Open Access
Add to BibSonomy
Abstract
Low quality (Q) factors of the intrinsic inductive–capacitive (LC) mode as well as the parasitic dipole oscillation mode restrict high-resolution sensing using split-ring resonators (SRR). Although the trapped Fano-mode of the high-Q factor is found in asymmetric SRR, the conventional design limits the scaling down of resonators. As such, excitation and manipulation of multiple trapped modes of SRR is significant for driving innovative designs of terahertz metamaterials and metasurfaces. In this work, we present a novel approach to manipulating multiple terahertz modes by increasing the fractal levels as well as the geometric symmetry of complementary SRR. It is found that the multiple trapped modes become achievable only in the case that the gap of adjacent fractal SRR opposes each other. By increasing the fractal level, the intrinsic resonance modes change slightly, and more trapped modes appear in between the frequency range of the two major intrinsic modes. The map of surface currents and magnetic field distribution reveal that intrinsic LC resonance in the first or second level SRR dominates the intrinsic modes. By contrast, the trapped mode arises from the hybridization of high-order localized dipole oscillation as well as the multiple localized LC resonances. These findings create new design opportunities for scalable metasurfaces across the terahertz spectrum and beyond, with ability to create high-resolution sensors.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Research employing terahertz radiation, is increasingly gaining huge attention, fulfilling practical applications in the fields of communication, sensing and imaging. In free space, the enabling devices for these applications are composed of sub-wavelength resonant bodies called metamaterials [1–12]. These engineered materials are simply a periodic arrangement of subwavelength resonators or meta-atoms whose frequency response can be tailored according to their shape or geometric size. The split-ring resonator (SRR) is the most popular meta-atom that is generally applied for sensing applications [13–15]. It consists of one or two rings or squares with split gaps in them that can be used to engineer a material’s magnetic permeability. The incident terahertz wave gives rise to a charge oscillation in inductive–capacitive (LC) resonance with the quality (Q) factors at the level of 10. Actually, the ohmic damping leads to a very large non-radiative loss, which limits the achievable Q-factors. A trapped mode of Fano-resonance can be excited by breaking the symmetry of the SRR structure, which exhibits extremely sharp resonance [16–28]. If one can achieve multiple trapped modes with high Q factors, the detection of molecule will be sensitive to the shift of multiple modes rather than one modes. This is able to increase the detection sensitivity for the application of bisosensor. In order to sense minimal amount of biochemical substances, the meta-atom can be designed as complementary structures [26–30]. Here, the complementary structures are entirely the inverse to those of metallic materials mentioned in the following Refs. [29–33]. According to the Babinet’s principle, the transmission coefficient, tc, for the complementary meta-atom is related to the transmission coefficient for its inversed metal meta-atom to by to + tc = 1. At resonance frequency, it is found that the to of metal structural SRR achieves minimum, while the tc of complementary SRR achieves maximum. By working within these limits, the trapped mode of complementary metamaterial can be triggered and tuned desirably. Recently, a new phenomenon is proposed that demonstrates the intrinsic Fano-resonance can collapse with an emergence of Lorentzian line-shape magnetic dipole oscillation in a complementary asymmetric SRR metamaterial [33]. Although the intrinsic mode or trapped mode can be tuned by engineering the structure of the meta-atom, the size of a single meta-atom needs to be ten times smaller than the operation wavelength, which restricts the device volume. In comparison, fractal structure-based meta-atoms are easy to engineer with room for scalability. Fractal structures are fragmented geometric shapes that can be split into sub-sections, for which, each sub-section or a group of sub-sections is identical to the entire meta-atom [34–42]. The most significant attribute therefore of a fractal structure is the self-similarity at different scales. It is found that one can achieve multi-frequency operation or broadband tenability in a metamaterial composed of fractal meta-atoms [41,42]. Its frequency response is attributed to the interaction between resonators of different sizes within a fractal meta-atom. Therefore, it is going to be a new approach to tuning the terahertz intrinsic-and-trapped mode by changing the fractal levels in a complementary meta-atom.
