Thickness-modulated Fourier-component-engineered metasurfaces supporting TE-and TM-polarized quasi-bound states in the continuum

Abstract The elimination of the first Fourier harmonic from a periodic thickness profile has been proposed as a way to suppress radiative leakage near the second stop band of zero-contrast gratings (ZCGs). However, the resulting enhancement of the radiative Q factor has so far been demonstrated only for the fundamental TE0 mode. Here, we extend this first-harmonic-elimination strategy to ZCGs that support coexisting TE-and TM-polarized guided-mode families, including both fundamental and first higher-order branches. We show that the resulting thickness-modulated Fourier-component-engineered metasurfaces exhibit enhanced radiative Q factors for the TE0, TE1, TM0, and TM1 modes, thereby forming continuous high-Q quasi-bound states in the continuum (quasi-BICs) near their respective second stop bands. By examining both silicon-nitride and silicon ZCGs, we confirm that this effect is robust across material platforms. We further show that discretized thickness profiles composed of finite rectangular segments preserve the essential high-Q characteristics of the non-discretized profiles. These results establish first-harmonic elimination in periodic thickness profiles as a general and practical route to continuous high-Q quasi-BICs across guided-mode branches, material platforms, and fabrication-accessible geometries.