Dispersion of the surface magnetoplasmons
We study the dispersion properties and transmission of a p-polarized electro-magnetic wave in a two-layer plasma structure in presence of an external magnetic field. The conditions for resonance transmission are found. The anomalous transparency is attributed to excitation of surface waves at plasma...
Gespeichert in:
| Datum: | 2010 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2010
|
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/17368 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Dispersion of the surface magnetoplasmons / S.V. Ivko, I.B. Denysenko, A.I. Smolyakov, N.A. Azarenkov // Вопросы атомной науки и техники. — 2010. — № 4. — С. 373-375. — Бібліогр.: 3 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-17368 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-173682011-02-26T12:04:47Z Dispersion of the surface magnetoplasmons Ivko, S.V. Denysenko, I.B. Smolyakov, A.I. Azarenkov, N.A. Приложения и технологии We study the dispersion properties and transmission of a p-polarized electro-magnetic wave in a two-layer plasma structure in presence of an external magnetic field. The conditions for resonance transmission are found. The anomalous transparency is attributed to excitation of surface waves at plasma-plasma interface. The dispersion relation for the surface mode at plasma-plasma interface in magnetic field is studied and compared with that for a plasma-vacuum system. Изучаются дисперсионные свойства и прохождение р-поляризованной электромагнитной волны в двухслойной плазменной структуре в присутствии внешнего магнитного поля. Получены условия резонансного прохождения. Аномальная прозрачность объясняется возбуждением поверхностной волны на границе плазма-плазма. Изучается дисперсионное соотношение для поверхностной волны на границе плазма-плазма в магнитном поле, проводится сравнение с дисперсией поверхностных волн в системе плазма-вакуум. Вивчаються дисперсійні властивості та проходження р-поляризованої електромагнітної хвилі в двошаровій плазмовій структурі за наявності зовнішнього магнітного поля. Отримано умови резонансного проходження. Аномальна прозорість пояснюється збудженням поверхневої хвилі на межі плазма-плазма. Вивчається дисперсійне співвідношення для поверхневої хвилі на межі плазма-плазма в магнітному полі, проводиться порівняння з дисперсією поверхневих хвиль в системі плазма-вакуум. 2010 Article Dispersion of the surface magnetoplasmons / S.V. Ivko, I.B. Denysenko, A.I. Smolyakov, N.A. Azarenkov // Вопросы атомной науки и техники. — 2010. — № 4. — С. 373-375. — Бібліогр.: 3 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/17368 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Приложения и технологии Приложения и технологии |
| spellingShingle |
Приложения и технологии Приложения и технологии Ivko, S.V. Denysenko, I.B. Smolyakov, A.I. Azarenkov, N.A. Dispersion of the surface magnetoplasmons |
| description |
We study the dispersion properties and transmission of a p-polarized electro-magnetic wave in a two-layer plasma structure in presence of an external magnetic field. The conditions for resonance transmission are found. The anomalous transparency is attributed to excitation of surface waves at plasma-plasma interface. The dispersion relation for the surface mode at plasma-plasma interface in magnetic field is studied and compared with that for a plasma-vacuum system. |
| format |
Article |
| author |
Ivko, S.V. Denysenko, I.B. Smolyakov, A.I. Azarenkov, N.A. |
| author_facet |
Ivko, S.V. Denysenko, I.B. Smolyakov, A.I. Azarenkov, N.A. |
| author_sort |
Ivko, S.V. |
| title |
Dispersion of the surface magnetoplasmons |
| title_short |
Dispersion of the surface magnetoplasmons |
| title_full |
Dispersion of the surface magnetoplasmons |
| title_fullStr |
Dispersion of the surface magnetoplasmons |
| title_full_unstemmed |
Dispersion of the surface magnetoplasmons |
| title_sort |
dispersion of the surface magnetoplasmons |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2010 |
| topic_facet |
Приложения и технологии |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/17368 |
| citation_txt |
Dispersion of the surface magnetoplasmons / S.V. Ivko, I.B. Denysenko, A.I. Smolyakov, N.A. Azarenkov // Вопросы атомной науки и техники. — 2010. — № 4. — С. 373-375. — Бібліогр.: 3 назв. — англ. |
| work_keys_str_mv |
AT ivkosv dispersionofthesurfacemagnetoplasmons AT denysenkoib dispersionofthesurfacemagnetoplasmons AT smolyakovai dispersionofthesurfacemagnetoplasmons AT azarenkovna dispersionofthesurfacemagnetoplasmons |
| first_indexed |
2025-07-02T18:36:48Z |
| last_indexed |
2025-07-02T18:36:48Z |
| _version_ |
1836561370219282432 |
| fulltext |
УДК 533.9
DISPERSION OF THE SURFACE MAGNETOPLASMONS
S.V. Ivko1, I.B. Denysenko1, A.I. Smolyakov2, N.A. Azarenkov1
1Department of Physics and Technology, V.N. Karazin Kharkov National University,
Kharkov, Ukraine
2Department of Physics and Engineering Physics, University of Saskatchewan,
Saskatoon, Canada
E-mail: sergey-ivko@yandex.ua
We study the dispersion properties and transmission of a p-polarized electro-magnetic wave in a two-layer plas-
ma structure in presence of an external magnetic field. The conditions for resonance transmission are found. The
anomalous transparency is attributed to excitation of surface waves at plasma-plasma interface. The dispersion rela-
tion for the surface mode at plasma-plasma interface in magnetic field is studied and compared with that for a plas-
ma-vacuum system.
