Investigation of properties of a spatial lattice formed by resonance dielectric spheres
The artificial dielectric model is used in creation of a material with the negative ε and µ and in describing electromagnetic wave interactions with vital tissues. The paper presents the theoretical study of the frequency properties and electric field distributions in the spatial cubic lattice at s...
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| Zitieren: | Investigation of properties of a spatial lattice formed by resonance dielectric spheres / G.A. Bryzgalov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 39-41. — Бібліогр.: 5 назв. — англ. |
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Bryzgalov, G.A. 2015-03-31T08:59:43Z 2015-03-31T08:59:43Z 2004 Investigation of properties of a spatial lattice formed by resonance dielectric spheres / G.A. Bryzgalov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 39-41. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 78.20.Ci, 41.20.Jb, 42.70.Qs, 73.20.Mf https://nasplib.isofts.kiev.ua/handle/123456789/79324 The artificial dielectric model is used in creation of a material with the negative ε and µ and in describing electromagnetic wave interactions with vital tissues. The paper presents the theoretical study of the frequency properties and electric field distributions in the spatial cubic lattice at sites of which 216 identical dielectric spheres are placed. Basic oscillation frequencies in the lattice have been defined. Splitting of the frequency performance into bands corresponding to the resonance values of the negative or positive value of εeff is observed. The method for determining the negative values of medium penetrations has been proposed. Модель штучного діелектрика використовується при створенні матеріалів з негативними ε і µ, а також при описі взаємодії електромагнітних хвиль з живими тканинами. Експериментально досліджуються частотні властивості і розподіл електричних полів в просторових кубічних гратках, у вузлах якої розміщено 216 однакових діелектричних сфер. Визначені частоти основних видів коливань в гратках. Спостерігається розщеплювання частотної характеристики на смуги, що відповідають резонансним значенням негативної або позитивної величини εэфф. Запропонований метод визначення негативного значення проникностей середовища. Модель искусственного диэлектрика используется при создании материалов с отрицательными ε и µ, а также при описании взаимодействия электромагнитных волн с живыми тканями. Экспериментально исследуются частотные свой- ства и распределение электрических полей в пространственной кубической решетке, и узлах которой размещены 216 одинаковых диэлектрических сфер. Определены частоты основных видов колебаний в решетке. Наблюдается расщепление частотной характеристики на полосы, соответствующие резонансным значениям отрицательной или положительной величины εэфф. Предложен метод определения отрицательного значения проницаемостей среды. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Новые и нестандартные ускорительные технологии Investigation of properties of a spatial lattice formed by resonance dielectric spheres Дослідження властивостей просторових решіток, утворених резонансними діелектричними сферами Исследование свойств пространственной решетки, образованной резонансными диэлектрическими сферами Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Investigation of properties of a spatial lattice formed by resonance dielectric spheres |
| spellingShingle |
Investigation of properties of a spatial lattice formed by resonance dielectric spheres Bryzgalov, G.A. Новые и нестандартные ускорительные технологии |
| title_short |
Investigation of properties of a spatial lattice formed by resonance dielectric spheres |
| title_full |
Investigation of properties of a spatial lattice formed by resonance dielectric spheres |
| title_fullStr |
Investigation of properties of a spatial lattice formed by resonance dielectric spheres |
| title_full_unstemmed |
Investigation of properties of a spatial lattice formed by resonance dielectric spheres |
| title_sort |
investigation of properties of a spatial lattice formed by resonance dielectric spheres |
| author |
Bryzgalov, G.A. |
| author_facet |
Bryzgalov, G.A. |
| topic |
Новые и нестандартные ускорительные технологии |
| topic_facet |
Новые и нестандартные ускорительные технологии |
| publishDate |
2004 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Дослідження властивостей просторових решіток, утворених резонансними діелектричними сферами Исследование свойств пространственной решетки, образованной резонансными диэлектрическими сферами |
| description |
The artificial dielectric model is used in creation of a material with the negative ε and µ and in describing electromagnetic wave interactions with vital tissues. The paper presents the theoretical study of the frequency properties
and electric field distributions in the spatial cubic lattice at sites of which 216 identical dielectric spheres are placed.
