Surface electromagnetic waves in left-handed material slab embedded in plasmalike media
This study is devoted to the dispersion properties of the electromagnetic surface eigen waves that propagate along the left-handed planar slab that is bounded by the air (vacuum) and the medium with positive plasma-like permittivity. Both the left-handed slab and the media are assumed to be isotropi...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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Galaydych, V.K. Azarenkov, N.A. Olefir, V.P. Sporov, A.E. 2015-05-13T16:05:16Z 2015-05-13T16:05:16Z 2014 Surface electromagnetic waves in left-handed material slab embedded in plasmalike media / V.K. Galaydych, N.A. Azarenkov, V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2014. — № 6. — С. 112-115. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.35g, 52.50.Dg https://nasplib.isofts.kiev.ua/handle/123456789/81210 This study is devoted to the dispersion properties of the electromagnetic surface eigen waves that propagate along the left-handed planar slab that is bounded by the air (vacuum) and the medium with positive plasma-like permittivity. Both the left-handed slab and the media are assumed to be isotropic and have zero losses. We present the results of the studying the phase and group velocities of the considered waves. Изучены свойства собственных поверхностных электромагнитных волн, распространяющихся вдоль плоской волноводной структуры, состоящей из слоя левостороннего материала, ограниченного вакуумом, и плазмоподобной средой с диэлектрической проницаемостью, зависящей от частоты. Слой левостороннего материала и окружающие среды предполагаются изотропными и бездиссипативными. Представлены результаты изучения фазовой и групповой скоростей рассматриваемых волн. Вивчено дисперсійні властивості власних поверхневих електромагнітних хвиль, які поширюються в пласкій хвилеводній структурі, яка складається з шару лівостороннього середовища, що межує з вакуумом та плазмоподібним середовищем з діелектричною проникливістю, яка залежить від частоти. Шар лівостороннього матеріалу та оточуючі середовища вважаються ізотропними та бездисипативними. Представлено результати дослідження фазової та групової швидкостей хвиль, що вивчаються. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Плазменная электроника Surface electromagnetic waves in left-handed material slab embedded in plasmalike media Поверхностные электромагнитные волны в слое левостороннего материала, погруженного в плазмоподобную среду Поверхневі електромагнітні хвилі в шарі лівостороннього матеріалу, зануреного в плазмоподібне середовище Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Surface electromagnetic waves in left-handed material slab embedded in plasmalike media |
| spellingShingle |
Surface electromagnetic waves in left-handed material slab embedded in plasmalike media Galaydych, V.K. Azarenkov, N.A. Olefir, V.P. Sporov, A.E. Плазменная электроника |
| title_short |
Surface electromagnetic waves in left-handed material slab embedded in plasmalike media |
| title_full |
Surface electromagnetic waves in left-handed material slab embedded in plasmalike media |
| title_fullStr |
Surface electromagnetic waves in left-handed material slab embedded in plasmalike media |
| title_full_unstemmed |
Surface electromagnetic waves in left-handed material slab embedded in plasmalike media |
| title_sort |
surface electromagnetic waves in left-handed material slab embedded in plasmalike media |
| author |
Galaydych, V.K. Azarenkov, N.A. Olefir, V.P. Sporov, A.E. |
| author_facet |
Galaydych, V.K. Azarenkov, N.A. Olefir, V.P. Sporov, A.E. |
| topic |
Плазменная электроника |
| topic_facet |
Плазменная электроника |
| publishDate |
2014 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Поверхностные электромагнитные волны в слое левостороннего материала, погруженного в плазмоподобную среду Поверхневі електромагнітні хвилі в шарі лівостороннього матеріалу, зануреного в плазмоподібне середовище |
| description |
This study is devoted to the dispersion properties of the electromagnetic surface eigen waves that propagate along the left-handed planar slab that is bounded by the air (vacuum) and the medium with positive plasma-like permittivity. Both the left-handed slab and the media are assumed to be isotropic and have zero losses. We present the results of the studying the phase and group velocities of the considered waves.
