From the viewpoint of quantum mechanics, a system must always be Hermitian since all its corresponding eigenvalues must be real. In contrast, the eigenvalues of open systems-unrestrained because of either decay or amplification-can be in general complex. Not so long ago, a certain class of non-Hermitian Hamiltonians was discovered that could have a completely real eigenvalue spectrum. This special class of Hamiltonians was found to respect the property of commutation with the parity-time (PT) operator. Translated into optics, this implies a balance between regions exhibiting gain and loss. Traditionally, loss has been perceived as a foe in optics and something that needs to be avoided at all costs. As we will show, when used in conjunction with gain, the presence of loss can lead to a host of counterintuitive outcomes in such non-Hermitian configurations that would have been otherwise unattainable in standard arrangements. We will study PT symmetric phase transitions in various optical settings that include semiconductor microrings and coupled fiber cavities, and show how they can allow mode-selectivity in lasers. One of the key outcomes of this effort was the realization of higher order degeneracies in a three-cavity laser configuration that can exhibit orders-of-magnitude larger sensitivity to external perturbations. We will also consider systems that display nonlinear effects such as gain saturation, thus allowing novel phase transitions. Some interesting properties associated with degeneracies in non-Hermitian settings will be investigated as well. Such degeneracies, called exceptional points (EPs), are much more drastic compared to standard degeneracies of eigenvalues because the corresponding eigenvectors also coalesce, which in turn reduces the dimensionality of the phase space. We will show that dynamic parameter contours enclosing or close to EPs can lead to a robust chiral mode conversion process – something that can be potentially used to realize omni-polarizing optical devices.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:etd-7011 |
| Date | 01 January 2018 |
| Creators | Ulhassan, Absar |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Electronic Theses and Dissertations |
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