Zero- and [pi]-States in a Periodic Array of Deep Photonic Wires

A one-dimensional periodic rectangular potential, also known as the Kronig-Penney (KP) potential, transforms the parabolic dispersion of a free particle into a set of bands separated by bandgaps. However, if the potential wells are deep enough, the lowest bands converge into a set of single discrete states, numbered from j = 1 to j = jmax, which can be even or odd, describing the number of extrema. Here, discrete and continuous KP states are experimentally observed within a periodically modulated metal-organic microcavity. Depending on the width of the photonic wires, the thickness of the cavity, and the added metal grating, the parity of the highest localized state jmax can be either even or odd, leading to a complementary parity of the first continuous mode. The apex of this Bloch-like state in turn either starts at k = 0, or a π-state at the edges of the Brillouin zone, formed by the periodic metallic wires. An easy analytical explanation and numerical confirmation of zero- or π-phase locking for laser modes in spatially modulated microcavities are provided.