PACS: 52.40.Db, 52.25.Os, 52.35.Hr
1. INTRODUCTION
The materials with negative dielectric permittivity
0<ε and magnetic permeability 0<μ (metamaterials)
have attracted much attention in recent years. The in-
creased interest to such media has been driven by their
potential applications in various branches of science and
technology. Such materials have much promises for
subwavelength optics, particularly, for imaging systems
without the diffraction limit [1], the so called super-
lense. 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 [2].
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2010. № 4.
Серия: Плазменная электроника и новые методы ускорения (7), с. 373-375.
373
Various remarkable properties in metamaterials are
based on the amplification of evanescent waves due to
surface mode resonances. In this paper, we study trans-
parency of a structure consisting of two plasma layers of
different electron densities. It was found earlier [3] that
at absence of magnetic field a p-polarized electromag-
netic wave obliquely incident at a layer with smaller
density can be totally transmitted through the two-layer
plasma structure. The transparency of the structure oc-
curs as a result of surface mode excitation. The surface
wave at the plasma-plasma interface amplifies the
transmitted wave, which is evanescent in plasma. In this
paper, we study the influence of an external magnetic
field on transparency of the two-layer structure. Voigt
geometry is considered.
2. TRANSPARENCY OF TWO-LAYER
PLASMA STRUCTURE
Consider a two-layer plasma structure surrounded by
vacuum (Fig.1). The structure is immersed in an exter-
nal magnetic field H
r
directed along z-axis. It is as-
sumed that the density of the first slab Pl1 is small
( 10 10 <ε< , 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 ). A
p-polarized electromagnetic wave with wave vector k
r
is obliquely incident at the first slab. The wave vector
has two non-zero components, x-component kx and y-
component ky. In the vacuum region V1, the wave con-
sists of the incident ( 0>kx ) and reflected ( 0<kx )
waves. The transmitted wave propagates into the semi-
infinite vacuum region V2. In the plasma regions Pl1
and Pl2, the waves are assumed to be non-propagating
(evanescent) in x-direction.
In a constant magnetic field the dielectric permittiv-
ity tensor of a plasma slab has the following non-zero
components
22
2
11 1
c
p
22 ωω
ω
=εε=ε
−
−≡ ,
( )22
2
2112
c
pc
ωωω
ωiω
=igε=ε
−
≡− ,
2
2
33 1
ω
ω
=ε p− ,
where ω , pω and cω are the wave, plasma and cyclo-
tron frequencies, respectively.
The expressions for components of electro-magnetic
field of the wave in different plasma and vacuum re-
gions may be obtained from Maxwell’s equations. Ob-
taining the components, we assumed that the plasma is
collisionless and ions are immobile (the wave frequency
is assumed to be large).
Fig.1. Schematic representation of propagation of elec-
tromagnetic wave through the two-layer structure
http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=FREESR&search=Search&smode=results&possible1=52.40.Db&possible1zone=pacs&bool1=and
http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=FREESR&search=Search&smode=results&possible1=52.25.Os&possible1zone=pacs&bool1=and
http://scitation.aip.org/vsearch/servlet/VerityServlet?KEY=FREESR&search=Search&smode=results&possible1=52.35.Hr&possible1zone=pacs&bool1=and
Assuming that the tangential components of electric
and magnetic field of the wave are continuous at inter-
faces and neglecting reflected wave in the vacuum re-
gion V1, one can obtain the condition of the absolute
transmission
( )
( ) ,
x222
222x
2
2
2
2
x111
111x
2
1
2
1
ikφcothξ+ψ
φcothξψikξψ
=
ikφcothξψ
φcothξ+ψikξψ
−
−−−
−−
−−
(1)
where )]([ 22 gεkκε=ξ − , )]([ 22 gεkgk=ψ y − ,
κa=ϕ , a is a layer thickness, θ=kx cos is the nor-
malized x-component of the wave vector, θ is the inci-
dence angle, ( ) εgεkk=κ y /2222 −− is the decay con-
stant, cωk /= , and c is the speed of light. Indexes 1 and
2 in Eq. (1) correspond to the parameters of the slabs
Pl1 and Pl2, respectively.
