## Abstract

We experimentally demonstrate a magnetically tunable left-handed metamaterial by introducing yttrium iron garnet rods into SRRs/wires array. It shows that the left-handed passband of the metamaterial can be continuously and reversibly adjusted by external dc applied magnetic fields. Retrieved effective parameters based on simulated scattering parameters show that tunable effective refraction index can be conveniently realized in a broad frequency range by changing the applied magnetic field. Different from those tuned by controlling the capacitance of equivalent LC circuit of SRR, this metamaterial is based on a mechanism of magnetically tuning the inductance via the active ambient effective permeability.

© 2008 Optical Society of America

## 1. Introduction

Metamaterial, especially left-handed metamaterial (LHM), which is founded on the concept of a material gaining its properties from structure rather than directly from composition, has opened a promising realm for physics as well as for engineering [1-3]. From the original work of negative refraction in microwave frequency [4] based on simultaneously negative effective permittivity and permeability [5, 6] to recent investigations on electromagnetic (EM) cloak [7], metamaterial has generated great interests with the potential to manipulate EM wave. However, the structure-determined property of metamaterial makes it generally an inactive device, which seems to be a bottleneck for practical applications. For instance, the reported cloak [7] is well functioned only in a faily narrow band or even at a single frequency.

Fortunately, however, considerable investigations have hitherto been devoted to the tunability of the metamaterial, especially to that of the LHM. It is known that an ideal single split ring resonator (SRR) can be seen as an equivalent LC circuit, with its resonance properties determined by the equivalent inductance and capacitance. By controlling the capacitance of the SRR, researchers have demonstrated the tunability of LHM in very different ways [8-17].

Conventional LHM uses SRRs to produce negative effective permeability over a particular frequency region and wire elements to produce negative effective permittivity in an overlapping frequency region [5, 6]. Therefore, despite the coupling effect which must be taken into account, it is true that the left-handed passband is primarily determined by the resonance frequency region of SRRs whenas the wires provide a negative permittivity “background”. Indicating a different mechanism of tunability from that of altering the equivalent capacitance, analyses on the correlation between equivalent inductance of the SRR and ambient permeability *µ _{am}* show that the resonance frequency of SRRs would increase with decreasing real part of

*µ*and vice versa, while the corresponding range of effective negative permeability would be tuned accordingly [18]. In this paper, by introducing yttrium iron garnet (YIG) rods into the SRRs/wires array and applying dc magnetic field, we experimentally demonstrate the tunable left-handed transmission properties of the LHM. From the simulated scattering parameters, we also study the tunable effective refraction indexes following the retrieval procedures [19].

_{am}It should be noted that there has been a controversy over the validity of this widely used retrieval procedure [20-22] which produces negative values for imaginary part of either permeability or permittivity. A common and simple method [21] to verify the causality condition of the retrieved effective parameters is to numerically calculate whether the corresponding energy absorption, which is a function of complex permeability and permittivity, is positive or not. In this publication, we concentrate on the tuning mechanism based on magnetically active inductance and its potential to realize desirable tuning properties of LHM. In addition, the causality condition of the retrieved effective parameters has been confirmed through the calculated positive energy absorption.

## 2. Experiments

Copper SRRs and wires are fabricated on opposite sides of the 0.9mm thick substrate (*ε*=4.4, loss tangent of 0.02) by shadow mask/etching technique. The copper thickness is 0.03 mm. The width and length of the wires are 0.4 mm and 10.1 mm, respectively. The outer ring length of the SRRs is 2.0 mm; and the linewidths of both rings are 0.2 mm. The gap in each ring is 0.4 mm; and the gap between the inner and outer rings is 0.2 mm. As shown in Fig. 1, the cells of copper SRRs/wires are arrayed to LHM with lattice constant l=5.0 mm; and then the square-sectioned YIG rods (with side length of a=0.8 mm, which is significantly smaller than the wavelength of the microwave; and longitudinal length b=10.0 mm), are introduced and placed at the symmetry axes of SRRs. Thereafter, we obtain the ferrite based tunable LHM with its unit cell composed of SRR/wire and corresponding YIG rod.