Herein, we propose three types of fractal meta-atoms made of complementary split-ring resonators (CSRR) of different sizes. The basic structure of the fractal meta-atom is made up of a circular CSRR and concentric CSRRs, where the diameter of the rings changes by 1/√2. That is, the shape and orientation of the generated CSRR is similar but different in size to the adjacent CSRR. The first type of fractal meta-atom, has the split gap of each subsequent CSRRs rotated by π radian, (Fig. 1(a) column 1). Since the gap of the generated SRR is opposite to the adjacent SRR, the metamaterial shall be termed opposite (O) gap metamaterial (O-gap). In the second type of fractal meta-atom, the split gaps are aligned on all CSRRs, and this will, in the course of this paper, be termed uni-directional gap (U-gap) metamaterial, (Fig. 1(a) column 2). In the third type of meta-atom, the orientation of the generated SRR is rotated by π/2 in the clockwise direction to adjacent SRRs. Metamaterial designs with such a fractal meta-atom will henceforth be referred to as clockwise gap (C-gap) metamaterial, (Fig. 1(a) column 3). The fractal level refers to the number of generated layers of CSRRs. Due to coupling effect; the terahertz response on these three types of meta-atoms must be compared at the same fractal level. Moreover, due to the difference is symmetry of the above-mentioned meta-atoms, the polarization sensitivity is also taken into account in both simulation and experimental measurements. The transmittance across metamaterials composed of either of these fractal meta-atoms is collected using a standard terahertz time domain spectroscopy (THz-TDS) setup. The surface current distribution and electric field strengths of resonance modes are also simulated. Finally, the evolution of terahertz intrinsic modes and trapped modes in fractal complementary metamaterials under different symmetric conditions and fractal levels are presented and discussed.
Fig. 1. Schematic representation of CSRR design. (a) Fractal meta-atoms of CSRR under different symmetric conditions: O-gap, U-gap, and C-gap, respectively, and fractal levels. (b) Pattern direction of fractal meta-atom, of which the z direction is the <100>-crystallographic orientation of SI-GaAs. P: lattice period, g: gap-size, r1: outer-radius, r2: inner-radius. (c) The top-view optical image of meta-atom. (d) Diagram of terahertz transmission spectroscopy
2. Experiments
Three types of fractal meta-atoms are illustrated in (Fig. 1(a)). The fractal level increases from 1 to 4 for each type of meta-atom. (Figure 1(b)) shows the coordination of free space, where the pattern of fractal meta-atom is in xy-plane, and the incident terahertz pulse is along the z-axis. P is the lattice period of the meta-atom, and is optimized to 100 µm. r1 and r2 are used to denote the outer-radius and inner-radius, respectively. r1 and r2 are optimized to 75 µm and 71 µm, respectively. The mean radius of the outermost CSRR is (r1+r2)/2 = 72 µm and the reduction ratio is given as S = 1/√2. The overall generated fractal level is N = 4, while the fractal dimension F is given as below [41]:
Figure 1(c) illustrates the microscopic images of as-fabricated meta-atoms. In the fabrication, the patterns of the meta-atoms are transferred onto 625 µm-thick <100>-oriented semi-insulating gallium arsenide (SI-GaAs) substrates by photolithography. Owing to the dielectric isotropy of <100>-oriented crystal, the normal line to the metal pattern layer is aligned with the crystallographic orientation of SI-GaAs. The effective area of the as fabricated fractal meta-atoms is 10 mm × 10 mm. The meta-atoms are metallized by a layer of 120 nm thick gold (Au) and 5 nm thick titanium (Ti). Ti is used enable good adhesion of Au to the substrate. Figure 1(d) illustrates the schematic diagram of terahertz transmittance measurement using a conventional THz-TDS. A couple of photoconductive antenna triggered by femtosecond pulse laser is used for terahertz generation and detection. The incident terahertz pulse is incident normally onto the metal surface of the meta-atom by a couple of 2 inch gold coated off-axis parabolic mirror. The detected terahertz signals are read out into an integrated lock-in amplifier at the time constant of 100 ms. The resonance modes are in the range from 0.2 THz to 1.0 THz. The frequency resolution is about 10 GHz. All terahertz measurements are conducted in nitrogen atmosphere so as to avoid water absorption in air. A bare SI-GaAs wafer identical to the sample substrate served as a reference. The transmission spectrum is extracted from Fourier transforms of the measured time-domain electric fields, which is defined as [33,34]:
3. Results and discussion
For a single CSRR, the electric component is perpendicular to the gap of the CSRRs, while the magnetic component is parallel to the gap. Normally, dual resonance modes occur when the incident terahertz polarization is perpendicular to the split gap of the SRR structure. However, only one mode is observed since the net electric dipole moment is large when the incident terahertz polarization is parallel to the gap. In the following two sub-sections, we shall discuss the electromagnetic response of the above mentioned three types of fractal meta-atom when excited by x- (Ex) and y-polarized (Ey) terahertz radiation.
