Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface
The possibilities of the slow surface electromagnetic waves propagation along the flat boundary of a metasurface with a dissipative dielectric are studied. The metasurface is a thin flat slab of metamaterial with simultaneously negative permittivity and permeability with “amplification”. All media w...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1946382023-11-28T12:34:07Z Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface Galaydych, V.K. Sporov, A.E. Olefir, V.P. Azarenkov, N.A. Basic plasma physics The possibilities of the slow surface electromagnetic waves propagation along the flat boundary of a metasurface with a dissipative dielectric are studied. The metasurface is a thin flat slab of metamaterial with simultaneously negative permittivity and permeability with “amplification”. All media were assumed to be isotropic. Dispersion dependences are obtained for the eigenmodes of such a waveguide structure. The possibility of full compensation of the energy losses of surface waves by the appropriate choice of the “gains” values is demonstrated. Вивчено властивості повільних поверхневих електромагнітних хвиль, що поширюються уздовж плоскої межі метаповерхні з дисипативним діелектриком. Метаповерхня є вузький плоский шар метаматеріалу з негативними як діелектричною, так і магнітною проникливостями з «підсиленням». Усі середовища вважались ізотропними. Отримано дисперсійні залежності власних мод такої хвилеводної структури. Продемонстровано можливість повної компенсації втрат енергії поверхневих хвиль відповідним вибором значень «підсилень». Изучены свойства медленных поверхностных электромагнитных волн, распространяющихся вдоль плоской границы метаповерхности с диссипативным диэлектриком. Метаповерхность представляет собой узкий плоский слой метаматериала с одновременно отрицательными диэлектрической и магнитной проницательностями с «усилением». Все среды считались изотропными. Получены дисперсионные зависимости для собственных мод такой волноводной структуры. Продемонстрирована возможность полной компенсации потерь энергии поверхностных волн соответствующим выбором значений «усилений». 2020 Article Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface / V.K. Galaydych, A.E. Sporov, V.P. Olefir, N.A. Azarenkov // Problems of atomic science and tecnology. — 2020. — № 6. — С. 30-35. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.35g, 52.50.Dg http://dspace.nbuv.gov.ua/handle/123456789/194638 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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Basic plasma physics Basic plasma physics |
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Basic plasma physics Basic plasma physics Galaydych, V.K. Sporov, A.E. Olefir, V.P. Azarenkov, N.A. Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface Вопросы атомной науки и техники |
| description |
The possibilities of the slow surface electromagnetic waves propagation along the flat boundary of a metasurface with a dissipative dielectric are studied. The metasurface is a thin flat slab of metamaterial with simultaneously negative permittivity and permeability with “amplification”. All media were assumed to be isotropic. Dispersion dependences are obtained for the eigenmodes of such a waveguide structure. The possibility of full compensation of the energy losses of surface waves by the appropriate choice of the “gains” values is demonstrated. |
| format |
Article |
| author |
Galaydych, V.K. Sporov, A.E. Olefir, V.P. Azarenkov, N.A. |
| author_facet |
Galaydych, V.K. Sporov, A.E. Olefir, V.P. Azarenkov, N.A. |
| author_sort |
Galaydych, V.K. |
| title |
Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface |
| title_short |
Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface |
| title_full |
Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface |
| title_fullStr |
Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface |
| title_full_unstemmed |
Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface |
| title_sort |
low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2020 |
| topic_facet |
Basic plasma physics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/194638 |
| citation_txt |
Low surface electromagnetic waves at the metasurface ⁄ dissipative dielectric interface / V.K. Galaydych, A.E. Sporov, V.P. Olefir, N.A. Azarenkov // Problems of atomic science and tecnology. — 2020. — № 6. — С. 30-35. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-16T22:02:06Z |
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2025-07-16T22:02:06Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2020. №6(130)
30 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2020, № 6. Series: Plasma Physics (26), p. 30-35.
https://doi.org/10.46813/2020-130-030
SLOW SURFACE ELECTROMAGNETIC WAVES AT THE
METASURFACE / DISSIPATIVE DIELECTRIC INTERFACE
V.K. Galaydych, A.E. Sporov, V.P. Olefir, N.A. Azarenkov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: galaydych@karazin.ua
The possibilities of the slow surface electromagnetic waves propagation along the flat boundary of a metasurface
with a dissipative dielectric are studied. The metasurface is a thin flat slab of metamaterial with simultaneously neg-
ative permittivity and permeability with "amplification". All media were assumed to be isotropic. Dispersion de-
pendences are obtained for the eigenmodes of such a waveguide structure. The possibility of full compensation of
the energy losses of surface waves by the appropriate choice of the “gains” values is demonstrated.