Saturation magnetization, linewidth and permittivity of the used YIG, which determine the magnetic permeability response of the ferrite under magnetic field, are 1700 Gs, 12 Oe and constant 14.7, respectively. As shown in Fig. 1, the ambient permeability *µ _{am}* would be determined by the magnetic effective medium composed of YIG rods and air. In presence of external dc magnetic field (H

_{0}) along the z axis,

*µ*would be a tensor with one dispersive element

_{am}*$\overline{\mu}$*, whose qualitative evolution could be obtained by computing the dependence of permeability of single YIG rod on magnetic field [23-28]. Accordingly, we qualitatively characterize the evolution of

_{x,am}=µ_{1x}+iµ_{2x}*$\overline{\mu}$*at 10.5 GHz, the resonance frequency of SRRs with YIG rods under zero magnetic field, as shown in Fig. 2(d) (the vertical axes are not labeled accordingly). Based on the evolution, Fig. 2(d) is divided into three regimes: “low” magnetic field, where

_{x,am}*µ*decreases from unity to lower values; “medium” magnetic field, where imaginary part of

_{1x}*$\overline{\mu}$*is found to play a significant role; and “high” magnetic field, where

_{x,am}*µ*decreases from higher values towards unity.

_{1x}With the sample (6×3 array) inserted into X-band rectangular waveguide WR90 with a cross section of 22.86×10.14 mm^{2}, the scattering parameters are measured by an HP8720ES network analyzer. In the presence of external dc magnetic fields (H0) (supplied by electromagnet) along the z axis, the tunable transmission coefficient (the S21 parameter) normalized against the transmission of the unloaded waveguide could be easily obtained. First of all, we observe the S21 parameter of the YIG rod array, and we find a very narrow forbidden-band that arises from the FMR and shifts to higher frequency with increasing magnetic field (not shown in the figures) [28]. We then measure the S21 parameters of the LHM sample with YIG rods under zero magnetic field (plotted as black solid lines in Fig. 2 for comparison). The left-handed passband (around 10.5 GHz) which occurs within the previously forbidden bands of the SRRs with YIG rods and wires array (as shown in the inset of Fig. 1) distinctly indicates the simultaneously negative *µ _{eff}* and

*ε*, i.e., the negative effective refraction index in this region [3]. Additionally, compared to that of sole wires, the plasma frequency decreases to about 13.0 GHz, which is attributed to the increase of ambient effective permittivity after the introduction of YIG rods. To clearly organize the documentation and create an opportunity for comparison among the results, we divide the transmission experiments into three sections (Fig. 2(a), (b) and (c)) based on the three regimes of

_{eff}*$\overline{\mu}$*evolution in Fig. 2(d).

_{x,am}First of all, it can be seen from Fig. 2(a) that, for “low” magnetic field region, as the applied dc magnetic field increases in the range of 0 to 1700 Oe, the left-handed passband keeps on shifting to higher frequency compared to that of the zero field. This indicates that the corresponding frequency range of negative refraction index could be effectively broadened towards higher frequency. Secondly, Fig. 2(b) shows that the left-handed passband of H_{0}=2700 Oe occurs in a region of relatively low frequency compared to that of the zero field; while passband corresponding to FMR emerges at about 12.0 GHz [23, 24]. And then, with continued increase of the applied magnetic field in “high” region, the left-handed passband continuously blueshifts and gradually returns to that of H_{0}=0 Oe. Additionally, the left-handed passband under “low” and “high” magnetic fields blueshift with gradually increasing and decreasing rates respectively, which indicates good accordance with the evolution of *µ _{1x}* in regime 1 and 3 of Fig. 2(d). On the other hand, after removal of the magnetic field, the passband would immediately return to its original state, i.e., the shift is completely continuous and reversible.

Compared to those under the “low” and “high” fields, the behavior of LHM with YIG rods under “medium” magnetic field between 1800 and 2700 Oe is much more complicated. The complexity arises from the strong coupling effects between LHM and FMR which occurs at the frequency range around 10.5 GHz (corresponding to the acutely varied *$\overline{\mu}$ _{x,am}* shown in regime 2 of Fig. 2(d)). Demonstrating the S21 parameter under H

_{0}=2300 Oe, Fig. 2(c) reveals that, except for the passband around 10.7 GHz originating from the coupling of FMR and wires [23, 24], an interesting observation of a pair of LHM’s passband indicates the complexity discussed above. We hereby propose a qualitative explanation of the appearance of this pair of passbands of LHM as follows: SRR cells located along the boundaries of the array actually ‘sense’ different ambient effective permeability from those in the center, and the large absolute value of

*µ*in this regime makes this difference more influential; and then the paired passband occurs in the corresponding ranges of simultaneously negative

_{1x}*µ*and

_{eff}*ε*. In addition, the difference between single YIG rod and the magnetic effective medium, in which the interactions among multiple rods must be taken into account of, causes the slightly different critical magnetic fields of regime 2 in Fig. 2(d) from those in the experiments [25, 26].

