A study on the electromagnetic mechanism of a flexible terahertz toroidal dipole metasurfaces

We have designed and fabricated metasurfaces structures generated toroidal dipole phenomenon by fabricating periodic metal pattern on polyimide substrate. The metasurfaces structure consists of two symmetric split rings along the Y-axis. The impact of structural parameters, gap, and SR, on the electromagnetic characteristics of metasurfaces at terahertz frequencies was investigated. An increase in gap results in a blue shift phenomenon in the amplitude transmission spectrum, while an increase in SR leads to a red shift phenomenon in the amplitude transmission spectrum. The intrinsic mechanism of the toroidal resonance is investigated more deeply by calculating the multipole scattering power and Q-factor. Q-factor values of 2.3 and 9.5 were obtained at low and high frequencies, respectively. Terahertz toroidal dipole metasurfaces made on flexible substrates like this have the potential for applications in terahertz functional devices, such as sensors and tuners.


Introduction
In 1964, the terahertz wave(0.2∼ 10 THz) was discovered by the researchers [1,2].Terahertz waves have a strong penetration and a fast propagation rate especially in a dry environment [3][4][5].Up to this point, terahertz technology has firmly captured the attention of researchers.Terahertz technology have been widely used in many fields, such as defense and security [6], radio communication systems [7], sub-millimeter positioning systems [8], and medical imaging [9], etc.The application of terahertz waves is severely limited by the scarcity of natural materials [10].The proposal of metamaterials allows terahertz to break the limitation of natural materials [11][12][13].Metamaterials are also known as artificial electromagnetic materials, and the electromagnetic properties rarely observed in natural materials are realized by artificially designed periodic or non-periodic arrangement of sub-wavelength structural units.As research progresses, the concept of metamaterials (MMs) has been proposed.Metasurfaces (MSs), compared to metamaterials, have significantly reduced dimensions in a certain dimension and can be considered as a two-dimensional metamaterials [14].With continuous research, a large number of metamaterial structures have been designed to compensate for the electromagnetic properties of natural materials [15][16][17][18].
Toroidal dipoles (TD) are the lowest-order class of toroidal multipoles, which is composed of a set of magnetic dipoles located in the meridional plane and are often neglected because of their weak coupling to the electromagnetic field [19,20].The effect of TDs was first considered by Zel'Dovich in 1958 in his explanation of ubiquitous destruction in nuclear physics [21].TDs have many unique electromagnetic properties, such as unidirectional refraction, resonance transparency and anisotropy et al [22][23][24][25][26][27][28].As shown in table 1, the comparison among the previous typically researches on the toroidal dipole MMs are listed.From the previous researches, a variety number of metamaterials is proposed.However, due to limitations in manufacturing processes, some of them have remained in the simulation phase [29][30][31][32][33].The dielectric materials were used to design the metamaterials, and the Q-factor is relatively high due to the low loss of the dielectric materials.Some of them can be realized both in the simulation and experiment, and the unit cell structure is often consisted of metallic pattern layer fabricated on the silicon/quartz substrate [34][35][36][37].The asymmetry structure including Fano structure is designed to construct the toroidal dipole resonance.However, the solid substrates lack of flexible restricts the application of the metamaterials.The flexible toroidal dipole metamateirals is also discussed, and the unit cell is consisted of the two metallic layers with polyimide spacer [38,39].Multilayer structures to some extent satisfy the flexible manipulation of terahertz waves, but the high-precision processing and cumbersome fabrication techniques required for preparation significantly limit the practical application of bilayer structures [39].Researchers are eager to develop easily manufacturable MSs structures to meet the demands of multifunctional terahertz devices [40,41].With the continuous research, it has enabled TD MSs to be applied under many scenarios, such as biosensing [42], medical detection [43], dichroic functional devices [44], and many other fields [45,46].In this paper, a terahertz TD MSs structure was prepared on a flexible medium, and the unit cell is consisted of one metallic layer and one substrate, which is easy to fabricate.The electromagnetic properties of the MSs were investigated by changing the structural parameters.The MSs structure consists of two symmetric split rings along the Y-axis.The electromagnetic properties of the MSs are investigated by varying the metal structure parameters gap and inner radius SR, then the TD generation mechanism is studied, and the distributions of the magnetic field and surface current are discussed.In order to study the intrinsic mechanism of TD resonance more deeply, the scattering power and Q-factor of the multipole are also calculated for a more in-depth discussion.TD MSs with high transmittance are of great research value for the fabrication of terahertz devices.Polyimide is used as a substrate for metamaterials because of its properties such as high transparency in terahertz and visible wavelength bands, low density, low dielectric constant, and ease of realizing processing [47].The MSs structure consists of two symmetric split rings along the Y-axis, where the outer radius of the split ring is R = 205 μm, and the inner radius is SR = 199 μm, respectively.And a metal strip is 189 μm length 20 μm width, which is placed in the middle of the open semicircular ring with an intermediate opening g = 20 μm.The thickness of polyimide Z is 20 μm, and the thickness of the metal structures is 200 nm.The monolithic structure forms a MSs in the X-Y plane by a periodic arrangement.The periodic dimensions of the unit cell structure are X × Y = 240 × 240 μm.In this thesis, the electromagnetic properties of the TD MSs samples are analyzed by fabricating samples with different structural parameters(Samples with gap values of 17, 27, and 37 and SR values of 169, 179, and 189 were prepared).During simulations and experiments, the electric field is polarized along the X-axis and terahertz waves are incident along the Z-axis.

