Controlled anomalous transmission through plasma layers
We study propagation of a p-polarized electromagnetic wave through a two-layer plasma structure in an external magnetic field perpendicular to the incidence plane. It is shown that normally opaque plasma layer can be made absolutely transparent. The conditions for resonant transmission are obtained...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2010
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| Cite this: | Controlled anomalous transmission through plasma layers / S. Ivko, A. Smolyakov, I. Denysenko, N.A. Azarenkov // Вопросы атомной науки и техники. — 2010. — № 6. — С. 129-131. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859867716817518592 |
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| author | Ivko, S. Smolyakov, A. Denysenko, I. Azarenkov, N.A. |
| author_facet | Ivko, S. Smolyakov, A. Denysenko, I. Azarenkov, N.A. |
| citation_txt | Controlled anomalous transmission through plasma layers / S. Ivko, A. Smolyakov, I. Denysenko, N.A. Azarenkov // Вопросы атомной науки и техники. — 2010. — № 6. — С. 129-131. — Бібліогр.: 7 назв. — англ. |
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| description | We study propagation of a p-polarized electromagnetic wave through a two-layer plasma structure in an external magnetic field perpendicular to the incidence plane. It is shown that normally opaque plasma layer can be made absolutely transparent. The conditions for resonant transmission are obtained and analyzed. The influence of the external magnetic field on resonant transmission is studied. We show that one can control electromagnetic radiation transmitted through the plasma structure by altering the magnetic field.
Изучается прохождение р-поляризованной электромагнитной волны через двухслойную плазменную структуру во внешнем магнитном поле, перпендикулярном плоскости падения. Показано, что непрозрачный плазменный слой может быть сделан абсолютно прозрачным. Условия резонансного прохождения получены и проанализированы. Изучено влияние магнитного поля на резонансное прохождение. Показано, что можно контролировать электромагнитное излучение, прошедшее через плазменную структуру, изменяя магнитное поле.
Вивчається проходження р-поляризованої електромагнітної хвилі крізь двохшарову плазмову структуру в зовнішньому магнітному полі, перпендикулярному до площини падіння. Показано, що непрозорий плазмовий шар може бути зроблено абсолютно прозорим. Умови резонансного проходження отримано та проаналізовано. Вивчено вплив магнітного поля на резонансне проходження. Показано, що можна керувати проходженням електромагнітного випромінювання через плазмову структуру, змінюючи магнітне поле.
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| first_indexed | 2025-12-07T15:49:35Z |
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CONTROLLED ANOMALOUS TRANSMISSION
THROUGH PLASMA LAYERS
S. Ivko1, A. Smolyakov2, I. Denysenko1, N.A. Azarenkov1
1Department of Physics and Technology, V.N. Karazin Kharkov National University, Ukraine;
2Department of Physics and Engineering Physics, University of Saskatchewan, Canada
E-mail: sergey-ivko@yandex.ua
We study propagation of a p-polarized electromagnetic wave through a two-layer plasma structure in an external
magnetic field perpendicular to the incidence plane. It is shown that normally opaque plasma layer can be made
absolutely transparent. The conditions for resonant transmission are obtained and analyzed. The influence of the
external magnetic field on resonant transmission is studied. We show that one can control electromagnetic radiation
transmitted through the plasma structure by altering the magnetic field.
PACS: 52.40.Db, 52.25.Os, 52.35.Hr
1. INTRODUCTION
Tunneling of particles and electromagnetic waves
through potential barriers has been widely studied in
physics. In optics, the light tunneling in the experiment
with frustrated total internal reflection occurs due to
penetration of the decaying field of the evanescent wave
inside the barrier. The transmission through the barrier
can be increased by amplifying the evanescent wave. One
of the amplification methods is interference with a
resonant surface mode excited on density discontinuities.