3.1 Ex-polarization
The simulated and experimentally measured transmittance across the three types of fractal meta-atoms excited by Ex-polarized terahertz wave is presented (Fig. 2). The results show good agreement between the simulated and experimental data. The first level meta-atom is composed of a single CSRR. Only a single resonance mode is observed. Dual modes occur in O-gap and U-gap meta-atoms when the fractal level increases from 2 to 4. Herein, the dual modes are termed as L1 and L2 respectively. As is shown (Fig. 2), the fractal level almost has no influence on the L1 and L2 modes. Although the smaller CSSR is able to induce a higher frequency mode, the metallic part of the generated CSRR is relatively smaller. It is well-known that the mode strength is proportional to the effective metal area [34]. Therefore, the high-order modes are supposed to be covered by the background of terahertz transmittance owing to its fable resonance strength. For C-gap meta-atom, however, there is only a single mode L1 that appears in the terahertz spectrum even though the fractal levels increase from 0 to 4. Any other high-order resonance frequencies of the meta-atoms are invisible even though the fractal level is above 2.
Fig. 2. Transmittance from simulation and measurement when excited with Ex-polarised terahertz waves. Simulated (blue solid line) and measured (red solid line) transmittance (a) O-gap; (b) U-gap; and (c) C-gap meta-atoms. Dashed line represents the central position of resonance modes.
The accurate position of above resonance modes of the three types of meta-atom are listed in Table 1 below:
Table 1. The resonance modes of fractal metamaterial excited by Ex-linearly polarized terahertz waves.
The L1 modes fluctuate between 0.5 and 0.53 THz, and the L2 mode fluctuates between 0.73 and 0.77 THz. There is a small redshift in the intrinsic modes, L1 and L2 as the fractal level grows from 1 to 4. This phenomenon is similar to the near-field coupled fractal meta-atom in previous work [34]. Actually, one can evaluate the strength of resonance damping modes by calculating the quality factors (Q factors). The Q factor is a ratio of the central frequency, ν to the line-width, Δν of the resonance mode. Here, the Δν is the full width at half-maximum (FWHM) of mode spectrum. The Q factors of all the resonance modes are listed in the Table 2.
Table 2. Q factors of resonance modes of fractal meta-atoms excited with Ex-polarized terahertz waves.
The Q factors of L1 modes increase from 3.8 to 5.4 or above. Obviously, the Q factors of L1 and L2 modes are below 10. The energy dissipation can be derived from the dielectric spectrum of the meta-atoms [44,45] while the permittivity can be derived from the measured amplitude and phase of the transmission spectra as given [44,45]:
where, ɛr is the real part of permittivity, and ɛi is the imaginary part of permittivity. The permittivity at resonance frequency can reflect the oscillation strength and loss of resonance modes. The Q factors as well as the intensity of the resonance modes relies on the imaginary part and real part of permittivity function in dielectric spectrum. Large imaginary part means large energy loss, while high real part of permittivity means strong oscillation. These explains the change in Q-factors at resonance.Figure 3 shows the retrieved complex permittivity of the meta-atoms under different symmetric conditions. For the intrinsic modes, L1 and L2, the real part of the complex permittivity shows a large negative value, while the imaginary part shows large positive values, describing a lossy medium at these frequencies [14,29]. With increasing the fractal level, the permittivity of L2 modes of O-gap and U-gap meta-atom appear to be red-shifted, which is in agreement with the measured terahertz spectra shown (Fig, 2 (a), (b)). There are fluctuations beyond the frequency of intrinsic L1 modes of the C-gap meta-atom in the dielectric spectrum shown (Fig. 3(c)), however, the intrinsic L2 modes disappear in transmission spectrum shown (Fig. 2(c)).
Fig. 3. Complex permittivity based on symmetry of meta-atoms with Ex-polarized incident terahertz waves. Dielectric spectra of (a) O-gap, (b) U-gap, and (c) C-gap meta-atom for Ex-polarized incident terahertz waves. Red solid line: imaginary part of permittivity. Blue solid line: solid part of permittivity. Dashed line: the central frequencies of resonance modes.