Simulation and production of samples
The samples of TD MSs structures in the paper were processed using conventional lithography and metallization process techniques.In the first step, a 20-μm thick substrate was obtained by spin-coating PI-5878G (fabricated by HD Micro Systems TM) liquid polyimide on a silicon wafer.During the process, the thickness of the polyimide is controlled precisely by controlling the temperature and the speed of rotation.PI-5878G is a high molecular weight, polyamic acid; precursor in an NMP [N-methyl-2-pyrrolidoline] based solvent system.After being applied to a silicon substrate, the precursor was thermally converted into an intractable polyimide film [48].The thickness of 10 μm polyimide layer was obtained, when the spin rate is 1500 rad/min.The silicon substate coated with polyimide were heated on the hotplate 80 °C for 10 min, then 120 °C for 10 min, then 180 °C for 10 min.The above process was executed twice, then the 20 μm polyimide layer was obtained.The thickness of polyimide layer was measured by the step tester.t In the third step, the TD MSs is peeled off from the silicon substrate.The terahertz TD MSs was characterized using a terahertz timedomain spectroscopy(THz-TDS) system.The THz-TDS system consists of four parabolic mirrors in an 8-F confocal geometry mechanism.The use of parabolic mirrors and a confocal geometry referenced by bare polyimide material significantly reduces dispersion effects.The MSs can be directly attached to a well-defined sample holder for measurements, then the sample holder was placed at the center of the terahertz spot, then the terahertz characteristics was measured using the THz time domain 8-F system in a dry environment at room temperature, thus excluding the absorption of terahertz waves by water vapor from affecting the experimental results, and thus reducing the experimental error to a certain extent.In order to investigate the electromagnetic properties of the TD MSs, numerical analysis was performed in the time domain using the commercial software CST Microwave Studio in the simulation analysis.In the simulation, the electric field is polarized along X and the Z direction is set as open add space, and the number of pulses was set as 10, and a hexahedral mesh was set as 15 cells per wavelength, in order to achieve a balance between computational efficiency and accuracy.

