Periodic structures have a large influence on propagating waves. This holds for various types of waves over a large range of length scales: from electrons in atomic crystals and light in photonic crystals to acoustic waves in sonic crystals. The eigenstates of these waves are best described with a band structure, which represents the relation between the energy and the wavevector (k). This relation is usually not straightforward: owing to the imposed periodicity, bands are folded into every Brillouin zone, inducing splitting of bands and the appearance of bandgaps. As a result, exciting phenomena such as negative refraction, autocollimation ofwaves and lowgroup velocities arise. k-space investigations of electronic eigenstates have already yielded new insights into the behaviour of electrons at surfaces and in novel materials. However, for a complete characterization of a structure, an understanding of the mutual coupling of eigenstates is also essential. Here, we investigate the propagation of light pulses through a photonic crystal structure using a near-field microscope. Tracking the evolution of the photonic eigenstates in both k-space and time allows us to identify individual eigenstates and to uncover their dynamics and coupling to other eigenstates on femtosecond timescales even when co-localized in real space and time.
Nature Phys.

Engelen, R. J. P., Sugimoto, Y., Gersen, H., Ikeda, N., Asakawa, K., & Kuipers, K. (2007). Ultrafast evolution of photonic eigenstates in k-space. Nature Phys., 3, 401–405. doi:10.1038/nphys576