Experimental Study of Fabry-Perot BICs in a Microwave Waveguide

Abstract

We study Fabry-Perot bound states in the continuum (FP-BIC) in the GHz frequency range, formed by two ceramic discs placed inside a metallic-walled rectangular waveguide, that act as perfect reflectors at the resonant frequency. The energy becomes perfectly trapped between the discs, forming a FP-BIC, when the distance between them matches the Fabry-Perot quantization condition. We present both theoretical and experimental analyses to investigate how the total and radiative quality factors (Q factors) depend on the inter-disk distance. We gain valuable insights into the Fano features observed in the transmission spectra using the quasi-normal mode technique and temporal coupled mode theory. Notably, we find that as the system approaches the BICs, the Fano asymmetry parameters diverge, resulting in a Lorentzian transmission profile. Experimentally, we measure a radiative Q factor on the order of $10^5$, while the total Q factor, limited by material losses, remains around $10^3$. These results offer new opportunities for the application of BICs in microwave technology, significantly advancing the potential for high-performance devices.

Figures (5)

• Figure 1: (a) Transmission spectrum of a single resonant mirror exhibiting a resonance at frequency $\omega_0$. The inset illustrates the schematic geometry of the mirror. (b) Schematic illustration of a Fabry-Pérot bound state in the continuum formed between two identical resonant mirrors.
• Figure 2: (a) Geometry of the rectangular waveguide with cross-sectional dimensions $a = 34$ mm and $b = 72$ mm (upper panel). The lower panel shows the dispersion relations of the three lowest-order waveguide modes. The shaded yellow region indicates the frequency range corresponding to single-mode (TE$_{10}$) operation. (b) Normalized extinction cross-section of a ceramic disc in free space (lower panel). The insets display the $E_z$-field distribution on the disc surface for the resonant eigenmodes corresponding to the peaks in the extinction spectra. The disc parameters are shown in the upper panel: radius $R = 10$ mm, thickness $h = 5$ mm, permittivity $\varepsilon = 80$, and loss tangent $\tan\delta = 10^{-3}$. (c) Transmission spectrum of the TE$_{10}$ mode through the waveguide loaded with the ceramic disc (lower panel). The insets illustrate the $E_z$-field profile of the disc eigenmode inside the waveguide. The upper panel shows the corresponding system geometry.
• Figure 3: (a) Transmission and (b) reflection spectra of the ceramic disc placed inside a waveguide. The solid red lines represent numerical results obtained using COMSOL Multiphysics, the black lines correspond to temporal coupled-mode theory (CMT) simulations, and the blue circles indicate experimental measurements. Inset in panel (a) show the electric field distributions at the resonant frequencies and the $Q$-factor of the resonance mode.
• Figure 4: (a) Schematic view of two disks in a waveguide. (b) The Q-factor depends on the distance between two disks with or without losses. (c) Electric field at different distances
• Figure 5: (a) Schematic diagram of the experiment equipment. (b) Schematic diagram of the experiment setup connection.(c) Transmission map of the experiment results. (d) Transmission map of the simulation results. (e) Transmission map of the coupled mode theory results. (f) Simulation calculation and experiment fitting of QNMs' Q-factor at different distances. (g) Simulation calculation and experiment fitting of QNMs'Fano parameter at different distances.