Coupled double-layer Fano resonance photonic crystal filters with lattice-displacement

We present here ultra-compact high-Q Fano resonance filters with displaced lattices between two coupled photonic crystal slabs, fabricated with crystalline silicon nanomembrane transfer printing and aligned e-beam lithography techniques. Theoretically, with the control of lattice displacement between two coupled photonic crystal slabs layers, optical filter Q factors can approach 211 000 000 for the design considered here. Experimentally, Q factors up to 80 000 have been demonstrated for a filter design with target Q factor of 130 000.