Q-band tunable negative refractive index metamaterial using ... - CM3IC

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JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 42 (2009) 155005 (5pp)

doi:10.1088/0022-3727/42/15/155005

Q-band tunable negative refractive index metamaterial using Sc-doped BaM hexaferrite P He1 , J Gao1 , Y Chen1 , P V Parimi1,2 , C Vittoria1 and V G Harris1 1 Center for Microwave Magnetic Materials and Integrated Circuits, Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115, USA 2 Department of Physics, Northeastern University, Boston, MA 02115, USA

Received 6 April 2009, in final form 23 June 2009 Published 17 July 2009 Online at stacks.iop.org/JPhysD/42/155005 Abstract A simple structured tunable negative refractive index (n) metamaterial (TNIM) has been designed, fabricated and tested in a Q-band rectangular waveguide. The structure consists of one slab of single crystalline scandium-doped barium hexaferrite (Sc-BaM), aligned parallel to two rows of periodic copper wires. The magnetic field tunable passband is measured indicating the occurrence of negative n. The centre frequency of the 5 GHz wide passband, having a transmission peak of −13 dB, is shifted linearly from 40.9 to 43.9 GHz by varying the bias field (H ) from 4.0 to 7.0 kOe. The impact of ferrite volume factor (FVF) of the Sc-BaM slab upon the performance of the TNIM composite has been studied qualitatively. A tradeoff effect is illustrated in which the desirable negative permeability (µ) of the ferrite is offset by the detrimental impact of its dielectric property in suppressing the negative permittivity (ε) of the nearby plasmonic wires. (Some figures in this article are in colour only in the electronic version)

tunability. In order to obtain negative n at different frequencies, one has to alter the periodicity or size of the elements. Recently, ferroelectric material has also been loaded into split rings to enable frequency tunability by varying the bias voltage [12]. However, the tunable bandwidth is still below 0.2 GHz mainly limited by the nature of split rings. It has long been known that ferrite materials can provide negative µ at the higher frequency side of their ferromagnetic resonance (FMR) in a transmission line [13, 14]. Since the frequency of the FMR shifts with the magnetic bias field H , the negative µ can be frequency tuned by H . Therefore, using ferrite materials instead of metallic resonators to generate negative µ can offer real-time frequency tunability. Ferrite films have been used as substrates combining with lumped elements to construct nonreciprocal left-handed transmission lines [15, 16]. TNIMs consisting of ferrite slabs and metal wires in parallel have also been demonstrated in C- and X- (7.0–12.5 GHz) bands [17, 18]. Such TNIM constructs used yttrium iron garnet (YIG) and periodic metal wires. The YIG provides negative µ, while the metal wires provide negative ε. The frequencies over which the µ and ε are coincidentally negative allow for negative n, which is usually

1. Introduction The developments in negative refractive index metamaterials (NIMs), or left-handed metamaterials (LHMs), have attracted a lot of interest in the past decade. Their simultaneous negative ε and µ properties make the electromagnetic (EM) field e
and
and the wave vector k
form a left-handed triplet without h, violating the Maxwell equations [1]. The NIMs exhibit many unusual EM properties such as backward wave propagation, negative refraction and near-field imaging [2]. These unusual properties allow for novel applications such as super lenses [3], leaky wave antennas [4] and miniature delay lines. The research on NIMs has been carried out in many frequency domains, which spread from microwave to infrared wave, and even visible light. And the mainstream design principle of NIMs is still to combine one material or structure of negative ε with another of negative µ together in a proper way to achieve negative n. Notable NIMs are resonant metamaterials [5, 6], photonic crystals [7–10] and planar periodic arrays of passive lumped circuit elements [11]. However, these metamaterials are all limited by inherent narrow bandwidths and lack the frequency 0022-3727/09/155005+05$30.00

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J. Phys. D: Appl. Phys. 42 (2009) 155005

