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Unconventional Surface Electromagnetic Waves at Plasma – Vacuum Boundary

Galaydych, V.K. and Galaydych, K.V.
Department of General and Applied Physics
School of Physics and Technology
V.Karazin Kharkiv National University
4 Svobody sq., Kharkiv 61077, Ukraine
E-mail: galaydych@pht.univer.kharkov.ua
galaydych@postmaster.co.uk
Tel: +38(057)3350509 Fax: +38(057)3353977
Abstract. As 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 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.
Keywords: Electromagnetic waves in plasma, circular surface electromagnetic waves, plasma-vacuum boundary.
PACS: 52.35.Hr.
PROBLEM STATEMMENT
Probably, first paper devoted to surface electromagnetic waves was published almost 100 years old [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
Let us consider a plane interface ( z = 0 ) between two semi restricted domains. Introduce a cylindrical
coordinate system with Z-axis perpendicular to the separating plane. First domain z > 0 is a vacuum with
permittivity 1 ε =1 and second domain is homogeneous free plasma with the frequency-dependent permittivity
( ) ( )2
2 1 /p ε =ε ω = − ω ω , where 2 4 2 p p e ω = π e n m is plasma frequency. In cylindrical coordinate system
(r,ϕ, z) the set of Maxwell’s equations split in two subsystems. One of them consists of { r E , z E ,Hϕ }, another
consists of { r H , z H , Eϕ }.We shall be interested in symmetric waves, i.e. all disturbances are independent of angle
ϕ .
RESULTS AND DISCUSSION
Consider the problem of describing wave propagation with nonzero components: an azimuth magnetic field Hϕ ,
a radial electric field r E and electric field z E , which is perpendicular to the boundary. We will find solution in
such form A(r, z,t ) = A(r )exp(mκ1,2z)exp(−ωt ) , 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 , 1,2 κ are real and positive). System of
equations for such wave disturbances is as follow.

There are experimental studies of circular surface electromagnetic waves [8]. 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 [8].
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 and E.M. Lifschitz, Electrodynamics of Continuous Media, (Butterworth, London, 1984)
2. J. Zenneck, Ann. der Physik, 23, 846-866 (1907).
3. A.D.Boardman, ed., Electromagnetic Surface Modes, (New York : John Wiley & Sons Ltd, 1982).
4. V.M.Agranovich and D.LMills, eds., Surface Polaritons, (Amsterdam, Elsivier, 1982).
5. N.L.Dmitruk et al., 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,” in Electromagnetic Surface Modes, edited by
A.D.Boardman, New York : John Wiley & Sons Ltd, 1982,

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