_{eff}## 3. Simulations

Although the transmission experiments intuitively show tunable properties of the left-handed passband, the effective parameters could distinctly reflect the intrinsic properties of this tunability. Nevertheless, because of the application of electromagnet in our experiment, it turns out difficult to obtain precise measurements of the transmission and reflection by repeatedly assembling the waveguides and matching loads. Accordingly, the effective parameters could not be retrieved from experimental data. Therefore, by using simulated scattering parameters of the model (for one unit cell length [19] with a cell dimension of 3.3 mm as shown in the inset of Fig. 3(d)) with geometrical and material parameter similar to that of the experiments, we investigate the tunable effective permeability *µ _{eff}*, permittivity

*ε*and refraction index

_{eff}*n*of LHM with YIG rods under different magnetic fields through the retrieval procedure [19].

_{eff}The retrieved *µ _{eff}* and

*ε*of the magnetically tunable LHMs corresponding to the “low” and “high” magnetic fields are shown in Fig. 3(a) and (b), and

_{eff}*n*is shown in (c). It seems to violate the positiveness of losses that the imaginary part of

_{eff}*ε*is negative even though those of

_{eff}*µ*and

_{eff}*n*are positive around the resonance frequency. Hereby we verify the causality condition of the retrieved effective parameters through calculation of the energy absorption (Im

_{eff}*(µ*[21]), as illustrated in the inset of (c). The real part of

_{eff})*|ε_{eff}|+Im(ε_{eff})*µ_{eff}|*n*is negative in the frequency range of the metamaterial resonance because of the simultaneously negative

_{eff}*µ*and

_{eff}*ε*. The frequency range of negative

_{eff}*n*is rather sensitive to the applied magnetic fields: f

_{eff}_{0}, the frequency related to the maximum of the passband blueshifts 260 MHz and redshifts 230 MHz for magnetic fields of 2000 Oe and 4000 Oe, respectively. This shifting behavior shown in Fig. 3(c) accords well with the prediction of

*µ*evolution and presents a physical essence of the passband shifting in the above transmission experiments. On the other hand, compared to that under zero magnetic field, real part of

_{1x}*n*shows larger negative amplitudes under “high” magnetic fields and smaller negative ones under “low” magnetic fields. Through analyses of the retrieved effective parameters show that, we found this phenomenon mainly arises from the rapid evolution of

_{eff}*ε*from a large negative value with increasing frequency in the concerned range [5]. Figure 3(c) also clearly shows that

_{eff}*n*for EM wave of certain frequency around passband could be tuned over a large range with appropriate applied magnetic fields. For instance, the real part of

_{eff}*n*corresponding to 10.2 GHz and 10.5 GHz alters in the ranges from -0.28 to -2.39 and from -0.81 to -1.65, respectively. With all dips of real parts in Fig. 3(c) included, Fig. 3(d) briefly summarizes the magnetically tuning effect of

_{eff}*n*with the dependence being the magnetic field.

_{eff}## 4. Conclusion

In summary, we experimentally demonstrate the magnetically tunable transmission behavior of hybrid LHMs composed of SRRs/wires and YIG rods. The fine tunability is clearly revealed by the distinct tuning effect even under very low magnetic field (e.g., 1000 Oe) when the frequency of FMR is far beyond the range of our concern. This is attributed to the high sensitivity of the equivalent circuit’s inductance to the ambient permeability. By using the simulated scattering parameters, we also show the broad tunability of the negative effective refraction index. It reveals that the tunable passband and negative effective refraction index of the metamaterial can be conveniently realized by altering the applied magnetic field. In addition, the causality condition of the retrieved effective parameters has been verified by numerical calculation of the energy absorption. This tunability would be useful for the construction of novel devices, e.g. broadband perfect lens.

## Acknowledgments

This work is supported by the National Science Foundation of China under Grant Nos. 50425204, 50572043, 50632030, and 60608016, and by the Postdoctoral Science Foundation under Grant No. 20060390043.

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