Basic oscillation frequencies in the lattice have been defined. Splitting of the frequency performance into bands corresponding to the resonance values of the negative or positive value of εeff is observed. The method for determining
the negative values of medium penetrations has been proposed.
Модель штучного діелектрика використовується при створенні матеріалів з негативними ε і µ, а також при описі
взаємодії електромагнітних хвиль з живими тканинами. Експериментально досліджуються частотні властивості і розподіл електричних полів в просторових кубічних гратках, у вузлах якої розміщено 216 однакових діелектричних
сфер. Визначені частоти основних видів коливань в гратках. Спостерігається розщеплювання частотної характеристики
на смуги, що відповідають резонансним значенням негативної або позитивної величини εэфф. Запропонований метод
визначення негативного значення проникностей середовища.
Модель искусственного диэлектрика используется при создании материалов с отрицательными ε и µ, а также при
описании взаимодействия электромагнитных волн с живыми тканями. Экспериментально исследуются частотные свой-
ства и распределение электрических полей в пространственной кубической решетке, и узлах которой размещены 216
одинаковых диэлектрических сфер. Определены частоты основных видов колебаний в решетке. Наблюдается расщепление частотной характеристики на полосы, соответствующие резонансным значениям отрицательной или положительной
величины εэфф. Предложен метод определения отрицательного значения проницаемостей среды.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/79324 |
| citation_txt |
Investigation of properties of a spatial lattice formed by resonance dielectric spheres / G.A. Bryzgalov // Вопросы атомной науки и техники. — 2004. — № 2. — С. 39-41. — Бібліогр.: 5 назв. — англ. |
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| first_indexed |
2025-11-25T20:43:13Z |
| last_indexed |
2025-11-25T20:43:13Z |
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| fulltext |
INVESTIGATION OF PROPERTIES OF A SPATIAL LATTICE FORMED
BY RESONANCE DIELECTRIC SPHERES
G.A. Bryzgalov
NSC “Kharkov Institute of Physics and Technology”
Akademicheskaya, 1, 61108, Kharkov, Ukraine, e-mail: bryzgalov@kipt.kharkov.ua
The artificial dielectric model is used in creation of a material with the negative ε and µ and in describing elec-
tromagnetic wave interactions with vital tissues. The paper presents the theoretical study of the frequency properties
and electric field distributions in the spatial cubic lattice at sites of which 216 identical dielectric spheres are placed.
Basic oscillation frequencies in the lattice have been defined. Splitting of the frequency performance into bands cor-
responding to the resonance values of the negative or positive value of εeff is observed. The method for determining
the negative values of medium penetrations has been proposed.
PACS: 78.20.Ci, 41.20.Jb, 42.70.Qs, 73.20.Mf
The artificial dielectric model is often used in differ-
ent theoretical considerations [1,2,3], though the sys-
tematic comparison between calculated and experimen-
tally measured values of effective permittivity had been
carried out only for the simplest lattices formed by infi-
nite thin ideally conducting discs [4].
In papers [2,3] it was shown that dispersive proper-
ties of an artificial dielectric formed by the regular lat-
tice of spherical particles can take any large positive and
negative values, .if dispersion is caused by the depen-
dence of a scattering coefficient on the frequency, val-
ues of εp and µp characterizing electromagnetic wave
scattering on spherical particles. It means that in the ar-
tificial dielectric lattice in cases when particles them-
selves have a high permittivity, the resonance frequen-
cies are possible, for that permittivity convert into infin-
ity. These frequencies are found from the following
transcendental equations
Cii
р
р δ=
ε−ωε
ε+ωε
1
12
)(
)(
, (1)
where C is the particle concentration, 1ε is the permit-
tivity of a particle material, iiδ are the components of
the tensor of penetrations of the spatial lattice formed by
spherical particles.
In this paper the dispersive performances of spatial
lattices formed by dielectric spheres, and the electrical
field distribution are experimentally studied. Firstly, the
simple method has been proposed to define the negative
value of effective permittivity.
