Diffraction of Modulated Electromagnetic Impulses on Periodical Grating
The problem of diffraction of amplitude-modulated impulses with linear frequency modulation on the planar periodical grating consisting of infinitely thin and ideally conducting strips has been considered. The ability to provide the group impulse delay without distorting of their forms and changing...
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Радіоастрономічний інститут НАН України
2002
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| Цитувати: | Diffraction of Modulated Electromagnetic Impulses on Periodical Grating / T.V. Gavrilova, Yu.B. Sidorenko // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 398-400. — Бібліогр.: 2 назв. — англ. |
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irk-123456789-1223452017-07-03T03:02:59Z Diffraction of Modulated Electromagnetic Impulses on Periodical Grating Gavrilova, T.V. Sidorenko, Yu.B. The problem of diffraction of amplitude-modulated impulses with linear frequency modulation on the planar periodical grating consisting of infinitely thin and ideally conducting strips has been considered. The ability to provide the group impulse delay without distorting of their forms and changing their duration has been shown. Dependencies of group delay on grating parameters and the velocity of frequency change in the field of long waves have been given. Рассмотрена задача дифракции амплитудно-модулированных импульсов с линейной частотной модуляцией на ленточной периодической решетке, состоящей из бесконечно тонких и идеально проводящих лент. Показано, что возможно осуществить групповую задержку сигналов без искажения их формы и изменения длительности. Приведены зависимости групповой задержки от параметров решетки и скорости качания частоты в длинноволновой области. Розглянуто задачу дифракції амплітудно-модульованих імпульсів з лінійною частотною модуляцією на стрічковій періодичній ґратці, що складається з нескінченно тонких та ідеально провідних стрічок. Показано, що існує можливість створити групову затримку сигналів не змінюючи їх форму та тривалість. Наведено залежності групової затримки від параметрів ґратки та швидкості качання частоти у довгохвильовій області. 2002 Article Diffraction of Modulated Electromagnetic Impulses on Periodical Grating / T.V. Gavrilova, Yu.B. Sidorenko // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 398-400. — Бібліогр.: 2 назв. — англ. 1027-9636 http://dspace.nbuv.gov.ua/handle/123456789/122345 en Радиофизика и радиоастрономия Радіоастрономічний інститут НАН України |
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The problem of diffraction of amplitude-modulated impulses with linear frequency modulation on the planar periodical grating consisting of infinitely thin and ideally conducting strips has been considered. The ability to provide the group impulse delay without distorting of their forms and changing their duration has been shown. Dependencies of group delay on grating parameters and the velocity of frequency change in the field of long waves have been given. |
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Article |
| author |
Gavrilova, T.V. Sidorenko, Yu.B. |
| spellingShingle |
Gavrilova, T.V. Sidorenko, Yu.B. Diffraction of Modulated Electromagnetic Impulses on Periodical Grating Радиофизика и радиоастрономия |
| author_facet |
Gavrilova, T.V. Sidorenko, Yu.B. |
| author_sort |
Gavrilova, T.V. |
| title |
Diffraction of Modulated Electromagnetic Impulses on Periodical Grating |
| title_short |
Diffraction of Modulated Electromagnetic Impulses on Periodical Grating |
| title_full |
Diffraction of Modulated Electromagnetic Impulses on Periodical Grating |
| title_fullStr |
Diffraction of Modulated Electromagnetic Impulses on Periodical Grating |
| title_full_unstemmed |
Diffraction of Modulated Electromagnetic Impulses on Periodical Grating |
| title_sort |
diffraction of modulated electromagnetic impulses on periodical grating |
| publisher |
Радіоастрономічний інститут НАН України |
| publishDate |
2002 |
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http://dspace.nbuv.gov.ua/handle/123456789/122345 |
| citation_txt |
Diffraction of Modulated Electromagnetic Impulses on Periodical Grating / T.V. Gavrilova, Yu.B. Sidorenko // Радиофизика и радиоастрономия. — 2002. — Т. 7, № 4. — С. 398-400. — Бібліогр.: 2 назв. — англ. |
| series |
Радиофизика и радиоастрономия |
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AT gavrilovatv diffractionofmodulatedelectromagneticimpulsesonperiodicalgrating AT sidorenkoyub diffractionofmodulatedelectromagneticimpulsesonperiodicalgrating |
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2025-07-08T21:32:59Z |
| last_indexed |
2025-07-08T21:32:59Z |
| _version_ |
1837116041459662848 |
| fulltext |
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4, pp. 398-400
DIFFRACTION OF MODULATED ELECTROMAGNETIC
IMPULSES ON PERIODICAL GRATING
T. Gavrilova, Yu. Sidorenko
Kharkov National Automobile and Highway University
25, Petrovsky St, 61002, Kharkov, Ukraine
E-mail: fizik@khadi.kharkov.ua
The problem of diffraction of amplitude-modulated impulses with linear frequency modulation on the pla-
nar periodical grating consisting of infinitely thin and ideally conducting strips has been considered. The ability
to provide the group impulse delay without distorting of their forms and changing their duration has been shown.
