Bound states in continuum in highly symmetric terahertz metasurfaces

Jie Ji1, Shihab Al-Daffaie2, and Jaime Gomez Rivas1,*

1Department of Applied Physics and Science Education, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlands
2Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven 5600 MB, The Netherlands


Bound states in the continuums (BICs) in optical resonant systems have attracted a great deal of attention because of their unique characteristics, such as infinite Q values. By building highly symmetric structures or tuning parameters in the resonant system, BICs can be formed within the continuum of radiating electromagnetic modes without any loss [1]. In this study, we describe symmetry-protected BICs in THz metasurfaces with a unit cell comprised of two detuned metallic rods. Theoretical findings support the notion that these BICs, supported by the lattice structure, are invariant even when slight adjustments are made to the lattice parameters [2]. However, the degree of this resilience can fluctuate depending on the distinctive characteristics and symmetries of the system.
Given their infinite radiative lifetime, detecting symmetry-protected BICs through normal-incident far-field measurements is impossible. Direct observation of BICs is only possible with near-field optical techniques [3]. Consequently, accessing BICs from the far field necessitates disrupting the lattice symmetry, causing the transformation of BICs into quasi-BICs with a finite radiative lifetime that resembles leaky or sub-radiant modes. From Figure 1(a-b), it can be observed that as the absolute value of asymmetry degree |𝜶| (defined by the difference in length between the two rods of the dimer) increases, the low-resonance frequency mode broadens due to radiation leakage by coupling to the continuum. This resonance is still much narrower than the high-frequency mode due to their different origin; namely, the out-of-phase oscillation of free electrons in the rods for the low-frequency resonance and the in-phase oscillation for the high-frequency resonance.

To investigate the robustness of the BIC mode with the lateral separation and shift displacement between the rods, Figure 1(c) shows the extracted resonance frequencies by fitting the simulated transmission spectra with the temporal coupled-mode theory [4]. When the lateral separation between the two rods is reduced, leading to a strong near-field coupling between the two rods, the low-frequency resonance shifts and the mode can be effectively tuned. When the lateral distance between the two rods is sufficiently large, the two resonances become insensitive to the shift displacement. This observation highlights that in highly symmetric THz metasurfaces, BIC modes are quite robust to the lattice parameters when near-field interactions can be neglected. This work provides valuable insights for applications of THz metasurfaces with the requirement of narrow resonances in tunable devices, including filters, sensors, and resonance-enhanced THz spectroscopy.

Figure 1: (a) Optical images of THz metasurface supporting a BIC mode and a quasi-BIC mode, and description of the unit cell parameters. (b) Transition from a BIC to a quasi-BIC mode as a function of the asymmetry degree of the metasurface, given by the normalized difference between the lengths of the rods, and for a lateral separation between rods of d=80 μm. (c) Investigation of the resonances shift of the THz metasurface when the lateral separation and shift displacement between the rods are varied.

[1] C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljacic, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), (2016)
[2] D. R. Abujetas, N. van Hoof, S. ter Huurne, J. Gómez Rivas, and J. A. Sánchez-Gil, “Spectral and temporal evidence of robust photonic bound states in the continuum on terahertz metasurfaces,” Optica 6(8), 996 (2019)
[3] N. J. J. Van Hoof, D. R. Abujetas, S. E. T. Ter Huurne, F. Verdelli, G. C. A. Timmermans, J. A. Sánchez-Gil, and J. G. Rivas, “Unveiling the Symmetry Protection of Bound States in the Continuum with Terahertz Near-Field Imaging,” ACS Photonics 8(10), 3010–3016 (2021)
[4] L. Cong and R. Singh, “Symmetry‐Protected Dual Bound States in the Continuum in Metamaterials,” Adv. Opt. Mater. 7(13), (2019)

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