The experimental research of electrodynamical pa-
rameters of cubic lattices at the sites of which there
were spherical dielectric scatters, was carried out. From
216 dielectric spheres in foam rubber holders the cubic
spatial structure of 6×6×6 elements is formed. The dis-
tance between spheres was chosen equal to 10 mm. The
dielectric sphere material is ceramics based on titanium
dioxide with the permittivity ε≈80, tgδ≈1⋅10-3. Spheres
of about 10 mm in diameter were prepared with deflec-
tion from the sphericity ≈1...2 µm. In the process of
sphere choice according to the frequency their tuning
was carried out by decreasing in diameter so that the
nominal frequency was equal to 3075 MHz with the ac-
curacy of choosing ±2.5 MHz. The resonance frequency
was defined according to the maximal value of the re-
flection coefficient of the H10 wave from the sphere
placed in the center of the cross section of 32×72 mm
waveguide. The resonance frequency corresponded to
the first magnetic resonance and structure of TE101 elec-
tromagnetic oscillations in the dielectric sphere. The
measuring section was placed between the waveguide
reflectometer and matched waveguide load. The power
supply was delivered from the high frequency generator
by the pin vibrator the axis of which was in the E vector
plane of excited in the structure oscillations correspond-
ing to TE101, TM101 and TM201 modes of oscillations in
the separate sphere. The probe in the shape of the pin vi-
brator placed on the opposite lattice side recorded a sig-
nal.
The electrical field intensity distribution in the space
between dielectric spheres by scatters was measured us-
ing the small perturbation method [5]. The method is
based on the measurement of resonance wavelength in
the structure during introducing a perturbating body of a
small volume ∆τ in the region under study. This shift of
a resonance wavelength is defined by the Slater pertur-
bation theorem that can be expressed by the equation
cp
HE
V
W
WWk
dVEH
drHdrE
k ∆−∆−=
ε+µ
µ−ε
−=
λ
λ∆
∫
∫ ∫
τ∆ τ∆
)( 22
22
2
, (2)
where EW∆ and HW∆ are the variations of a stored
energy in the electrical and magnetic fields of the cavity
during introducing the perturbating body, cpW is the av-
erage energy stored in the cavity at a high frequency os-
cillation period, k is the proportionality factor defined
by the geometry and electromagnetic properties of the
perturbating body material ( 1→k for 0→τ∆ ).
For the resonance structure with the positive value
of the effective permittivity the measured frequency
shift will be directed to the side of resonance frequency
decreasing. Fig.1,a shows the resonance curve shifted to
the left side Fр→Fр1 at introducing the perturbating body
in the Е-field region, and the signal amplitude at the
operating point 1 will increase (the arrow direction 1→1
′). On the high frequency slope at the operating point 2
the signal amplitude will decrease (2→2′). If the effec-
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.39-41. 39
mailto:bryzgalov@kipt.kharkov.ua
tive permittivity will vary its sign then the sign cpW of
the stored energy in the electrical field of the
resonance structure will vary. It will result in the reso-
nance curve shift to the right side Fр→Fр2, as it is shown
in Fig. 1b. The signal amplitude decrease will be ob-
served at the operating point 1 (1→1′), and the increase
will be at the operating point 2 (2→2′). Thus, we shall
define resonance frequency bands with positive and
negative values of the effective permittivity.
In our case for the reliable recording of the frequen-
cy shift we have used the perturbating body in a shape
of the thin copper cylinder 10 mm long and 3 mm in di-
ameter. The signal from the output probe was detected
and amplified by the correlated amplifier B8-6 and syn-
chronously with the movement of the perturbating body
recorded by the recorder.
The lattice passbands for the first magnetic reso-
nance corresponding to the ТЕ101 mode were defined in
the single spherical dielectric cavity. It is the band of
2960...3130 MHz. The amplitude – frequency perfor-
mance in this passband of a lattice is presented in Fig.2.
The second passband corresponding to the first electri-
cal resonance and ТМ101 mode in the single dielectric
sphere equals to 4328...4390 MHz. The third passband
corresponding to the ТЕ201 mode equals to
6040...6280 MHz.
In general case the dispersion equation for ТЕ
modes of the single sphere has two groups of roots [3].
