Symmetric surface electromagnetic waves at flat interface plasma –vacuum
As it is known the surface electromagnetic waves (SEW) can propagate along surface, which separates two media with the permittivity of different signs . A lot of works devoted to studies and applications of plane SEW. We have shown that new type of SEW can propagate along the boundary of free plasma...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
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| Cite this: | Symmetric surface electromagnetic waves at flat interface plasma –vacuum / V.K. Galaydych, K.V. Galaydych // Вопросы атомной науки и техники. — 2007. — № 1. — С. 96-98. — Бібліогр.: 9 назв. — англ. |
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| author | Galaydych, V.K. Galaydych, K.V. |
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| citation_txt | Symmetric surface electromagnetic waves at flat interface plasma –vacuum / V.K. Galaydych, K.V. Galaydych // Вопросы атомной науки и техники. — 2007. — № 1. — С. 96-98. — Бібліогр.: 9 назв. — англ. |
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| description | As it is known the surface electromagnetic waves (SEW) can propagate along surface, which separates two media with the permittivity of different signs . A lot of works devoted to studies and applications of plane SEW. We have shown that new type of SEW can propagate along the boundary of free plasma with vacuum. The equiphase surfaces of these waves are the circular cylinders in contrast to planes in case of conventional surface waves. The properties of these unconventional SEW are presented. The dispersion characteristics, the field distribution and Poynting vector for these waves were obtained. Comparison of properties of conventional and unconventional SEW have been analysed.
Відомо, що поверхневі електромагнітні хвилі (ПЕХ), можуть поширюватись уздовж поверхні, що розділяє два середовища з діелектричними сталими різних знаків . Багато робіт присвячено вивченню плоских ПЕХ. Ми показали, що ПЕХ нового типу можуть поширюватись уздовж межі вільної плазми з вакуумом. Еквіфазними поверхнями у цих хвиль є кругові циліндри, а не площини, як у випадку звичних поверхневих хвиль. Отримано дисперсію, розподіл полів та вектор Пойнтинга для цих хвиль. Проведено порівняння властивостей звичайних та вивчених в даній роботі ПЕХ.
Известно, что поверхностные электромагнитные волны (ПЭВ), могут распространяться по поверхности, которая разделяет две среды с диэлектрическими постоянными различных знаков . Много работ посвящено изучению плоских ПЭВ. Мы показали, что ПЭВ нового типа могут распространяться по границе свободной плазмы с вакуумом. Эквифазными поверхностями у этих волн есть круговые цилиндры, а не плоскости, как в случае обычных поверхностных волн. Получены дисперсия, распределение полей и вектор Пойнтинга для этих волн. Проведено сравнение свойств обычных и рассмотренных в данной работе ПЭВ.
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| first_indexed | 2025-12-07T19:03:48Z |
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96 Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 96-98
SYMMETRIC SURFACE ELECTROMAGNETIC WAVES
AT FLAT INTERFACE PLASMA –VACUUM
V.K. Galaydych 1, K.V. Galaydych 2
1 V. N. Karazin Kharkov National University, School of Physics and Technology,
Department of General and Applied Physics, Svobody sq. 4, 61077 Kharkov, Ukraine;
2 NSC “Kharkov Institute of Physics and Technology”,
Academicheskaya Str. 1, 61108 Kharkov, Ukraine
As it is known the surface electromagnetic waves (SEW) can propagate along surface, which separates two media
with the permittivity of different signs [1]. A lot of works devoted to studies and applications of plane SEW. We have
shown that new type of SEW can propagate along the boundary of free plasma with vacuum. The equiphase surfaces of
these waves are the circular cylinders in contrast to planes in case of conventional surface waves. The properties of
these unconventional SEW are presented. The dispersion characteristics, the field distribution and Poynting vector for
these waves were obtained. Comparison of properties of conventional and unconventional SEW have been analysed.
