1 Introduction
Periodic gratings made of
dielectric rods of rectangular cross-section (Fig. 1) exhibit clear-cut
resonance characteristics in the range of wavelengths comparable with the grating
period. The advantage of these gratings over conventional frequency-selective
surfaces is that the transmission and reflection characteristics of such
gratings can be controlled by external fields. For example, in [1] we
demonstrated that the transmission coefficient of a ferrite rod grating could
be efficiently controlled by a magnetic field applied along the rods.
Fig. 1. Cross-section of the grating.
In [2], we showed that a
magnetic field applied to the grating in the propagation direction of the
incident wave might have a crucial effect on the polarization and transmission
characteristics of the grating.
In [3], we investigated the
transmission characteristics of a grating made of high-resistivity
silicon rods. In this case, the characteristics of the grating can be
controlled by illuminating the grating by a quartz halogenic
lamp.
2 Experimental Setup and
Measurements
The measurements were
carried out on an R2-69 network analyzer operating in the 54-78-GHz range. The gratings
were placed either between transmitting and receiving horns or between the
lenses of a beam waveguide line. The ferrite grating was made of ten
5.5-cm-long rods of 2´3-mm
cross-section cut out of a low-loss (tand @ 10-3) slab of NiZn ferrite with a permittivity of e = 13.8. The silicon grating was made of high-resistivity silicon (r > 2 10 W cm), which shows extremely
low losses in the millimeter-wave range at room temperature. The parameters of
the grating material were measured to be e = 11.7 and tand < 10-4 in the
range of wavelengths from 1 to 6 mm.
2 Magnetically Controlled
Ferrite Gratings
The effect of a magnetic
field on the transmission characteristics of a ferrite grating was investigated
for two different geometries of magnetization: (1) when the magnetic field is
applied along the roods of the grating and (2) when the magnetic field is
applied perpendicular to the plane of the grating (along the wave vector of the
incident wave in the case of normal incidence). The grating was made of the same
ferrite rods in both cases.
In the first case, the
ferrite rods were glued to a rectangular iron frame. The magnetization of the
grating was performed by magnetizing coils wound around two opposite sides of
the frame that are parallel to the ferrite rods. A bias magnetic current of
about 1 A was enough to magnetize the grating up to saturation. The
transmission characteristics of the grating versus the dimensionless parameter k = p / l (p is the grating period and l is the wavelength) are
shown in Fig. 2: the solid and dashed curves correspond to nonmagnetized
and magnetized gratings, respectively. Figure 3 represents the same
characteristics calculated by a mode-matching technique. These results show
good qualitative agreement.
Fig.2. Measured transmission coefficient T versus dimensionless parameter k = p / l for the nonmagnetized (solid line) and magnetized (dashed line) grating.
In the second case, the ferrite rods
were pasted to a 1-cm-thick plate of foamed polystyrene with a period of 2.8
mm. The latter plate served as a support that allowed us to fix the grating at
the center of 8-cm-long solenoid, so that the plane of the grating was
perpendicular to the solenoid axis. The permittivity of foamed polystyrene was
less than 1.1 and had no appreciable effect on the
transmission characteristics
of the grating.
Fig.3. Transmission coefficient T versus dimensionless parameter k = p / l calculated by the mode matching technique for the nonmagnetized (solid line) and magnetized (dashed line) grating.
The solenoid was wound of a
copper wire 1.3 mm in diameter. The total number of turns was about 1000; the
maximum magnetic field of 720 Oe at the center of the
solenoid was attained for an electric current of 10 A through the coil. The
grating was fixed at the center of the solenoid with its plane perpendicular to
the solenoid axis. The solenoid was placed between transmitting and receiving
horns. The measurements were carried out in three different configurations: the
E polarization (when the polarization vectors of the feed and receiving horns
are parallel to the axes of the grating rods), the H-polarization (when the
above vectors are perpendicular to the axes of the rods), and the
cross-polarized configuration (when the polarization of the feed horn is
parallel while that of the receiving horn is perpendicular to the rods).
Fig.4. Transmission coefficient of the grating in the absence of magnetic field; the solid and dashed curves represent the measured and calculated transmission coefficients, respectively.
The transmission coefficient
versus frequency for the first configuration is shown in Fig. 4 (solid line).