Изучены свойства собственных поверхностных электромагнитных волн, распространяющихся вдоль плоской волноводной структуры, состоящей из слоя левостороннего материала, ограниченного вакуумом, и плазмоподобной средой с диэлектрической проницаемостью, зависящей от частоты. Слой левостороннего материала и окружающие среды предполагаются изотропными и бездиссипативными. Представлены результаты изучения фазовой и групповой скоростей рассматриваемых волн.
Вивчено дисперсійні властивості власних поверхневих електромагнітних хвиль, які поширюються в пласкій хвилеводній структурі, яка складається з шару лівостороннього середовища, що межує з вакуумом та плазмоподібним середовищем з діелектричною проникливістю, яка залежить від частоти. Шар лівостороннього матеріалу та оточуючі середовища вважаються ізотропними та бездисипативними. Представлено результати дослідження фазової та групової швидкостей хвиль, що вивчаються.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/81210 |
| citation_txt |
Surface electromagnetic waves in left-handed material slab embedded in plasmalike media / V.K. Galaydych, N.A. Azarenkov, V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2014. — № 6. — С. 112-115. — Бібліогр.: 8 назв. — англ. |
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2025-11-27T09:13:03Z |
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2025-11-27T09:13:03Z |
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ISSN 1562-6016. ВАНТ. 2014. №6(94)
112 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2014, №6. Series: Plasma Physics (20), p. 112-115.
SURFACE ELECTROMAGNETIC WAVES IN LEFT-HANDED
MATERIAL SLAB EMBEDDED IN PLASMALIKE MEDIA
V.K. Galaydych, N.A. Azarenkov, V.P. Olefir, A.E. Sporov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: viktor.galaydych@gmail.com
This study is devoted to the dispersion properties of the electromagnetic surface eigen waves that propagate
along the left-handed planar slab that is bounded by the air (vacuum) and the medium with positive plasma-like
permittivity. Both the left-handed slab and the media are assumed to be isotropic and have zero losses. We present
the results of the studying the phase and group velocities of the considered waves.
PACS: 52.35g, 52.50.Dg
INTRODUCTION
At last decades both theoretical and experimental
studies of new composed materials which are often
called as metamaterials are carried out in the whole
world. Such metamaterials possess many unique
physical properties which are not found among the all
usual substances [1].
The basic feature of these materials is the fact that
the directions of the group and phase velocities of
electromagnetic eigen waves in such materials are
opposite directed, that’s why such materials are called
left-handed materials (LHM). These unique properties
give the opportunity to design innovative devices with
previously unavailable characteristics [2]. Possible
technological applications include many areas, such as
superlensing, optical cloaking, image processing and so
on. In addition it should be mentioned the research
carried out at the Argonne Wakefield Accelerator
Facility; specifically, the investigation of the LHM
application to control the dispersion relation in a loaded
waveguide [3, 4].
Designing such new devices is impossible without
detail theoretical investigation of the electromagnetic
properties of the waveguide structures with
metamaterials. At present planar waveguide structures
with metamaterials are widely used in the
investigations. In different leading scientific laboratories
of the world it was considered various planar waveguide
structures which contains LHM embedded either by
vacuum or by different ordinary dielectrics with
constant permittivity [5-7]. But using ordinary
dielectrics which bound the metamaterial slab leads to
the narrowing of possible wavenumbers range for the
eigen surface electromagnetic waves of such structures
as compared with vacuum bounds.
In the present work we study the planar waveguide
structure that consists of the left-handed metameterial
slab immersed in the non-magnetic plasma-like media
which permittivity depends on the wave frequency.
Plasma, metals, semi-metals and metamaterials with
appropriate parameters [8] possess such electric and
magnetic properties in some frequency ranges.