PACS: 52.35.Hr
1. PROBLEM STATEMENT
Probably, first paper devoted to surface
electromagnetic waves was published almost 100 years
ago [2]. These waves satisfy Maxwell’s equations and
may be excited on the boundary between two media with
different permittivity. These modes are localized near the
separating surface, i.e. their amplitudes are biggest at this
surface and decays inside both of media. Vast deal of
problems surface waves involved were solved and
published (see [3]-[6] and references therein).
Consideration in all these works concern with plane
waves, i.e. the equiphase surfaces are the planes. Surface
electromagnetic waves in solids of spherical and
cylindrical shape have been investigated in [7].
We study the possibility of existence of solutions of
Maxwell’s equations with the equiphase surfaces giving
circles at separating surface. In a sense, we are interested
in such type of waves which are analogous to established
circular waves on water surface. Mode of excitation is out
of consideration in this report; one of possibilities was
studied in [8].
Let us consider a plane interface ( 0z = ) between two
half-spaces. Introduce a cylindrical coordinate system
with Z-axis perpendicular to the separating plane. First
domain 0z > is a vacuum with permittivity 1 1ε = and
second is homogeneous free plasma with the frequency-
dependent permittivity ( ) ( )2
2 1 /pε ε ω ω ω= = − , where
2 24p p ee n mω π= is a plasma frequency. In cylindrical
coordinate system ( ), ,r zϕ the set of Maxwell’s
equations split in two subsystems. One of them consists
of { rE , zE , Hϕ }, another consists of { rH , zH , Eϕ }. We
will be interested in symmetric waves, i.e. all disturbances
are independent of angle ϕ .
Let’s consider the problem of describing wave
propagation with nonzero components: an azimuth
magnetic field Hϕ , a radial electric field rE and electric
field zE , which is perpendicular to the boundary. We will
find solution in such form:
( ) ( ) ( ) ( )1,2, , exp expA r z t A r z i tκ ω= −m , where ω is a
wave frequency, 1/κ is a depth of field penetration in
both media, indexes 1, 2 correspond to vacuum and
plasma (ω , 1,2κ are real and positive).
2. RESULTS AND DISCUSSION
System of equations for such wave disturbances is as
follow:
1,2 1,2 ,rH ik Eϕκ ε=m (1)
1,2 ,z
r
dEikH E
drϕ κ= −m (2)
( ) 1,2
1 ,z
d rH ik E
r dr ϕ ε = −
(3)
where k cω= , c is a speed of light.
Expressions for the electric fields rE , zE with Hϕ are:
( )1,2 1,2/rE i k Hϕκ ε= ± (4)
( )2
1,2 1,2/zdE i k k H
dr ϕκ ε= − + . (5)
Substituting (4), (5) in (3) we obtain equation for Hϕ
2
2 2
1,22 ( ) 1 0
d H dH
r r K r H
drdr
ϕ ϕ
ϕ + + − = , (6)
where 2 2 2
1,2 1,2 1,2K kκ ε= + . Equation (6) is a well-known
Bessel’s equation and its solution is any linear
combination of independent Bessel functions of first
order: ( )1 1,2H Z K rϕ = . This equation describes both
divergent and convergent circular wave, according to
choice of Bessel functions as a solution. Let us obey the
boundary conditions consisting in a continuity of
tangential component of electric and magnetic field of a
wave on plasma - vacuum boundary. It gives dispersion
equation for circular surface electromagnetic waves that
can propagate along plasma - vacuum boundary:
( ) ( ) ( )( )1 2 / 1K K K kω ε ω ε ω= = = + , (7)
97
from which follows conditions of existence for these
waves / 2pω ω< and expressions for the inverse depths
of penetration:
( )( )1 / 1kκ ε ω= − + , ( ) ( )( )2 / 1kκ ε ω ε ω= − − + . (8)
The electric fields of such circular surface
electromagnetic waves are:
( ) ( )1,2 1,2 1/rE i k Z Krκ ε= ± , (9)
( ) ( )2
1,2 1,2 0/ /zE i k k K Z Krκ ε = + . (10)
Evidently, both the range of existence and dispersion
law for circular surface electromagnetic waves are the
same as for plane surface electromagnetic waves [1-5].
