Retrieving Dispersion Diagrams of Waveguide-Coupled Planar Photonic-Crystal-Embedded Microresonators

We report a numerical study on retrieving the dispersion diagrams of waveguide-coupled planar photonic-crystal-embedded microresonators (PCEMs) that comprise a finite-size square photonic crystal lattice of air-holes embedded in a high-index-contrast square microcavity. We extract the projected dispersion diagram of the waveguide-coupled PCEM by means of spatial Fourier transform of the simulated waveguide field patterns over a span of frequencies. We use various coupled waveguide widths in order to span a selected range of wavevectors. The retrieved PCEM dispersion diagram exhibits discrete flat bands near resonance frequencies over a relatively wide scope of wavevectors