Emission control in broad periodic waveguides and critical coupling

Broad periodic channel waveguides, with a corrugation on their edge, exhibit a remarkable structure in their dispersion diagram, in the form of stripes of minigaps, whose hyperbolic shape is demonstrated. Around the Brillouin zone edge, the contra-directional feedback borrows the geometry of Littrow diffraction. Spontaneous emission from a large subset of modes then acquires a strong modulation. Lasing on these modes, the so-called “Littrow lasing”, offers also the lowest lasing threshold of the open resonator system. Reviewing our recent studies of this system, we discuss slow light and critical coupling phenomena: for a properly adjusted contra-directional coupling, the bands become substantially flat in a sizable area of the dispersion diagram, opening various perspectives. The band engineering tools to master these phenomena and the physical implications in other domains are briefly reviewed.