1 Introduction
Periodic gratings made of dielectric rods of rectangular cross-section 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 the fact 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.
In this paper, we consider the transmission characteristics of a ferrite grating when the external magnetic field is perpendicular to the plane of the grating (or is parallel to the propagation direction of the incident wave in case of normal incidence) (see Fig. 1).
Fig. 1. Cross-section of the ferrite grating.
Here, we only present the results of experimental investigation. Theoretical analysis of such a configuration is substantially complicated as compared with the case when the magnetic field is parallel to the rods. In this configuration, the waves of two orthogonal polarizations are coupled; therefore, one cannot reduce the problem to scalar problems for each polarization as before. The most important factor is that, due to the high demagnetizing field in the rods, the total magnetic
field is strongly inhomogeneous and contains both x and y components, whereby the permeability tensor is a function of x and y coordinates. In this paper, we restrict ourselves to the experimental investigation of ferrite gratings.
2 Experimental
Setup and Measurements
The grating was made of ten 5.5-cm-long rods of 2´3-mm cross-section cut out of a slab of NiZn ferrite with a permittivity of 13.8. The 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. 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 measurements were carried out on an R2-69 network analyzer operating in the 54-78-GHz range. The grating was fixed at the center of the solenoid with its plane perpendicular to the solenoid axis. The solenoid was placed between the feed 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).
The transmission coefficient versus frequency for the first configuration is shown in Fig. 2 (solid line).
Fig.2. 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 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. 3.
Fig.3. 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 (cf. [1]). 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 4 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. 4 and the examination of the dispersion curves of the grating shown in Fig. 5 allow us to tentatively suggest that the Faraday effect is attributed to various types of transitions between different branches of the dispersion characteristics.
Fig.4. Transmission coefficient of the grating measured in the cross-polarized configuration.
Fig.5. Dispersion curves of the ferrite grating for E (solid curves) and H (dashed curves) polarizations.
For example, the transmission peak at about 58 GHz can be associated with the transitions he2 + he2 « he1 or he2 + he2 « hh1 induced by the magnetic field (see Fig. 4).
3 Metal-Dielectric
Grating
Metal-dielectric gratings,
otherwise known as "knife-type" gratings, were shown to be quite
versatile for designing frequency selective surfaces [2]. These gratings
consist of alternating dielectric rods of different values of permittivity that
are separated by thin conductive layers. One of the most interesting properties
of these gratings is the appearance of
rather wide stopbands in their transmission vs frequency characteristics. The
bandwidth and the shape of these stopbands
were shown to depend on the dielectric and geometric parameters of the rods. In
this paper, we consider a particular case of a metal-dielectric grating made of
a dielectric with permittivity 2, the permittivity of most fiber-optic
materials. Figure 6 shows the transmission coefficient of the metal-dielectric
grating versus the ratio of the grating period p to the wavelength l for the H-polarized (H vector of the wave is parallel to the
axes of the rods) incident wave. The dimensions of the rods are as follows: the
width b (the size in the y direction) is 0.7 p and the grating thickness c
(the size in the x direction) is p (solid curve) and 0.75 p (dashed curve). Figure 6 clearly shows
that the grating provides an efficient bandstop filter with a relative
bandwidth of about 3%; the central frequency of the stopband can be controlled
by varying the thickness c of the
grating.
Fig. 6. Transmission coefficient of a
metal-dielectric grating versus the ratio of the grating period p to the wavelength for various
thicknesses c of the grating; (solid curve) c
= p and (dashed curve) c = 0.75 p.
References
[1] Meriakri,
V.V., Nikitin, I.P., Parkhomenko, M.P., Sivov, A.N., and Shatrov, A.D., Radiotekhnika i Elektronika, 1990, vol 35,
no. 10, pp. 2061-2065.
[2] Meriakri, V.V. and Nikitin, I.P., Int. J. Infrared and Millimeter Waves,
1996, vol. 17, no. 10, pp. 1769-1778.