Dependencies of group delay on grating parameters and the velocity of frequency change in the field of long
waves have been given.
Constructing and elaborated making of functional
devices and devices of the radar-tracking systems
based on using of peculiarities of interaction of the
composite electromagnetic impulses with different
hindrances, including periodic shields, remains an
essential problem of mm and sub-mm waves tech-
niques. With their help the optimum filters providing
the compression and the delay of signals dividers,
transcribers of the velocity of the frequency sweeping
can be constructed.
Expansion of initial frequency band, in view of
modulated signal of presence additional parameter
(frequency deviation) leads to the occurrence of idio-
syncrasies of distribution and interaction with the
periodic shields possessing different continuous
properties.
Diffraction of amplitude-modulated (AM) elec-
tromagnetic impulses with the Gaussian enveloping
and linear frequency modulation on the strip periodic
grating, consisting of infinitely thin and perfectly
conductive strips are investigated.
Initial and scattered fields satisfy the homoge-
neous Maxwell equations, the conditions of radiation,
boundary conditions on the surface of periodic struc-
ture as
( ) ( ) ( )0 0,U t t= Φ , (1)
( ) ( ) ( ) ( )0
1
1, dU z t t t
z c dt
∂ = Φ ≡ Φ
∂
,
where
( )
( ) ( )0
2
0
2
0
exp
2
i tt tt e
T
ψ− − Φ = −
,
( ) ( ) ( )20 0 0 0 0
1
2
t t t t tψ ω β= − + − .
Here 0β is a velocity of a frequency sweeping,
0ω is a carrier frequency of the signal, ( ),U z t
stands for the xE or xH -components of the electri-
cal or magnetic field accordingly.
The solution to the wave equation is obtained as
an expansion in Fourier integral on frequencies
( ) ( )
( ) ( ) ( )
, ,
1 , , ,
2
j
j i t
U y z t
F y z e dωω ϕ ω ω
π
∞
−
−∞
=
∫ (2)
where j is the number of the domains to which the
solution concerns; ( )F ω is a spectral function of the
initial field; ( ) ( ), ,j y zϕ ω are the functions, which
provide realization of the above-stated requirements.
Proceeding from periodicity of considered hin-
drance along the axis Oy , we shall present the spec-
tral function ( ) ( ), ,j y zϕ ω for each domain as a Fou-
rier-series expansion. Unknown complex decomposi-
tion values will be determined thus from the solution
of boundary problem for the plane simple harmonic
wave normally incident on the strip grating, with the
fixed frequency ω and amplitude ( )F ω . The scat-
tered field is determined via its integral representa-
tion. Amplitude and phase characteristics of scattered
field will depend on properties of spectral function of
initial field ( )F ω and the kind of transfer functions
for the grating which are evaluated by a strict
mathematical method for solution of boundary prob-
lems of diffraction.
