Linear and nonlinear wave dynamics in amorphous photonic lattices

Conventional intuition in solid-state physics holds that in order for a solid to have an electronic band-gap, it must be periodic, allowing the use of Bloch's theorem. Indeed, the free-electron approximation seems to imply that Bragg scattering in periodic potentials is a necessary condition for the formation of a band-gap. But this is obviously untrue: looking through a window reveals that glassy silica (SiO ₂), although possessing no order at all, still displays a band-gap spanning the entire photon energy range of visible light, without absorption. Several experimental studies have probed the properties of the band-gap in such "amorphous" electronic systems using spectroscopic techniques [1], time-of-flight measurements [2], and others. With the major progress in photonic crystals [3, 4], it is natural to explore amorphous photonic structures with band-gaps, where the actual wavefunction can be observed directly, and hence, many physical issues can be studied at an unprecedented level. Indeed, amorphous photonic media have been studied theoretically in several pioneering papers (e.g., [5, 6]), and experiments in the microwave regime have demonstrated the existence of a band-gap [5]. However, amorphous band-gap media have never been studied experimentally in the optical regime. Particularly in optics, the full beauty of disorder can be revealed: optics offers the possibility to precisely engineer the potential strength and period, as well as the unique opportunity to employ nonlinearity under controlled conditions, which could unravel unknown features that are much harder to access experimentally in other systems. Here, we present the first experimental study of amorphous photonic lattices: a two-dimensional array of randomly organized evanescently coupled waveguides. We demonstrate that the bands in this medium, comprising inherently localized Anderson states, are separated by gaps, despite the total lack of Bragg scattering. We find that amorphous photonic lattices support the existence of strongly localized defect states, whose widths is much narrower than the Anderson localization length. We show the existence of a region of negative effective mass (anomalous diffraction), which could be demonstrated experimentally by superimposing a weak spatial modulation on the random potential (refractive index), and observing transport. In this setting, a wavepacket with a negative effective mass moves opposite to the direction it would have moved had it had positive effective mass. Finally, we numerically demonstrate the existence of discrete solitons in amorphous photonic lattices and discuss their similarities and differences from discrete solitons in a periodic setting.