A tunable dual-band ferrite-based metamaterial has been investigated by experiments and simulations. The negative permeability is realized around the ferromagnetic resonance (FMR) frequency which can be influenced by the dimension of the ferrites. Due to having two negative permeability frequency regions around the two FMR frequencies, the metamaterials consisting of metallic wires and ferrite rods with different sizes possess two passbands in the transmission spectra. The microwave transmission properties of the ferrite-based metamaterials can be not only tuned by the applied magnetic field, but also adjusted by the dimension of the ferrite rods. A good agreement between experimental and simulated results is demonstrated, which confirms that the tunable dual-band ferrite-based metamaterials can be used for cloaks, antennas and absorbers.
©2013 Optical Society of America
Since Veselago  predicted the negative refractive index (NRI) material with simultaneously negative effective permittivity and permeability, these materials have been recently stimulated tremendous fundamental and practical interests because of their unusual electric and magnetic features and due to their potential applications in different regimes of the electromagnetic spectrum [2–5]. Because NRI materials are not found in nature, metamaterials have been a major resort to obtain NRI materials . Hence, much attention has been focused on the unusual electromagnetic properties of these metamaterials such as the reversals of both Doppler shift and Cherenkov radiation, enhancement of evanescent wave, and subwavelength resolution imaging, etc [7–9]. Most up-to-date metamaterials are artificial structures, like well-known composite periodic structures composed of thin metallic wires (ε < 0) and split-ring resonators (SRRs) (μ < 0) [10–14]. Such metamaterials usually obtain their unique electromagnetic properties from the designed structures rather than the composition.
Dual-band and multi-band metamaterials have been drown considerable attention because of multi-frequency applications [15–17]. Some researchers have presented some dual-band or multi-band metamaterials by designing composite structures or the same structures with different sizes to broaden the bandwidth. However, characteristic metamaterial frequency band is difficult to tune in such metamaterials, since the dimension of the periodic composite structure should be small enough compared to the wavelength which creates challenges in the fabrication . Recently, new ferrite-based metamaterial structures have been reported in which negative magnetic permeability is achieved by substituting SRR elements with ferrites [19–22]. The negative permeability appears when the ferromagnetic resonance (FMR) of the ferrite taking place . The FMR of the magnetic materials is influenced by a lot of factors such as the bias magnetic field, magnetocrystalline anisotropy field, and demagnetization field. Hence, we can control the characteristic metamaterial frequency band by tuning these factors. A lot of researches on the negative index frequency band shifted by adjusting the bias magnetic field have been reported, but there are few reports on frequency band influenced by shape demagnetization factor. In this work, we designed a dual-band NRI ferrite-based metamaterial. In order to demonstrate the microwave transmission characteristics of the dual-band NRI ferrite-based metamaterial, a single-band NRI ferrite-based metamaterial was also prepared. The microwave transmission properties of ferrite-based metamaterials tuned by the different shape demagnetization factor were investigated by experiments and simulations.
The commercial yttrium iron garnet (YIG) rods were sliced with dimensions of l × w × h mm3, where l = 0.8, 1.6, and 2.4 mm, w = 0.4 mm, h = 10 mm, respectively. Saturation magnetization 4πMs, linewidth ΔH, and relative permittivity εr of the YIG rods are 1950 Gs, 10 Oe, and 14.5, respectively. Using a shadow mask/etching technique, we prepared 0.4 mm thick FR-4 dielectric substrates (εr = 4.4 and tanδ = 0.014) with copper wires spacing of 3 mm on one side. The size of the copper wires is 0.5 × 0.03 × 10 mm3. The other 0.4 mm thick FR-4 dielectric substrates without copper wires were pasted on the side of dielectric substrates with copper wires, which made two sides of the copper wires covered by the dielectric substrates. The YIG rods with the dimension of 0.8 × 0.4 × 10 mm3 were pasted back-to-back with copper wires on one side of the substrate/wire/substrate structure. The other YIG rods with a series of dimensions were pasted on the other side of the substrate/wire/substrate structure. The dual-band NRI ferrite-based metamaterials were obtained by assembled the rod-wire-rod units into an array, as shown in Fig. 1(a). For comparison, the single-band NRI ferrite-based metamaterials were also obtained by assembled the rod-wire units into an array, as shown in Fig. 1(b). The distance d between the rods is 3 mm.