1. STATEMENT OF THE PROBLEM
The considered electromagnetic waves propagate
along the planar waveguide structure that is made of
isotropic LHM slab of thickness . This material is
characterized by effective permittivity and
permeability which depend on the wave
frequency and are commonly expressed with the help of
experimentally obtained expressions [2]:
2
2
1)(
p
, (1)
2
0
2
2
1)(
F
, (2)
here p is effective plasma frequency, 0 is the
characteristic frequency of LHM. In further study we
consider the LHM with / 2 10p GHz,
0 / 2 4 GHz and parameter 0,56F [5].
This LHM slab is bounded on one side by the
artificial isotropic nonmagnetic (
2 1 ) material with
no losses and the effective permittivity
2
2
2 2
( ) 1
p
, (3)
here 2p is effective plasma frequency for
neighbourhood medium, we choose
2 / 2 3,2p GHz. Such parameters ratio leads to the
existence of the frequency range within which
0 and 20 1 simultaneously. The semi-
bounded conventional dielectric with constant dielectric
permittivity 1 1 and permittivity 1 1 is located on
the other side of LHM slab.
Let’s consider electromagnetic wave that propagates
along this structure. It is assumed that wave disturbance
tends to zero far away from LHM and the dependence
of the wave components on time t and coordinate z is
chosen in the following form:
3, ( ), ( )exp[ ( )]E H E x H x i k z t , (4)
here x is the coordinate rectangular to the wave
propagation direction and to the LHM slab.
In this case it is possible to split the system of
Maxwell equations into two subsystems. One of them
describes the waves of H -type and the other – wave of
E-type.
The wave of E-type possesses the dispersion relation
in the following form:
ISSN 1562-6016. ВАНТ. 2014. №6(94) 113
2 1 1 2
2 2
1 2 1 2[ ] tanh 0
h h
h h
, (5)
here 2
11
2
31 kkh , 2 2
2 3 2 2h k k ,
22
3 kk , ck / , c is the speed of
light in vacuum.
In the region of LHM slab the wave field
components, normalized by the )0(yH , can be written
as:
xx
y eCeCxH 21 ,
keCeCkxE xx
x /213
, (6)
keCeCixE xx
z /21
,
here 1C and 2C are wave field constants.
In the air (vacuum) region the wave field
components, normalized on the )0(yH , possess the
form:
xh
y exH 1
13 /1 kekxE
xh
x (7)
11 /1 keihxE
xh
z
In the plasma-like half-space the wave field
components, normalized by the )0(yH , can be written
as:
2h x
yH x Ae
,
2
3 2/
h x
xE x Ak e k
, (8)
2
2 2/
h x
zE x i A h e k
,
here A is wave field constant. These constants are of
the following form:
2
1 2 12 ( ) /
h
EA h e
,
1 1 2 2 1( ) ( ) / EC h h , (9)
2
2 1 2 2 1( ) ( ) / EC h h e ,
2 2
2 2( 1) ( ) ( 1)E e h e .
Similarly wave of H-type possesses the dispersion
relation in the following form:
2 1 1 2
2 2
1 2 1 2[ ] tanh 0
h h
h h
.
(10)
In the region of LHM slab the wave field
components, normalized by the )0(yE , can be written
as:
1 2
x x
yE x D e D e ,
3 1 2 /x x
xH x k D e D e k , (11)
1 2 /x x
zH x i D e D e k ,
here 1D and 2D are wave field constants.
Wave field components, normalized on the )0(yE ,
in the air (vacuum) region:
xh
y exE 1 ,
13 /1 kekxH
xh
x , (12)
11 /1 keihxH
xh
z .
In the plasma-like half-space the wave field
components, normalized by the )0(yE , can be written
as:
xh
y BexE 2
,
23 /2 keBkxH
xh
x
, (13)
22 /2 kehBixH
xh
z
,
here B is wave field constant. These constants are of
the following form:
2
1 2 12 ( ) /
h
HB h e
,
1 1 2 2 1( ) ( ( ) ) / HD h h , (14)
2
2 1 2 2 1( ) ( ( ) ) / HD h h e ,
2 2
2 2( 1) ( ) ( 1)H e h e .
