Electron beam excitation of left-handed surface electromagnetic waves at artificial interfaces
Yu. O. Averkov,* A. V. Kats, and V. M. Yakovenko
A. Ya. Usikov Institute for Radiophysics and Electronics, Ukrainian National Academy of Sciences, 12 Acad. Proskura Str.,
61085 Kharkov, Ukraine
Received 8 October 2008; revised manuscript received 14 January 2009; published 6 May 2009
In this Brief Report we present the theoretical analysis of excitation of the surface plasmon polaritons by a
thin electron beam propagating in the vacuum gap separating a plasmalike medium metal from an artificial
dielectric with negative magnetic permeability. We have obtained and discussed the dispersion relation for the
vacuum-gap-localized waves for an arbitrary vacuum-gap width. We have shown that the interface-localized
waves with the negative total energy flux can be excited.
DOI: 10.1103/PhysRevB.79.193402 PACS numbers: 41.60.Bq, 52.35.Fp
Nowadays a good deal of attention is focused on studies
of the electromagnetic properties of artificial media, espe-
cially left-handed media LHM, and combined structures
made of the juxtaposed planar slabs of epsilon-negative
ENG and mu-negative MNG media. These media sustain
the propagation of electromagnetic waves EMWs possess-
ing negative group velocity i.e., their group velocity v
gr
is
antiparallel to the phase velocity v
ph
, v
gr
↑↓ v
ph
.
1,2
Such
waves are also referred to as backward or left-handed waves
LHWs.
3
The bulk LHWs demonstrate a number of unusual
properties which are of great interest for different applica-
tions. As a matter of fact, there can possibly exist left-handed
surface electromagnetic waves LHSWs that also possess
exotic properties as their volume counterparts. In close anal-
ogy to the media supporting bulk LHWs and thus often
called LHM, such interfaces could be called left-handed sur-
face. The LHSWs are existent at different interfaces starting
with a thin metallic layer sandwiched between two dielectric
half spaces see Ref. 4, supporting well-known surface plas-
mon polaritons SPPs, and the most advanced interfaces in-
cluding artificial media such as double negative and double
positive ones see Ref. 5, and ENG/MNG interfaces see,
e.g., Ref. 6 and references therein. The electrodynamic
properties of ENG/MNG interfaces have been theoretically
investigated in Ref. 7. Examination of surface EMWs prop-
erties and excitation of these waves are of considerable in-
terest both from the scientific point of view and due to their
possible role in subsequent miniaturization of the devices for
light manipulation, which is currently a top-priority issue.
Surface wave excitation can be achieved by different
methods, but if one of the neighboring media forming an
interface that supports the surface EMWs is transparent, then
excitation can be realized using optical methods the total
internal reflection in Otto or Kretschmann geometry and dif-
fraction by appropriate periodic structures; see Ref. 8 and
references therein. However, if both the media are opaque,
say, ENG/MNG interface, then surface waves cannot be ex-
cited by the above methods.
In the present Brief Report we deal with this particular
case and analyze the excitation of left-handed quasisurface
waves by means of an electron beam instability. The electron
beam is supposed to propagate within a very narrow vacuum
gap separating the ENG and MNG media. This method is
shown to be an effective one for surface waves excitation
over the GHz frequency range and it is really difficult to
indicate other appropriate methods for the case under study.
Existence of a narrow gap between the media results in the
eigenmodes of the system differing from the media interface
surface EMWs. However, for rather thin vacuum gap these
hybridized eigenmodes possess the negative energy flux and
thus they are left handed backward. It should be empha-
sized that as the gap vanishes, these modes strictly revert to
the surface waves of the ENG/MNG media interface.
We consider the simplest case where the wave vector q
of
the EMWs excited is parallel to the beam velocity v
0
, q
v
0
.
Below it will be shown that in this instance the TM-polarized
waves can only be excited. Note that the excitation of nega-
tive group-velocity TM- and TE-polarized surface waves at a
vacuum/LHM interface by an electron bunch over the GHz
frequency range has been theoretically examined in Ref. 9.
The system under consideration is shown in Fig. 1. This
three-layer system consists of half space 1 with negative di-
electric permittivity
1
0 and positive magnetic permeabil-
ity
1
0 say, plasmalike or metal-like medium, and arti-
ficial dielectric half space 3 with
3
0,
3
0 separated by
vacuum gap 2 of thickness h. The coordinate system is cho-
sen so that the z axis is directed normal to the interfaces and
media 1 and 3 correspond to z -h / 2 and z h / 2, respec-
tively. Let an electron beam moves with velocity v
0
in the
positive Ox direction in z =0 plane. We suppose that the
beam is infinitely thin in Oz direction and infinitely wide in
Oy direction. Such an approximation implies that we sup-
pose the radiation wavelength, , to be much greater than the
beam thickness. Examine the excitation of TM-polarized
EMWs propagating along Ox axis with electric and magnetic
field components E
= E
x
,0, E
z
and H
= 0, H
,0, where
Plasma-like medium
Artificial dielectric
Vacuum
Gap
Electron beam
O
E
x
z =-h/2
x
z
1
3
2
j
E
z
H
E
z = h /2
y
FIG. 1. Color online Geometry of the problem.
PHYSICAL REVIEW B 79, 193402 2009
1098-0121/2009/7919/1934024 ©2009 The American Physical Society 193402-1