Note that the resonance transmission condition (1)
depends on the layer widths, while the condition at
0=H is independent on a1 and a2 [3].
The equation (1) is equivalent to the set of two real
transcendental equations (for its real and imaginary
parts), those in general case may be solved only numeri-
cally. An analytical solution of Eq. (1) is possible only
for the limits of thin ( 1<<ϕ ) and thick ( 1>>ϕ ) layers.
If the layer is thin, the equation (1) reduces to the set of
the following two equations
02
2
2
2
2
1
1
2
1
2
=φ
ξ
ψξ+k+φ
ξ
ψξ+k 2
2x
2
1x −−
and
02
2
2
1
1
1 =φ
ξ
ψ+φ
ξ
ψ .
374
In the case 1>>ϕ , Eq. (1) transforms to the follow-
ing equation
( ) ( )
.2ξ
2ξ
2
2
22
2
1
11
1
1221
φ
x2
x
φ
x
x1
1
e
ik+ξ+ψ
ik+ξψ
e
ik+ξψ
ik+ξ+ψ=ξψξ+ψ
−
−
−
−
−
−
−−−
(2)
3. DISPERSION PROPERTIES OF SURFACE
WAVES AT PLASMA-PLASMA AND
PLASMA-VACUUM INTERFACES
In zero approximation, neglecting the right-hand
side of Eq. (2), 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 − . (3)
The equation (3) may be presented in the form
2
2
2
2
222
2
1
2
1
111
gε
κεgk
gε
κε+gk yy
−
−
=
−
. (4)
Eq. (4) may be solved analytically only in some lim-
iting cases. Therefore, we found its solution numeri-
cally. In Fig.2, the dispersion dependencies for waves
with 0<ky and 0>ky are shown. The curves were
obtained for 125.0/ 2=pc ωω and .25.0/ 21 =pp ωω
Note that surface waves at plasma-vacuum interface
are always slow ( c<vph , where phv is the wave phase
velocity). It is connected with the fact that dielectric
permittivity larger than unity doesn’t allow surface
modes with phase velocities greater than the speed of
light. In plasmas with 1<ε , propagation of fast waves
( c>vph ) is possible. Thus, in the plasma slabs Pl1 and
Pl2 the surface modes can couple to incident electro-
magnetic waves, which are evanescent in the plasmas.
Fig.2. Dispersion of the surface waves
at plasma-plasma interface.
The curves were obtained for 25.0/ 21 =pp ωω and
125.0/ 2=pc ωω
The waves in magnetized plasmas are non-
reciprocal, i.e. dependent on the sign of yk . We term
the wave with 0>ky a positive branch and the wave
with 0<ky a negative branch. The positive and nega-
tive branches exist in different frequency ranges (Fig.2).
To find the upper limit of the frequency range, we
let kky >> , that gives us
211 ε±g=εg 2m , (5)
( ) ( ) 02
2
2
2
1 =
ωω±ω
ω
ωωω
ω
c
p
c
p −−
m
. (6)
Here, the upper sign is for the positive and lower for
the negative branch, correspondingly.
In the case of weak magnetic field ( pc ωω << ),
Eq. (6) has the following solution:
( )
2
p1p2
ppc0
ω+ω
ωωω±ω=ω 2
2
2
2
1
infinf 2
−
⋅± ,
where ( ) ( ) 2/20
inf
2
p2p1 ω+ω=ω is the asymptotic frequency
(at kky >> ) for the case of non-magnetized plasma. For
the surface waves at plasma-vacuum interface ( 0=ωp1 )
the equation (6) is quadratic. It has solutions
⎟
⎠
⎞⎜
⎝
⎛
± c
2
cp
v ωω+ω=ω m2)(
inf 2
2
1
. hybrid frequency 2
cp1H1 ω+ω=ω 2 (see Fig.2), which is
smaller than the onset frequency for the positive branch.