PACS: 52.35g, 52.50.Dg
INTRODUCTION
The noteworthy progress was made in the manufac-
turing of metasurface [1, 2] based on the metamaterials
[3] during the last years. The metamaterials are com-
posite materials consisting of cells that play the role of
atoms for electromagnetic disturbances, the wave-
length of which is much larger than the cell’s size.
For these artificial “substances” it is possible to get
such combination of electromagnetic characteristics
which so far unknown for natural substances.
In particular, it can manage to achieve simultane-
ously negative value of permittivity and permeability.
Such double negative metamaterials (DNM) are often
referred as left-handed materials or negative refractive
media.
In our previous paper [4] it was demonstrated the
full loss compensation for the surface electromagnetic
wave that propagates in plane waveguide structure
along the interface between the thin layer of the high-
permittivity dielectric with strong losses and the iso-
tropic DNM material with gain.
The aim of this work is to determine the possibility
of propagation of the plane slow surface electromag-
netic waves in the plane structure consisting of the
metasurface and the dissipative dielectric. The task
geometry has shown in Fig. 1.
Fig. 1. The geometry of problem
A dissipative dielectric (DD) possesses the moderate
value of power losses. The metasurface we call the one
side of a thin flat slab of the metamaterial with "gain"
and simultaneously negative both dielectric permittivi-
ty and magnetic permeability. At another side, this
metamaterial layer is adjacent to dissipative dielectric
material. Similarly to our previous paper [4] it was
assumed the existence of the gains in the metamaterial
to compensate the wave energy losses and is not dis-
cussed mechanisms of such gains [3].
1. TASK SETTINGS
We investigate the electromagnetic waves propagat-
ing along a plane waveguide structure in the Z - axis
direction. Let the X - axis been perpendicular to the
interface. The semi-infinite region 0x is occupied by
dissipative dielectric without dispersion, but with losses
described with help the imaginary part of the permittivi-
ty
1 4 0.05 i ,
1 1 .
The gap 0 x d is filled by metamaterial that
characterized by the commonly used the effective per-
mittivity and permeability [5]:
2
( ) 1
( )
p
Gi
, (1)
2
2
0
( ) 1
( )G
F
i
, (2)
Throughout it was considered the metamaterial with
/ 2 10p GHz,
0 / 2 4 GHz, and 0.56F [5]
with thickness 0.716d cm, so
0 0.6 d c .
Such choice of the metamaterial parameters leads to
the appearance of the frequency interval
01 1.5 where 0 and 0
simultaneously (DNM). The values of ,G G are en-
tered for modelling the “electric and magnetic gains” of
electromagnetic waves in the metamaterial.
The semi-infinite region x d is occupied by the
air or vacuum without both dispersion and losses with
constant permittivity 2 1 and permeability 2 1 .
We will consider the slow surface electromagnetic
wave that can propagate in this structure. We will find
the solutions for the plane wave disturbances that de-
creasing exponentially far away from the boundaries.
The spatial-temporal dependence of the wave compo-
nents has such a form:
3, ( ), ( )exp[ ( )]E H E x H x i k z t . (3)
https://doi.org/10.46813/2020-130-026
ISSN 1562-6016. ВАНТ. 2020. №6(130) 31
Here the amplitudes of the wave fields decrease expo-
nentially from the boundaries, axis Z lies at the sepa-
ration plane, and x is the coordinate perpendicular to
the wave propagation direction and
3 3 3Re( ) Im( ) k k i k .
Just like [5] it is possible to split the Maxwell
equations on two independent sub-systems. One of
them describes the waves of H-type that contain
( , , )x y zH E H – components, and another – waves of E-
type that contain ( , , )x y zE H E – components.
The dispersion equation for E-type mode of struc-
ture considered has the form:
1 2 2 1
2 2
1 2 1 2
( )cosh[ ]
( )sinh[ ] 0
h h d
h h d
,
(4)
where
2 2
1,2 3 1,2 1,2h k k , 2 2
3k k -
are the transverse wave vectors, /k c , were c is the
light speed.
The wave of H-type possesses the dispersion relation
of the similar form:
1 2 2 1
2 2
1 2 1 2
( )cosh[ ]
( )sinh[ ] 0
h h d
h h d
.
(5)
2. MAIN RESULTS
Two dispersion equations (4), (5) were solved nu-
merically. From the beginning these equations was
solved for ideal structure: both losses and gains were
assumed to be zero (Fig. 2). The inclined line Q and
curve S correspond to the conditions
1 0h and 0 ,
respectively. They separate the region, where the am-
plitudes of the wave fields decrease exponentially
from the boundaries. So the slow surface electromag-
netic waves can exist in that region of Figs. 2, 3. Three
solutions have been obtained of the dispersion equa-
tions (4), (5): one solution for E – wave and two solu-
tions for H – waves.