The dashed curve represents the corresponding transmission coefficient
calculated by the mode-matching technique. The application of the external
magnetic field leads to a slight change in the transmission characteristic,
which is illustrated in Fig. 5.
Fig.5. Transmission coefficient of the grating measured in the absence of magnetic field (dashed curve) and in a magnetic field of 720 Oe.
Here, the dashed curve
represents the transmission coefficient in the absence of magnetic field, and
the solid curve illustrates the effect of the longitudinal magnetic field. The
change caused by the magnetic field is somewhat similar to that observed in the
grating with the rods magnetized along their axes (see Figs. 2 and 3). However,
in the present case, it takes much higher magnetic-field strength to change the
characteristics of the grating.
The most important and
interesting result is that the grating exhibits a Faraday rotation, which is
observed in the cross-polarized configuration at certain narrow frequency
intervals. Surprisingly, despite the very large demagnetizing field in the
rods, this phenomenon clearly manifests itself in a rather low magnetic field.
Figure 6 shows the transmission coefficients of the grating measured in the
cross-polarized configuration for various values of the applied magnetic field.
One can see that, even at a magnetic field of about 70 Oe,
two pronounced peaks at frequencies of about 58 and 70 GHz appear against the
background of at least –15 dB (the lower solid curve). As the magnetic field
increases to about 200 Oe, the transmission peaks
become higher and broader (dashed curve). A further increase
in the magnetic field to its maximum value of 720 Oe
results in the transmission pattern shown by the upper solid curve. The
position of the transmission peaks in Fig. 6 and the examination of the
dispersion curves of the grating shown in Fig. 7 allow us to tentatively
suggest that the Faraday effect is attributed to
various types of transitions between different branches of the dispersion
characteristics.
Fig.6. Transmission coefficient of the grating measured in the cross-polarized configuration.
Fig.7. Dispersion curves of the ferrite grating for E (solid curves) and H (dashed curves) polarizations.
3 Optically Controlled
Semiconductor Grating
The transmission
characteristics of a semiconductor grating are also investigated in the case of
normal incidence of a plane linear polarized wave. Figures 8 and 9 show these
characteristics versus the dimensionless parameter k = p / l for the E and H
polarizations of the incident wave, respectively. The solid curves correspond
to the measured characteristics, and the dashed curves correspond to the
characteristics calculated by a mode-matching technique. When the grating is
illuminated by a quartz halogenic lamp, the
transmission is leveled and suppressed to –15 dB throughout the frequency range
(dotted curves). Similar measurements of the reflection coefficient resulted in
a suppression of reflection coefficients to about –5 dB.
Fig.8. Transmission coefficient of the silicon grating versus k (the case of E polarization).
Fig.9. Transmission coefficient of the silicon grating versus k (the case of H polarization).
4 Controlled
Metal-Dielectric Grating
Metal-dielectric gratings,
otherwise known as "knife-type" gratings, were shown to be quite
versatile for designing frequency selective surfaces. These gratings consist of
alternating dielectric rods of different values of permittivity that are
separated by thin conductive layers. In [2, 3], we have shown that these
gratings are promising for the design of frequency selective surfaces. Moreover, they may provide another kind of
controlled gratings, where the control can be performed by an electric field.
Specifically, the control can be performed by changing the resistance of the
conductive layers of metal-dielectric gratings. This type of control seems to be more attractive since it
can be substantially more efficient provided thin films with strongly variable
conductivity are available. The results of numerical calculations for such
structures have been carried out for the H-polarization case for a grating with
the following parameters: a = 1.3 mm, b = 0.8 mm, c = 1.5 mm, 1 = 13, and 2 = 4. The curves in Fig. 10 correspond to the values of the surface
resistance of conducting films that are represented on the top of this figure.
The curves that correspond to the perfectly conducting films and the perfectly
isolating films (or to the absence of films) are not represented, because these
curves are fairly similar to the curves that correspond to the surface
resistance of 1 W and 1000 W, respectively.
One can see that it takes rather sharp change in the surface resistance of the
conductive films to efficiently control the frequency-selective properties of
the grating.
Fig. 10. Transmission characteristics of an
electrically controlled metal-dielectric grating.
References
[1]
[2]
[3] V.V.
[5] V.V.
[6] V.V.
