m. It is important to note that this kind of sensor is meant to sense thin-film analytes, i.e., a thickness of 4 m or less.   Finally, we studied the effect of different values of the refractive index of the analyte on the sensor performance. We carried out a series of simulations by sweeping the refractive index between 1.0 and 2.0, while the analyte thickness was fixed at 4 µm, as shown in Figure 6a. The resulting resonance shift (df ) is shown to be 56.6, 100.6, 140.8, 184, and 213.6 GHz for the refractive index of 1.2, 1.4, 1.6, 1.8, and 2.0, respectively. Figure 6b shows the resonance shifts and the linear fitting, which gives a slope of 213.6 GHz per refractive index unit (RIU). This slope is sometimes considered a measure of the sensor sensitivity. However, the well-known measure is the wavelength sensitivity using [14,17]: where "c o " is the speed of light in free space. The latter is a more comprehensive approach, as the resonance frequency is considered in the calculations. For the proposed mirrored design in this paper, very high sensitivity of 1.14 × 10 5 nm/RIU has been achieved. As actual biomolecules contain water, the effect of the imaginary part of the refractive index has been investigated in this regard [29]. As expected, no resonance shift was observed at all. However, there was a reduction in the amplitude depth of the resonance. This suggests that resonances with a large amplitude modulation are preferred in order to get reasonable measurements at the detector side.
Crystals 2020, 10, x FOR PEER REVIEW 6 of 8 Finally, we studied the effect of different values of the refractive index of the analyte on the sensor performance. We carried out a series of simulations by sweeping the refractive index between 1.0 and 2.0, while the analyte thickness was fixed at 4 m, as shown in Figure 6a. The resulting resonance shift (df) is shown to be 56.6, 100.6, 140.8, 184, and 213.6 GHz for the refractive index of 1.2, 1.4, 1.6, 1.8, and 2.0, respectively. Figure 6b shows the resonance shifts and the linear fitting, which gives a slope of 213.6 GHz per refractive index unit (RIU). This slope is sometimes considered a measure of the sensor sensitivity. However, the well-known measure is the wavelength sensitivity using [14,17]:

= ×
where "co" is the speed of light in free space. The latter is a more comprehensive approach, as the resonance frequency is considered in the calculations. For the proposed mirrored design in this paper, very high sensitivity of 1.14 × 10 5 nm/RIU has been achieved. As actual biomolecules contain water, the effect of the imaginary part of the refractive index has been investigated in this regard [29]. As expected, no resonance shift was observed at all. However, there was a reduction in the amplitude depth of the resonance. This suggests that resonances with a large amplitude modulation are preferred in order to get reasonable measurements at the detector side.

Conclusions
In conclusion, we have demonstrated complementary THz metasurfaces consists of a freestanding supercell composed of four complementary mirrored asymmetric split-rectangular resonators. A careful evaluation of the performance of the mirrored design has been carried out. Clear evidence of high field confinement is observed in the supercell of the four CM-ASRs. Moreover, we demonstrated that the mirrored design outperforms its counterpart nonmirrored supercell by at least 250%. More importantly, we investigated the performance of this design for biosensing applications. A high sensitivity level of 1.14 × 10 5 nm/RIU has been attained. Such devices represent potential candidates for future biomedical sensors to identify very small amounts of analytes.

Conclusions
In conclusion, we have demonstrated complementary THz metasurfaces consists of a free-standing supercell composed of four complementary mirrored asymmetric split-rectangular resonators. A careful evaluation of the performance of the mirrored design has been carried out. Clear evidence of high field confinement is observed in the supercell of the four CM-ASRs. Moreover, we demonstrated that the mirrored design outperforms its counterpart nonmirrored supercell by at least 250%. More importantly, we investigated the performance of this design for biosensing applications. A high sensitivity level of 1.14 × 10 5 nm/RIU has been attained. Such devices represent potential candidates for future biomedical sensors to identify very small amounts of analytes.
Funding: This research received no external funding.