Curves H1-wave, H2-wave correspond to the
waves of H-type and the curve E-wave corresponds to
wave of E-type.
Let’s introduce such dimensionless quantities: the
frequency
0/ , the wavenumber
3 0Re( ) /k c , the decrement
3 0Im( ) /k c , the
“electric”
0/G and “magnetic” gains
0/G .
The considered E-wave and H2-wave are forward
(both phase and group velocities are positive) and H1-
wave is backward (phase velocity is positive and group
velocity is negative).
It can be argued that the losses do not put an
appreciable changes the dispersion dependences of the
considered waves (see Figs. 2, 3)
Fig. 2. The dependence of the normalized frequency
on the wavenumber for the metamaterial layer with
zero gains 0 G G and for non-dissipative dielec-
tric with
1 4
Fig. 3. The dependence of the frequency and decre-
ment on the wavenumber for the metamaterial
gains values 0 , and for dissipative dielectric:
1 4 0.001 i
Fig. 4. The normalized phase velocity
3/phV ck versus normalized frequency
32 ISSN 1562-6016. ВАНТ. 2020. №6(130)
Fig. 5. The normalized group velocity
1
3/grV c d dk versus normalized frequency
Fig. 6. The dependence of the normalized decrement
and the frequency of the E wave versus normalized
wavenumber for different values of “magnetic” gain
(1 0.0;2 0.005;3 0.01;4 – 0.015; 5 – 0.02 for
1 4 0.05 i and 0
According to Fig. 4 the phase velocities of modes
considered in 2...3 times less then the light speed. The
group velocity of the forward modes decrease with
increasing frequency, but increases for the backward
mode H1 (Fig. 5).
The Figs. 6-11 illustrate the separate influences of
the DNM “electric and magnetic gains” on the depend-
encies of the decrements and the mode frequencies ver-
sus wavenumber in the presence of dielectric’s dissipa-
tion.
It's remarkable that the influence of “electric and
magnetic gains” on the modes dispersive curves is ra-
ther weak. At the same time, the influence of "electric
and magnetic amplification" on the values of the damp-
ing decrements of the modes under consideration is sig-
nificant.
Fig. 7. The dependence of the decrement and the
frequency of the H2-wave versus wavenumber
for different values of “magnetic” gain
(1 0.0; 2 0.01; 3 0.02; 4 0.03; 5 0.05)
for
1 4 0.05 i and 0
Fig. 8. The dependence of the normalized decrement
and the frequency of the H1-wave versus normalized
wavenumber under different values of “magnetic”
gain (1 0.0;2 0.005;3 0.01; 4 0.02; 5 0.03;
6 0.04) for
1 4 0.05 i and 0
The type of influence of "electric and magnetic
gains" on the damping decrements is enough different.
That’s why we represent all of them.
ISSN 1562-6016. ВАНТ. 2020. №6(130) 33
Fig. 9. The dependence of the decrement and the
mode frequency of the E-wave versus wavenumber
for different values of “electric” gain
(1 0.0;2 0.005;3 0.01;4 0.015;5 0.02) for
1 4 0.05 i and 0
Fig. 10. The dependence of the normalized decrement
and the mode frequency of the H2-wave versus
wavenumber for different values of “electric” gain
(1 0.0;2 0.01;3 0.02;4 0.03;5 0.04;
6 0.05) for 1 4 0.05 i and 0
The Figs. 12-17 present the full compensation
( 0 ) for set of the system parameters for three
modes.
We figure out that condition of full dissipative
compensation 0 is reachable for each of the three
modes. We see that both the “magnetic” and “electric
gains” can to compensate the losses for the all consid-
ered modes.
We have established a rather unexpected fact. It
turned out that it is possible to compensate the dielectric
losses for each mode with the help of only one non-zero
"gain" at a zero value of the other "gain".
Thus, such full compensations (for a given 4.0 )
are possible:
for the E-wave:
a) 0 , 0.007 ; b) 0 , 0.01 ;
for H2-wave:
a) 0 , 0.0003 ; b) 0 , and 0.015 ;
for H1-wave:
a) 0 , 0.00015 ; b) 0 , and 0.005 .
It was shown, that the gain values needed for the full
compensation of the electromagnetic surface waves en-
ergy losses in the dissipative dielectric are quite reason-
able.
