"JOURNAL
OF RADIOELECTRONICS" N 4, 2000 |

**STUDY OF
ELECTROMAGNETIC WAVE BACKSCATTERING FROM STRUCTURES WITH ANISOTROPIC
CONDUCTIVITY**

**Yu. N. Kazantsev, V. N. Apletalin, V. S. Solosin, A. S.
Zubov**

The Diffraction Problem Laboratory, the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences

Received April 20, 2000

*A possibility of backscattering controlling by means of
structures with anisotropic conductivity is considered. It is shown that
applying of this structures allowed to reduce the backscattering from leading
and rear edges and from metal-impedance border.*

**1. Introduction.**

Electromagnetic wave scattering from anisotropic structures, and specifically, from ones with anisotropic conductivity was investigated by many authors [1-7]. Here we concentrate on the possibility of controlling the backscattering from some typical scattering centres by means of structures with anisotropic conductivity.

The so-called leading and rear edges as well as the boundaries between surfaces with different electrical properties are considered as typical scattering centres. As an efficiency criterion of using the structures with anisotropic conductivity, the extent of the backscattering reducing from the centres mentioned above is considered. The results presented below do not claim to completeness, however, they confirm the efficiency of application of anisotropic structures to control the backscattering from physical bodies.

**2. Methods and facilities for the backscattering
measurements.**

Since the principal results presented in the article were obtained experimentally, we consider briefly the methods and facilities used to obtain these results.

Fig.1

Two experimental sets were employed - the Radiocollimator
(Compact Range) and the Reflectometer. The Compact Range is shown schematically
in Fig. 1, where *1* - anechoic chamber,* 2* - collimator, *3* -
system of transmit/receive horns, *4* rotary arrangement, *5* -
measuring set involving the Frequency Sinthesizer and Microwave Network
Analyzer.

The collimator quiet zone represents an elliptical cylinder
with sizes of 1.0 x 0.6 x
1.0 m^{3}. The RCS sensitivity of the facility is 10^{-6} m^{2}.
The Compact Range is used as basic measurement facility of *ISAR* method.
The backscattering is measured at discrete frequencies of the operating range
for various object's aspect angles. The data obtained are transformed in Time
Domain to provide the object image where the backscattering centers are
appeared. One can distinguish separate zones in the object image to study them
in more detail.

The Reflectometer is shown schematically in Fig. 2 where *1*
- the Frequency Synthesizer, *2* - three operating *LM*_{11}
mode transducers, *3* - directional power divider,* 4* - coincide and
cross polarization discriminator,* 5* - two matched loads, *6 *-
microwave switch, *7* - the Microwave Network Analyzer, *8* - rotary
arrangement and the object under test.

Fig.2

The Reflectometer operating aperture is 0.2
x 0.2 m^{2}. The RCS sensitivity is 10^{-8} m^{2}. The *ISAR
*method is used to discern the scattering centers on the object under test.

The backscattering from typical scattering centers was studied by means of physical models. The leading edge was modeled by the sharp wedge, and a half-plane was considered as the rear edge. The boundary between metal and "impedance" surfaces is modeled the boundary between surfaces with different electrical properties. The "impedance" surface is assumed to be any non-metal surface, and particularly, metal surface coated by a layer of either radio-absorbing or radio-transparent material.

As a rule, the measurements in Compact Range were duplicated by measurements carried out with the Reflectometer.

**3. The backscattering from a leading edge (sharp wedge).**

Fig.3.

Two-dimensional RCS , or echowidth, for a conducting wedge (Fig 3) is described by the well-known formula (see, for example, [8]):

where ,
- wavelength, ,
- angle between wedge
faces, - angle
between a wedge face and wave incident direction. The upper sign in brackets
corresponds to* E-*polarization (*E* vector of incident wave is
parallel to wedge edge) and the lower one corresponds in turn to *H*-polarization
(*H* vector of incident wave is in parallel to wedge edge).