Analysis and discussion of results
Figures 2(a), (b) and (c) show the simulated and measured transmission spectra of the TD MSs at gap = 17 μm, 27 μm and 37 μm, and the black solid line is the simulated amplitude transmission spectrum and the red dotted line is the experimental amplitude transmission spectrum.It can be clearly observed from the figure 2 that the simulated and experimental results are basically the same within a certain error range, and two resonance points can be clearly observed.Certain errors between the experiment and simulation can be explained by the following reason: firstly, errors caused by processing during the manufacturing process of the sample, such as uneven coating of polyimide thickness and misalignment of the metal pattern.Secondly, the experimental instrument itself caused defects in the measurement process, such as the limited resolution of the measurement, resulting in the results of the measurement and simulation error.Through experiments and simulations, resonances were generated at frequencies of ∼0.45 THz and ∼0.79 THz, and the resonance at ∼0. 45 THz was termed the lowfrequency resonance (LF) and the resonance at ∼0.79 THz was termed the high-frequency resonance (HF).In TD MSs, LF produces a blueshift phenomenon with the gradual increase of gap, the blue shift decreased from 0.008 to 0.006 THz, indicating a gradual weakening of the blue-shifting capability with the increase in gap.The resonance frequency of the sample can be analyzed using capacitive and inductive coupling, and the resonance is similar in nature to an inductive capacitive (LC) resonance, which is interpreted through equation (1): Where: L denotes the inductance attributed in the unit cell, and C denotes the capacitance attributed in the unit cell.Due to the gradual increase of gap, the inductance of the metal patterned layer decreases, while the distance between the two split rings is increased lead to the decrease of the capacitance, so the resonant frequency moves to a high frequency.In the fabricated sample, the processed sample consists of ∼400 unit cell.According to equation (1), additional capacitance is introduced between neighboring unit cells, which lead to shift the experimental amplitude transmission spectrum to lower frequencies compared with the simulated frequency, and the same tendencies can be observed in figure 2, both in (a), (b) and (c).
The magnetic field distributions at the TD MSs (gap = 17 μm) are shown in figures 3(a) and (b) show the distribution of the magnetic field at LF and HF.The magnetic field distribution in figures 3(a) and (b) are concentrated in the circular region of the MSs in the YZ plane, and the vortex magnetic field with the head and tail in the clockwise direction can be observed at the LF resonance, and the vortex magnetic field with the head and tail in the anticlockwise direction can be observed at the HF resonance, respectively.The vortex magnetic field is the typical characteristics of TD phenomenon.
As in figure 4(a), the intrinsic mechanism of the TD resonance on the LF MSs can be explained more graphically.At LF, the polarization of the incident terahertz wave causes the surface current to form a circular current path in the upper and lower half-circles, resulting in a capacitive-inductive (LC) resonance.In the upper semi-circular toroidal, the surface current moves in the counterclockwise direction, and the surface current moves in the clockwise direction in the lower semi-circular toroidal, and the direction of surface current flow the middle metal bar is the same as the electric field.The oscillating structure flowing along the semicircle is similar to a magnetic dipole, and according to the right-hand rule, the magnetic field in the upper half-circle points to the negative half-axis of the Z-axis, and the magnetic field in the lower half-circle points to the positive half-axis of the circle.In addition, the surface current passing through the intermediate metal structure generates a magnetic field around the metal rod, as indicated by the black circular arrows in figure 4(a).The magnetic field generated by the intermediate metal rod opposites the directions of the magnetic field direction at the upper and lower half rings.
Figures 4(b) and (c) depict the surface current distribution of the TD MSs under LF and HF conditions, respectively.Compared with figures 4(b) and (c), it is evident that the current intensity in the upper and lower metal rings is relatively weak, and the current intensity is mainly concentrated in the middle metal bar.This observation becomes clearer when analyzed in conjunction with figure 3(b), where the enhanced current on the central metal bar is primarily attributed to the distribution of the strongest head-to-tail magnetic field.