Fig. 11. The dependence of the normalized decrement
and the mode frequency of the H1-wave versus
wavenumber for different values of “electric” gain
(1 0.0;2 0.01; 3 0.02; 4 0.03; 5 0.04;
6 0.05) for
1 4 0.05 i and 0
Fig. 12. The dependences of the of the decrement
and the mode frequency of E-wave on the value of
gain if 0 for 4.0
34 ISSN 1562-6016. ВАНТ. 2020. №6(130)
Fig. 13. The dependences of the decrement and the
mode frequency of E-wave on the value of gain if
0 for 4.0
Fig. 14. The dependences of the decrement and the
mode frequency of H2-wave on the value of gain
if 0 for 4.0
Fig. 15. The dependences of the of the decrement
and the mode frequency of H2-wave on the value of
gain if 0 for 4.0
Fig. 16. The dependences of the of the decrement and
the mode frequency of H1-wave on the value of gain
if 0 for 4.0
Fig. 17. The dependences of the decrement and
the mode frequency of H1-wave on the value of gain
if 0 for 4.0
CONCLUSIONS
It was obtained that slow surface electromagnetic
waves can be sustained by boundary between
metasurface and dissipative dielectrics. The loss of
wave energy is compensated by the use of the met-
amaterials with "gains".
The results obtained in this work can be useful for
the various practical applications of metamaterials in
technology, life science, and medicine.
This work was supported by the Ministry of Edu-
cation and Science of Ukraine, under the grants
0118U002023.
ISSN 1562-6016. ВАНТ. 2020. №6(130 35
REFERENCES
1. O. Quevedo-Teruel et al. Roadmap on metasurfaces //
J. Opt. 2019, v. 21, p. 073002.
2. S.S. Bukhari J.C. Vardaxoglou, W. Whittow. A
metasurfaces review: Definitions and applications //
Appl. Sci. 2019, v. 9(13), p. 2727.
3. Nonlinear, tunable and active metamaterials / Ed. by
Ilya V. Shadrivov, Mikhail Lapine, Yuri S. Kivshar.
Springer, 2015.
4. V.K. Galaydych, N.A. Azarenkov, V.P. Olefir,
A.E. Sporov. Modelling of the electromagnetic surface
waves propagation on the interface between the left-
handed metamaterial and the dissipative dielectric //
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«Plasma Physics» (25). 2018, № 6, p. 109-112.
5. I.V. Shadrivov, A.A. Sukhorukov, Yu.S. Kivshar.
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// Phys. Rev. 2003, E 67, p. 057602-4.
Article received 22.09.2020
МЕДЛЕННЫЕ ПОВЕРХНОСТНЫЕ ЭЛЕКТРОМАГНИТНЫЕ ВОЛНЫ НА ГРАНИЦЕ РАЗДЕЛА
МЕТАПОВЕРХНОСТЬ / ДИССИПАТИВНЫЙ ДИЭЛЕКТРИК
В.К. Галайдыч, А.Е. Споров, В.П. Олефир, Н.А. Азаренков
Изучены свойства медленных поверхностных электромагнитных волн, распространяющихся вдоль плос-
кой границы метаповерхности с диссипативным диэлектриком. Метаповерхность представляет собой узкий
плоский слой метаматериала с одновременно отрицательными диэлектрической и магнитной проницатель-
ностями с «усилением». Все среды считались изотропными. Получены дисперсионные зависимости для соб-
ственных мод такой волноводной структуры. Продемонстрирована возможность полной компенсации по-
терь энергии поверхностных волн соответствующим выбором значений «усилений».
ПОВІЛЬНІ ПОВЕРХНЕВІ ЕЛЕКТРОМАГНІТНІ ХВИЛІ НА МЕЖІ ПОДІЛУ МЕТАПОВЕРХНЯ /
ДИСИПАТИВНИЙ ДІЕЛЕКТРИК
В.К. Галайдич, О.Є. Споров, В.П. Олефір, М.О. Азарєнков
Вивчено властивості повільних поверхневих електромагнітних хвиль, що поширюються уздовж плоскої
межі метаповерхні з дисипативним діелектриком. Метаповерхня є вузький плоский шар метаматеріалу з
негативними як діелектричною, так і магнітною проникливостями з «підсиленням». Усі середовища вважа-
лись ізотропними. Отримано дисперсійні залежності власних мод такої хвилеводної структури. Продемонс-
тровано можливість повної компенсації втрат енергії поверхневих хвиль відповідним вибором значень «під-
силень».
http://www.rsphysse.anu.edu.au/nonlinear/papers/IlyaShadrivov.shtml#PRE_2003_67_57602
http://www.rsphysse.anu.edu.au/nonlinear/papers/AndreySukhorukov.shtml#PRE_2003_67_57602
http://www.rsphysse.anu.edu.au/nonlinear/papers/YuriKivshar.shtml#PRE_2003_67_57602
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