Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium
Transient electromagnetic (EM) wave scattering from a stratified anisotropic medium with temporal and spatial dispersion is considered. The dispersive anisotropic medium is modeled by constitutive relations that involve four second rank tensor susceptibilities, containing time convolution integrals....
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| Zitieren: | Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium / A.V. Malyuskin, S.N. Shulga // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 401-403. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-1223462017-07-03T03:03:00Z Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium Malyuskin, A.V. Shulga, S.N. Transient electromagnetic (EM) wave scattering from a stratified anisotropic medium with temporal and spatial dispersion is considered. The dispersive anisotropic medium is modeled by constitutive relations that involve four second rank tensor susceptibilities, containing time convolution integrals. Scalarization approach to the solution of transient EM scattering problems in layered anisotropic medium is outlined. As a practical application the physical model of the effective absorber was proposed and numerically investigated. В работе исследуется нестационарное рассеяние электромагнитных волн в анизотропной слоистой среде с пространственной и временной дисперсией. Анизотропная среда описывается материальными уравнениями типа временной свертки с ядрами восприимчивости, представляющими собой тензоры второго ранга. Предложена и численно исследована модель широкополосного поглощающего покрытия. У роботі досліджується нестаціонарне розсіяння електромагнітних хвиль в анізотропному шаруватому середовищі з просторовою і часовою дисперсією. Анізотропне середовище описується матеріальними рівняннями типу часової згортки з ядрами сприйнятливості, що являють собою тензори другого рангу. Запропонована і чисельно досліджена модель широкосмугового поглинаючого покриття. 2002 Article Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium / A.V. Malyuskin, S.N. Shulga // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 401-403. — Бібліогр.: 6 назв. — англ. 1027-9636 http://dspace.nbuv.gov.ua/handle/123456789/122346 en Радиофизика и радиоастрономия Радіоастрономічний інститут НАН України |
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Transient electromagnetic (EM) wave scattering from a stratified anisotropic medium with temporal and spatial dispersion is considered. The dispersive anisotropic medium is modeled by constitutive relations that involve four second rank tensor susceptibilities, containing time convolution integrals. Scalarization approach to the solution of transient EM scattering problems in layered anisotropic medium is outlined. As a practical application the physical model of the effective absorber was proposed and numerically investigated. |
| format |
Article |
| author |
Malyuskin, A.V. Shulga, S.N. |
| spellingShingle |
Malyuskin, A.V. Shulga, S.N. Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium Радиофизика и радиоастрономия |
| author_facet |
Malyuskin, A.V. Shulga, S.N. |
| author_sort |
Malyuskin, A.V. |
| title |
Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium |
| title_short |
Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium |
| title_full |
Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium |
| title_fullStr |
Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium |
| title_full_unstemmed |
Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium |
| title_sort |
transient electromagnetic wave scattering from dispersive anisotropic layered medium |
| publisher |
Радіоастрономічний інститут НАН України |
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2002 |
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http://dspace.nbuv.gov.ua/handle/123456789/122346 |
| citation_txt |
Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium / A.V. Malyuskin, S.N. Shulga // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 401-403. — Бібліогр.: 6 назв. — англ. |
| series |
Радиофизика и радиоастрономия |
| work_keys_str_mv |
AT malyuskinav transientelectromagneticwavescatteringfromdispersiveanisotropiclayeredmedium AT shulgasn transientelectromagneticwavescatteringfromdispersiveanisotropiclayeredmedium |
| first_indexed |
2025-07-08T21:33:05Z |
| last_indexed |
2025-07-08T21:33:05Z |
| _version_ |
1837116046009434112 |
| fulltext |
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4, pp. 401-403
TRANSIENT ELECTROMAGNETIC WAVE
SCATTERING FROM DISPERSIVE ANISOTROPIC
LAYERED MEDIUM
A.V. Malyuskin, S.N. Shulga
Kharkiv National University, Chair of Theorertical Radiophysic
61077, Svobody Sq. 4, Kharkiv,Ukraine
E-mail: Sergey.N.Shulga@univer.kharkov.ua , malyuskin@univer.kharkov.ua
Transient electromagnetic (EM) wave scattering from a stratified anisotropic medium with temporal and
spatial dispersion is considered. The dispersive anisotropic medium is modeled by constitutive relations that in-
volve four second rank tensor susceptibilities, containing time convolution integrals. Scalarization approach to
the solution of transient EM scattering problems in layered anisotropic medium is outlined. As a practical appli-
cation the physical model of the effective absorber was proposed and numerically investigated.