Resonant structures exploiting this principle are well-
known. The resonant transmission of a p-polarized
electromagnetic wave through a symmetrical three-layer
structure composed of a media with negative dielectric
permittivity, that was placed between layers with positive
permittivity, was demonstrated both theoretically and
experimentally [1]. Lately [2,3], it was shown that
symmetry of the system is not a necessary condition, and
total brightening of an asymmetric two-layer system is also
possible. It was suggested that the total transparency was
due to a surface mode excitation at the interface between
layers. The surface waves with phase velocity exceeding
the speed of light couple with the incident electromagnetic
wave and transmit energy through the opaque layer.
Recently, structures, that can resonantly transmit
evanescent waves, attracted much interest. It was shown
by Pendry [4], that amplification of evanescent spectrum
of the incident light can be used to create a subwavelength
optical imaging system without the diffraction limit
(superlens). Manipulation of light at the subwavelength
scale also opens the possibilities for all optical computer
components which would combine advantages of wide
band photonics and nanoscale electronics [5].
In this paper we study propagation of a p-polarized
electromagnetic wave through a two-layer plasma
structure in an external magnetic field perpendicular to
the incidence plane. We find the conditions when total
transparency occurs. It is shown that transparency of the
system can be controlled by changing the magnetic field.
2. TRANSMISSION THROUGH
A TWO-LAYER PLASMA STRUCTURE
Consider a two-layer plasma structure surrounded by
vacuum (Fig. 1). The structure is immersed in an external
magnetic field H
r
directed along z-axis. It is assumed that
the density of the first slab Pl1 is small ( 10 <ε< 10 ,
where 10ε is the dielectric permittivity of the first layer at
absence of magnetic field), while the second layer Pl2 is
dense with 020 <ε (here 20ε is the dielectric permittivity
of the second layer at 0=H ). Consider propagation of a
p-polarized (with field components zyx H,E,E )
electromagnetic wave with the wave vector
yyxx ek+ek=k
rrr
through the structure. The wave
propagating from the half-infinite vacuum region V1 is
obliquely incident at the plasma layer Pl1. In the vacuum
region V1, there are the incident ( 0>kx ) and reflected
( 0<kx ) waves. The transmitted wave propagates into the
half-infinite vacuum region V2. In the plasma regions Pl1
and Pl2, which have widths 1a and 2a , the waves are
assumed to be non-propagating (evanescent) in x-
direction.
Fig. 1. Schematic representation of propagation of the
electromagnetic wave through the two-layer structure
We assume that ions in plasma are motionless and
electron collision frequencies are much smaller than the
wave frequency. Thus, the components of the dielectric
permittivity tensor of plasma in magnetic field has the
following form
22
2
1
c
p
ωω
ω
=ε
−
− ,
( )22
2
c
pc
ωωω
ωω
=g
−
,
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 6. 129
Series: Plasma Physics (16), p. 129-131.
where ω , pω and cω are the wave, plasma an electron
cyclotron frequencies, respectively.
From Maxwell’s equations we obtain the expressions
for components of electromagnetic field of the wave
130
( ) ( ) ⎟
⎠
⎞
⎜
⎝
⎛
−
−
dx
dHg+εHk
gεk
=xE z
zyx 22
0
1 , (1)
( ) ( ) ⎟
⎠
⎞
⎜
⎝
⎛
−
−
dx
dHε+gHk
gεk
i=xE z
zyy 22
0
, (2)
0
2
=Hκ+
dx
Hd
z
2
2
z , (3)
where ( ) εkgεk=κ 2
y /2
0
222 −− , cω=k /0 , c is the
speed of light. The equations (1) - (3) are valid for both
plasma and vacuum regions. For the vacuum regions,
1=ε and 0=g .
In the following we use wave impedance to match
boundary conditions. The local wave impedance is
defined as
( ) ( )
( )xH
xE
=xZ
z
y .
In the first vacuum region V1, the local impedance for
the electromagnetic wave is
( ) ( ) (
( ) (
)
)xikΓ+xik
xikΓxikZ=xZ
xvx
xvx
vv1 −
−−
expexp
expexp , (4)
where 0/ kk=Z xv is the characteristic impedance of the
vacuum region, vΓ is the reflection coefficient of the
wave incident from the half-infinite vacuum region onto
the plasma-vacuum interface. It follows from (4) that
)(Z+Z
)(ZZ=Γ
v1v
v1v
v 0
0− , (5)
where ( )0v1Z is the impedance at plasma-vacuum
interface.
