High-quality factor Quasi-BIC mode via selective symmetry-breaking approach in a terahertz metasurface

This study numerically and experimentally presents a novel approach to excite bound state in the continuum (BIC) mode with a high Q-factor in the THz meta-molecule (composition of meta-atoms) system, leveraging a unique method of selective symmetry breaking in a ring-shaped metamolecule system. Unlike conventional strategies that uniformly disrupt the symmetry across all resonators to excite a quasi-BIC mode, this innovative technique targets only half of the unit cell for symmetry perturbation. This selective symmetry breaking minimizes radiative losses and enhances the Q-factor of the quasi-bound states in continuum (quasi-BIC) modes. The selective symmetry breaking is achieved in a ring-shaped metamolecule system by simple radial perturbation. The results depict a notable improvement in the Q-factor, achieving values as high as 107 in simulation, a significant enhancement compared to the uniformly symmetry-breaking approach, which exhibits Q-factors around 25.80. The experimental transmission spectrum and the near-field scanning images firmly validate the existence of the high Q BIC mode under this strategic symmetry-breaking approach. This work may open new avenues for developing advanced THz devices with promising applications in sensing, filtering, and non-linearity in the THz domain.


Introduction
The investigation of high Q resonances in optics and photonics is motivated by the phenomena like nonlinearity [1], strong light-matter interaction, sensing [2], optical switch [3,4] etc.Recently, THz technology has garnered significant interest in areas such as sensing [5], filtering [6], and slow light modulation [7], mainly due to its unique ability to penetrate dielectric materials, its low photon energy interactions, distinct spectral signature to some elements and applicability in 6G communications.The fundamental research and development of THz metamaterial with high Q resonant response is always very important in such a context.Controlling losses is essential in metamaterials to obtain a narrow spectral response.The losses can be classified as non-radiative and radiative, which can be minimized by choosing the material properly and optimizing the design.In the THz frequency range, the Drude metals show high conductivity and, hence, less non-radiative loss than optical communication or visible bands [8].In such cases, the radiative losses are a significant cause of loss in metallic metamaterials.Therefore, in the THz frequency range, the major challenge to minimize the losses in metallic metamaterials shifts towards addressing radiative losses.Metallic structures are mostly preferred for their ease of fabrication.Furthermore, the metallic structures offer an additional advantage over all-dielectric counterparts by potentially reducing etching errors, which are very common in fabricating all-dielectric structures.Several works have reported high Q resonance mode excitation using a metallic metamaterial system at terahertz frequencies [9][10][11].Jansen et al studied the excitation of trapped mode resonances in metallic THz metasurfaces [12].The trapped modes with in-phase oscillations of antisymmetric currents lead to a Q factor 27.5.Chen et al proposed a nested square split ring resonator metamaterial as a sensing application in the THz range [13], which shows an improvement of the Q factor with a value of 30.5.In another approach, a sharp resonance has been excited in a planar metallic metasurface by exploiting the intrinsic nature of the toroidal resonance [14].The passive tunability of the design shows a maximum Q factor of 42.5 in the THz spectral regime.Zhang et al theoretically and experimentally demonstrated multiple bound state in the continuum (BIC) in a split ring resonator using the symmetry-breaking approach [15].Thanks to the ultra-high Q nature of the symmetry-protected BIC, a quasi-BIC Fano line shape resonance is manifested under the breaking of the structural symmetry.This characteristic allows for observing sharp resonances with a high Q factor, which is crucial for enhancing the performance of various photonic and terahertz applications.The symmetry-protected quasi-BIC approach garners attention for its straightforward physical picture and the extensive tunability of both Q factor and resonance frequency through asymmetry.However, the relatively low Q factor and the structural complicacy of the existing works show ample room to improve the Q factor further and create a design with less complicacy.The standard strategy to observe symmetry-protected quasi-BIC is to perturb the structural symmetry of a unit cell uniformly [2,16].In such a scenario, all the resonators contribute to the far-field radiation.Recent studies have demonstrated promising results in the metasurface-based quasi-BIC resonance.Zhou et al reported an all-metal metasurfaces achieving high-Q and high figure of merit (FOM) resonances based on BICs in the visible wavelength range [17].Aigner et al demonstrated the excitation of quasi-BIC mode in a plasmonic nanofin metasurfaces, which support symmetry-protected bound states in the continuum in the mid-infrared (MIR) region.By breaking the out-of-plane symmetry of the nanofins, a high-quality factor mode is excited under normal incidence [18].However, it is important to investigate the emergence of high Q mode in the terahertz frequency region.Compared to the visible and MIR region, there are fundamental differences in material properties and dispersion effect when interacting with terahertz radiation.We have introduced a generalized selective or non-uniform symmetry-breaking scheme in a simple ring-shaped metamolecule system.This method stands out as it strategically breaks the symmetry of only half the resonators in the metamolecule, unlike previous methods that uniformly perturb the symmetry of all the resonators.This approach effectively reduces the radiation density, a significant advancement in controlling radiative losses.The design consists of simple ring shape geometry, and we have strategically applied radial perturbation to break the symmetry selectively.The simplicity of both the design and the symmetry-breaking approach significantly reduces the chances of fabrication errors.Such a selective symmetry-breaking strategy with a simple ring resonator design to excite a high Q quasi-BIC mode has not been demonstrated in previous studies.In our approach, a high Q resonance mode appears because of dipole detune due to selective symmetry breaking.The improved Q factor and a straightforward design approach can have significant implementations in sensing, filtering, and slow light applications at terahertz frequencies.