The NRI ferrite-based metamaterials were placed in an X-band rectangular waveguide WR90 (22.86 × 10.16 mm2) under various applied magnetic fields which is generated by an electromagnet along the z direction. The microwave with TE10 mode propagates along y direction with an electric field polarized along the x direction. The microwave properties were measured by an HP 8720ES network analyzer. In addition, the microwave properties of ferrite rod and ferrite-based metamaterials were simulated by using CST Microwave Studio, a Maxwell’s equations solver. The geometry, dimensions and materials’ parameters for the simulation are chosen to be consistent with the experimental ones.
3. Results and discussion
The negative permeability of the ferrite can be obtained when the FMR takes place. The effective permeability of the ferrite can be expressed by Eqs. (1)-(4), it can be predicted that the permeability of the ferrite strongly desponds on the FMR frequency. The FMR frequency ωr is influenced by the demagnetization factor N.
Because of applying the electromagnet in this work, it is difficult to obtain precise measurements of the transmission and reflection by repeatedly assembling the waveguides and matching loads. Thus, instead of experimental data, the simulated scattering parameters are used to retrieve the effective material properties. The material parameters are obtained by S-parameter retrieval method which is described in detail elsewhere . The unit cell of a ferrite rod alone with the dimension of 3 × 3 × 10 mm3 is shown in Fig. 2(a). The geometry, dimensions and materials’ parameters used in the simulation are the same as the experimental ones. The retrieved effective permeability μeff of the ferrite rod with a series of length l is shown in Fig. 2(b). The applied magnetic field was set at H0 = 2300 Oe. Firstly, in all cases, there is one remarkable frequency dispersion in the range of 8-12 GHz and the negative Re(μeff) has appeared at the upper resonant frequencies. Secondly, one observes that the FMR frequency decreases as the rod length l increases.
The demagnetization factor N is determined by the dimension of the samples. The demagnetization factor N for one direction varies inversely with the dimension in that direction. On increasing l from 0.8 mm to 2.4 mm, the demagnetization factor Ny for y direction and the value of (Ny – Nz) decrease. Based on Eq. (4), the ωr decreases as the (Ny – Nz) decreases, which leads to the negative Re(μeff) frequency region shifting to the lower frequency.
Figure 3(a) shows the measured transmission spectra for rods-only, wires-only and the single-band NRI ferrite-based metamaterials with the rod length l = 0.8 mm, respectively. There is a band gap and stop band in the transmission curve for YIG rods alone and wires alone, which are induced by the negative permeability of the ferrite around the FMR frequency and negative permittivity of the wires array within a wide region below the electric plasma frequency, respectively. Besides, a passband, which emerges just in the region where both permittivity and permeability are negative , was observed for the ferrite-based metamaterials consisting of YIG rods and copper wires. The measured transmission spectra for the single-band NRI ferrite-based metamaterials with a series of rod length l were shown in Fig. 3(b). It can be seen that the passband measured under different l reveals a tunable property. The passband frequency decreases from 10.6 to 10.2 GHz as l increases from 0.8 to 2.4 mm, which shows that the transmission property is influenced by the dimensions of the samples related to the demagnetization factor N. This characteristic can be used to prepare the dual-band metamaterials consisting of metallic wires and ferrite rods with different dimensions.