In the plasma regions, the wave field is evanescent and
the impedance takes the form
( ) ( ) (
( ) (
)
)κxΓ+κx
κxΓκxiξ+iψ=xZ
expexp
expexp
−
−−
− ,
where )]g(ε[kκε=ξ 22
0/ − , )]g(ε[kgk=ψ y
22
0/ − .
The wave impedance in the second vacuum region v2Z is
spatially independent
vv2 Z=Z .
Since tangential components of the electric and
magnetic fields are continuous at x = 0, a1 , a1 + a2 , the
impedances are also continues at the interfaces. We match
impedance at each interface
( ) ( )00 1v1 Z=Z , (6)
( ) ( )111 aZ=aZ 2 , (7)
( ) v2 Z=a+aZ 12 , (8)
where the indexes 1 and 2 correspond to the plasma
regions Pl1 and Pl2, respectively.
Using the boundary conditions (6) - (8), we calculate
impedance at the first plasma-vacuum interface ( )0v1Z .
Then, using the obtained ( )0v1Z , we get the reflection
coefficient vΓ . The transmission coefficient T is defined
as
21 vΓ=T − , (9)
where ( )
( )0
0
1v
1v
v Z+Z
Z–Z=Γ , (10)
( ) ( )( )
( )( )11
11
11 iψ+aZ+iξ
Liξ+iψ+aZiξ+iψ=Z
12
112
1 0 − , (11)
( ) ( )
( )2v2
22v
22 iψ+Z+iξ
Liξ+iψ+Ziξ+iψ=aZ 2
12 − , (12)
( )lll aκ=L tanh and l = 1,2.
3. CONDITIONS FOR THE TOTAL
TRANSPARENCY
From (10) it follows that the total transparency
( 0=Γv ) occurs only if ( )01v Z=Z . Using the relation,
from (11) - (12) we find the condition for the total
transparency
( )
( )
( )
( )2
22
2
11
111
11 Lψ+Z+iξ
Lξ+ψi+Zξψ=
LψZiξ
Lξψi+Zξψ
2v2
2v
2
v1
v −
−−
−
− . (13)
The equation (13) is equivalent to the set of two real
transcendental equations (for its real and imaginary parts),
those in general case may be solved only numerically. If
the layers are thick ( 12,1 ≈L ), we obtain the equation
which coincides with the dispersion relation for the
surface waves at interface between two semi-infinite
plasmas:
21 ξψ=ξ+ψ 21 − .
Note that at plasma-plasma interface, propagation of
fast ( c>vph , where phv is the wave phase velocity) and
slow ( cv ph < ) surface waves is possible. At plasma-
vacuum and plasma dielectric interfaces, the surface
waves are always slow [6,7]. Thus, in the plasma slabs
Pl1 and Pl2 the surface modes can couple to incident
electromagnetic waves, which are evanescent in the
plasmas. Since for the incident waves we have 0k<k y ,
the resonant transmission is possible only in the frequency
range, where the surface waves are fast. Dispersion of
waves in magnetized plasmas depends on sign of yk . We
term the wave with 0>ky a positive branch and the
wave with 0<ky a negative branch.
For the both branches transition from slow mode to
fast mode occurs at frequency
2
42
2
1 42 p2
2
p1
cc ωω+ω+ω=ω .
The branches start from the frequency determined by
the inequality 02 >κ . In particular, the negative branch
starts at the hybrid frequency 2
cp1H1 ω+ω=ω 2 , which is
smaller than the onset frequency for the positive branch.
Below H1ω the Voigt dielectric constant
1
2
1
2
1 /)( εε gεV1 −= is large and positive, and, as a result,
02
1 <κ for a finite propagation vector, i.e. the surface
wave doesn't exist.