Difference from conventional plane surface waves
consists in the spatial dependence of wave amplitude.
To concretize the task let’s choice the type of solution
of equation (6) in the form ( )1J Kr . It means that we
have divergent circular surface electromagnetic waves. Its
fields are
( ) ( ) ( )1, , , ,H r z t J Kr z tϕ = ⋅Θ (11)
( ) ( ) ( ) ( )1,2 1,2 1, , / ,rE r z t i k J Kr z tκ ε= ± ⋅ Θ , (12)
( ) ( ) ( ) ( )2
1,1 1,2 0, , / / ,zE r z t i k k K J Kr z tκ ε = + ⋅Θ , (13)
where ( ) ( )1,2, expz t z i tκ ωΘ = −m . At large distance from
origin (for 1Kr >> ) we may use asymptotic forms for
Bessel’s functions 0J and 1J :
( ) ( )
( ) ( )
0
1
2 cos 4
2 cos 4 2
J Kr Kr Kr
J Kr Kr Kr
π π
π π π
≈ ⋅ −
≈ ⋅ − −
, (14)
It can be seen that the divergent circular surface
electromagnetic waves becomes quasi-plane surface
electromagnetic waves (TM-polarization) with harmonic
dependence on radial coordinate and slowly (~ 2 Krπ )
decreasing amplitude that propagate in radial direction.
The time averaged (per period 2T π ω= ) Poynting
vector for the wave with components { Hϕ , rE , zE }, is
8r z
cS H Eϕπω
= . (15)
If the wave components { Hϕ , rE , zE } are set by
expressions (11)-(13), then the values of time averaged
Poynting vector near to the separating surface ( 0z = )
are:
( ) ( )
( ) ( ) ( )
1 0 1
2 0 1
8
8
r
r
S K J Kr J Kr
S K J Kr J Kr
π
πε ω
= ⋅
= ⋅
. (16)
We can see from (16) that directions of energy flows in
vacuum and plasma are the opposite at any distance from
origin:
( )1 2 1r rS S ε ω= < − (17)
Dependence of normalized averaged per period Poynting
vector (in vacuum) versus normalized radius is shown in
the Figure. There are the circular regions of alternation of
sign of Poynting vector, that is typical for plane SEW [4].
Normalized averaged per period Poynting vector
(in vacuum) versus normalized radius.
Experimental studies of circular surface
electromagnetic waves is presented in [9]. These waves
were exited in thin metal films. In this experiment the
optical probe of a scanning near-field microscope
operated as transmitting aerial. It should be noted that our
results are in good qualititative agreement with [9].
CONCLUSIONS
Starting from Maxwell’s equations we have obtained
the solutions in the form of divergent (or convergent)
circular surface electromagnetic waves. Equiphase
surfaces of these waves are circles. These waves have
dispersion law similar to well-known plane surface
electromagnetic waves. At large distance from centre of
excitation these waves become quasi-plane.
REFERENCES
1. L.D. Landau, E.M. Lifschitz. Electrodynamics of
Continuous Media. London: “Butterworth”, 1984.
2. J. Zenneck // Ann. der Physik. 1907, v. 23, p.846-866.
3. A.D. Boardman. Electromagnetic Surface Modes.
New York: “John Wiley & Sons Ltd”, 1982.
4. V.M. Agranovich, D.L. Mills. Surface Polaritons.
Amsterdam: “Elsivier”, 1982.
5. N.L. Dmitruk, V.G. Litovchenko, V.L. Strizhevsky.
Surface Polaritons in Semiconductors and Dielectrics.
Kiev: “Naukova Dumka”, 1989 (in Russian).
6. A.N. Kondratenko. Surface and Bulk Waves in
Bounded Plasmas. Moscow: “Energoatomizdat”, 1985 (in
Russian).
7. R. Ruppin. Spherical and cylindrical surface
polaritons in solids: Electromagnetic Surface Modes/ ed.
by A.D. Boardman. New York: “John Wiley & Sons
Ltd”, 1982, Chap.9, p. 345-398.