Simulation and sample fabrication details
We have designed a meta-molecule system comprising four resonators or meta-atoms made of aluminum rings positioned on the top of a quartz substrate, collectively referred to as a meta-molecule system.Figure 1 illustrates the schematic of the proposed meta-molecule system, including a detailed view of a unit cell (as shown in the inset).The optimized geometrical parameters of the meta molecule system are periodicity (P) = 200 µm, width (w) = 6 µm, outer ring radius: r 1 = 27 µm, r 2 = r 3 = 34 µm, and r 4 = 41 µm.Finite element solver-based CST Microwave studio suite software has been used to design and optimize the proposed metasurface design.The boundary conditions are chosen as unit cell along X and Y direction, and Open (add space), Open along Zmax and Zmin, respectively.The transmission spectrum is simulated under the excitation of TE polarized (Y-polarized) normal incident electromagnetic plane wave.Following theoretical optimization, the proposed design is fabricated in a clean room environment.Quartz wafer is used as a substrate material for the proposed meta-molecule system.The thickness of the one-sided polished quartz wafer was 500 µm.A thin film of aluminum with a thickness of 200 nm was deposited on the quartz substrate using thermal evaporation.It was then spin-coated with hexamethyldisilane (HMDS) and S1813 positive photoresist, followed by a complementary patterning using a direct laser mask writer.This step defined the areas to be etched out and those to be masked based on our intended metasurface design.The HMDS acts as an adhesive for the positive photoresist.After development for 50 s, the sample was etched using an aluminum etchant to remove the undesired metallic part, while the photoresist served as a protective mask for regions intended to be part of the final metasurface structure.Finally, acetone is used to strip away the residual photoresist.

