Visualization of photonic band structures via far-field measurements in SiN_x photonic crystal slabs

Band structures of the photonic crystal slabs play a significant role in manipulating the flow of light and predicting exotic physics in photonics. In this Letter, we show that the key features of photonic band structures can be achieved experimentally by the polarization- and momentum-resolved photoluminescence spectroscopy utilizing the light emission properties of SiNx. The two-dimensional spectra clearly reveal the energy-momentum dispersion of band structures, which is in perfect agreement with the simulation results. The isofrequency contours can be measured easily by adding a bandpass filter with a desired photon energy. Furthermore, it is convenient to observe clearly and directly the optical singularity - the optical bound states in the continuum featured by dark point in three-dimensional photoluminescence spectra. The polarization-resolved isofrequency contours clearly show that this dark point is the center of an azimuthally polarized vortex. Finally, the helical topological edge states can be easily observed in photonic topological insulators with deformed hexagonal lattices. Our work provides a simple and effective approach for exploring topological photonics and other intriguing phenomena hidden in the photonic crystal slabs.