P He et al

identified by a passband. The interacting mechanism between the ferrite and metal wires has also been theoretically studied using the transfer function matrix technique [19]. Although TNIMs continue to face the challenge of large insertion loss, their frequency tunability and highly frequency dispersive properties are ideal for microwave devices such as delay lines, phase shifters and antennas. In this paper, we report the work of constructing a TNIM performing near 40 GHz in a Q-band rectangular waveguide. The simple structured TNIM composite consists of one Sc-BaM slab and two rows of copper wires. The theoretically calculated µ of the Sc-BaM slab shows a negative region near its FMR, which is coincident with the negative ε generated by the copper wires. The tunable passband indicating the negative n is demonstrated in both experiments and simulations. The effect of ferrite volume factor (FVF) of the Sc-BaM slab is studied experimentally. The tradeoff between the desirable negative µ and the undesirable high dielectric constant of the ferrite is also illustrated.

2. Design and test results There are two major challenges to realize TNIMs in Q-band comparing with previous works at lower frequencies. First, the smaller wavelength results in higher sensitivity to geometric parameters of the assembly. Second, a suitable low loss ferrite material with high frequency FMR is needed. The small linewidth (H ∼ 50 Oe of the polycrystalline and H < 1 Oe of the single crystalline) YIG material is no longer suitable because of its relatively small anisotropy field (Ha ∼ 200 Oe) and subsequent low frequency FMR. On the other side, the Ha of barium hexaferrite (i.e. magnetoplumbite or Ba M-type ferrite) is too large, ∼17 000 Oe, resulting in a FMR frequency much higher than 40 GHz. The doping of Ba M-type ferrite with Sc has been shown to shift the FMR to frequencies as low as X-band [20]. Appropriate doping will allow for the tuning of FMR near 40 GHz by varying the bias field. Figure 1(a) shows an intuitive TNIM design consisting two rows of copper wires and two Sc-BaM slabs. Because of the ferrite’s anisotropy, the composite performance is nonreciprocal in nature [21, 22]. The field distribution analysis in simulations shows that there is little field concentrating in the right ferrite slab sandwiched by the two rows of wires. Therefore, the design can be simplified by removing the right ferrite slab resulting in a design as in figure 1(b). The wave propagation behaviour remains largely unchanged between the two designs. In figure 1(b), the thicknesses of the KaptonTM substrate, copper wires and the Mylar TM spacer are 0.14 mm, 0.025 mm and 0.72 mm, respectively. The width of individual wires is 0.3 mm and their longitudinal centre to centre spacing is 1.0 mm. The thickness of the Sc-BaM slab is 1.0 mm to achieve the optimal performance. Its easy axis is parallel to the magnetic bias field H . The height of all elements is 2.84 mm, the same as the inner height of the Q-band rectangular waveguide. The composite length along the direction of propagation is 6.0 mm. The two rows of copper

Figure 1. (a) Top views of the TNIM design consisting of two Sc-BaM slabs, two rows of copper wires on Kapton substrate, and a Mylar spacer and (b) the simplified TNIM consisting of only one Sc-BaM slab. The magnetic bias field H , the propagation constant β and the directional vector from copper wires to their vicinal ferrite slab Y form a right-handed triplet. (c) The schematic drawing of the TNIM composite mounted in a Q-band rectangular waveguide.

wires ensure sufficient plasmonic effect to generate negative ε while maintaining simplicity for fabrication and assembly. The Kapton substrates serve as spacers to reduce the coupling between the ferrite and copper wires [23]. The composite is mounted at the centre of the Q-band waveguide as shown in figure 1(c). The Sc-BaM slab is specially positioned to the lefthand side of copper wires because of its anisotropic nature. The bias field, H , the wave propagation constant, β, and the direction from the copper wires to their vicinal Sc-BaM slab, noted as Y , form a right-handed chirality. For the high quality single crystal Sc-BaM, the anisotropy field, Ha , is 9000 Oe, the linewidth, H , 400 Oe, the saturation magnetization, 3300 G, the dielectric constant, 12, and the dielectric loss tangent, √ tan δe , 0.0002. Its FMR frequency can be estimated by γ  (H + Ha )(H + Ha + 4π Ms ), where the gyromagnetic ratio γ  = 2.8 GHz kOe−1 . But in real cases, the demagnetization field determined by the form factor of the ferrite crystal also needs to be subtracted from H . 2

J. Phys. D: Appl. Phys. 42 (2009) 155005

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Figure 2. (a) The theoretically calculated effective µ versus frequency of a Sc-BaM slab under the extraordinary wave mode in the Q-band rectangular waveguide. The bias field and easy axis are both in the slab plane. (b) The retrieved effective ε of the simulated scattering parameters of the copper wires. (c) The calculated effective n from the µ and ε in (a) and (b). (d) The calculated FOM from the complex n.