In order to reveal the origin of different terahertz responses in the three types of fractal meta-atoms, the current distribution of the intrinsic modes, L1 and L2 of U-gap, O-gap and C-gap meta-atoms are simulated, shown (Fig. 4(a), (b), and (c)), respectively. In this case, the electrical field polarization is parallel to the metallic split gap of CSRR, as shown (Fig. 1). It is clear that the incident terahertz field drives a couple of anti-parallel surface currents in the upper and lower halves of the outermost CSRR unit cell, which dominates the L1 modes of the all meta-atoms. Similarly, anti-parallel surface currents in the upper and lower halves of the second level CSRR unit cell dominates the L2 modes, of which the direction of current is opposite to the current of L1 modes. For a symmetric structure, only dipolar resonance modes are naturally excited due to the constructive interference of charge oscillation in the two equal metal edges of the loop, which is able to couple strongly with the incident terahertz wave [13–15]. Such a couple of localized dipoles oscillating constructively in phase and amplitude will trigger a couple of magnetic dipole oscillations, as shown (Fig. 4(d), (e), and (f)). The magnetic dipole on first level and second level of CSRR result in intrinsic L1 and L2 modes of O-gap and U-gap meta-atoms, correspondingly. When the fractal levels increase up to 3 or 4, the outermost CSRR and the innermost CSRR undergo much weaker coupling to the incident terahertz radiation field, hence the terahertz response for meta-atoms mainly derives from the mode coupling of the biggest two adjacent CSRR. However, C-gap meta-atoms generated at higher levels are rotated by π/2 there by distorting the magnetic dipole oscillations. Therefore, the L2 modes disappear in terahertz spectrum. The outermost CSRR dominate the L1 modes. There is no trapped mode to be observed in the case of Ex-polarization.
Fig. 4. Surface current and magnetic field distribution at resonance modes. Surface currents at resonance modes for (a) O-gap, (b) U-gap, (c) C-gap; Magnetic field distribution of resonance modes of meta-atom in the layout of (d) O-gap, (e) U-gap, (f) C-gap. Where polarization of electric field is parallel to split gaps. Color bars denote the relative strength of surface current and magnetic field accordingly.
3.2 Ey-polarization
Simulated and measured transmittance across all three types of fractal meta-atoms excited with Ey-polarized terahertz wave is presented (Fig. 5(a), (b) and (c)). For a single CSRR, there exist two intrinsic resonance modes, I1 and I2. According to the Babinet’s principle, the intrinsic LC modes I1 as well as a parasitic dipole oscillation I2 are excited when the incident terahertz polarization is perpendicular to the metal gap. With the increase in the fractal level, more and more resonance modes appear in terahertz spectrum, as shown (Fig. 5(a)). In comparison, only three resonance modes are excited by the incident terahertz wave in the U-gap and C-gap meta-atoms, even though the fractal level increases from 2 to 4. The details of resonance modes are listed in Table 3.
Fig. 5. Transmittance from simulation and measurement when excited with Ey-polarised terahertz waves. Simulated (blue solid line) and measured (red solid line) transmittance for (a) O-gap, (b) U-gap, and (c) C-gap meta-atoms. Dashed line: the central position of resonance modes
Table 3. The resonance modes of fractal meta-atoms excited by Ey-polarized terahertz waves.
Herein, the three intrinsic modes are denoted Ii, where i = 1,2,3; while the trapped modes are denoted Tj, j = 1,2. It is obvious that the intrinsic modes I1, I2 and I3 of O-gap, U-gap and C-gap meta-atoms are almost identical. It should be noted that, the resonance modes are sensitive to the polarization of the incident terahertz wave. In this case, L1, L2, and L3 denote the intrinsic resonance modes in response to Ex polarized incident terahertz waves. While I1, I2, and I3, indicate the intrinsic resonance modes in response to Ey polarized incident terahertz waves. In O-gap meta-atom, the first trapped mode T1 occurs at around 0.5 THz between the intrinsic modes I2 and I3 at the fractal level of 4. The second trapped mode T2 occurs at 0.82 THz beyond intrinsic mode, I3. The resonance properties of above modes can be described from the Q factors, which is listed in Table 4
Table 4. The Q factors of fractal meta-atoms excited by Ey-polarized terahertz waves.
Interestingly, Q factors of the intrinsic and trapped modes are below 10. The relatively low Q factors are attributed to the high energy loss at resonance frequency, which can be drawn from careful observation of the dielectric spectrum of the meta-atoms.
Figure 6 shows the derived complex permittivity of the meta-atoms under different symmetric conditions. Compared to Fig. 3, the oscillation of permittivity at resonance modes are much stronger than modes under Ex-polarization. For L1 modes, the real part of the function of complex permittivity shows a large negative value, while the imaginary part shows large positive values, describing a lossy medium at these frequencies. For the L2 modes, however, both the real part and the imaginary parts become weakened. This phenomenon is the same as in our previous result of teeter-totter effect in single CSRR [46]. For the L3 modes, complex permittivity is weaker than L1 modes but stronger than L2 modes. In the O-gap meta-atom, however, the complex permittivities of the other two trapped modes are very faint as well. Correspondingly, the Q-factors of trapped modes are higher than the L1 modes but lower than the L2 modes.
