IPR - 01 Electromagnetic Wave Propagation Characteristics on ...

DGFS-PHD PROJECT PROPOSAL, INSTITUTE FOR PLASMA RESEARCH, GANDHINAGAR,382428
<strong>IPR</strong> - <strong>01</strong>
<strong>Electromagnetic</strong> <strong>Wave</strong> <strong>Propagation</strong> <strong>Characteristics</strong> on Helical Slow <strong>Wave</strong>
Structure Loaded with Metamaterials
Metamaterials are artificially engineered materials which can have negative effective
electric permittivity and/or negative effective magnetic permeability. Different from
conventional materials, which have both positive electric permittivity and positive
magnetic permeability [i.e., double positive (DPS)], metamaterials show different
electromagnetic and optical properties. For instance, when electric permittivity and
magnetic permeability of the material are both negative [i.e., double negative (DNG)],
negative refraction happens and direction of phase velocity is reversed. DNG
metamaterials are also called Left Handed Materials (LHM) because electric field,
magnetic field and the direction of phase velocity form a left handed coordinate
system for these materials. On the other hand, when only one of the constitutive
parameters of the metamaterial is negative [i.e., single negative (SNG)] evanescent
waves appear.
Due to their aforementioned exceptional properties, metamaterials are being
investigated for many possible utilizations in different scientific and engineering
applications, which otherwise cannot be easily accomplished with conventional
materials. Recently, reducing scattering from various structures, and in the limit
achieving transparency and building cloaking structures, have been investigated by
many researchers [1-7]. On the other hand, resonant structures aimed at increasing
the electromagnetic intensities, stored or radiated power levels have also been
studied extensively [7-14]. Similarly, metamaterial layers have been proposed to
enhance the power radiated by electrically small antennas [15-17]. While some of
these studies are based on utilization of non-linear metamaterial structures, some of
them rely on pairing slabs, spheres or cylinders with their electromagnetic conjugates
(e.g., pairing/coating DPS materials with DNG metamaterials or mu-negative (MNG)
metamaterials with epsilon-negative (ENG) metamaterials).
In proposed project work wave propagation along a helical waveguide loaded with a
longitudinal metamaterial cylinder adjacent to air, will be studied. The analytical
dispersion relations will be solved numerically for the . - ß diagrams in guided mode of
electromagnetic wave propagation.
Background/Interest of Student: <strong>Electromagnetic</strong> theory and computational as well as
programming skill
Surya K Pathak

DGFS-PHD PROJECT PROPOSAL, INSTITUTE FOR PLASMA RESEARCH, GANDHINAGAR,382428
Microwave & ECE Group
<strong>IPR</strong>-02
GUIDED AND LEAKY MODE CHARACTERISTICS OF FLEXIBLE PLASMA TUBE WAVEGUIDE IN
MILLIMETER WAVE FREQUENCIES
Generally, once electromagnetic waves are incident upon the surface of two different
dielectric media, reflection and refraction phenomena occur between the two media due to
the dissimilar refractive indexes. At a certain critical angle of incidence or above, the
transmitted ray disappears and all the electromagnetic energy becomes confined to the
incidence region. This is total internal reflection, and the fields in the upper regions exist in an
evanescent form, i.e., decaying exponentially in the +y direction. This is the principle of a
guided surface wave and optical fibers and other guided planar integrated optical circuits use
this type of electromagnetic wave.
Figure 1: Reflection and refraction of electromagnetic wave on surface of two dissimilar
materials. a is the angle of incidence
Figure 2: Reflection and refraction of electromagnetic wave with several incident angles.
Figure 3: Geometrical optic descriptions of simplest guided surface and leaky wave along
dielectric film. The refractive index of the film is assumed to be higher than that of the
surrounding free space.
(a) Guided mode with total internal reflection. The electromagnetic wave energy is confined
to the waveguide region.
(b) Leaky mode configuration. <strong>Electromagnetic</strong> energy is constantly leaked into the free space
region.
As in the general case of refraction shown in Figure 1, the refracted rays can be viewed as
leaky rays, because even though the electromagnetic waves are guided to propagate in the
+x-direction, the electromagnetic energy can also propagate in the +y-direction, thus the
energy of the electromagnetic wave is constantly leaked in the transverse direction to the free
space when the wave is propagated in the + x direction [1-2]. Figure 3 shows a more apparent
view using dielectric slab waveguide geometry. Figure 3(a) is the purely guided mode based
on total internal reflection, whereas Figure 3(b) shows the leaky rays. The guided surface
wave is guided by total internal reflection. However, when a critical incident angle is
exceeded, the electromagnetic power is constantly leaked downward in the traveling
direction. When the electromagnetic power is constantly leaked, the amplitude of the axial
field is attenuated, yet this is not due to material absorption. Mathematically, these waves are
improper, because the amplitude of the wave increases transversely and the radiation
condition at infinity is violated [3-5]. Thus, it would seem that leaky waves are nonphysical.
However, leaky waves are physically measurable and used in many electromagnetic
applications. Yet, since leaky waves are mathematically improper, they can only exist in a
restricted region of a wedge shape within which the field stays finite, as shown in Figure 4.
This is because the location of the source is finite (or fixed).

