Bandwidth tunable optical filter based on a tri-mode high-contrast grating

We propose a monolithic optical bandpass filter with a transmission bandwidth tunable by the incident angle in a tri-mode high-contrast grating (HCG). We attribute this extraordinary phenomenon to the destructive interference between the TM$_{0}$ and TM$_{2}$ modes and the Fabry-P\'erot resonance of the TM1 mode, which can only be excited at the oblique incidence. The transmission bandwidth can be tuned from zero at normal incidence and increases quadratically with incident angle, while the center wavelength reds shifts slightly. The corresponding Q factor can be continuously tuned from 10$^{6}$ to 10$^{2}$ as the incident angle increases from nearly 0$^{\text{o}}$ to 10$^{\text{o}}$.