For the case when the parameters of initial im-
pulse satisfy the requirement of quasi monochro-
maticity 0ω ω∆ , in the paper [1] the analytical
expressions for the scattered fields, allowing gener-
alization on solving of diffraction for АМ and LFМ
Diffraction of Modulated Electromagnetic Impulses on Periodical Grating
Radio Physics and Radio Astronomy, 2002, v. 7, No. 4 399
fields on some class of periodic structures, are ob-
tained.
It is determined that in case of the frequency
modulation of an initial signal owing to expansion of
the frequency band occupied in initial impulse, and
the account of the aspect of continuous curves of the
module and phase of transfer functions for grating
among the parameters describing the scattered field,
occur additional ones (a phase and batch delay, shift
of a carrier frequency). Such performances as spades
amplitude, efficient duration, a velocity of the fre-
quency sweeping, additional phase attack have more
composite dependence on parameters of periodic
structure.
Let's analyze the properties of zero harmonics of
scattered field. Analytical expression for scattered
field has in this case the form
( ) ( )
( )
( )
( )
( )
0
0
0 0
0 2
0
, ,
exp ,
2
j
i
j
j i
j
U y z t
zt t tcQ e
T
ψ−
=
− − − ∆ −
(3)
and in the case when the dependence of amplitude
and phase of transmission coefficients of the grating
on frequency is practically linear, expressions for
performances of scattered field look like
( ) ( )
( )0 0
j jQ C ω= ; (4)
( )
00
jT T≈ ; (5)
( ) ( )( )
( )( ) ( )
0 00 0
2
0 0 0 0
1 ;
2
j j
j j
zt t tc
zt t tc
ψ ω
β δ
≈ − ± −∆ +
+ − ± −∆ + (6)
( ) ( )
00 00; ;j jω β β∆ = ≈ (7)
( ) ( )
( ) ( )
2
0 00
2
0 0 0 0 0 2 0
1 arctg
2
1 ;
2
j Tδ β
ω ϕ ω ϕ ω α β
= − +
′ − − (8)
( )
( ) 2
0 0 2 0 00
jt Tϕ ω α β′∆ ≈ + . (9)
From the expressions (3)–(9) it follows, that as
compared to incident impulse the zero harmonics of
scattered field has a series of differences. At first, the
smaller spades amplitude stipulated by factor
( )
( )00
jC ω , representing the module of coefficient
of transfer function of a strip diffraction grating. And
we shall mark, that parameters of zero harmonics will
differ for domains above the grating ( )1j = and
under grating ( )2j = owing to the available con-
nection between coefficients ( )
( )00
jC ω
( )
( )
( )
( )1 2
0 0 0 01 C Cω ω+ = – for E-polarization,
( )
( )
( )
( )1 2
0 0 0 01 C Cω ω− = − – for H-polarization.
Secondly, the zero harmonics have additional
phase attack and the group delay, the phases of trans-
fer function of the grating stipulated by linear de-
pendence on frequency in the frequency band occu-
pied by the initial impulse and presence of the linear
modulation of frequency.
Thirdly, efficient duration, bearing frequency
and the frequency deviation of zero harmonics, prac-
tically coincides with the corresponding magnitudes
of initial impulse.
Thus, selection of parameters of a diffraction
grating and initial impulse makes it is possible to
realize group delay of LFМ of impulses without dis-
tortion of its shape and modification of efficient du-
ration.