Fig. 6. Complex permittivity based on symmetry of meta-atoms with Ey-polarized incident terahertz waves. Dielectric spectra of (a) O-gap, (b) U-gap, and (c) C-gap meta-atom in the case of Ey-polarization. Red solid line: imaginary part of permittivity. Blue solid line: solid part of permittivity. Dashed line: the central position of resonance modes.
In order to reveal the origin of the aforementioned resonance modes in all three types of fractal meta-atoms, the surface currents as well as the magnetic field at the resonance frequency are simulated accordingly. In this case, the polarization of terahertz electrical field is perpendicular to the metal gap of CSRR, as shown (Fig. 1). The gap becomes the symmetric axis of the surface current.
The surface current distribution of O-gap meta-atom is as shown (Fig. 7(a)). In Fig. 7(a) the incident terahertz field drives a couple of circulating surface currents in the gap of the CSRR at I1 and I3 modes. The surface current distribution and direction is seen as mirror images between the left and right halves of the CSRR structure. Since the circulating current is the evidence of the LC resonance, we propose that the localized LC on first level and second level of CSRR dominate the intrinsic modes, I1 and I3. However, the magnetic dipole momentum of mode I3 is opposite to that of mode I1, as shown (Fig. 7(b)). For the modes I2, however, the current flow becomes more complex. A couple of conjugated circulating surface current exist around the metal gap of CSRR, of which the direction of current is opposite to the circulating current of I1. The circulating current strengths and flowing area of modes I2 is distinctly weaker than that of modes I1. Meanwhile, two counter-circulating surface current occur at the lower-halves of CSRR unit cells, which cancel the electrically driven magnetic dipoles but form the electrical dipoles. To a symmetric structure, only dipolar resonance are naturally excited due to the constructive interference of charge oscillation in the two equal metal edges of the loop, which is able to strongly couple with the incident terahertz wave [14,46]. In our case, there are several localized dipoles oscillating constructively in phase and amplitude, which cause the modes I2. To the trapped mode T1 shown (Fig. 7(a)), a couple of circulating surface currents in the third level CSRR of O-gap meta-atom dominate the T1 mode, which is an evidence of LC resonance. Such a LC resonance results in a magnetic dipole shown (Fig. 7(b)). To the trapped mode T1, however, it is much more complex than the trapped mode T1. There are different current loops flowing simultaneously on each fractal level of CSRR. There are several localized dipole oscillations on the first and second level of CSRR, in company with a couple of circulating surface currents in the fourth level of CSRR. As such, all these localized LC resonances oscillate simultaneously with the multiple localized electric dipoles. Accordingly, the multiple localized magnetic dipoles oscillating constructively in phase and amplitude, as shown (Fig. 7(b)), creates the trapped mode T2.
Fig. 7. Surface current and magnetic fields distribution at resonance modes. (a) Surface currents and (b) magnetic field at resonance modes of O-gap meta-atom. Where polarization of electric field is perpendicular to the split gaps. Color bars denotes the relative strength of surface current and magnetic field accordingly. I refers to the intrinsic modes. T refers to the trapped modes.
For the U-gap meta-atom, however, there are only three intrinsic modes, I1, I2 and I3. As shown (Fig. 8), the circulating currents on first level of CSRR dominate the intrinsic mode I1, and that on second level of CSRR dominate the intrinsic mode I3. The multiple localized electric dipole oscillators on first level of CSRR generate the intrinsic mode I2. With the fractal levels increasing from 1 to 3, however, similar localized dipole oscillators occur on the second level of the CSRR structure. As such, the hybridization of multiple localized electric dipoles gives rise to the intrinsic mode I2. When the fractal level increases to 4 another couple of circulating current appears on the most-inner CSRR. Thus, such a couple of LC resonance hybrids with the other multiple localized electric dipole on first, second, and third level CSRR, which leads to the mode I2. Figure 8 shows the surface current distribution as well as the magnetic field distribution of resonance frequencies in C-gap meta-atoms, correspondingly. In a single CSRR, the LC resonance and localized dipole oscillation dominate I1 and I2 modes. When the fractal level is greater than 1, the generated CSRR is rotated by π/2, as such, the LC resonance modes is unable to be excited by the incident terahertz wave. However, the outermost CSRR play the role of a bright resonator, which excites the dark LC resonance on the second level of CSRR. Herein, the bright LC resonance on the first level of CSRR hybridizing with the dark LC resonance on second level of CSRR, constructing the I1 modes in C-gap meat-atom at the fractal level of 2. With a further increase of fractal level, the dark resonance on third level and fourth level of CSRR are excited simultaneously. As such, the collective oscillation of aforementioned modes dominates the evolution of I1 modes. Similarly, a couple of intrinsic LC resonance on the second level of CSRR gives rise to I3 modes in the beginning. With increasing the fractal levels, the higher order LC resonance can be excited, leading to I3 modes. As shown (Fig. 8(b)), there is a single magnetic dipole on the second level of CSRR oscillating with the other two localized magnetic dipole on first level giving rise to the I2 modes. Since the second level of CSRR is rotated by π/2, the incident Ey-polarized terahertz beam generates a couple of dipoles similar to the case of Ex-polarization. As such, the multiple dipoles on the first level and the second level CSRR are both bright resonances. There is no dark resonance to be excited in this case. Single trapped modes have also been demonstrated elsewhere [16–28], however, our work demonstrate a feasibility study to achieve multiple trapped modes by changing the fractal symmetry.
