Applied Science and Convergence Technology 2022; 31(1): 31-34
Published online January 30, 2022
Copyright © The Korean Vacuum Society.
Department of Physics and Institute of Quantum Convergence Technology, Kangwon National University, Chuncheon 24341, Republic of Korea
Metasurfaces with high quality factor resonances can be fabricated by breaking the symmetry of the constituent resonators, thereby converting symmetry-protected dark states to quasi-bound states in the continuum. As the quality factor is inversely proportional to the degree of the asymmetry, high quality factor metasurfaces typically comprise fine-tuned resonators requiring state-of-the-art lithographic technologies to fabricate. In this study, a method is proposed to create quasi-bound states in the continuum in dielectric metasurfaces without high-resolution lithography. The results show that quasi-bound states in the continuum can be formed by introducing a non-vertical sidewall in an array of cube resonators, such that the resonator symmetry breaks in an out-of-plane direction. The proposed method enables fabrication by controlling the dry etching angle without extensive use of high-resolution lithography. Using full-wave electromagnetic simulations and multipole analyses, high quality factor resonances are observed in the proposed metasurface structure, the connections of which to the quasi-bound states in the continuum are clarified. Our work enables fabrication of high quality factor metasurfaces with low cost and high controllability, and is expected to greatly benefit the field of enhanced light-matter interactions in nanophotonics.
Keywords: Metasurface, Quasi-bound states in the continuum, Quality factor, Lithography, Cube resonators, Symmetry breaking
A metasurface is a two-dimensional array of resonators with subwavelength dimensions and periods, which can be engineered to have desirable properties absent in natural materials. Several photonic applications such as flat optics, sensors, and photodetectors are based on metasurfaces due to their flexibility in manipulating electromagnetic fields at the sub-wavelength scale [1–6]. In particular, dielectric metasurfaces can support Mie resonances with various types of multipole moments capable of efficiently boosting nanoscale light-matter interactions [7–9]. Such metasurfaces have been utilized to enhance photoluminescence, harmonic generation, and nonlinear mixing, etc. in optically active materials including III-V semiconductors and lowdimensional materials [10–14]. Further enhancement is possible by realizing resonances with high quality factors (Q), which increase local photonic density of states. In metasurfaces, high quality factor resonances are typically realized by introducing an asymmetry into an otherwise symmetric unit cell. This distorts the symmetr
Metasurfaces with quasi-BIC are known to have a quality factor of resonance that is inversely proportional to the square of the asymmetry parameter. Therefore, high-Q resonances can be achieved through minimal adjustments using a symmetric resonator. For metasurfaces designed for visible or near-infrared wavelengths, the typical size of an individual resonator is of the order of 100–300 nm and introduced asymmetry must be of the order of a few tens of nanometers. This critical dimension requisite is extremely difficult to achieve with commonly used, scanning electron microscope (SEM)-based electron beam lithography (EBL) systems and generally require extremely expensive e-beam writers with acceleration voltage of ~100 kV. Therefore, a high-Q metasurface that can be fabricated without expensive lithographic tools is expected to significantly benefit research on metasurfaces and enhanced light-matter interactions.
In this study, a fabrication method for high-Q metasurfaces operating at near-infrared wavelengths without employing a high-end e-beam writer. Typically, asymmetric dielectric metasurfaces are fabricated in a particular order . First, a hard mask with an asymmetric pattern is created using EBL atop a dielectric film. Then, the asymmetric pattern is transferred to the underlying dielectric film in the process of dry etching. This standard process creates resonators with in-plane asymmetry. The proposed method begins with the creation of a hard mask with a large, symmetric pattern that can be easily handled with common SEM-based EBL systems (Fig. 1). Following this, the pattern is transferred to the film in the dry etching step, as in the conventional method. Subsequently, an additional dry etching is applied at a non-vertical angle, thereby creating non-vertical sidewalls and out-of-plane oriented asymmetry. The etching angle can be controlled either by tilting the loading surface of the handling wafer, or by using etching facilities with angle controllability such as argon ion beam millers. Therefore, the metasurface with out-of-plane asymmetry can be practically realized but, nevertheless, remains unexplored. Finally, using full wave electromagnetic simulations, the optical properties of such metasurfaces are analyzed and the physical origin of their resonances is discussed.
For electromagnetic simulations, a python-based finite difference time domain (FDTD) method library called MEEP was employed . The proposed metasurface comprised an array of silicon cubes with slightly non-vertical sidewalls along one side (Fig. 2). The length of each side of the cube (
Post simulation, the Q-factor of the resonances was extracted by fitting the transmission spectra with the following Fano formula ,
Here, ω is angular frequency,
Mie modes contributing to the resonances are analyzed with multipole decomposition studies. From electric field distribution within the resonators, multipole moments can be calculated using the following equations [20, 23],
Figures 3(a) and 3(b) show the calculated transmission spectra of asymmetric (
For a more quantitative analysis, Q-factors of the resonances were extracted using Eq. (1) and plotted in Fig. 4. The Q-factors increase divergently as
The electric field distribution of the resonant mode for a sample with
Further quantitative analysis of the nature of the resonance was performed through multipole decomposition studies using Eqs. (2)-(7), the results for which are shown in Fig. 6. For a metasurface with perfectly symmetric resonators (
Furthermore, the role of the undercut in the coupling of the bound and continuum states can be explained as follows. In a perfectly symmetric cube,
The aforementioned mechanism implies that the coupling between two modes could potentially be absent for a different polarization. If the incident magnetic field is polarized in the
In this study, the formation of quasi-BIC induced by out-of-plane symmetry breaking was investigated in metasurfaces. A sharp resonance with a Q-factor inversely proportional to the degree of undercut was observed, which is strongly dependent on the polarization of incident radiation. Multipole decomposition studies revealed the detailed nature of the resonances and the role of undercut in establishing the quasi-BIC. The proposed method presents an additional tool for controlling the high-Q resonances which offers great tunability for metasurface applications. Furthermore, the proposed fabrication method of tilted dry etching can be applied to dielectric resonators that are considerably smaller or larger for operation in different wavelength ranges spanning from visible to far-infrared. While our calculation does not include effect of a substrate and may not fully reflect optical properties of metasurfaces in realistic systems, qualitative agreement may still be expected due to a relatively low refractive index of commonly used substrates (~1.52 for glass) compared to that of the resonators (~3.6). Therefore, this study is expected to introduce several possibilities for application of high-Q metasurfaces in enhancing light-matter interactions in various semiconductors and low-dimensional quantum materials.
This project is supported by a National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIT: NRF-2021R1C1C1010660) and a 2020 Research Grant from Kangwon National University. The authors would like to thank Editage (www.editage.co.kr) for English language editing.
The authors declare no conflicts of interest.