DGFS-PHD PROJECT PROPOSAL, INSTITUTE FOR PLASMA RESEARCH, GANDHINAGAR,382428
The mathematically improper character of leaky waves is derived from their source-free
condition. Various basic articles and recent reviews are useful to understand the general
physics of leaky waves [1-5]. The earliest and most widely utilized engineering application of
the leaky wave phenomenon is leaky wave antennas [3] and this application of leaky waves is
still being actively studied [7]. Meanwhile, other leaky wave applications in the microwave/
millimeter/sub-millimeter wave band are low-loss waveguides [8], microwave applicators [9],
dielectric resonators [10], leaky wave filters [11], directional couplers [12], and so on.
Figure 4: Radiation from semi-infinite leaky waveguide: (a) Leaky waveguide is fed by closed
waveguide [8]. When viewed from point z’, the amplitude of the field increases as the
distance from
the waveguide increases. (b) Expected field pattern along x direction (transverse direction)
[9].
Plasma Column <strong>Wave</strong>guides
<strong>Electromagnetic</strong> wave propagation along plasma columns was extensively studied in the
1950s and
1960s, when much attention was paid to the surface and leaky wave problems in an
unmagnetized
and magnetized plasma layer (slab) and column involving communications between missiles
and the
earth [13, 14]. High-speed rockets or missiles with high-temperature exhaust fumes can make
the
surrounding atmosphere into plasma due to friction and thermal ignition. As such, the
atmosphere
around a high-speed vehicle can be considered as a metal rod plasma cladding system and the
atmosphere affected by high-speed vehicles considered as a plasma column. The
communications
between such vehicles and earth stations can be affected by the electromagnetic properties
of the
plasma.
A plasma column has also been applied as a plasma antenna with cylindrical geometry in the
RF
band [15]. Another strong research area related to plasma columns is surface wave plasma
sources

DGFS-PHD PROJECT PROPOSAL, INSTITUTE FOR PLASMA RESEARCH, GANDHINAGAR,382428
with circular geometry. (See references [16] and references therein.) Lastly, from a broader
perspective, light propagation in cylindrical metal or cylindrical geometry with a negative
dielectric
constant can also be included as applications of plasma column waveguides. This case involves
cylindrical surface Plasmon or surface Plasmon polariton1) where the field energy is strongly
confined near the cylindrical surfaces. Surface Plasmons with a planar geometry have already
been
extensively studied (see reference [17] and references therein.) and remain a very attractive
research
topic [16]. However, surface Plasmons on cylindrical surfaces [19, 20] have received more
attention
recently due to the probe structure of NSOM (Near-field Scanning Optical Microscopy).
All the above applications use the guided modes of a plasma column. Nonetheless, the guided
modes
of a plasma column are limited in their operating frequency due to high frequency cutoffs. S.
S.
Martinos and E. N. Economou previously studied the existence of a “virtual” radiation mode
for
surface Plasmon above the plasma frequency [20].
This Ph.D. proposal deals with propagation and radiation characteristics, both in guided and
leaky
mode, of flexible plasma tube waveguide. Initial mathematical foundation has been
formulated.
Computational methodology has been established.
Surya Pathak
Microwave & ECE Group
Institute for Plasma Research, Bhat, Gandhinagar 382428
bhusurya@gmail.com