Fig. 8. Surface current and magnetic fields distribution for different fractal levels of U-gap meta-atom, at resonance modes. (a) Surface currents and (b) magnetic field at resonance modes of meta-atom in the layout of U-gap. Color bars: the relative strength of surface current and magnetic field accordingly. I refers to the intrinsic modes.
4. Summary
Fractal meta-atoms of complementary circular split-ring resonators (CSRR) are investigated under different symmetric conditions at the terahertz frequency range. Three types of fractal meta-atoms based on two factors; fractal number and split gap alignment (symmetry) are investigated: That is, opposite gap (O-gap), having the spilt gaps of adjacent SRR rotated by π in radian; the uni-directional gap (U-gap), with split gaps uni-directionally aligned; and clockwise gaps (C-gaps) having the split gaps of adjacent SRR rotated by π/2 radians in a clockwise direction. Simulated transmittances across these CSRR meta-atoms are investigated using CST microwave Studio Suit software package for different polarization of the incident terahertz waves. Experimental measurements on the fabricated metamaterials are conducted using terahertz-time domain spectroscopy. For normally incident terahertz beam with polarization along the x-axis, two intrinsic modes are excited in the U-gap and O-gap cases, while only one intrinsic mode is excited in C-gap meta-atom. Correspondingly, the Q factors of intrinsic modes increase with increasing in the fractal levels. When the incident terahertz beam is polarized along the y-axis, three intrinsic modes appear in all three types of meta-atoms with fractal level greater than 1. Furthermore, two trapped modes are observed in O-gap meta-atom when the fractal level reaches 4. All the intrinsic modes as well as trapped modes appear slightly red-shifted in frequency domain. The map of surface currents and magnetic field distribution reveal that intrinsic capacitive-inductive (LC) resonance on first level or second level SRR dominate the intrinsic modes; while the trapped mode is due to the hybridization of high-order localized dipole oscillation as well as the multiple localized LC resonance. Our results pave a new way to design the metamaterials for biosensor application and high-resolution thin film sensors.
Funding
Joint Fund of Astronomy (U1631112) from Natural National Science Foundation of China (NSFC).
Acknowledgments
Zhenyu Zhao and Zhidong Gu contributed equally in this work.
References
1. S. A. Jackson, “The nexus: where science meets society,” Science 310(5754), 1634–1639 (2005). [CrossRef]
2. E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Mikhaylovskiy, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadodwala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5(11), 783–787 (2010). [CrossRef]
3. N. Liu and A. Pucci, “Plasmonic biosensors: Know your molecules,” Nat. Mater. 11(1), 9–10 (2012). [CrossRef]
4. G. Brolo, “Plasmonics for future biosensors,” Nat. Photonics 6(11), 709–713 (2012). [CrossRef]
5. X. Wu, B. Quan, X. Pan, X. Xu, X. Lu, C. Gu, and L. Wang, “Alkanethiol-functionalized terahertz metamaterial as label-free, highly-sensitive and specific biosensor,” Biosens. Bioelectron. 42, 626–631 (2013). [CrossRef]
6. S. J. Park, J. T. Hong, S. J. Choi, H. S. Kim, W. K. Park, S. T. Han, J. Y. Park, S. Lee, D. S. Kim, and Y. H. Ahn, “Detection of microorganisms using terahertz metamaterials,” Sci. Rep. 4(1), 4988 (2015). [CrossRef]
7. L. Xie, W. Gao, Jie Shu, Y. Ying, and J. Kono, “Extraordinary sensitivity enhancement by metasurfaces in terahertz detection of antibiotics,” Sci. Rep. 5(1), 8671 (2015). [CrossRef]
