| Abstract |
This master’s thesis’ subject is to provide a systematic theoretical study on
the properties of photonic systems characterized by non-Hermitian disorder.
Disordered systems have been extensively studied for decades, both due to
their fundamental importance in Physics and their direct relevance to numerous technological applications. On the other hand, non-Hermiticity is a
property of “open” systems - that is, of those that allow the exchange of
energy with their environment - which has been recently revisited in optical physics in a totally different context, that of parity-time symmetry. The
aforementioned twist led to the discovery of a plethora of new and exotic phenomena, which in turn led to the development of a whole new research field:
that of non-Hermitian Photonics. In this work, we focus on the interplay
between non-Hermiticity and disorder, along with the new properties that
arise from the combination of these two features. At first, we study the phenomenon of Anderson localization in systems with uniform non-Hermitian
disorder, by calculating the localization length and the spatial extent of the
system’s eigenstates, as well as the density of states and eigenvalue statistics on the complex plane. Next, we examine the properties of systems with
non-Hermitian binary disorder. Emphasis is placed on the physical-behavior
differences that they exhibit concerning their Hermitian analogs. Interestingly, several unexpected and intriguing effects make their appearance in our
model. The relation of our findings to recent experimental results is also
discussed. Finally, we present a method for achieving perfect and shapepreserving beam transmission through discrete photonic environments characterized by disorder. This is achieved by carefully combining the effects of
disorder and non-Hermiticity, in such a way that one phenomenon negates
the influence of the other. Remarkably, the effects of both diagonal and offdiagonal disorder can be efficiently eliminated by our non-Hermitian design.
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Non-Hermitian disordered photonic systems
