Ph.D Thesis


Ph.D StudentIdo Kaminer
SubjectLight in Complex Settings
DepartmentDepartment of Physics
Supervisor Full Professors Segev Mordechai
Full Thesis textFull thesis text - English Version


Abstract

The PhD dissertation is divided to three major parts:

1. Shape-preserving accelerating beams in nonlinear media.

Accelerating beams were introduced into optics in 2007, drawing much interest, with applications like trapping particles along curved paths and self-bending plasma channels - mostly related to nonlinear interactions of light and matter. In 2008-2010, several groups studied dynamics of accelerating beams in nonlinear media, yet, the prevailing opinion was that shape-preserving nonlinear accelerating beams do not exist. Our 2011 paper in PRL showed that a specific design of the beam can make it accelerate in a shape-preserving manner while propagating in almost any kind of nonlinearity.


2. Non-diffracting self-accelerating solutions of the full Maxwell equations.

The growing interest in accelerating beams raised an important fundamental question: Can a beam bend itself to high angles, maybe even 90°? Several experimental and numerical studies revealed that such beams tend to breakup or decay. In the end of 2011, we were the first to resolve this challenge, finding the full vector solutions of Maxwell’s equations for shape-preserving accelerating beams. Interestingly, this actually predicts a new family of nondiffracting beams which also self-bend. Our work in PRL predicted this novel dynamics of accelerating waves to exist in almost any linear and nonlinear wave system in nature, including many classical waves, as sound waves and surface waves. This led many groups around the world to pursue followups in optics, acoustics, and other systems.


3. Solitonets: networks of interacting solitons exhibiting complex nonlinear dynamics.

Complex networks emerged simultaneously over the last decade in biology, computer science, economy, sociology, and physics. They model systems displaying complex topology, which results in overall behaviour that cannot be simply explained by the properties of the individual parts of the networks. Examples range from metabolic networks and the World Wide Web to social networks. We came into this field with a new concept in mind - to analyse networks where the carrier of information was a field instead of a discrete set of values, thus immensely increasing the complexity of the network. To make the problem tractable, we proposed using solitons as those carriers. Each soliton still has an infinite number of degrees of freedom, but also behaves as a particle, with conservation laws controlling its interactions. The network of solitons (Solitonet) exhibits a huge variety of new phenomena, such as surprising noise-enhanced memory effects, spontaneous self-synchronization, and stochastic recurrent behaviour.