M.Sc Thesis

M.Sc StudentSharabi Yonatan
SubjectAspects of Waves in Aperiodic Structures
DepartmentDepartment of Electrical and Computer Engineering
Supervisors PROFESSOR EMERITUS Gad Eisenstein
Mordechai Segev


My master’s thesis focuses on wave propagation in aperiodic structures. While the propagation of waves in periodic structures is well understood, with solutions in the form of Bloch modes, wave propagation in aperiodic structures is much less understood. In my work, I examine wave propagation in two specific types of aperiodic systems - one dimensional (1D) quasiperiodic structures, and 1D disordered media. in each one of these systems, we find unique behavior, uncommon to that type of aperiodic system.

The first aperiodic structure I examine is a family of one-dimensional quasiperiodic crystals which display properties normally exclusive to periodic structures. While general quasiperiodic structures have a fractal band structure with critically decaying eigenmodes, the quasicrystal that we study can behave as a quasiperiodic or periodic structure, depending on some parameters. In the sub-wavelength regime, our quasiperiodic structure shows periodic behavior with a non-fractal bandstructure and Bloch-like modes.

In the second aperiodic structure, we studied weak localization in a medium that is homogenous in its linear properties, but disordered in its NL coefficients. The NL coefficient is spatially random in the medium, and therefore the propagating field induces the NL change itself according to its intensity. 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 the 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.