| Abstract: | We present a family of one-dimensional quasiperiodic crystals which display properties normally exclusive to periodic structures. While typical quasiperiodic structures have a fractal band structure with critically decaying eigenmodes, our family of structures can behave as a quasiperiodic or periodic system, depending only on the wavelength and the variance in the potential. In certain regimes we witness non-fractal band structure and propagation of light as Bloch-like modes, while in the other regime the structure exhibits all the features of a quasiperiodic potential. On a related subject, we study the propagation of waves in a linearly- homogenous medium with a spatially-random nonlinear coefficient. We find that waves propagating in this nonlinearly-disordered medium exhibit weak localization (coherent backscattering), with power-law decay instead of the exponential decay characteristic of Anderson localization. This anomalous behavior is a result of a negative feedback mechanism caused by the interplay between localization and nonlinearity, which also gives rise to unique statistical features where the fields in all realizations of disorder converge to the same intensity as the light penetrates deeper and deeper into the disordered medium. |