The first group of roots determines dielectric sphere
electromagnetic oscillations concentrated in the internal
sphere region. They have been named as internal or “in-
put” modes of oscillations. The second group of roots
determines proper dielectric sphere oscillations concen-
trated basically outside the sphere volume in the space
around it, therefore such oscillations have been named
“output” modes of oscillations of the dielectric cavity.
“Input” and “output” modes are intercollected and have
the similar structure of the electromagnetic field. They
do not exist separately. We observed it during measure-
ments of the amplitude – frequency performance of a
lattice. Each resonance splits into two ones correspond-
ing to “input” and “output” modes. These resonances
are without fail overlapped in the frequency providing
0 20 40 60 80 100 120 140
0.0
0.2
0.4
0.6
0.8
1.0
a)
3123,57 IHz
A
m
p
lit
u
d
e
Z, ii
0 20 40 60 80 100 120 140
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
b)
3123,0 IHzA
m
p
li
tu
d
e
Z, ii
0 20 40 60 80 100 120 140
0.0
0.2
0.4
0.6
0.8
1.0
c)
3121,9 МHz
A
m
p
li
m
u
d
e
Z, мм
0 20 40 60 80 100 120 140
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
d)
3121,3 МHz
A
m
p
li
tu
d
e
Z, мм
Fig.1. Resonance frequency shift Fp of a structure during introducing a perturbating body in the E-field region: a –
the effective permittivity of a structure is positive, b – the effective permittivity of a structure is negative
3000 3020 3040 3060 3080 3100 3120
0.0
0.2
0.4
0.6
0.8
1.0
IIIIII
A
m
pl
it
ud
e
Frequency, MHz
Fig.2. Amplitude – frequency performance of an artificial dielectric with the cubic structure of a lattice at sites of
these dielectric spheres of 10 mm in diameter and distance between them 10 mm are placed. Power supply is in
the E – field plane of the TE101 mode
Fig.3. Electrical field distribution in a cubic lattice be-
tween spheres along the Z coordinate at frequencies of
apexes of the double resonance curve: a,c – on high
frequency slope; b,d - on the low frequency slope. The
coordinate of the first sphere center is 18 mm
40
40
intermode coupling. Fig.3 shows the structure of an
electric field distribution in the lattice along the Z direc-
tion, when the cylinder axis of a perturbating body coin-
cides with the plane of the Е – field of a single sphere.
Fields have been measured on slopes of apexes of the
double resonance with frequencies Fp1=3121.5 MHz and
Fp2=3123,3 MHz. Frequency values of an operating
point on slopes of the resonance curve without perturbat-
ing body are given in the figure. We observe the frequen-
cy increase during introducing the perturbating body both
on left – hand and right – hand apexes of resonances. The
signal decreases on low frequency slopes and increases
on high frequency ones. This is the evidence of the nega-
tive value of the effective permittivity of a spatial lattice
in this resonance band. Fields of all lattice resonances
shown in Fig.2 have been researched. Resonances in the
region Ι have positive values of εeff. Resonances in the re-
gion ΙΙΙ have negative values of εeff. Resonances in the re-
gion ΙΙ have both positive and negative values of εeff at
various distances of the perturbating body motion, i.e. in
separate layers of the spatial lattice.
The thin copper disc has measured the direction and
value of magnetic fields in a lattice for one from reso-
nance bands of 3120...3123 MHz. Obtained values of
fields correspond to negative values of permittivity.
Since the permittivity of this band is also negative then
these preliminary results allow to say about the simulta-
neous existence of negative values of ε and µ.
The electrical field distribution along the Z coordi-
nate has shown that together with modulation by
spheres there is the spatial modulation by structure
boundaries. Thus, for the resonance frequency of
3129 MHz there is one sinusoidal variation modulated
by six layers of a sphere. The double resonance
3121.5 MHz and 3123.3 MHz has two spatial variations
modulated by six layers of spheres, and so on. The max-
imum number of observed variants of a field equals to
six. There is such a number of double resonances in Ι
and ΙΙΙ frequency bands. There are three double reso-
nances in the frequency band ΙΙ.
The investigation of the electrical field distribution
between lattice spheres along Х and Y coordinates has
shown that each resonance is due to basic resonances on
one from three mutually perpendicular planes and reso-
nances in two other ones. It is the evidence of
anisotropy of properties of the cubic lattice at sites of
that spherical dielectric scatters are placed.