Analysis of the high Q Fano resonance
We have strategically broken the structural mirror symmetry of the metamolecule system to reduce the radiation density of the system.The proposed design shows a high Q Fano-like resonance under the non-uniform mirror symmetry breaking of the metamolecule (as shown in figure 2(b)).Figure 2(a) shows the different schemes of symmetry breaking applied in the design to strategically enhance the Q factor by reducing the radiation loss.To minimize inter-unit cell near-field interactions and study the resonance behavior primarily due to symmetry-protected BIC, we arranged the four-ring resonators with a center offset of 6 µm, as shown in figure S4 of supplementary material.Figure 2(b) shows the simulated transmission spectrum corresponding to a symmetric structure, a uniform symmetry-broken structure, and a non-uniform symmetry-broken (or selectively symmetry-broken) structure.The symmetric metasurface design exhibits a broad resonance dip at a frequency of 1.1 THz.As per already reported studies, it is known that such a metallic design shows a polarization-independent broad dipole resonance [19].An additional Fano line shape resonance appears in the spectrum as we introduce a uniform mirror symmetry-breaking effect in the system.However, we can adopt a smart strategy to further enhance the Q factor of the meta-molecule system by breaking the symmetry in a non-uniform or selective way.A significant enhancement in the Q factor from 25.8 to 107 is observed under the non-uniform symmetry-breaking effect.The sharp spectral dip arises in a narrow frequency window with an additional resonance dip.Hence, the sharp resonance dip (marked as A for the convenience of discussion) seems to be spectrally squeezed in a narrow frequency range.The resonance dips are marked as A, B, and C with different color for the convenience of discussion.The first resonance dip shows significantly narrower linewidth compared to the second.Under the symmetry-breaking effect, the usually uncoupled dark resonance interacts with the bright, broad radiation continuum and manifests a Fano line shape embedded in the broad radiation continuum [20][21][22].The broad dipolar resonance splits as soon as the mirror symmetry of the structure is broken and Fano-like resonance dip evolves in the background of broad resonance.To get a more in-depth qualitative realization of the splitting of the broad dipole mode, a plasmonic mode hybridization scheme is presented in figure 3.In a coupled ring system, both symmetric and antisymmetric modes are observed as a result of hybridization [23,24].The size of the rings is smaller than the exciting wavelength, allowing the micro-ring to be treated as an electrical dipole.Four different eigenmodes are possible, as depicted in figure 3 (for both transverse and longitudinal polarization of the incident electric field).Two of them are described as an in-phase oscillation of the electric dipoles in both rings.They are known as symmetric or bright eigenmodes since they can radiate into the far field.An out-of-phase oscillation of the electric dipoles in both rings designates the remaining two modes.These modes are known as dark modes, which cannot be directly coupled to the radiation continuum.However, as structural symmetry is broken, the dark mode couples to the continuum with a net reduced dipole moment and manifests as a sharp Fano line shape resonance.The coupling between two resonators depends on the spatial and respective spectral position [25,26].To further understand the mechanism of coupling in the proposed design, we have simulated the near-field distributions of the electric field, as shown in figure 4. The field profiles at three resonance dips are depicted by different color frames, keeping in a match with the distinguishing font color for the three-resonance dips marked as A, B, and C, respectively, in figure 2(b).Figure 4 shows that at two distinct resonance dips, A and B, dipole modes in each pair are antisymmetric.Longitudinally aligned pairs (axis parallel to polarization) couple more effectively due to their spectral proximity and small gaps.This effect arises because a circular ring resonator's dipole mode resonance depends on its radius and ring width [27].If the resonance wavelength of the three-ring resonator of radius 41 µm, 34 µm and 27 µm are denoted by λ 41 , λ 34 and λ 27 then λ 41 ⩾ λ 34 ⩾ λ 27 .So, the pair of resonators with radius 41 µm and 34 µm; 27 µm and 34 µm will be coupled due to their spectral overlapping.The Z-component of the electric field corresponding to the resonance dip A and B (as shown in figure 4) are combinations of symmetric and antisymmetric modes generated for each longitudinal pair.At resonance dip A, rings 3 and 4 oscillate in phase, creating a sharp linewidth resonance due to ring 2's role in reducing the net dipole moment.In contrast, at dip B, rings 2 and 4 oscillate strongly in phase, with rings 1 and 3 showing weaker antiphase oscillations.This pattern is also evident from the absolute field profile for dip B, resulting in a larger net dipole moment, leading to a broader Fano resonance.For resonance dip C, the Ez component shows uniform oscillation across the rings, producing a significant net dipole moment.At resonance dip A, the rings 4 and 3 behave as bright resonators, and the coupling with oppositely oscillating dark resonators gives the Fano dip A. Similarly, at resonance dip B, the diagonal ring pair 2,4 strongly oscillates in phase and acts as a bright resonator.The coupling with the indirectly excited dark resonators gives the Fano dip B. The explanation of the relation between the sharp resonance dip and the dark resonance mode is depicted in figure 5(a).The resonant state |ψ 1 ⟩ can be an interaction between the unperturbed or bound state and the broad radiation continuum [28].The perturbation causes a frequency shift as well as dipole detuning in the system, as a result of which the state manifests as a sharp Fano resonance with a finite Q factor [28,29].The green arrow in figure 5(a) shows the direction of the net dipole moment.Figures 5(b) and (c) give firm quantitative evidence of the dipole detuning in the metamolecule system.Figures 5(b) and (c) validate the asymmetric field strength under the perturbation effect and symmetric field strength with a zero-dipole moment for the unperturbed system.The field strength for the unperturbed mode corresponding to Γ point (K x = K y = 0) is calculated by using the eigenmode analysis in CST microwave studio suite simulation.

