Angle- and polarization-dependent spectral characteristics of circular grating filters

We design and implement one type of guided mode resonance (GMR) circular grating filters (CGFs) on an HfO₂-on-silicon platform. Taking advantage of an angle-resolved micro-reflection measurement system, we achieve their incident angle- and polarization-dependent reflection spectra. For normal incident arbitrary linear polarization, a pair of reflection peaks is experimentally observed due to the coexistence of the azimuthal component E_a and the radial component E_r of the incident wave electric field (E-field). For oblique incident s-polarization (E-field perpendicular to the incident plane), the peak excited by the E_a component splits into two sub-peaks due to the removal of degeneracy, while that excited by the E_r component gradually fades away with the increase of the incident angle. For oblique incident p-polarization (E-field parallel to the incident plane), the spectrum appears to be reversed; that is, the peak corresponding to the E_r component gets split while that corresponding to the E_a component gradually disappears when the incident angle increases. Moreover, we experimentally demonstrate the spectral relationships between CGFs and linear grating filters under not only normal incidence but also oblique incidence; these relationships greatly facilitate the spectral design and tailoring of the CGFs.