2. MAIN RESULTS
The results of numerical calculation of dispersion
relations for E and H-waves for the selected set of
parameters are shown at Fig. 1. There are four solutions
of two dispersion equations (5) and (9).
Curves marked by the numbers 1, 2 correspond to
the waves of E-type and curves marked by the numbers
3, 4 correspond to the waves of H-type. For the chosen
set of parameters the condition that the central
metamaterial demonstrates left-handed properties
( 0)( and 0)( simultaneously) is valid for
the normalised frequency 1 1.5 . The lines (a) and
(b) represent the curves 2 and 1 , and
the line(c) – ( ) ( ) .
Fig. 1. The dependence of the normalised frequency
0/ on dimensionless wave number 3 0/k c
for LHM slab thickness
0 / 0,5c , 11 , 121
Let's consider the phase 3/phV k and group
velocity 3grV d dk for E- and H-waves which
correspond to lines 2, 3, 4 on Fig. 1.The dependence of
the normalized phase velocity on normalized frequency
for fixed different values of slab thickness is shown
on Figs. 2, 3.
For the one of H-waves (its dispersion is represented
by the line 3 on Fig. 1), dependence of the phase
velocity on the frequency varies substantially with
decreasing of the slab thickness (see Fig. 2). Number 1
http://www.multitran.ru/c/m.exe?t=2926706_1_2
114 ISSN 1562-6016. ВАНТ. 2014. №6(94)
on Fig. 2 corresponds to the slab thickness 0/c=1,
number 20/c=1.5, number 3 0/c=2.
For the other H-mode (its dispersion is given by the
line 4 on see Fig. 1), dependence of the phase velocity
on the frequency does not change with decreasing of the
slab thickness (see Fig. 3).
It is shown that the surface waves are slow and
strong frequency dependent in that frequency range
where central slab material demonstrates the left-
handedness.
Phase velocity of the considered waves at fixed
frequency changes with changing the value of slab
Fig. 2. The dependence of the phase velocity /phV c of
the one H-wave which dispersion is shown by the line 3
on Fig. 1 on the frequency 0/ for different left-
handed material slab thickness
0 / 1;1.5;2c
Fig. 3. The dependence of the phase velocity /phV c of
the other H-wave which dispersion is presented by the
line 4 on Fig. 1 on the frequency 0/ for
different left-handed material slab
thickness 0 / 1;1.5;2c
thickness . This dependence is called as geometric
dispersion it is shown on Fig. 4.
Dependence of phV and grV on the slab thickness is
most strong for those values of metamaterial thickness,
which, as we know, are not succeeded to be produced
up to now. Practical possibility of managing the waves
velocities will be run in such structures when rather thin
metamaterials will be produced.
On Fig. 5 the line 1 corresponds to E –wave which
dispersion is represented by the line 2 on see Fig. 1. The
lines 2 and 3 correspond to H –waves which dispersions
are given by the lines 3 and 4 on see Fig. 1. As we can
see the modes considered are both forward and
backward. Especially it should be noted the presence of
H-mode with zero group velocity.
The modes on see Fig. 5 show strong group velocity
dependence on frequency, including linear dependence.
These features can be very useful for practical
applications.
CONCLUSIONS
The possibility of existence of surface
electromagnetic eigen waves which propagate along the
left-handed planar slab bounded by the vacuum and the
medium with positive plasma-like permittivity is shown.