Theoretical analysis of the bright-dark coupling for the proposed system
We have used the analytical formula based on Gallinet and Martin's ab initio theory [30,31], which facilitates a quantitative approach for a deeper understanding of the resonance behavior in metamaterials.This theory reveals the roles played by the electromagnetic modes and material losses in forming Fano resonance in metallic subwavelength structures.The theory is based on the interference between radiative broad resonance mode (continuum) and non-radiative asymmetric mode (dark mode).According to ab initio theory, the resonance magnitude of the system can be expressed as the product of the symmetric (bright) and antisymmetric (dark) resonance modes respectively [31], where the superscript i(j) = 1, 2 indicates the ith(jth) dark(bright) mode.The dark and bright resonance profile can be expressed as, where ω is the frequency, ω d (ω b )is the central resonance frequency of the dark and bright modes, γ d (γ b ) is the linewidth of the dark(bright) mode spectrum, K is the relative amplitude of the resonance, q is the asymmetric parameter, and b is the modulation damping parameter corresponding to the damping effect due to the intrinsic losses.The parameters q and b are shape parameters that describe the Fano line shape of the resonance.By using these analytical functions and considering bright-dark interaction, the complete transmission spectrum for the proposed system can be obtained.The excellent agreement between the numerically simulated and theoretically calculated transmission spectrum is shown in figure 6(a).The parameters of the analytical expression are obtained by fitting with the spectrum obtained using numerical simulation.The values of the extracted fit parameters are reported in table 1.The contributing bright mode, which is decomposed from the analytical modeling, is shown in figures 6(b) and (c) shows the corresponding discrete line shape.Equation (1) gives the collective influence of all the radiant continuum and the discrete dark resonance mode, which gives the complete transmission profile.

The influence of geometrical perturbation and BIC characteristics
To investigate the asymmetry dependence of the transmission spectrum, we have simulated the meta-molecule system for different degrees of asymmetry.The degree of asymmetry in the meta-molecule system is defined as δ = (r1−r2) (r1+r2) × 100%.Figure 7(a) depicts the transmission plot under the different degrees of geometrical perturbation.It is evident from figure 7(a) that the resonance mode ceases to couple with the radiation continuum as we decrease the asymmetry.This can be understood as an ideal BIC mode that cannot be accessed due to its infinite Q factor or zero linewidth.This BIC mode transforms into quasi-BIC mode under the influence of geometrical perturbation and manifests as a high Q Fano resonance.The Q factor of the resonance mode can be calculated by extracting the overall damping rate from Fano fitting [29,[32][33][34]: , where c 1 , c 2 andα are real value constants, γ is the overall damping rate, and ω 0 is the resonance frequency.The radiative Q factor, Q = ω0 2γ is plotted against the respective degree of asymmetry as shown in figure 7(b).The Q factor of the resonance mode shows a (5.9×10 4 ) fitting with a correction term −33.97.The inverse square dependence of the Q factor demonstrates the existence of the structural symmetry-protected BIC in the meta-molecule system [15,29].The calculated transmission against varying degrees of asymmetry is shown in figure 7(c) (see supplementary section for fitting details).The resonance becomes sharper as we reduce the asymmetry and finally disappears from the spectrum for a perfectly symmetric structure.The BIC mode can be distinguished by the property that for zero asymmetry, it has an infinite Q factor and hence cannot be detected in the spectrum.The presented approach is based upon the solid foundation established by the previous works reported in this field.To convey the improvement in the Q factor observed in the current study, we have presented a comparison in table 2, which shows an enhancement in the excitation of the Q factor compared to earlier studies.