When and ,
two-dimensional RCS for *E-*polarization
is much greater in magnitude when that for *H*-polarization .
Therefore, the problem was to find a way of decreasing ,
such that
at least do not increase, or, what is still better, would also decrease. The
effect mentioned has been attained when the faces of the metal wedge were coated
by a layer of a material which turns initial *E-*polarization to 90^{0}
and, at the same time, does not affect, or weakly affects, the *H-*polarization
(Fig. 4).

Fig.4.

The coating represents a multi-layer structure consisting of
several polarization gratings separated by thin dielectric layers, each grating
being turned to a small angle with respect to an adjacent one. A polarization
grating consists of thin parallel conductors, and the grating period is small as
compared with the wavelength. The conductors of upper (outer) grating (*1*)
are perpendicular to the wedge edge and the conductors of lower (nearest to the
metal surface) grating (*2*) make a small angle with the edge direction.
The coating of the models under test was formed by 5 gratings separated by mylar
layers of 0.25 mm thick. Every separate grating was fabricated from woven
material of 0.25 mm thick. The grating period was equal to 0.25 mm, the diameter
of the copper conductors forming the gratings was equal to 0.1 mm. The total
coating thickness was equal to 2.5 mm. The coating was stuck on both faces of
metal wedge a such manner as it is shown in Fig.4. Fig.
5 shows the measured frequency dependence of
for a

Fig. 5.

sharp wedge ()
with coating (solid line) for the incidence angle .
The calculated backscattering levels from a metal wedge without coating are
presented for* E*- and *H*-polarizations (dotted and dot-and-dash
lines respectively). Figure 5 shows that
for the wedge with anisotropic coating is by (15-20) dB lesser than the similar
parameter for the metal wedge without coating in a broad frequency range. The
low-frequency boundary of coating's operating band can be shifted to the left
(to lower frequencies) by increasing the dielectric layer thickness between
gratings. From the high-frequency side, no essential restriction of the
operating band has been observed at least in the X-band. As for ,
it proves to be approximately the same as in the case of a metal wedge without
coating.

**4. Backscattering from the rear edge (half-plane edge).**

Two-dimensional RCS (echowidth) from the metal half-plane edge is described by the same formula (1) with . As a result, formula (1) reduces to

When , (the lower sign in brackets) is much greater then (the upper sign). The problem was there to find a method for decreasing which would not be accompanied by an essential increase in . This can be realized by attaching a metallized anisotropic film, to the rear edge (See Fig. 6).

Fig. 6.

The anisotropic structure (*1*) is formed by narrow
circular gaps in a metal layer. The centres of circles lie at the film edge
attached to the metal half-plane. It is evident that the currents induced at the
half-plane edge by an *H*-polarized wave are not perturbed in the place
where the half-plane and the anisotropic film are joined since these currents
are parallel to the gaps. On the other hand, the opposite (outer) film edge
moves to be transparent for the *H*-polarized wave, and therefore the field
is not perturbed in this area. A thin resistive film (*2*) is placed
underneath the anisotropic film. It absorbs the surface waves excited by an *E*-polarized
wave.

Fig. 7 shows the values of measured from the half-plane with the anisotropic film attached to it. The film dimensions are shown in Fig. 6. The thickness of the resistive film is equal to 70 mkm, and permittivity .

Fig. 8 shows similar results for .
For comparison, the backscattering level from the metal half-plane edge for *H*-polarized
wave with is
shown in both figures by dotted lines.

**5. Backscattering from the boundary between metal and
impedance surfaces.**

It is well known that a toothed structure can be used to decrease the backscattering from the boundary between the metal and impedance surfaces. It is also known that the use of a toothed boundary gives rise to certain directions perpendicular to the teeth edges, in which the backscattering turns out to be considerable. This undesirable property of conventional toothed structure can be removed by the use of teeth with anisotropic conductivity. The teeth are made on the base of gratings in which the conductors are parallel to the tooth bisector.