In order to go deeper into the intrinsic mechanism of the TD resonance from the theoretical aspect, the volumetric current density distribution was extracted from the simulation results to calculate the power of the five strongest multipoles.Their contributions were quantified through multipole scattering theory [49][50][51].For normal incidence of terahertz waves, the magnetic dipole (MZ) is parallel to the Z-axis, the electric dipole (Ex) is parallel to the X-axis, and the TD (Tx) is parallel to the X-axis, and at the same time the magnetic quadrupole (Qm) and the electric quadrupole (Qe) are generated, which can be calculated as five vectors by equations (2)-( 6), respectively: r j r 2r j d r 4 2 3  Where j is the current density, c is the speed of light in vacuum and r is the coordinate vector from the origin to the center of the toroidal distance.We calculated the current density(j) via the commercial software CST with a step size of 0.01 THz.Then the power of the five strongest multipoles was calculated according to the equations (2)-( 6) with MATLAB software.Then the curve of decomposed scattering power for different multipole moments in TD MSs were obtained.As shown in figure 5, Tx is almost dominant and the density of Tx is stronger than that of almost any other multipoles.Tx and Mz have the same trend, with the density of Tx being eight times that of Mz.At LF, the density of Tx decreases to almost zero.At HF, The density of Tx increases with the increase in frequency, while the density of Qm increases sharply.From figure 4(c), it can be observed that the surface current on the two side rings weakens, while the surface current on the central metal rod strengthens, leading to enhanced TD resonance, which is consistent with the increase in Tx density.As the surface current on the central metal rod increases, the generated magnetic field is enhanced, So the strongest magnetic field can be observed in figure 3(b) with the head and tail connected.
Table 2 gives the Q-factor at LF and HF for different gaps (gap = 17 μm, 27 μm and 37 μm).The Q factor was defined as the ratio of resonance frequency to the full width at half maximum.The radiative and nonradiative losses determine the value of the Q factor.In this paper, the Q-factor increases with the increase of the gap.At gap = 17 μm, the values of 2.3 and 9.5 are obtained at LF and HF, respectively.At HF, the Q-factor is greater than at LF, indicating reduced radiation loss and increased coupling strength for TD MSs at HF.As shown in figure 5, Tx at HF is significantly larger than at LF, which is why the strongest head-to-tail magnetic field is observed at HF, as depicted in figure 3(b).As shown in figure 6, we simulated and studied the amplitude transmission spectrum of the TD MSs structure parameter SR ranging from 169 μm to 189 μm with a step size of 0.2.By creating a 2.5D plot, we clearly demonstrated the impact of SR on the electromagnetic properties of the TD MSs.In figure 6, we can discern that the first resonance point ∼0.50 THz, followed by the appearance of the second resonance point at approximately ∼0.70 THz, and the third resonance point at ∼0.96 THz, as the frequency steadily increases.It's worth noting that as SR increases, three resonance points undergo varying degrees of leftward shifting, as vividly depicted.Furthermore, with the gradual increase of SR, the transmittance at the second and third resonance points steadily rises.This allows us to predict that when SR reaches a certain threshold, the second and third resonance points will disappear.To validate the accuracy of our predictions, we conducted simulations for SR values of 169 μm,179 μm and 189 μm and compared them with the experimentally measured data, as depicted in figure 7, shows the transmission spectra of simulated and measured amplitudes of SR with different inner radii.The simulated and measured results are basically the same, and the errors may be due to the mixing of impurities in the sample processing and the interference of uncontrollable factors in the measurement process.With the gradual increase of the outer radius, the amplitude-transmission spectra are red-shifted to different degrees.Through the comparison, it was evident that the results of all three values were consistent within the margin of error.

