Exploring light propagating in photonic crystals with Fourier optics

Photonic crystals (PhCs) act on light in two different ways: confinement and modification of propagation. Both phenomena rely on the complex interplay between multiply scattered waves that can form what is known as a Bloch mode. Here, we present a technique that allows direct imaging of Bloch modes, both in real space and in k-space. The technique gives access to the location of the field maxima inside the PhC, the dispersion relation, equifrequency surfaces, as well as reflection and transmission coefficients. Our key advance is that we retrieve the desired information comprehensively, without postprocessing or cumbersome near-field scanning techniques, even for modes that are nominally lossless, i.e., below the light line. To highlight the potential of the technique, we extract the dispersion curve of a coupled cavity waveguide consisting of as many as 100 cavities, as well as the equifrequency surfaces and polarization properties of a PhC beam splitter.