Resonance transparency occurs when the wave
frequency ω , y-component of the wave vector yk and
CONCLUSIONS the plasma layer widths 1a and 2a are connected by the
resonance condition (13). Without magnetic field the
resonance condition is independent on sign of yk , and the
structure is totally transparent at the same wave frequency
for both 0<yk and 0>yk (Fig.2 solid line).
It has been shown that an overcritical plasma slab (with
negative dielectric permittivity) in a magnetic field can be
made transparent to a p-polarized electromagnetic wave.
The condition for total transparency has been obtained.
The anomalous transmission is explained by interference
between the evanescent field of the incident wave and the
field of the resonant mode in the two-layer structure. In
the limit of thick layers, the dispersion of the resonant
mode coincides with the dispersion of the surface waves
at plasma-plasma interface in a magnetic field.
Structures consisting of alternating layers of media
with positive and negative permittivity are potential
building blocks of various plasmonic devices. Applying a
magnetic field to the structure, additional possibility to
control transmission of electromagnetic energy through
the structure appears. This possibility may be used in
constructing various gate devices.
Fig. 2. The transparency coefficient over the normalized
wave vector for different values of magnetic field:
0/ =p2c ωω (solid line), 2.0/ =p2c ωω (dashed line) . The
dependencies are obtained for 67.0/ =p2ωω ,
p2ωc=a /3.711 , p2ωc=a /1.342 and 5.0/ =p2p1 ωω
This work was supported by the NATO Collaborative
Linkage Grant CBP.NUKR.CLG.983378.
Applying an external magnetic field to the system, which
is totally transparent at H=0, we decrease the
transparency of the system (Fig. 2, dashed line). We can
restore the absolute transparency by changing width of a
layer, for instance, 1a . The resonance width 1a is
different for the positive and negative branches (Fig. 3).
REFERENCES
1. R. Dragila, B. Lutherdavies, S. Vukovic // Phys. Rev.
Let. 1985, v. 55, N 10, p. 1117.
2. R. Ramazashvili // JETP Letters. 1986, v. 43, N 5,
p. 298.
3. E. Fourkal, I. Velchev, C.M. Ma, A. Smolyakov// Phys.
Plasmas. 2006, v. 13, N 9, p. 092113.
4. J. B. Pendry //Phys. Rev. Lett. 2000, v. 85, p. 3966.
5. R. Zia, J.A. Schuller, A. Chandran, M.L. Brongersma //
Materials Today. 2006, v. 9, N 7-8, p. 20-27.
6. I.B. Denysenko, A.V. Gapon, N.A. Azarenkov,
K.N. Ostrikov, M.Y. Yu // Phys. Rev. E. 2002, v. 65,
p. 046419.
7. N.A. Azarenkov, I.B. Denysenko, A.V. Gapon,
T.W. Johnston // Phys. Plasmas. 2001, v. 8, N 5,
p. 1467. Fig. 3. The transparency coefficient over the normalized
wave vector for different widths of the first plasma
layer: p2ωc=a /2.571 (solid line), p2ωc /8.7 (dashed
line). The dependencies are obtained for 67.0/ =p2ωω ,
p2ωc=a /1.342 , 2.0/ =p2c ωω and 5.0/ =p2p1 ωω
Article received 7.10.10
УПРАВЛЯЕМОЕ АНОМАЛЬНОЕ ПРОХОЖДЕНИЕ ЧЕРЕЗ ПЛАЗМЕННЫЕ СЛОИ
С. Ивко, А. Смоляков, И. Денисенко, Н.А. Азаренков
Изучается прохождение р-поляризованной электромагнитной волны через двухслойную плазменную
структуру во внешнем магнитном поле, перпендикулярном плоскости падения. Показано, что непрозрачный
плазменный слой может быть сделан абсолютно прозрачным. Условия резонансного прохождения получены и
проанализированы. Изучено влияние магнитного поля на резонансное прохождение. Показано, что можно
контролировать электромагнитное излучение, прошедшее через плазменную структуру, изменяя магнитное
поле.