Let's consider for example expression for a
group delay of zero spatial harmonic for E-
polarization. For the long wavelength case
( 0
0 2
l
c
ωκ
π
≡ << ; – the grating constant) from
known dependences of transmission coefficients on
dimensionless frequency κ ( cos du π= ; d is a
breadth of a slot of the grating) it is obtained [2]:
( )
( ) ( )
( )
( ) ( )
( )
( )
1/2
1 2 2
0 0 0
1
0 0 0
2
0 0
0
11 ln ,
2
1arg arctg ln ,
2
1arg arctg .12 ln
2
uC
uC
C u
κ κ
κ κ
κ
κ
−+= +
+= −
= +
(10)
Relations (10) allow to determine immediately
( )
( )
1
0
2 2
0
2
0 0 0
1ln
2
12 1 ln
2
11 ln ,
2
u
lt uc
u T
π κ
κ β
+
∆ = ×++
++ (11)
( )
( )
2
0
2 2
0
1
2
0 0 0
1ln
2
12 1 ln
2
11 ln .
2
u
lt uc
u T
π κ
κ β
−
+
∆ = − ×++
+ × −
T. Gavrilova, Yu. Sidorenko
400 Radio Physics and Radio Astronomy, 2002, v. 7, No. 4
Apparently, that the group delay has major
magnitude for past impulse; depends on the phase
and fill factor of grating, and also from the primal
pulse duration, its carrier frequency.
In Fig. 1 the graphic dependences of the relative
group delay 0
0
t
T
∆ on the parameter of grating fill-
ing d for the case АМ ( 0β = , a dotted line) and
LFМ impulse ( 0.2β = , solid curves), calculated
with the formulas (11) are presented. One can see
that with increasing of breadth of the slot in the field
of admissible structure parameters, defined by the
inequality 0
1ln 1
2
uκ + , the group delay in-
creases, reaching at 0.7d = the maximum values
(
0
~ 2 4 %t
T
∆ … ).
The broadening of the frequency band occupied
of the initial signal by the frequency modulation or
the decreasing of initial duration leads to the increas-
ing of group delay. So at the modulation of the initial
signal with the frequency deviation
0
~ 1 %ω
ω
∂
( 0 0.2β = ) at 0 0.05T = ns the group delay in-
creases on 0.5 %, and at 0 0.03T = ns on 1 % as
compared to АМ signal. Graphics in Fig. 2 illustrate
the dependence of the relative group delay on pa-
rameter 0Tβ ω∂= for reflected (solid curves) and
transmitted (dotted line) fields.
References
1. T. Gavrilova. Izv. Vuzov. Radiofisika, 23, №9 (1980)
(in Russian).
2. V.P. Shestopalov. Method. Problems of Riemann of
Hilbert in the theory of a diffraction. Kharkov Press
House in Kharkov University. (1971) (in Russian)
ДИФРАКЦИЯ МОДУЛИРОВАННЫХ
ЭЛЕКТРОМАГНИТНЫХ ИМПУЛЬСОВ
НА ПЕРИОДИЧЕСКОЙ РЕШЕТКЕ
Т.В. Гаврилова, Ю.Б. Сидоренко
Рассмотрена задача дифракции амплитудно-
модулированных импульсов с линейной частотной
модуляцией на ленточной периодической решетке,
состоящей из бесконечно тонких и идеально проводя-
щих лент. Показано, что возможно осуществить груп-
повую задержку сигналов без искажения их формы и
изменения длительности. Приведены зависимости
групповой задержки от параметров решетки и скорости
качания частоты в длинноволновой области.
ДИФРАКЦІЯ МОДУЛЬОВАНИХ
ЕЛЕКТРОМАГНІТНИХ ІМПУЛЬСІВ НА
ПЕРІОДИЧНИХ ГРАТКАХ
Т.В. Гаврилова, Ю.Б. Сидоренко
Розглянуто задачу дифракції амплітудно-модульо-
ваних імпульсів з лінійною частотною модуляцією на
стрічковій періодичній ґратці, що складається з нескін-
ченно тонких та ідеально провідних стрічок. Показано,
що існує можливість створити групову затримку сиг-
налів не змінюючи їх форму та тривалість. Наведено
залежності групової затримки від параметрів ґратки та
швидкості качання частоти у довгохвильовій області.
AM impulse (β=0)
LFM impulse (β=0,2)
Fig. 1.
Fig. 2
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