Analysis of guided and leaky modes of circular waveguides and realization of mechanical tunable metamaterial and devices

Yang, Siming
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The guided and leaky mode characteristics for planar dielectric structures are relatively

well known, due to its various kind of applications. However, the investigation to the modes

characteristics for a circular rod structure is relatively rare, especially for the leaky modes,

despite the rod structure is very simple and useful.

Accordingly, in the first part of the thesis, we analyze the guided and leaky modes for

a circular dielectric rod in detail. The analysis is carried out in several steps. First, by

considering the field distributions outside the rod, the modes are well defined and classified

based on their physical meanings. The relations for the mode solutions using different types of

special functions and Riemann sheets are figured out. Further, completed forms of characteristic

equations used to solve different modes are presented explicitly. Second, in order to solve this

nonlinear characteristic equation efficiently and accurately, we employ iterative methods and

spent lots of efforts in deriving the initial guess expression in a simply but efficient form.

Through using the asymptotic expansion method and employing the Lambert W function, we

derive the initial guesses around the cutoff frequency, low frequency limit and high frequency

limit for both TM and TE cases. Finally, the numerical results are presented for the complex

transverse propagation constants of proper and two types of improper modes for both cases.

Some of the improper modes have not been shown in literatures.

Next, we extend the analysis to the circular rod with negative permittivity and permeability

(double negative material (DNG)). Following the same analysis procedure for the conventional

dielectric circular rod, first, we derive the characteristic equation for the DNG case and de

fine different types of modes. Second, we expand the characteristic equation asymptotically

and then find the initial guess expression for different types of modes around the cutoff, high

frequency limit and low frequency limit. Finally, using these initial guesses we solve the char

acteristic equation with iterative methods and find the dispersion curves.


The electromagnetic (EM) material property of simultaneous negative permittivity and per

meability we use for the DNG rod analysis actually can not be found in nature so far. The

method in generating material with DNG property is using metamaterials. In the second part

of the thesis we introduce metamaterials, and discuss our work of realizing tunable metamate

rials in detail. This type of tunable property allows the metamaterial device to overcome the

drawback of fixed and limited bandwidth from the conventional metamaterials.

We start it from presenting a novel tunable and flexible SRR-based meta-atom capable

of tuning its EM response characteristics over a broad frequency range by simple mechanical

stretching. First, we design and simulate a meta-atom with a liquid metal as the resonator

material. The liquid metal is patterned to be a SRR structure and embedded inside a highly

stretchable silicone elastomer. Due to its liquid nature, the liquid metal-based SRR could flow

in response to an applied strain, and compliant to change from the encasing elastomer as the

meta-atom being stretched and twisted. Therefore, through simple mechanical stretching, the

shape of the SRR is changed. Correspondingly, the equivalent capacitance and inductance of

the SRR are adjusted, thus tuning the resonance frequency of the meta-atom. The shifting

trend of the resonance frequency with different stretching orientations is predicted by a simple

circuit mode, and verified from the experiment.

Next, we extend the idea of meta-atom to the meta-skin, which is composed of an array

of meta-atoms. This meta-skin performed as a tunable selective surface with a wide resonance

frequency tuning range when being stretched. Further, due to its flexibility, this meta-skin can

function as a flexible “cloaking” surface in suppressing the scattering from the dielectric ob

ject. As examples, we demonstrate frequency selective responses of multilayer meta-skins with

different stretching ratio in the planar direction. Also, we investigate scattering suppression

effect of the meta-skin coated on a finite-length dielectric rod in free space.

Benefit from the liquid metal and highly stretchable elastomer, we design and realize a

directivity reconfigurable two-arm spiral antenna. This new device has the ability to reconfig

urate the radiation pattern along the main lobe direction by control the shape of the antenna,

as the radiation pattern becomes sharper, directivity is optimized. Finally, the directivity,

efficiency, and axial ratio with different dome height, operating frequencies are presented.

Antenna, Leaky Mode, Metamaterials, Waveguide