КЕРОВАНЕ АНОМАЛЬНЕ ПРОХОДЖЕННЯ КРІЗЬ ПЛАЗМОВІ ШАРИ
С. Івко, А. Смоляков, І. Денисенко, М.О. Азарєнков
Вивчається проходження р-поляризованої електромагнітної хвилі крізь двохшарову плазмову структуру в
зовнішньому магнітному полі, перпендикулярному до площини падіння. Показано, що непрозорий плазмовий
шар може бути зроблено абсолютно прозорим. Умови резонансного проходження отримано та проаналізовано.
Вивчено вплив магнітного поля на резонансне проходження. Показано, що можна керувати проходженням
електромагнітного випромінювання через плазмову структуру, змінюючи магнітне поле.
131
УПРАВЛЯЕМОЕ АНОМАЛЬНОЕ ПРОХОЖДЕНИЕ ЧЕРЕЗ ПЛАЗМЕННЫЕ СЛОИ
КЕРОВАНЕ АНОМАЛЬНЕ ПРОХОДЖЕННЯ КРІЗЬ ПЛАЗМОВІ ШАРИ
|
| id | nasplib_isofts_kiev_ua-123456789-17480 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:49:35Z |
| publishDate | 2010 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Ivko, S. Smolyakov, A. Denysenko, I. Azarenkov, N.A. 2011-02-26T22:09:01Z 2011-02-26T22:09:01Z 2010 Controlled anomalous transmission through plasma layers / S. Ivko, A. Smolyakov, I. Denysenko, N.A. Azarenkov // Вопросы атомной науки и техники. — 2010. — № 6. — С. 129-131. — Бібліогр.: 7 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/17480 We study propagation of a p-polarized electromagnetic wave through a two-layer plasma structure in an external magnetic field perpendicular to the incidence plane. It is shown that normally opaque plasma layer can be made absolutely transparent. The conditions for resonant transmission are obtained and analyzed. The influence of the external magnetic field on resonant transmission is studied. We show that one can control electromagnetic radiation transmitted through the plasma structure by altering the magnetic field. Изучается прохождение р-поляризованной электромагнитной волны через двухслойную плазменную структуру во внешнем магнитном поле, перпендикулярном плоскости падения. Показано, что непрозрачный плазменный слой может быть сделан абсолютно прозрачным. Условия резонансного прохождения получены и проанализированы. Изучено влияние магнитного поля на резонансное прохождение. Показано, что можно контролировать электромагнитное излучение, прошедшее через плазменную структуру, изменяя магнитное поле. Вивчається проходження р-поляризованої електромагнітної хвилі крізь двохшарову плазмову структуру в зовнішньому магнітному полі, перпендикулярному до площини падіння. Показано, що непрозорий плазмовий шар може бути зроблено абсолютно прозорим. Умови резонансного проходження отримано та проаналізовано. Вивчено вплив магнітного поля на резонансне проходження. Показано, що можна керувати проходженням електромагнітного випромінювання через плазмову структуру, змінюючи магнітне поле. This work was supported by the NATO Collaborative Linkage Grant CBP.NUKR.CLG.983378. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Плазменная электроника Controlled anomalous transmission through plasma layers Управляемое аномальное прохождение через плазменные слои Кероване аномальне проходження крізь плазмові шари Article published earlier |
| spellingShingle | Controlled anomalous transmission through plasma layers Ivko, S. Smolyakov, A. Denysenko, I. Azarenkov, N.A. Плазменная электроника |
| title | Controlled anomalous transmission through plasma layers |
| title_alt | Управляемое аномальное прохождение через плазменные слои Кероване аномальне проходження крізь плазмові шари |
| title_full | Controlled anomalous transmission through plasma layers |
| title_fullStr | Controlled anomalous transmission through plasma layers |
| title_full_unstemmed | Controlled anomalous transmission through plasma layers |
| title_short | Controlled anomalous transmission through plasma layers |
| title_sort | controlled anomalous transmission through plasma layers |
| topic | Плазменная электроника |
| topic_facet | Плазменная электроника |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/17480 |
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