Studies of the lattice fields for ТМ101 and ТЕ201
modes in the single sphere have also shown the pres-
ence of passbands with negative and positive values of ε
eff. In case if the number of spheres in a lattice increases
then the frequency spectrum is condensed and separate
resonances form one band.
Thus, studies of electromagnetic properties of a cu-
bic lattice at sites of which the resonance spherical di-
electric scatters are placed, where the ТЕ101 mode is ex-
cited, have shown that the lattice has passbands corre-
sponding to positive and negative values of permittivity.
Resonance bands have been defined, in which the alter-
nation of positive and negative values of permittivity is
observed in lattice layers. Preliminary measured results
demonstrating the simultaneous presence of negative
values of ε and µ have been obtained. These effects may
be used for the creation of novel artificial dielectrics
with negative ε and µ and for researching electromag-
netic wave interactions with tissues in vivo, sells of
which form the regular spatial lattice, and their nuclei
are the resonance scatters. The simple and effective
method has been proposed to define the negative value
of medium penetrations.
REFERENCES
1. Ya.B. Fainberg, N.A. Khizhnyak. Artificial
anisotropic medium // Zhournal Teoreticheskoj
Fiziki. 1955, v.25, №5, p.711-720.
2. N.A Khizhnyak. Artificial anisotropic dielectrics //
Zhournal Teoreticheskoj Fiziki. 1957, v.27, №9,
p.2006-2038.
3. N.A. Khizhnyak. Integral equations of macroscop-
ic electrodynamics. Kiev: Naukova Dumka, 1986,
p.280.
4. V.B. Kazansky, L.N. Litvinenko, R.V. Shapiro,
V.P. Shestopalov. Theoretical and experimental
study of properties of artificial metal dielectrics //
Izvestiya Vuzov. Radiofizika. 1979, v.22, №8,
p.1002-1011.
5. J. Slater. Electronics of M.W. Frequencies // Sov.
Radio. 1948, p.250. (In Russian).
ИССЛЕДОВАНИЕ СВОЙСТВ ПРОСТРАНСТВЕННОЙ РЕШЕТКИ,
ОБРАЗОВАННОЙ РЕЗОНАНСНЫМИ ДИЭЛЕКТРИЧЕСКИМИ СФЕРАМИ
Г.А. Брызгалов
Модель искусственного диэлектрика используется при создании материалов с отрицательными ε и µ, а также при
описании взаимодействия электромагнитных волн с живыми тканями. Экспериментально исследуются частотные свой-
ства и распределение электрических полей в пространственной кубической решетке, и узлах которой размещены 216
одинаковых диэлектрических сфер. Определены частоты основных видов колебаний в решетке. Наблюдается расщепле-
ние частотной характеристики на полосы, соответствующие резонансным значениям отрицательной или положительной
величины εэфф. Предложен метод определения отрицательного значения проницаемостей среды.
ДОСЛІДЖЕННЯ ВЛАСТИВОСТЕЙ ПРОСТОРОВИХ РЕШІТОК,
УТВОРЕНИХ РЕЗОНАНСНИМИ ДІЕЛЕКТРИЧНИМИ СФЕРАМИ
Г.О. Бризгалов
Модель штучного діелектрика використовується при створенні матеріалів з негативними ε і µ, а також при описі
взаємодії електромагнітних хвиль з живими тканинами. Експериментально досліджуються частотні властивості і
___________________________________________________________
PROBLEMS OF ATOMIC SIENCE AND TECHNOLOGY. 2004. № 2.
Series: Nuclear Physics Investigations (43), p.39-41. 41
розподіл електричних полів в просторових кубічних гратках, у вузлах якої розміщено 216 однакових діелектричних
сфер. Визначені частоти основних видів коливань в гратках. Спостерігається розщеплювання частотної характеристики
на смуги, що відповідають резонансним значенням негативної або позитивної величини εэфф. Запропонований метод
визначення негативного значення проникностей середовища.
42
42
G.A. Bryzgalov
REFERENCES
Г.А. Брызгалов
Г.О. Бризгалов
|