1. Introduction
Performance of virtually all modern wide-band
communication systems, e.g. mobile services and
multimedia wireless networks can be enhanced with
the use of novel composite materials with specially
designed EM properties. Among such materials
photonic crystals [1], chiral and omega media [2] and
left-handed materials [3] have been thoroughly inves-
tigated recently. These media can be manufactured
by embedding conductive or magnetodielectric reso-
nance inclusions in the host medium. As a rule com-
plex microstructure of composite materials leads to
their macroscopic anisotropy. The main reasons for
such anisotropy are the complicated shape of inclu-
sions, ordered spatial arrangement of the particles,
electromagnetic anisotropy of the host medium and
in some cases electromagnetic interaction between
particles.
2. Statement of the Problem and Solution
Scheme
We consider impulse plane wave
( )exp( )in in inE e F t ik R= ⋅ obliquely incident in
the direction of the vector ink on a homogeneous
anisotropic layer that occupies the domain of
space ,x y−∞ < < ∞ , 0 z d< < . EM properties
of the medium are modeled by the constitutive equa-
tions [4]:
( )
( )
ˆ ˆ4 ,
ˆ ˆ4 ,
ee em
me mm
D E E H
B H E H
π χ χ
π χ χ
= + ∗ + ∗
= + ∗ + ∗
(1)
where the asterisk stands for the time convolution
integral
( ) ( ) ( )ˆ ˆ, , ,
t
E R t R t t E R t dtντ ντχ χ
−∞
′ ′ ′∗ = − ⋅∫ ,
involving second rank tensor susceptibilities
ˆντχ ( ), ,e mν τ = . The cross-susceptibilities ˆ ,em meχ
arise due to spatial dispersion of the medium. The
boundary value problem includes the Maxwell equa-
tions along with standard boundary conditions. Be-
sides, the susceptibilities kernels ˆντχ are assumed to
be identically zero for 0t < due to causality.
EM scattering problems in stratified anisotropic
medium can be efficiently solved by reducing the
vector boundary problem to the equivalent scalar one
for the so called potentials [5]. This procedure is
based on the EM field decomposition on the trans-
versal and longitudinal, with respect to the stratifica-
tion axis, components
0 0,z zE E z E H H z H⊥ ⊥= + = + ,
projecting the Maxwell equations on the special spa-
tial basis 0 0, ,z z ⊥ ⊥×∇ ∇ with subsequent elimina-
tion of the longitudinal components. As a result we
have the coupled system of two integral-differential
equations for the scalar functions Ε,Η
[ ]( ) [ ]( )0, , .
t
r z t z E H dt⊥ ⊥ ⊥
−∞
′Ε Η = ⋅ ∇ ×∫ (2)
The basic advantages of such approach are reduction
of the number of unknown quantities, coordinate
A.V. Malyuskin, S.N. Shulga
402 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4
invariance and the possibility of various numerical
methods to be applied. The vector EM field can be
reconstructed straightforwardly from potentialsΕ,Η ,
but some physical quantities, e.g. reflection and
transmission coefficients, are represented directly in
terms of potentials (2).
3. The Physical Model for Composite
Wideband EM Absorber
The concept of perfectly matched layer (PML), re-
flectionless for any angle of monochromatic plane
wave incidence has been discussed lately. In [6] the
model of PML for the wideband signals was pro-
posed using the concept of time-derivative Lorentz
medium (TDLM). In such medium field time deriva-
tives contribute to the polarization provided that the
medium possesses both electric and magnetic proper-
ties. Physically time derivative behaviors allow one
to broaden the frequency region in which a well-
known matching condition ε µ= is satisfied [6].
The main problem with PML however is that it
is principally unrealizable with only passive compo-
nents. Idea proposed in [6] can be realized with the
use of spatially dispersive anisotropic medium with
tensor susceptibilities of the special kind
|| 0 0 0
ˆ ˆˆ ˆ,I z z z Iνν νν νν ντ ντχ χ χ χ χ⊥ ⊥ ⊥= + = × , (3)
where 0 0 0 0Î x x y y⊥ = + . These materials can be
engineered using single- or multi-resonance non-
closed conductive elements with complex shape. As
a particular example of physically realizable alterna-
tive of PML we consider below the material formed
by the cubic lattice of “omega” [2] particles with
ferrite cores.