8. X. Yang, X. Zhao, K. Yang, Y. Liu, W. Fu, and Y. Luo, “Biomedical applications of terahertz spectroscopy and imaging,” Trends Biotechnol. 34(10), 810–824 (2016). [CrossRef]
9. S. Wang, L. Xia, H. Mao, X. Jiang, S. Yan, H. Wang, D. Wei, H.-L. Cui, and C. Du, “Terahertz biosensing based on a polarization-insensitive metamaterial,” IEEE Photonics Technol. Lett. 28(9), 986–989 (2016). [CrossRef]
10. Z. Geng, X. Zhang, Z. Fan, X. Lv, and H. Chen, “A route to terahertz metamaterial biosensor integrated with microfluidics for liver cancer biomarker testing in early stage,” Sci. Rep. 7(1), 1–11 (2017). [CrossRef]
11. D.-K. Lee, J.-H. Kang, J. Kwon, J.-S. Lee, S. Lee, D. H. Woo, J. H. Kim, C.-S. Song, Q.-H. Park, and M. Seo, “Nano metamaterials for ultrasensitive Terahertz biosensing,” Sci. Rep. 7(1), 8146 (2017). [CrossRef]
12. W. Xua, L. Xie, J. Zhu, L. Tang, R. Singh, C. Wang, Y. Ma, H.-T. Chen, and Y. Ying, “Terahertz biosensing with a graphene-metamaterial heterostructure platform,” Carbon 141, 247–252 (2019). [CrossRef]
13. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84(18), 4184–4187 (2000). [CrossRef]
14. W. J. Padilla, A. J. Taylor, C. Highstrete, M. Lee, and R. D. Averitt, “Dynamical Electric and Magnetic Metamaterial Response at Terahertz Frequencies,” Phys. Rev. Lett. 96(10), 107401 (2006). [CrossRef]
15. I. V. Shadrivov, P. V. Kapitanova, S. I. Maslovski, and Y. S. Kivshar, “Metamaterials controlled with light,” Phys. Rev. Lett. 109(8), 083902 (2012). [CrossRef]
16. R. Singh, I. A. I. Al-Naib, M. Koch, and W. L. Zhang, “Asymmetric planar terahertz metamaterials,” Opt. Express 18(12), 13044–13050 (2010). [CrossRef]
17. R. Singh, I. A. I. Al-Naib, Y. P. Yang, D. R. Chowdhury, W. Cao, C. Rockstuh, T. Ozaki, R. Morandotti, and W. L. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phys. Lett. 99(20), 201107 (2011). [CrossRef]
18. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99(14), 147401 (2007). [CrossRef]
19. J. H. Shi, Z. Zhu, H. F. Ma, W. X. Jiang, and T. J. Cui, “Tunable symmetric and asymmetric resonances in an asymmetrical split-ring metamaterial,” J. Appl. Phys. 112(7), 073522 (2012). [CrossRef]
20. J. Wallauer and M. Walther, “Fano line shape and phase reversal in a split-ring resonator based metamaterial,” Phys. Rev. B 88(19), 195118 (2013). [CrossRef]
21. D. R. Chowdhury, X. F. Su, Y. Zeng, X. S. Chen, A. J. Taylor, and A. Azad, “Excitation of dark plasmonic modes in symmetry broken terahertz metamaterials,” Opt. Express 22(16), 19401–19410 (2014). [CrossRef]
22. D. J. Park, J. H. Shin, K. H. Park, and H. C. Ryu, “Electrically controllable THz asymmetric split-loop resonator with an outer square loop based on VO2,” Opt. Express 26(13), 17397–17406 (2018). [CrossRef]
23. S. Y. Yang, Z. Liu, X. X. Xia, E. Yiwen, C. Tang, Y. J. Wang, J. J. Li, L. Wang, and C. Z. Gu, “Excitation of ultrasharp trapped-mode resonances in mirror-symmetric metamaterials,” Phys. Rev. B 93(23), 235407 (2016). [CrossRef]
24. J. A. Burrow, R. Yahiaoui, A. Sarangan, I. Agha, J. Mathews, and T. A. Searles, “Polarization-dependent electromagnetic responses of ultrathin and highly flexible asymmetric terahertz metasurfaces,” Opt. Express 25(26), 32540–32549 (2017). [CrossRef]
25. E. Bochkova, S. Han, A. D. Lustrac, R. Singh, S. N. Burokur, and A. Lupu, “High-Q Fano resonances via direct excitation of an anti-symmetric dark mode,” Opt. Lett. 43(16), 3818–3821 (2018). [CrossRef]
26. W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. 37(16), 3366–3370 (2012). [CrossRef]
