COL 11(8), 080102(2013) CHINESE OPTICS LETTERS August 10, 2013
Analytical model of amplitude-weighted array technology in
forming symmetrical radiation patterns
Lanxiang Zhong (
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1,2
, Zhiyong Zhang (
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1
, and Jianlang Li (
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2∗
1
Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710068, China
2
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
∗
Corresponding author: apuli@siom.ac.cn
Received March 26, 2013; accepted May 31, 2013; posted online August 2, 2013
A method on amplitude-weighted array technology is proposed based on an analytical formula in which
the radiation amplitudes of array elements are evaluated analytically by a random symmetrical far-field
radiation pattern. Using this formula, any desired spatial radiation pattern in the far field could be built
by applying the analytical solutions of radiation amplitudes of array elements. To check the validity of this
formula as well as the proposed technique, an annular intensity distribution as target far-field pattern is
designed, and the respective radiation amplitude of array elements are determined by solving the formula
analytically. The available far-field pattern is calculated by applying these solutions and then compared
with the target far-field pattern. The theoretical results show the capabilities of the analytical derivation
as well as the proposed technique in forming specific radiation patterns.
OCIS codes: 010.3640, 030.1670, 070.6110.
doi: 10.3788/COL201311.080102.
Phased array technology, originally developed in the
1 950s
[1]
, has re c e ntly been used in a broad range of appli-
cations in satellite communications, weather radar, non-
destructive detection, medical diagnosis, underground
exploration, smart antenna, etc.
[2−7]
. The primary o b-
jective of this technique is to build far-field radiation
patterns with high main lobe and low side lobes in a
desired direction by the coherent radiation superposi-
tion of the array elements. To reinforce the radiation
pattern, the relative phases of individual elements are
precisely adjusted while their respective amplitudes are
equal
[8−14]
. In ge neral, the phased array encounters
diffic ulty in forming any targe t radiation pattern, such
as a ring or rectangular shape, despite the ring-shaped
radiation pattern’s applications in directed and wartime
communications and specific shape ultrasonic therapy.
In addition, delay lines applied in pha sed arrays be-
come short especially at the optical wavelength a nd are
diffic ult to fabricate, making phase shifters complicated
and costly.
In describing radiation fields, amplitude is another im-
portant factor aside from the phase. In this study, the
radiation pattern in the far field is theoretically inves-
tigated by manipulating the ra diation amplitudes in an
in-phase radiation array. As a result, a universal formula
which determines the relationship between the radiation
amplitudes of array elements and a random symmetri-
cal radiation pattern in the far field is derived. This
formula provides a novel discovery that any desired radi-
ation pattern could be for med by simply co ntrolling the
respective radiation amplitude (i.e., amplitude weight)
of array elements with these radiation amplitudes de-
termined by solving the formula analytically. Distinct
from phas ed ar ray technology, this amplitude-weighting
array technology only requires the utilization of variable
attenuators in each radiation element and avoids the use
of phase shifters.
Furthermore, to confirm the va lidity of this method,
an annular radiation pattern is chosen as target far-field
pattern, after which the ra diation amplitude of each
array element is determined by solving the formula an-
alytically. The available far-field pattern is calculated
by applying these solutions and comparing it with the
target far-field pattern.
We will build the universal formula for amplitude-
weighting array technology to describe the relationship
between the radiation amplitudes of array elements and
a symmetrical radia tion pattern in the far field. Figure 1
illustrates a planar array with (2N +1)×(2M +1) ele-
ments in an isotropic media a nd Cartesian coordinate
system. The elements of this array are distributed s ym-
metrically in pla ne xoy with the axial spacing of a and
b in the x-axis and y-axis directions, respectively. The
coordinates of the far-field point P is (x
0
, y
0
, z
0
),
−→
L
0
denotes the vector from origin o to point P , θ denotes
the angle between z-axis and the projection of
−→
L
0
in
plane xoy, and φ denotes the angle between the z-axis
and the projection of
−→
L
0
in plane yoz. To simplify, all
the ar ray elements are regarded as ideal point radiation
sources with identical circular frequency ω and polariza-
tion direction.
Starting with a random array element C with coordi-
nates (na, m b) (–N 6 n 6 N, –M 6 m 6 M ), a line
Fig. 1. Planar array elements distributed symmetricall in
plane xoy.
1671-7694/2013/080102(6) 080102-1
c
2013 Chinese Optics Letters
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