8. S.M. Levitsky, I.A. Anisimov. Surface waves
excitation by the modulated electron beam normally
incident on plasma boundary // Radiotehnika i
Elektronika. 1986, v. 41, N3, p. 614-615 (in Russian).
9. B. Hecht, H. Bielefeldt et al. Local exitation,
scattering, and interference of surface plasmons//
Phys.Rev.Lett. 1996, v. 77, N 9, p. 1889-1892.
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| id | nasplib_isofts_kiev_ua-123456789-110416 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T19:03:48Z |
| publishDate | 2007 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Galaydych, V.K. Galaydych, K.V. 2017-01-04T12:21:59Z 2017-01-04T12:21:59Z 2007 Symmetric surface electromagnetic waves at flat interface plasma –vacuum / V.K. Galaydych, K.V. Galaydych // Вопросы атомной науки и техники. — 2007. — № 1. — С. 96-98. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.35.Hr https://nasplib.isofts.kiev.ua/handle/123456789/110416 As it is known the surface electromagnetic waves (SEW) can propagate along surface, which separates two media with the permittivity of different signs . A lot of works devoted to studies and applications of plane SEW. We have shown that new type of SEW can propagate along the boundary of free plasma with vacuum. The equiphase surfaces of these waves are the circular cylinders in contrast to planes in case of conventional surface waves. The properties of these unconventional SEW are presented. The dispersion characteristics, the field distribution and Poynting vector for these waves were obtained. Comparison of properties of conventional and unconventional SEW have been analysed. Відомо, що поверхневі електромагнітні хвилі (ПЕХ), можуть поширюватись уздовж поверхні, що розділяє два середовища з діелектричними сталими різних знаків . Багато робіт присвячено вивченню плоских ПЕХ. Ми показали, що ПЕХ нового типу можуть поширюватись уздовж межі вільної плазми з вакуумом. Еквіфазними поверхнями у цих хвиль є кругові циліндри, а не площини, як у випадку звичних поверхневих хвиль. Отримано дисперсію, розподіл полів та вектор Пойнтинга для цих хвиль. Проведено порівняння властивостей звичайних та вивчених в даній роботі ПЕХ. Известно, что поверхностные электромагнитные волны (ПЭВ), могут распространяться по поверхности, которая разделяет две среды с диэлектрическими постоянными различных знаков . Много работ посвящено изучению плоских ПЭВ. Мы показали, что ПЭВ нового типа могут распространяться по границе свободной плазмы с вакуумом. Эквифазными поверхностями у этих волн есть круговые цилиндры, а не плоскости, как в случае обычных поверхностных волн. Получены дисперсия, распределение полей и вектор Пойнтинга для этих волн. Проведено сравнение свойств обычных и рассмотренных в данной работе ПЭВ. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma dynamics and plasma wall interaction Symmetric surface electromagnetic waves at flat interface plasma –vacuum Симетричні поверхневі електромагнітні хвилі на плоскій межі плазма - вакуум Симметричные поверхностные электромагнитные волны на плоской границе плазма - вакуум Article published earlier |
| spellingShingle | Symmetric surface electromagnetic waves at flat interface plasma –vacuum Galaydych, V.K. Galaydych, K.V. Plasma dynamics and plasma wall interaction |
| title | Symmetric surface electromagnetic waves at flat interface plasma –vacuum |
| title_alt | Симетричні поверхневі електромагнітні хвилі на плоскій межі плазма - вакуум Симметричные поверхностные электромагнитные волны на плоской границе плазма - вакуум |
| title_full | Symmetric surface electromagnetic waves at flat interface plasma –vacuum |
| title_fullStr | Symmetric surface electromagnetic waves at flat interface plasma –vacuum |
| title_full_unstemmed | Symmetric surface electromagnetic waves at flat interface plasma –vacuum |
| title_short | Symmetric surface electromagnetic waves at flat interface plasma –vacuum |
| title_sort | symmetric surface electromagnetic waves at flat interface plasma –vacuum |
| topic | Plasma dynamics and plasma wall interaction |
| topic_facet | Plasma dynamics and plasma wall interaction |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110416 |
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