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A Highly-confined Dielectric Waveguide Enabled by
Conformal Anisotropic Impedance Surfaces
Zhi Hao Jiang
Lei Kang, Taiwei Yue, and Douglas H. Werner
State Key Laboratory of Millimeter Waves,
School of Information Science and Engineering,
Southeast University
Nanjing, 210096, P. R. China
Department of Electrical Engineering
The Pennsylvania State University
University Park, PA 16802, USA,,
Keywords—anisotropic impedance surface; conformal coating;
dielectric waveguide; metasurface
scenarios that require dense deployment. Previous methods for
overcoming this drawback often involve the inclusion of threedimensional structured claddings and/or cores. For example,
totally reflecting coatings [12], photonic band gap claddings
[13], and anisotropic artificial multilayered metallo-dielectric
coatings [14] or cores [15], have been used for accomplishing
sub-wavelength guidance. These approaches, however,
unavoidably limit the operation in a narrow frequency range and
increase the volume, weight, and cost of the dielectric
waveguides. Here, we propose and demonstrate an anisotropic
impedance surface (AIS) coating, which is extremely thin and
lightweight, for achieving a highly-confined mode in a dielectric
waveguide within a broad bandwidth.
Artificial impedance surfaces, also referred to metasurfaces,
are a class of quasi-two-dimensional textured structures
composed by an array of sub-wavelength unit cells in a periodic
or aperiodic arrangement [1]. The constituent unit cells can have
either uniform or non-uniform electromagnetic responses,
thereby offering greatly increased degrees of freedom as
compared to conventional frequency selective surfaces. Unlike
their three-dimensional metamaterial counterparts, these
artificially structured surfaces possess several advantages
including lower losses, ease-of-fabrication, and more diversity,
providing a fully-planar and even conformal platform for
manipulating the flow of electromagnetic waves [2]. Due to
these superiorities, in recent years, they have been exploited to
enable new physical wave phenomena like abnormal refraction
and reflection [3], unconventional propagation and radiation of
surface waves [4, 5], and so on. Moreover, the impedance
surfaces have been utilized for expanding the functionality of
electromagnetic devices or enhancing the performance of
existing components, such as flat lenses for far-field and nearfield focusing [6, 7], shaped-beam leaky-wave antennas [8],
ultrathin wave-plates [9], cloaks for antennas [10], and much
We consider a cylindrical dielectric rod waveguide coated
by an AIS, which has its axis along the z direction. The
homogeneous dielectric waveguide has a radius of r and a
relative dielectric constant of εr. The AIS coating is conformed
to the outer surface of the rod so that it does not increase the size
of the waveguide. The electromagnetic property of the AIS is
characterized by a surface impedance tensor (!" ) in cylindrical
coordinates with non-zero off-diagonal elements, which can be
defined as
Abstract—In this paper, we report the analysis, design, and
experimental validation of a conformal coating approach for
achieving a highly-confined mode in a dielectric waveguide with a
low dielectric constant. By controlling the surface electromagnetic
response of the anisotropic impedance surface, it is shown that the
original loose confinement of the guided mode of the dielectric
waveguide can be dramatically improved over a broad bandwidth.
The tensor impedance surface was further realized by an array of
short dipole elements and characterized. The good agreement
between simulated and measured results confirms the proposed
concept and associated design methodology.
As one of the fundamental building blocks for various
microwave, millimeter wave and photonic systems, dielectric
waveguides (DWs) have the advantage of being extremely lowloss [11]. However, when using a low dielectric constant
material for achieving a lighter weight, poor mode confinement
hampers the wide usage of DWs in highly integrated systems or
978-1-5386-3284-0/17/$31.00 ©2017 IEEE
= !"
!"$% '$
The tensor elements !"%$ and !"$% are purely imaginary
numbers. The boundary conditions on such an AIS indicate that
the tangential electric fields are continuous across the coating
surface while the tangential magnetic fields have discontinuities.
The properties of the fundamental guided mode, i.e. the HE11
mode, were derived by writing out the fields in the regions inside
and outside the rod and applying the boundary conditions taking
the AIS coating into account. It was found that !"%$ has a more
prominent impact on the propagation constant of the HE11 mode
than !"$% . For a rod made of Teflon with εr = 2.1 and r = 0.144
λ0, the propagation constant normalized to that of free space for
different values of !"$% is shown in Fig. 1, as a function of the
reactance of !"%$ . It can be seen that when !"$% = ∞, i.e. an
open circuit condition, a real number solution of the propagation
constant can be obtained for a value of !"%$ within the range
AP-S 2017
from -300j to 200j. Importantly, as the power distribution in the
transverse plane shows for the cases when kz/k0 = 1.444 and
1.024, i.e. !"%$ = −140- and 40-, respectively, the majority of
the power is concentrated inside the rod. This is drastically
different from that of a bare Teflon rod, where most of the power
locates outside the rod and is loosely-confined to the surface [11].
By setting the value of !"$% to be inductive or capacitive but
with a large reactance, similar properties of the guided HE11
mode can be maintained. This indicates that, by artificially
modifying the boundary conditions using an AIS coating, the
strong mode confinement can be achieved within a broad
to the original waveguide. The measured transmission curves for
the waveguide with and without the coating are displayed in Fig.
2, which agree well with the numerical predictions, thereby
confirming the proposed idea as well as the corresponding
design approach.
Fig. 3. Simulated snapshots of electric field distribution in the x-z plane at 3.2
GHz for the Teflon rod waveguide w/wo the AIS coating.
In conclusion, we have presented the idea of using an
ultrathin and low-loss flexible AIS coating for achieving a
strongly-confined mode in a sub-wavelength dielectric
waveguide. The theory and associated design methodology were
validated by an experimental demonstration. Based on such a
versatile platform, a number of interesting wave phenomena can
be envisioned and further explored.
Fig. 1. Normalized propagation constant (kz/k0) as a function of !"%$ for different
values of !"$% . The power distribution in the transverse plane when kz/k0 = 1.444
and 1.024, respectively, for the case !"$% = ∞.
Fig. 2. Measured and simulated co-polarized transmission between the
transmitting and receiving probes for a Teflon rod waveguide (25.4 mm in
diameter) w/wo the AIS coating. The inset shows a unit cell of the AIS.
To implement the required anisotropic surface impedance in
the microwave range, an array of end-loaded short dipoles
oriented along the z-direction was employed. Two linearlypolarized dipoles were used as probes at the two ends of the
waveguide for characterizing its transmission property. As Fig.
2 shows, within a broad frequency range from 2.5 to 4 GHz, an
enhanced transmission of more than 10 dB can be observed for
the case with the presence of the AIS coating as compared to
that without the coating. The snapshots of the electric field
distribution in the x-z plane clearly reveal the fact that the AIS
coating greatly improves the mode confinement, whereas the
electric field is primary located outside the rod for the uncoated
dielectric open waveguide (see Fig. 3). The AIS coating was
fabricated and assembled with the Teflon rod. The coating has a
thickness of only 0.1 mm (~λ0/1000) and adds almost no weight
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This work was funded by the Penn State MRSEC under the award NSF DMR-1420620.
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