Conclusion
In this paper, a two-dimensional MSs structure consisting of a metal layer and a polyimide layer is designed and fabricated.Amplitude transmission spectra are obtained by simulation and experiment, and the results of both  are highly consistent.The LF and HF resonances are clearly observed in the amplitude transmission spectra, and it is concluded from numerical analyses and simulations that the TD resonance is generated at the rings on upper and lower sides of the MSs, and the enhancement of the surface current at the HF is mainly due to the TD resonance.With the gradual increase of the structural parameter gap, the amplitude transmission spectrum is shifted to high frequencies.At the same time, the inner radius SR of the metal structure can also regulate the electromagnetic properties of the MSs.Therefore, the electromagnetic properties of TD MSs can be adjusted by changing the structural parameters, and thus more terahertz-functional devices can be developed.

Figure 1 (
Figure1(a) shows the schematic structure of the TD MSs unit, where the MSs consists of a top metal layer and a bottom polyimide layer.Polyimide is used as a substrate for metamaterials because of its properties such as high transparency in terahertz and visible wavelength bands, low density, low dielectric constant, and ease of realizing processing[47].The MSs structure consists of two symmetric split rings along the Y-axis, where the outer radius of the split ring is R = 205 μm, and the inner radius is SR = 199 μm, respectively.And a metal strip is 189 μm length 20 μm width, which is placed in the middle of the open semicircular ring with an intermediate opening g = 20 μm.The thickness of polyimide Z is 20 μm, and the thickness of the metal structures is 200 nm.The monolithic structure forms a MSs in the X-Y plane by a periodic arrangement.The periodic dimensions of the unit cell structure are X × Y = 240 × 240 μm.In this thesis, the electromagnetic properties of the TD MSs samples are analyzed by fabricating samples with different structural parameters(Samples with gap values of 17, 27, and 37 and SR values of 169, 179, and 189 were prepared).During simulations and experiments, the electric field is polarized along the X-axis and terahertz waves are incident along the Z-axis.The samples of TD MSs structures in the paper were processed using conventional lithography and metallization process techniques.In the first step, a 20-μm thick substrate was obtained by spin-coating PI-5878G (fabricated by HD Micro Systems TM) liquid polyimide on a silicon wafer.During the process, the thickness of the polyimide is controlled precisely by controlling the temperature and the speed of rotation.PI-5878G is a high molecular weight, polyamic acid; precursor in an NMP [N-methyl-2-pyrrolidoline] based solvent system.After being applied to a silicon substrate, the precursor was thermally converted into an intractable polyimide film[48].The thickness of 10 μm polyimide layer was obtained, when the spin rate is 1500 rad/min.The silicon substate coated with polyimide were heated on the hotplate 80 °C for 10 min, then 120 °C for 10 min, then 180 °C for 10 min.The above process was executed twice, then the 20 μm polyimide layer was obtained.The thickness of polyimide layer was measured by the step tester.t In the third step, the TD MSs is peeled off from the silicon substrate.The terahertz TD MSs was characterized using a terahertz timedomain spectroscopy(THz-TDS) system.The THz-TDS system consists of four parabolic mirrors in an 8-F confocal geometry mechanism.The use of parabolic mirrors and a confocal geometry referenced by bare

Figure 1 .
Figure 1.(a) Schematic unit structure of TD MSs (b) Microscope image of TD MSs sample at gap = 17 μm.

Figure 2 .
Figure 2. Transmittance profiles of TD MSs with different gaps (a) gap = 17 μm, (b) gap = 27 μm, (c) gap = 37 μm (the black solid line denoted the simulated amplitude transmission spectrum and the red dotted line denoted the experimental amplitude transmission spectrum).

Figure 4 .
Figure 4. (a) Schematic diagram of LC resonance-induced surface currents in TD MSs under LF (green line labels surface currents, brown labels Tx), (b) Surface current distribution at the LF, (c) Surface current distribution at the HF.

Figure 6 .
Figure 6.2.5-dimensional plot of the paired-amplitude transmission spectrum for the structural parameter Sr.

Table 1 .
The comparison among the previous TD MMs researches.

Table 2 .
Q -factor corresponding to different gaps under LF and HF.