It is demonstrated that the surface E-wave is a direct
Fig. 4. The dependence of the phase velocity /phV c on
left-handed material slab thickness. 1: E-wave (with
dispersion shown by the line 2 on Fig. 1, 1,64 );
2: H-wave (with dispersion shown by the line 3 on
Fig. 1, 1,23 ); 3: H-wave (with dispersion shown by
the line 4 on Fig. 1 , 1,154 )
Fig. 5. The dependence of the group velocity /grV c on
of the frequency 0/ for left-handed material
slab thickness 0 / 1c . 1: E-wave (with dispersion
shown by the line 2 on Fig. 1); 2: H-wave (with
dispersion shown by the line 3 on Fig. 1); 3: H-wave
(with dispersion shown by the line 4 on Fig. 1)
http://www.multitran.ru/c/m.exe?t=5292580_1_2
ISSN 1562-6016. ВАНТ. 2014. №6(94) 115
one (group and phase velocities coincide in the
direction) and H-polarized wave is backward one (phase
and group velocities are directed oppositely).
It is shown that the phase velocity of one of the H-
waves is weakly dependent on the thickness of the
metamaterial slab, that is important for technological
applications. The absolute value of the group velocity of
H-waves can be quite low, down to zero. The linear
frequency dependence of group velocity of E-waves in a
combination with a relatively broad range of its
existence makes this mode very perspective one.
In particular it should be noted that the length of the
surface waves is much less than the length of bulk
electromagnetic waves, which significantly reduces the
size of technological devices.
The results obtained in this work can be useful for
the modelling and designing of modern nanodevices
based on metamaterials.
REFERENCES
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2. Theory and phenomena of metamaterials / Edit. by
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3. S. Antipov, L. Spentzouris, W. Gai, M. Conde,
F. Franchini, et al. Observation of wakefield generation
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// J. Appl. Phys. 2008, v. 104, p. 014901.
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Article received 20.10.2014
ПОВЕРХНОСТНЫЕ ЭЛЕКТРОМАГНИТНЫЕ ВОЛНЫ В СЛОЕ ЛЕВОСТОРОННЕГО
МАТЕРИАЛА, ПОГРУЖЕННОГО В ПЛАЗМОПОДОБНУЮ СРЕДУ
В.К. Галайдыч, Н.А. Азаренков, В.П. Олефир, А.Е. Споров
Изучены свойства собственных поверхностных электромагнитных волн, распространяющихся вдоль
плоской волноводной структуры, состоящей из слоя левостороннего материала, ограниченного вакуумом, и
плазмоподобной средой с диэлектрической проницаемостью, зависящей от частоты. Слой левостороннего
материала и окружающие среды предполагаются изотропными и бездиссипативными. Представлены
результаты изучения фазовой и групповой скоростей рассматриваемых волн.
ПОВЕРХНЕВІ ЕЛЕКТРОМАГНІТНІ ХВИЛІ В ШАРІ ЛІВОСТОРОННЬОГО МАТЕРІАЛУ,
ЗАНУРЕНОГО В ПЛАЗМОПОДІБНЕ СЕРЕДОВИЩЕ
В.К. Галайдич, М.О. Азарєнков, В.П. Олефір, О.Є. Споров
Вивчено дисперсійні властивості власних поверхневих електромагнітних хвиль, які поширюються в
пласкій хвилеводній структурі, яка складається з шару лівостороннього середовища, що межує з вакуумом
та плазмоподібним середовищем з діелектричною проникливістю, яка залежить від частоти. Шар
лівостороннього матеріалу та оточуючі середовища вважаються ізотропними та бездисипативними.
Представлено результати дослідження фазової та групової швидкостей хвиль, що вивчаються.
http://ufn.ru/en/articles/1968/4/d/
http://ufn.ru/en/articles/1968/4/d/
http://en.wikipedia.org/wiki/Taylor_%26_Francis
http://www.rsphysse.anu.edu.au/nonlinear/papers/IlyaShadrivov.shtml#PRE_2003_67_57602
http://www.rsphysse.anu.edu.au/nonlinear/papers/AndreySukhorukov.shtml#PRE_2003_67_57602
http://www.rsphysse.anu.edu.au/nonlinear/papers/YuriKivshar.shtml#PRE_2003_67_57602
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