In Fig. 1 the reflection coefficient for the case of
normal incidence of quasimonochromatic [6], Gaus-
sian
( ) ( )( ) ( )[ ]327 7 /6 2 1 1 2 1F t x x= − − − − ,
and Laguerre
( ) ( ) ( )[ ]
( )
( )
( )[ ]
2 00.7 ,
exp 2
exp , /
!
m
m
m m
F t L x L x
x d
L x x x x t T
m dx
= − −
= − =
E-polarized pulses on anisotropic composite slab
backed with the perfect conductor is shown as a func-
tion of parameter βχ . Parameter βχ measures the
contribution of time derivative terms in the electric
and magnetic transversal susceptibility kernels
( )
( ) 0
2 2, 0
0
cos
1
2 sin
2
t
at
t e
at
a
β
νν β
α
ω χ
χ χω χ
ω
Γ−
⊥
−
= Γ − −
,
where 2 2 2
0 / 4a ω= − Γ , 0ω is the resonance fre-
quency, Γ is the damping coefficient, αχ is the usual
Lorenz susceptibility term [6]. For the numerical
computations we choose these parameters to fit the
results presented in [6], particularly period
100T = fs. In Fig. 1 curves 1 and 2 correspond to
the Gaussian and quasi monochromatic pulse scatter-
ing from PML TDLM [6], curve 3 corresponds to the
case of Laguerre pulse scattering from composite
layer with material parameters(3). Fig. 1 demon-
strates that non-reflecting properties of anisotropic
composite material (3) can be made very efficient, in
principle the same order as the PML TDLM ones.
0 10 20 30 40
-120
-100
-80
-60
-40
-20
0
1- Gaussian pulse scat. (PML TDLM)
2 - Quasimonochromatic pulse scat. (PML TDLM)
3 - Laguerre pulse scat. (bianisotropic slab)
3
2
1R
ef
le
ct
io
n
co
ef
ic
ie
nt
, d
B
χ
β
(105)
Fig. 1. EMP reflection coefficient for anisotropic
composite layer backed with PEC
4. Conclusion
In this report the general scheme for handling tran-
sient EM problems in layered dispersive anisotropic
medium is outlined. The model of wideband absorber
is proposed and numerically investigated.
References
1. T. Krauss, R. De La Rue. Progress in Quantum Elec-
tronics. 23, 51(1999).
2. I.V. Lindell, A.H. Sihvola. IEICE Trans. Electronics.
7, 114 (1996).
3. N. Engheta. Int. Conf. MMET*02. 175 (2002).
4. A. Karlsson, G.Kristensson. J. Electromagn. Waves
Applicat. 6, 537 (1992).
5. A. Malyuskin, V. Shulga, S. Shulga. Radio Physics
&Radio Astronomy. 5(3), 291 (2000).
6. R. Ziolkowski. IEEE Trans. AP-45, 656 (1999).
Transient Electromagnetic Wave Scattering from Dispersive Anisotropic Layered Medium
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 403
НЕСТАЦИОНАРНОЕ РАССЕЯНИЕ
ЭЛЕКТРОМАГНИТНЫХ ВОЛН
В АНИЗОТРОПНОЙ
ДИСПЕРГИРУЮЩЕЙ СЛОИСТОЙ
СРЕДЕ
А.В. Малюскин, С.Н. Шульга
В работе исследуется нестационарное рассеяние
электромагнитных волн в анизотропной слоистой среде
с пространственной и временной дисперсией. Анизо-
тропная среда описывается материальными уравне-
ниями типа временной свертки с ядрами восприимчи-
вости, представляющими собой тензоры второго ранга.
Предложена и численно исследована модель широко-
полосного поглощающего покрытия.
НЕСТАЦІОНАРНЕ РОЗСІЯННЯ
ЕЛЕКТРОМАГНІТНИХ ХВИЛЬ В
АНІЗОТРОПНОМУ ДИСПЕРГУЮЧОМУ
ШАРУВАТОМУ СЕРЕДОВИЩІ
О.В. Малюскін, С.М. Шульга
У роботі досліджується нестаціонарне розсіяння
електромагнітних хвиль в анізотропному шаруватому
середовищі з просторовою і часовою дисперсією. Ані-
зотропне середовище описується матеріальними рів-
няннями типу часової згортки з ядрами сприйнятливо-
сті, що являють собою тензори другого рангу. Запро-
понована і чисельно досліджена модель широкосмуго-
вого поглинаючого покриття.
|