A study of the backscattering has been carried out using the models of single teeth with isotropic and anisotropic conductivity. The samples under test are shown schematically in Fig. 9.

Fig. 9.

We studied the following structures.

a) A single tooth with anisotropic conductivity and the vertex angle
150^{o}, 110^{o}, 90^{o}, 70^{o} and 50^{o}
on the impedance substrate. The anisotropic tooth was cut from the technical
fabric of 0.23 mm thickness containing one-dimensional wire grid. The substrate
(the same for all specimens) was a thin radio-absorbing dielectric layer with
(the permittivity of dielectric
in the X-band) of 1 mm thickness on a ground plate.

b) Identical (for comparison) isotropic metal tooth. It was cut from the aluminium foil.

The backscattering measurements were carried out in the Compact Range
conditions in frequency range 8.0 - 16.0 GHz. A conducting cylinder with RCS of
600 cm^{2} at frequency 10 GHz was used to normalize the scattering
data. The geometry of the experiment is shown in Fig. 10. The sample under test
was placed on a rather small support in the form of inclined plane (with an
inclination angle of ).
The support was placed on the support unit. By turning the sample in inclined
plane, one can realise two various orientations of examined toothed structure
relative to the vector of the
incident *H*-polarized wave. For the first orientation, the incoming plane
wave is directed along the tooth bisector (bisector illumination). For the
second orientation, the vector
of the incident plane wave is perpendicular to the tooth side edge (side
illumination, see Fig. 10).

Fig. 10.

Fig. 11 shows typical starting experimental backscattering results in time domain obtained for an isotropic metal tooth (tooth vertex angle ).

Fig. 11.

Fig. 11*a* corresponds to the case of bisector
illumination, and Fig. 11*b* - to the case of side illumination. Peaks *2*
and *3* in the figures are non-informative since they are associated with
the backscattering from the sample edges. Peak *1* is of interest since
with peak is associated with the backscattering from the vertex and the side of
the tooth in Figs. 11*a* and 11*b*, respectively.

In Figs. 12*a, b** *the
backscattering impulse response amplitudes are presented as function of the
tooth vertex angle for the bisector and side illumination respectively.

Fig. 12.

The dotted lines are related to the isotropic metal toothed
structure shown in Fig. 9*b*, while the solid lines correspond to the
anisotropic tooth (See Fig. 9*a*). As one can see, the
anisotropic toothed structure provides low backscattering level for any type of
illumination for the tooth vertex angles .
A metal tooth offers low backscattering for ,
but only in the case of bisector illumination. For the side illumination (Fig.
12*b*), the metal tooth exhibits the backscattered signal by (20-25) dB
higher as compared with the anisotropic tooth structure for the tooth vertex
angle .
However, this difference tends to zero for obtuse angles.

**Conclusion.**

The structures with anisotropic conductivity reveal new
possibilities for controlling the backscattering from typical scattering centres
(leading and rear edges, boundaries between surfaces with different
electromagnetic properties). For example, anisotropic coating on the faces of a
sharp wedge edge enables one to decrease the backscattering of *E-*polarized
waves by (15 - 20) dB in a wide frequency range keeping down the backscattering
of *H*-polarized waves.

The modification of a toothed boundary between metal and impedance surfaces by using a film with anisotropic conductivity enables one to eliminate the main drawback of such boundaries, namely, substantial backscattering level when the illumination is perpendicular to the teeth sides.

**References**

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*Authors: *

Yuri Nikolaevich Kazantsev, e-mail: kaz@ms.ire.rssi.ru

Vladimir Nikolaevich Apletalin, e-mail: apl@ms.ire.rssi.ru

Vladimir Sergeevich Solosin, e-mail: vsolosin@ms.ire.rssi.ru

Alexander Sergeevich Zubov

The Diffraction Problem Laboratory, the Institute of Radioengineering and Electronics of the Russian Academy of Sciences