The effective µ of the ferrite slab under the extraordinary wave mode in the rectangular waveguide can be theoretically calculated as plotted out in figure 2(a) [21, 22]. A negative region of effective µ is obtained near 40 GHz with H ≈ 5000 Oe. The effective ε retrieved from the simulated scattering parameters of the copper wires is also plotted in figure 2(b). It is negative over the whole frequency range, which allows for no wave propagation by itself. In the frequency region where ε and µ are coincidentally negative, the effective n is negative. And the wave propagation is allowed and a passband is expected. The ordinary wave mode propagating through the ferrite is neglected here because it does not propagate when the ferrite is combined with the copper wires. √ Because n = ± εµ, where ε = ε − jε , µ = µ − jµ ,   n = n − jn , and the plus and minus signs are chosen by making n > 0, the frequency response of n can be calculated as plotted out in figure 2(c). The n shows a prominent negative (0.5) over the whole frequency range except between 42 GHz and 45 GHz. From the complex n, the figure of merit (FOM) can be calculated as |n /n | in figure 2(d). The FOM has a peak value of 3.9 at 42.6 GHz. The bandwidth is 3.2 GHz of FOM > 2 and 2.1 GHz of FOM > 3. Because the peak of FOM is relatively low and narrow, we would expect large insertion loss only in the negative n region. We can also tell that the drawback mainly comes from the contribution of µ near FMR by reviewing

figure 2(a). Therefore, in order to improve FOM, the main focus should be on reducing the H of the ferrite. In experiments, the high quality single crystalline Sc-BaM slab was grown by liquid phase epitaxy. Thin slabs were cut out from the parent crystal to make the easy magnetic axis in the slab plane. The copper wires were fabricated from copper clad on Kapton sheets using traditional lithographic procedures. The composite was assembled by fixing individual components to form the construct as in figure 1(b), and was mounted in the centre of a Q-band rectangular waveguide as in figure 1(c). Silver paint was used to ensure low resistance contact between the wires’ upper and bottom ends to the inner wall of waveguide, which was found essential to generate the plasmonic effect and subsequent negative ε. The Q-band waveguide is calibrated to the two ends by the thru-reflect-line (TRL) method. The scatter parameters are measured using Agilent vector network analyzer. In figure 3, the measured scattering parameters, S21 and S12, of a 6 mm long TNIM composite at a bias field of 5.5 kOe are presented in comparison with the S21 of the copper wires. There is no transmission allowed by the copper wires as expected. Therefore, the passband allowed in S21 for the TNIM composite is the result of adding the ferrite slab. As analyzed in the theoretical calculation, the passband signals the occurring of negative n. The S12 near 40 GHz is weakened because of the nonreciprocal property of the Sc-BaM slab, where the copper wires and the ferrite interact destructively. The static bandwidth of the passband is approximately 5 GHz with >−20 dB transmission. The peak transmission is −15 dB 3

J. Phys. D: Appl. Phys. 42 (2009) 155005

P He et al

The major advantage of TNIMs is the frequency tunability of the passband. In figure 4(a), the tuning of the passband is demonstrated by varying the bias field H . The inset to figure 4(a) is a plot of the passband’s centre frequency versus H . The centre frequency shifts from 40.9 to 43.9 GHz with H changing from 4.0 to 7.0 kOe. The tuning is close to linear with a tuning factor of 1.0 GHz kOe−1 . In response to a field variation of 3 kOe, the dynamic bandwidth of this TNIM design is around 8 GHz, adding the 5 GHz static bandwidth and 3 GHz of centre frequency shift. Figure 4(b) shows the simulated results for comparison, which agree well with the experiments. The large insertion loss in the experiments is mainly because of the magnetic loss in the ferrite and the eddy current loss on the copper wires and silver paint. To overcome this drawback, the linewidth of the ferrite needs to be reduced. Finer fabricating and assembling technique needs to be explored in future.