Below H1ω the Voigt dielectric constant V1ε is large
and positive, implying that 02
1 <κ for a finite propaga-
tion vector, i.e. no surface magnetoplasmon is allowed.
Thus, at large yk the wave frequency is close
to )(
inf
vω± (Fig.3).
CONCLUSIONS
375
Fig.3. Dispersion of the surface wave at plasma-vacuum
interface. The curves were obtained for 125.0/ =pc ωω
We can also find a partial solution of Eq. (3), if we
request
021 =ψψ − , (7)
01 =ξ+ξ 2 . (8)
In conclusion, we have studied the resonant proper-
ties of a two-layer plasma configuration in an external
magnetic field. We have found the conditions at which
the structure becomes absolutely transparent for an inci-
dent p-polarized electromagnetic wave. The case when
the magnetic field is perpendicular to the wave vector
and is parallel to the plasma-vacuum and plasma-plasma
interfaces has been considered (Voigt geometry). It has
been shown that in the case of infinitely thick layers the
condition of anomalous transparency reduces to the dis-
persion relation for the surface waves at plasma-plasma
interface. The dispersion relation has been studied in
detail. The unique properties of the plasma-plasma sys-
tem in magnetic field have been noted. Among them are
existence of the fast surface mode and non-reciprocity
of the waves. The frequency region, where the surface
waves exist, has been found. We have also determined
the upper frequency limit for the fast wave, what is im-
portant for the problem of resonant transmission.
The partial solution of the system (7), (8) is
k=ky ,
2
42
2
1 42 p2
2
p1
cc ωω+ω+ω=ω .
This work was supported by the NATO Collabora-
tive Linkage Grant CBP.NUKR.CLG.983378.
REFERENCES
The frequency 1ω corresponds to the upper frequency
limit for the fast waves. 1. J.B. Pendry and D.R. Smith, The quest for the super-
lens // Sci. Amer. 2006, v.295, №1, p.60-67. The field of the surface mode decays from the inter-
face, i.e. the decay constant κ is a real number. Requir-
ing 02 >κ , we determine the onset frequency. For the
wave propagating in positive direction, the frequency is
determined by inequality V1y εkk ≥ , where
1
2
1
2
1 /)( εε gεV1 −= is the Voigt dielectric constant for
the plasma slab Pl1. The negative branch starts at the
2. R. Zia, J.A. Schuller, A. Chandran, and
M.L. Brongersma. Plasmonics: the next chip-scale
technology // Materials Today. 2006, v.9, №7-8,
p.20-27.
3. E. Fourkal, I. Velchev, C.M. Ma, A. Smolyakov.
Evanescent wave interference and the total transpar-
ency of a warm high-density plasma slab // Physics
of Plasmas. 2006, v.13, №9, 092113.
Статья поступила в редакцию 05.07.2010 г.
ДИСПЕРСИЯ ПОВЕРХНОСТНЫХ МАГНЕТОПЛАЗМОНОВ
С.В. Ивко, И.Б. Денисенко, А.И. Смоляков, Н.А. Азаренков
Изучаются дисперсионные свойства и прохождение р-поляризованной электромагнитной волны в двух-
слойной плазменной структуре в присутствии внешнего магнитного поля. Получены условия резонансного
прохождения. Аномальная прозрачность объясняется возбуждением поверхностной волны на границе плаз-
ма-плазма. Изучается дисперсионное соотношение для поверхностной волны на границе плазма-плазма в
магнитном поле, проводится сравнение с дисперсией поверхностных волн в системе плазма-вакуум.
ДИСПЕРСІЯ ПОВЕРХНЕВИХ МАГНЕТОПЛАЗМОНІВ
С.В. Івко, І.Б. Денисенко, А.І. Смоляков, М.О. Азарєнков
Вивчаються дисперсійні властивості та проходження р-поляризованої електромагнітної хвилі в двошаро-
вій плазмовій структурі за наявності зовнішнього магнітного поля. Отримано умови резонансного прохо-
дження. Аномальна прозорість пояснюється збудженням поверхневої хвилі на межі плазма-плазма. Вивча-
ється дисперсійне співвідношення для поверхневої хвилі на межі плазма-плазма в магнітному полі, прово-
диться порівняння з дисперсією поверхневих хвиль в системі плазма-вакуум.
ДИСПЕРСИЯ ПОВЕРХНОСТНЫХ МАГНЕТОПЛАЗМОНОВ
ДИСПЕРСІЯ ПОВЕРХНЕВИХ МАГНЕТОПЛАЗМОНІВ
|