The unit cell of two ferrite rods is shown in Fig. 4(a). The dimension of the YIG rod A is 0.8 × 0.4 × 10 mm3. The width w and height h of the YIG rod B are the same as that of the YIG rod A, while the length l of the YIG rod B is 0.8, 1.6, and 2.4 mm, respectively. The retrieved effective permeability μeff of two ferrite rods with a series of length l of rod B at H0 = 2300 Oe is shown in Fig. 4(b). The rod-wire-rod unit shows the two negative permeability properties, which is different from the rod-wire unit shown in Fig. 2(b). When the length l of rod B is equivalent to that of rod A (l = 0.8 mm), there is only one frequency dispersion observed due to the same demagnetization factor for rod A and rod B. when l > 0.8 mm, there are two remarkable frequency dispersions in the range of 8-12 GHz. One can see that the first FMR frequency controlled by rod B decreases as the rod B length l increases, while the second FMR frequency controlled by rod A is constant. It is obvious that the two negative permeability frequency regions can be tuned by the dimension of the ferrites.
The dual-band NRI ferrite-based metamaterials were composed of the rod-wire-rod units. Figure 5(a) shows the measured transmission spectra for rods A and rods B, wires-only and the dual-band NRI ferrite-based metamaterials with the rod B length l = 2.4 mm, respectively. There are two band gaps in the transmission curve for two YIG rods alone, which is induced by the negative permeability around the two FMR frequency regions. Two passbands were observed for the ferrite-based metamaterials consisting of rod-wire-rod units, which is different from the ferrite-based metamaterials consisting of rod-wire units. The measured transmission spectra for the dual-band NRI ferrite-based metamaterials with a series of rod B length l were shown in Fig. 5(b). When the length l of rod A and rod B equals 0.8 mm, a passband was observed. When the length l of rod B is different from that of rod A (l > 0.8 mm), there are two passbands observed in the range of 8-12 GHz. The first passband frequency controlled by rod B decreases as the rod B length l increases, while the second passband frequency controlled by rod A is constant. The passband tunable characteristic is in agreement with the behavior of effective permeability, which is influenced by the dimension of the ferrites.
The unit cell of ferrite rod A-copper wire-ferrite rod B is shown in Fig. 6(a). The dimensions of the ferrite rod A, rod B and copper wire are the same as that described above. The real part of effective refractive index neff is retrieved from the simulated scattering parameters for the rod-wire-rod unit, as shown in Fig. 6(b). It can be seen that the real part of the index Re(neff) is negative in the frequency range where the passband appears, indicating that the dual-band ferrite-based metamaterials should be the NRI metamaterials. When the length l of rod B is different from that of rod A (l > 0.8 mm), there are two negative refractive index frequency region observed in the range of 8-12 GHz and the first negative refractive index frequency decreases as the rod B length l increases, which is in agreement with the behavior of transmission spectra.
Figure 7(a) shows the simulated transmission spectra for the dual-band NRI ferrite-based metamaterials with rod B length l = 2.4 mm under a series of applied magnetic fields. There are two passbands in the simulated transmission curves, which is in agreement with the behavior of the experimental ones. The passbands simulated under different H0 reveals its magnetically tunable property. As H0 rises from 1900 to 2300 Oe, the first passband frequency increases from 9.1 to 10.2 GHz, while the second passband frequency increases from 9.5 to 10.6 GHz. The real part of effective refractive index neff of the rod-wire-rod unit under a series of applied magnetic fields is shown in Fig. 7(b). It can be seen that the two negative refractive index frequencies increase as the H0 increases, which in good agreement with the behavior of transmission spectra.
The single-band and dual-band NRI ferrite-based metamaterials consisting of metallic wires and ferrite rods with various dimensions have been prepared. The microwave transmission properties can be tuned not only by changing the applied magnetic field, but also by adjusting the dimensions of the ferrite rods. For the single-band NRI ferrite-based metamaterials consisting of rod-wire units, the passband frequency decreases as rod length increases. For the dual-band NRI ferrite-based metamaterials consisting of rod-wire-rod units, there are two passbands observed in the range of 8-12 GHz when the length of rod B is different from that of rod A, and the passband frequencies are also decrease as the rod length increases. The results provide a new way to fabricate the tunable dual-band metamaterials cloaks, antennas and absorbers.
This work was supported by the Shandong Natural Science Foundation under Grant No. ZR2010AM025, National Natural Science Foundation of China under Grant Nos. 51032003, 11274198, 51102148, and National High Technology Research and Development Program of China under Grant No. 2012AA030403.
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