27. Y. K. Srivastava, L. Cong, and R. Singh, “Dual-surface flexible THz Fano metasensor,” Appl. Phys. Lett. 111(20), 201101 (2017). [CrossRef]
28. L. Cong and R. Singh, “Symmetry-Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7, 1900383 (2019). [CrossRef]
29. H. T. Chen, J. F. O’Hara, A. J. Taylor, and R. D. Averitt, “Complementary planar terahertz metamaterials,” Opt. Express 15(3), 1084–1095 (2007). [CrossRef]
30. F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007). [CrossRef]
31. J. Keller, J. Haase, F. Appugliese, S. Rajabali, Z. X. Wang, G. L. Paravicini-Bagliani, C. Maissen, G. Scalari, and J. Faist, “Superradiantly limited linewidth in complementary THz Metamaterials on Si-membranes,” Adv. Opt. Mater. 6(16), 1800210 (2018). [CrossRef]
32. P. Forn-Díaz, L. Lamata, E. Rico, J. Kono, and E. Solano, “Ultrastrong coupling regimes of light-matter interaction,” Rev. Mod. Phys. 91(2), 025005 (2019). [CrossRef]
33. Z. Gu, Z. Zhao, H. Zhao, W. Peng, J. Zhang, and W. Shi, “Fano-resonance collapse induced terahertz magnetic dipole oscillation in complementary meta-atoms via local symmetry breaking,” J. Appl. Phys. 125(14), 143102 (2019). [CrossRef]
34. Z. Song, Z. Zhao, W. Peng, and W. Shi, “Terahertz response of fractal meta-atoms based on concentric rectangular square resonators,” J. Appl. Phys. 118(19), 193103 (2015). [CrossRef]
35. H. X. Xu, G. M. Wang, Z. Tao, and T. J. Cui, “High-directivity emissions with flexible beam numbers and beam directions using gradient-refractive-index fractal metamaterial,” Sci. Rep. 4(1), 5744 (2015). [CrossRef]
36. G. Y. Song, B. Huang, H. Y. Dong, Q. Cheng, and T. J. Cui, “Broadband focusing acoustic lens based on fractal metamaterials,” Sci. Rep. 6(1), 35929 (2016). [CrossRef]
37. G. Volpe, G. Volpe, and R. Quidant, “Fractal plasmonics: subdiffraction focusing and broadband spectral response by a Sierpinski nanocarpet,” Opt. Express 19(4), 3612–3618 (2011). [CrossRef]
38. F. Miyamaru, S. Kubota, and M. W. Takeda, “Terahertz response of split-ring resonators with fractal structures,” Appl. Phys. Express 5(7), 072001 (2012). [CrossRef]
39. S. Sederberga and A. Y. Elezzabi, “The influence of Hausdorff dimension on plasmonic antennas with Pascal’s triangle geometry,” Appl. Phys. Lett. 98(26), 261105 (2011). [CrossRef]
40. X. Q. Huang, S. Y. Xiao, D. X. Ye, J. T. Huangfu, Z. Y. Wang, L. X. Ran, and L. Zhou, “Fractal plasmonic metamaterials for subwavelength imaging,” Opt. Express 18(10), 10377–10387 (2010). [CrossRef]
41. F. Miyamaru, Y. Saito, M. W. Takeda, B. Hou, L. Liu, W. Wen, and P. Sheng, “Terahertz electric response of fractal metamaterial structures,” Phys. Rev. B 77(4), 045124 (2008). [CrossRef]
42. Q. Du, H. Yang, T. Lv, and X. Wang, “Multiband and polarization-independent left-handed metamaterial with cross fractal structure,” Opt. Commun. 301-302, 74–77 (2013). [CrossRef]
43. B. Mandelbrot, Fractals and Chaos (Springer, 2014) p. 38.
44. X. Liu, S. MacNaughton, D. B. Shrekenhamer, H. Tao, S. Selvarasah, A. Totachawattana, R. D. Averitt, M. R. Dokmeci, S. Sonkusale, and W. J. Padilla, “Metamaterials on parylene thin film substrates: Design, fabrication, and characterization at terahertz frequency,” Appl. Phys. Lett. 96(1), 011906 (2010). [CrossRef]
45. J. Neu and C. A. Schmuttenmaer, “Tutorial: An introduction to terahertz time-domain spectroscopy (THz-TDS),” J. Appl. Phys. 124(23), 231101 (2018). [CrossRef]
46. Z. Song, Z. Zhao, H. Zhao, W. Peng, X. He, and W. Shi, “Teeter-totter effect of terahertz dual modes in C-shaped complementary split-ring resonators,” J. Appl. Phys. 118(4), 043108 (2015). [CrossRef]