Figure 3. Measured S21 and S12 of a 6.0 mm long TNIM composite containing a 1.0 mm thick Sc-BaM slab in comparison with the S21 of copper wires mounted in the centre of a Q-band rectangular waveguide.

3. Discussion In order to obtain negative n with acceptable insertion loss, both µ and ε need to be negative as illustrated in figure 2(c). For the TNIM composite, both of them are collective effects of all the elements including the ferrite slab, copper wires, Kapton substrates, Mylar spacer and the surrounding air. Because the dielectric constant of the ferrite is much higher comparing with the ones of Kapton and Mylar, the FVF plays an important role in realizing not only negative µ but also negative ε. In order to study the FVF in the TNIM composite, albeit qualitatively, another two TNIM composites have been measured consisting of 0.3 mm and 1.3 mm thick Sc-BaM slabs, respectively. In the 0.3 mm thick Sc-BaM slab case, weaker tunable passbands are observed as in figure 5(a). The peak transmission is only −22 dB and the static bandwidth is much narrowed down. The reduction in bandwidth coincides with the decrease in the negative µ region as the result of a smaller FVF. Therefore, in order to obtain negative µ, the FVF must be big enough. In the 1.3 mm thick Sc-BaM slab case, the passbands disappear completely. The whole composite behaves like a ferrite slab exhibiting FMR absorption peaks. The reason lies in the dielectric effect of the ferrite. It overwhelms the plasmonic wires. In another word, the effective ε of the composite turned positive. Therefore, in order to achieve negative ε and so negative n, the ferrite’s dielectric effect must be considered when determining the geometry of the periodic copper wires. The FVF cannot be too big, although it can ensure negative µ. And the carrier density in the copper wires must be sufficient so that the plasmonic effect can be strong enough to withstand the destructive dielectric effect of the ferrite.

Figure 4. (a) Measured and (b) simulated S21s of the TNIM composite containing a 1.0 mm thick Sc-BaM slab under bias fields of 5.0, 5.5 and 6.0 kOe, respectively. Inset: measured centre frequency of the TNIM passband versus the magnetic bias field.

near 40 GHz, where S12 shows a dip of −60 dB. The isolation is around 40 dB. Due to the existence of positive µ elements in the TNIM composite, the experimental µ is a collective effect and is different from the theoretically calculated one in figure 2(a). The bandwidth of the negative µ region depends upon the FVF of the Sc-BaM slab. And in all cases it should be smaller than the theoretic estimation of the one of the bulk Sc-BaM material as γ  · 2πMs ≈ 2.8 × 1.65 ≈ 4.6 GHz [19, 22].

4. Conclusions In summary, a simple structured TNIM composite consists of one Sc-BaM slab and two rows of periodic copper wires is demonstrated in Q-band waveguide. The theoretically calculated µ, ε, n and the FOM, together with the measured and simulated tunable passbands of the TNIM composite, are 4

J. Phys. D: Appl. Phys. 42 (2009) 155005

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Acknowledgment The authors gratefully acknowledge Anton L Geiler of the CM3IC and Zhuhua Cai of the Department of Chemical Engineering at Northeastern University for beneficial discussions and assistance.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]

Figure 5. Measured S21s of 6.0 mm long TNIM composites under bias fields of 5.0, 5.5 and 6.0 kOe. The contained Sc-BaM slab is (a) 0.3 mm and (b) 1.3 mm thick, respectively.

[16] [17] [18]

sufficient to explain the negative n effect. The effect of FVF of the Sc-BaM slab is studied to confirm the tradeoff between the desirable negative µ and the detrimental dielectric property of the ferrite. It gives out a qualitative design guide of future metamaterial works utilizing ferrites. In order to reduce the insertion loss and improve the FOM of the TNIM for device applications such as tunable phase shifter, smaller linewidth ferrite material with high frequency FMR and finer assembling technique will be needed.

[19] [20] [21] [22] [23]

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