Fig.2 curves of dependence of
()
2
|
(,,)|
i
xd
,
0,1,
i=
on the slot width d, when the
angular value of the conical gratings is constant, are shown.
a
b
Figure 2. Dependence of coefficients
(2)
||
n
x
on slot width d with different value
and
1
=: a -
0
n=; b -
1
n=.
In the model problem of waves diffraction on the conical diffraction gratings the
diffraction characteristics of the field are completely defined by coefficients
()
2
(,,)
n
xd
.
From the given numerical results it is possible to describe the dependence of
coefficients
()
2
(,,)
n
xd
on number and geometric parameters of the problem. In the
model problem of wave diffraction on the considered conical diffraction gratings the
coefficient
()
2
0
(,,)
xd
corresponds to the reflected field from the gratings and other
coefficients (
1
n) characterize transmitted field through the gratings. Increase of
()
2
0
|
(,,)|
xd
and decrease of
()
2
1
|
(,,)|
xd
are observed as the slots narrow (for the
fixed cone opening angle ). In the limiting case when slots are absent (
0
d=) we
obtain
()
2
0
|
(,,)|1
xd
=
and
()
2
1
|
(,,)|0
xd
=
that corresponds to the process of total
reflection from the solid perfectly conducting cone [9].
Mathematical model of wave diffraction on the conical diffraction gratings
with variable surface properties. It should be noted that the considered first and
second boundary value problems are model ones for problems of electromagnetic
waves diffraction on perfectly conducting simple periodic conical diffraction gratings.
Tapes of such gratings have high conductivity and model metal tapes with high degree
of electric conductivity (for example, copper tapes).
The used methods of integral transforms and SIE can be used for the solution of
problems with more difficult conical geometry. The obtained results of the research of
- 1540 -