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