Experimental demonstration 4.1. Measurement of transmission using THz time-domain spectroscopy
Intending to demonstrate the above-discussed numerical results experimentally, we prepared samples using quartz wafers.Metasurfaces were fabricated for three degrees of asymmetries δ = 0, 20.5%, 29.4%.The transmission amplitude of the proposed metasurface is measured using an in-built fiber-coupled terahertz time-domain spectroscopy setup (THz-TDS) in a dry environment with humidity less than 14%. Figure 8 presents the schematic of the fiber-coupled in-built THz time-domain spectroscopy setup.The characterization setup consists of a photoconductive-based THz transmitter and a THz receiver with a pair of identical gold-coated parabolic mirrors.The metasurface sample is placed in the focal plane of the parabolic mirrors to ensure less spatial dispersion of incidence [15].An array size of approximately 1 cm × 1 cm is fabricated to assure excitation homogeneity.The transmitted time domain signal is transformed to the frequency domain through Fourier transformation and normalized with an identical bare quartz substrate as a reference, T (ω) = Es(ω)  Er(ω) , where E s (ω) and E r (ω) are the Fourier-transformed frequency domain transmission spectra of the sample and bare quartz substrate.The transmission spectra are measured for three samples with different degrees of asymmetries.The results show a signature of the quasi-BIC resonant response and a good agreement of resonance frequency of the simulated and experimental results.Figure 9(a) presents the transmission spectrum obtained from the symmetrical metasurface configuration, revealing a distinct resonance dip at 1.1 THz, matching with simulation predictions.However, the discrepancies in the observed linewidth and amplitude compared to simulations are likely due to edge scattering losses and inevitable fabrication inaccuracies.Figures 9(b) and (c) illustrate the measured transmission spectrum corresponding to structural asymmetry δ = 20.5% and δ = 29.4%.The results show a signature of the existence of quasi-BIC resonance mode at frequency 0.7 THz as we introduce the asymmetry.Since the results correspond to an asymmetry degree of 29.4%, showing a prominent dip, we have calculated the experimental and simulated Q factors for this asymmetry for comparison (see supplementary material for details).The experimentally determined Q factor is 5.96, whereas the simulated Q factor is 33.7.This mismatch between simulation and experimental result is mainly due to the experimental set-up's minimum resolution limit, which is insufficient to resolve a resonance with ultra-narrow linewidth resonance.Moreover, the quartz substrate with a thickness of 500 µm is used as a mechanical support to the metasurface design, producing an etalon effect due to the reflection from the incident surface.The presence of the etalon pulses creates a noisy oscillation in the time domain transmission spectrum.The sharp resonance dip somewhat loses its existence as a cumulative effect of the limited resolving power and the etalon effect.To avoid this etalon effect, the data  have been truncated before the emergence of etalon noises.However, a finite amount of information is lost due to this effect, and that causes an observable mismatch between the simulation and experiment.

Measurement of the near field distributions
We investigated the near-field distribution of the electric field associated with the resonance mode of the fabricated metasurface sample by using near-field scanning terahertz microscopy (NSTM) setup.Figures 10(a  (Protemics GmbH).The generated terahertz beam is focused on the tip using off-axis parabolic mirrors.The sample is mounted on an XYZ motorized stage to construct the spatial profile.The transient THz Electric field mapping in the temporal domain is done using a delay line.The current induced in the microprobe, due to the THz electric field, is amplified (using trans-impedance amplifier) and detected using the standard lock-in measurement technique (SR865).The THz microprobe was placed 10 µm (< λ 10 ) above the metasurface for this measurement.An area of 400 µm × 400 µm was scanned around a meta-molecule with a step of 10 um.The measured spatio-temporal THz electric field distribution is then Fourier transformed to the frequency domain to obtain the electric field profile at different frequencies.Due to the spatial resolution limitation of the microprobe, the measured field profiles appear convoluted compared to the profiles obtained in the simulation (For details, see section 2 in the supplementary information).

