First Advisor

Jay Gopalakrishnan

Term of Graduation

Spring 2024

Date of Publication


Document Type


Degree Name

Doctor of Philosophy (Ph.D.) in Mathematical Sciences


Mathematics and Statistics




Anti-Resonant Reflecting Fiber, Confinement Loss, Leaky Modes, Microstructured Fiber, Optical Fibers, Waveguides



Physical Description

1 online resource (x, 172 pages)


Several important classes of modern optical waveguides, including anti-resonant reflecting and photonic bandgap fibers, make use of geometries that guide energy in low refractive index material, a property that makes them of significant interest in numerous applications, notably including high-power delivery and guidance. These waveguides frequently exhibit resonance phenomena, in which their ability to propagate an input signal is sharply curtailed at particular operating frequencies. In this work we detail new advances in understanding these resonance effects and their implications for numerical modeling of these structures.

Part 1 focuses on the fields of slab waveguides, relatively simple structures for which the fields induced by a given input source may be calculated semi-analytically. The focus is on forming an integral over a continuum of modes to calculated the radiation fields in these devices. This is done as preparation for future work examining the robustness of the leaky mode representation, the primary method of measuring confinement loss used in this work.

Part 2 focuses on resonance effects in optical fibers. It begins with semi-analytic results for radially symmetric optical fibers, supplying insight into resonance effects directly and allowing for benchmarking of numerical methods. These methods are then applied to microstructured optical fibers to demonstrate that the loss profiles of these devices are distinctly sensitive to choices regarding the modeling of outer material layers. Further investigation shows this sensitivity is moderated by including a material loss layer, corresponding to polymer coatings or jackets in the real fiber. This sensitivity is also shown to be present in studies of loss associated with varying a geometric parameter of the device. Finally, implications for numerical modeling are considered, in particular regarding choices for construction of finite element meshes.


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This work was supported in part by NSF Grant DMS-2136228 and the Air Force Office of Scientific Research Grant FA9550-23-1-0103.

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