Date of Award


Degree Type


Degree Name

Doctor of Philosophy in Physics



First Advisor

Leonard Kahn


The research conducted in this dissertation is the theoretical investigation into the transmission properties of one dimensional inversion symmetric quaternary photonic crystals and heterostructures created by combining quaternary and binary crystals. A photonic crystal is a device constructed from dielectric or conducting scattering elements arranged in a periodic manner. Saying a crystal has inversion symmetry simply means that the individual unit cells do too. Inversion symmetry is needed to ensure the system remains reciprocal and that topological phase of bands in a band structure remains discrete. The terms "binary" and "quaternary" refer to the number of layers in a unit cell, in this case, two and four, respectively. Similar to how an ionic lattice manipulates the ow of electrons, the periodicity of a photonic crystal can control the flow of photons. This leads to interesting physical properties in a device, such as photonic band gaps, regions in frequency space where photonic states cannot exist, and interface modes, localized states that can form at the boundary between two different crystals due to some change in material parameters or geometry.

In the first manuscript, we investigate interface modes in a heterostructure composed of a single binary photonic crystal and single quaternary photonic crystal. Several papers have already investigated modes in structures solely consisting of binary crystals. Being one dimensional, quaternary crystals are still relatively simple to fabricate while providing more interesting behavior compared with a binary system. In the work, this is done by inserting a tunable layer in between every original layer of the binary crystals. By setting other parameters in the heterostructure constant, it is possible to smoothly transform one binary photonic crystal into another through an intermediate quaternary state. The transfer matrix method is used in the simulation of these crystals and their resultant properties. Identifying topological phase in the band structure for quaternary crystals is discussed and compared to that of binary crystals. Band gap closings are also discussed. Examples of topological interface modes in the transmission spectra of binary/quaternary structures are provided showing that modes only exist in certain band gap when the quaternary crystal is tuned from one binary to another.

In the second manuscript, the single binary/quaternary system mentioned previously is generalized to a periodic array of crystals with each crystal still being periodic itself. Interface modes are shown to display different behavior as the tunable layer in the quaternary crystal(s) increases. Topological modes in the band gap are shown to vanish, split in two, or be surrounded by additional modes. Investigations are done for systems consisting entirely of lossless dielectrics and for systems where the tunable layer has a frequency dependent refractive index via the Drude model. Also, examples are given of how modes couple as the number of unit cells in the central crystal of a heterostructure changes.

In the third manuscript, effective medium theory is applied to both isolated quaternary photonic crystals and heterostructures. Effective medium theory has been used on photonic crystals and metamaterials in previous works to recover effective parameters, such as refractive index and impedance from transmission and reflection coefficients. We briefly compare analytic and numerical techniques for recovering effective parameters. We then examine how branch point singularities in the real part of the effective refractive index evolve as various parameters in the quaternary crystal, such as tunable layer thickness and loss components of permittivity, change. Construction of the effective refraction index analytically requires knowing the correct branches across the index profile in order to ensure it is both continuous and smooth. Understanding how branch crossings change with other parameters can help prevent abrupt profile changes/discontinuities.



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