Conclusion
In conclusion, we have reported a robust high quasi-BIC mode with a ring-shaped metamolecule system.The system's symmetry is broken innovatively to reduce the radiation density, resulting in a high Q quasi-BIC resonance that surpasses the Q factor achieved by the typical symmetry-breaking approach.The Q factor of the resonance and the resonance frequency can be tuned by changing the geometrical degree of asymmetry.The experimental results of the simulation and theoretical modeling corroborate the new approach to excite a high Q quasi-BIC resonance mode in the THz frequency range.To the best of our knowledge, this type of high Q quasi-BIC mode excitation in a simple metallic meta-molecule through a non-uniform approach of symmetry breaking is reported for the first time.This kind of simple, experimentally well-accessible, yet effective method can open new avenues for the exciting field of applications like sensing and nonlinearity in the THz frequency range.

Figure 2 .
Figure 2. (a) The arrangements of four ring resonators in a metamolecule unit cell with three approaches: symmetric, uniform symmetry breaking, and selective symmetry breaking.Olive background resonators have a radius of 27 µm, red background resonators 41 µm, and gray background resonators 34 µm.(b) Simulated transmission spectrum of the symmetric meta-molecule system, non-uniformly symmetry broken structure, and uniformly symmetry broken structure.

Figure 3 .
Figure 3.The mode hybridization scheme for a micro ring pair unit cell, where the dark mode manifests as a result of dipole detuning due to the introduction of the structural asymmetry.

Figure 4 .
Figure 4.The simulated Z-component of the electric field, normalized surface current density profile, and absolute of the normalized electric field profile distributions at the three-resonance dip.The color of the frame is consistent with the font color used to depict the three-resonance dip in figure 2.

Figure 5 .
Figure 5. (a) A schematic description of the decomposition of the sharp resonance mode into an unperturbed dark mode and the radiation continuum.The size of the sign represents the strength of the field, (b) the 1D field plot along Y-direction at x = −44 µm and X = 44 µm for the symmetry-perturbed metamolecule system, (c) the 1D field plot along Y direction for the symmetric structure, calculated using eigenmode analysis.

Figure 6 .
Figure 6.(a) The theoretically calculated transmission spectrum for a structural asymmetry δ = 26.4%.The Theoretical matching validates the evidence of the bright-dark coupling mechanism.(b) The broad radiation continuum was extracted using the analytical model, and (c) the corresponding dark or discrete line shape was extracted using the analytical fit.

Figure 7 .
Figure 7. (a) The simulated transmission contour plot as a function of frequency and degree of asymmetry, (b) the asymmetry versus calculated Q factor of the sharp resonance dip.The solid line represents the fitting with the expression Q = Aδ −2 + Correction term, (c) evolution of the quasi-BIC in the transmission spectra vs the degree of asymmetry.

Figure 8 .
Figure8.The Fiber-coupled THz time domain setup, the transmitted THz radiation is focused to a beam spot size 8 mm using a parabolic mirror of a focal length of 10 cm.The focused THz beam is passed through a metasurface sample area of 1 cm × 1 cm and then is detected in the detector.
) and (b) show the normalized (abs(E z )) electric field distribution mapped over an area of 400 um × 400 um with the measurements on the left panel and simulated results on the right panel.The simulated near-field distributions are accurately reproduced in the experimental abs(E z ) field distribution associated with the quasi-BIC mode at a frequency of 0.71 THz.The working principle of the NSTM setup is similar to that of a conventional THz-TDS system (For details, see figureS3in the supplementary information).A 35 fs optical pulse, with 800 nm central wavelength, from Spectra-Physics MaiTai laser is split to generate a single cycle THz pulse using a photoconductive antenna (BATOP GmbH) and detect the THz pulse using a polarization-sensitive micro-structured photoconductive antenna based THz microprobe

Figure 10 .
Figure 10.The measured near field scanning microscopy image and simulated abs(Ez) field distributions of metasurface with asymmetry α = 29.4% at frequencies (a)f = 0.71 THz and (b)f = 0.92 THz.The field distributions are scanned and calculated at 10 µm above the metasurface.The ring resonators are highlighted with black dashed circles.

Table 1 .
Extracted parameters from the analytical fitting.

Table 2 .
Comparison with already reported works.