Investigation of Electromagnetic Wave Propagation Across Achiral-Chiral Interfaces and Fabry-Perot Type Slab Resonators Including Material Dispersion and Dielectric Loss

Date of Award

2022

Degree Name

Ph.D. in Electrical and Computer Engineering

Department

Department of Electrical and Computer Engineering

Advisor/Chair

Monish Chatterjee

Abstract

In this dissertation, Fresnel coefficients are examined for electromagnetic (EM) propagation across an achiral/chiral (ACC) boundary, and thereafter extended to cases involving slab-type resonator structures. An important factor to be noted is that while the numerical results presented in this research are accurate to the limits of our assumptions, one feature of a chiral material not taken into consideration in the early stages of work is the presence of dielectric losses. It turns out that a chiral (meta) material is usually also lossy via a complex dielectric permittivity. In the research presented in several chapters of this dissertation, the chiral dielectric has been assumed to be lossless, whereby all three material parameters (permittivity, permeability and chirality) are assumed to be real. Towards the latter chapters, dielectric losses are taken into account to make the results more compatible with practical cases. The results presented are aimed at observing the effects of loss on both the propagated fields themselves as decaying vectors, as well as on the amplitude and phase characteristics of the relevant Fresnel coefficients (amplitude as well as power or intensity). As is well known, upon both transmission and reflection from a chiral interface, the incident plane (specifically perpendicularly or s-polarized) wave transforms into two modes (right circular polarization (RCP) and left circular polarization (LCP)), propagating non-collinearly and collinearly for the transmitted and reflected modes respectively. This work focuses on certain anomalous properties pertinent to the chirality itself which provide novel insights into chiral materials. The dissertation highlights anomalies relative to the emergence of Brewster effects, tunability of Brewster angles and critical angles via the (dimensionless) chirality coefficient (? ?) over specific bands, total internal reflection (TIR), non-complementarity, mode evanescence, and also possible effective negative-index-like behavior in the chiral material. Extending the problem to include dispersive chiral dielectrics and discrete components may lead to potential applications such as tunable superlenses (with imaging and vision implications) and also devices including chiral Fabry-Perot etalons. Specific test cases for the propagation of a pulse-like waveform, as well a 2-D transparency with color and grey-scale variations have also been analyzed using appropriate dispersive models and Fresnel coefficients by use of MATLAB simulations. Extension to the cases involving two planar interfaces (ACC in the front and chiral/achiral (CAC) in the back), leading to entirely different optical characteristics compared with the standard achiral, lossless Fabry-Perot resonator. Results are first derived for the corresponding FCs in the case of a (CAC) propagation environment. Continuing with the lossless assumption, amplitude and intensity reflection and transmission characteristics of a chiral slab have been investigated in some detail. It is found that under chirality, there emerge singularities along the incident angle scale which in the limit exhibit total power coefficients exceeding 1 or drop below 1, which within an assumed ±10% variation are considered acceptable within computational errors, while when exceeding the assumed bound are interpreted as non-physical. The special cases of a chiral slab resonator in the thin film limit are also examined in some detail. The thin-film resonator is configured in both a uniform background and also a lithographic structure with three layers. Overall, chiral slabs (in those cases where energy conservation is satisfied) generally exhibit non-uniform transverse modes, with mode densities dependent on the slab thickness, chirality and also the permittivities of the layers. When dielectric loss is introduced in the chiral layer, the physics and related mathematical analyses of the problem become more complicated, with special attention being required to track the effect of a complex dielectric permittivity in the chiral region on the complex phasor fields, the boundary conditions applied at z = 0, and emergent Snell's laws, and the interpretations of decaying fields in the chiral region and beyond, both in terms of their amplitude and phase behavior, as well as their intensity and energy conservation implications. Some results in this regard are presented with the understanding that further investigations with lossy chiral materials are currently ongoing.

Keywords

Electrical Engineering, Electromagnetics, Energy, Materials Science, Optics, Chirality, propagation, thin film, chiral Fabry-Perot, transverse modes, total internal reflection (TIR), Fresnel coefficients, Brewster phenomenon, materials, polarization, mode density, free spectral range, dielectric loss, energy conservation

Rights Statement

Copyright © 2022, author

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