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We propose a new approach to control the propagation of electromagnetic (EM) wave with certain polarization by a split ring resonator (SRR) array. Interactions between SRR and the EM wave in the array are analyzed and it is found that the H field is always perpendicular to the SRR plane around the magnetic resonance frequency. Based on this property, a semicircular waveguide is designed to realize a 180 degrees bending with high performance. The structure of this approach is simple and feasible, providing an alternative way to construct bending waveguide with low loss.
©2010 Optical Society of America
1. Introduction
Since the split ring resonator (SRR) was first proposed as a structure unit of left-handed media by Pendry [1], it has been widely used in various metamaterial to achieve negative refraction [2–5]. At the resonance frequency range, SRR shows some exceptional properties such as negative permeability [6], high resonance loss and even negative permittivity [7]. Various derivations of the SRR are applied to fabricate zero index material [8], invisible cloak [9], permeability tunable devices [10] and realize perfect wave absorber [11–13] based on these properties. However, up till now, rarely investigation on change of the EM field of a rotating SRR around the magnetic resonance frequency is reported [14]. In this work, we analyzed the interactions between SRR and a TM wave whose H field penetrate through the loop of the SRR. It is found that the H field induced by magnetic resonance is always perpendicular to the SRR plane even if the SRR is rotated by a certain angle. Based on this property, the propagation of the EM wave can be guided by a series of SRRs. Comparing with established designs [15,16], this approach provides a simple and effective method for realization of bent waveguide devices with high transmittance.
2. Theory
Considering a TM electromagnetic wave whose H field penetrates through the loop of a SRR, a ring current would be induced in the SRR when the beam encounters the SRR. Figure 1 depicts the response of a SRR to the TM wave. The current vanishes at the proximity of the gaps and rises to maximum at the middle of the opposite side. This current also generates H field around the SRR itself. The total magnetic field of the SRR is a superposition of the induced H field and the TM wave. At the frequency of magnetic resonance, the induced H field is so large that it can be treated as the total magnetic field whose direction is perpendicular to the SRR plane. If we rotate the SRR around the z axis by an angle of θ (Fig. 2(a) ), it seems that the magnetic flux decreases because the H field of the TM wave does not penetrate through the SRR loops perpendicularly, which will weaken the magnetic resonance. However, the magnetic resonance does not reduce sharply until SRR loop is almost perpendicular to the wave propagation. As a result, the direction of the total H field is always along the normal of the SRR plane, rotating with the SRR to a relatively large angle.
Fig. 1 Interactions between a TM wave and a SRR. Ring currents are excited by the H field penetrate through the SRR loops and then generate an induced H field.
Fig. 2 a. The wave vector k is deflected when the SRR is rotated by an angle of θ. The H field is always perpendicular to the SRR plane, and the rotation does not affect E field. Thus, the wave vector k will rotate with the SRR by an angle of θ. b. The typical size of the SRR unit used in the simulations in this paper.
3. Simulation
We use CST 5 Microwave Studio to compute the H field of this system with a rotating SRR of different angles. Figure 2(b) illustrates the typical size of the SRR and the simulation results at the resonance frequency of 14.2 GHz are shown in Fig. 3 . The arrows in Fig. 3 indicate the direction of the total H field when a TM wave passes through a SRR. The H field still penetrates through the SRR loops perpendicularly when the rotation angle is smaller than 60 degrees. For rotation angles larger than 60 degrees, the initially induced H field is not strong enough with respect to the H field of the TM wave because too little H field penetrates through the loop. When the rotation angle approximates to 90 degrees, the SRR loop is almost parallel to the H field and the magnetic flux is close to zero. Thus, no magnetic resonance occurs and the SRR is transparent to the TM wave (Fig. 3(f)). On the other hand, The SRR is a symmetry structure to the E field of the TM wave and the electric resonance is rather weak that can be ignored during the rotation. Therefore, the total H field is rotating with rotation of the SRR, keeping perpendicular to the SRR plane with a maximum of 60 degrees. There is little interaction between E field and SRR and no change on the direction of the E vector. According to right hand rule, the wave vector k will also rotate and keep parallel to the plane of the SRR.
Fig. 3 H field distribution at resonance frequency of 14.2 GHz with different rotation angles of the SRR. In our simulation, the distance to the SRR from each port is 20 mm. The unit of the scale is A/m.
We also obtain the transmission properties of the SRR during the rotation. As shown in Fig. 4 , there is a bandstop at the resonance frequency which can be attributed to a high reflection of the negative permeability of the SRR. The transmittance of the bandstop begins to rise until the rotation angle is larger than the 60 degrees and returns to 100% when the rotation angle is 90 degrees. This result is in agreement with the simulation results of H field. Moreover, the inset of Fig. 4 shows that the resonance frequency is nearly fixed despite of the rotation.
Fig. 4 The S21 spectrum of the SRR system at frequency range of 10~20 GHz. SRR is rotated from 10° to 90°.
Hence, we can conclude that the rotating SRR is able to align the wave vector k of the TM wave along the plane of it at the resonance frequency and this resonance frequency is almost constant during the rotation. Based on this principle, a trajectory consisting of a series of SRRs can conduct the propagation of the TM wave. In order to assure a high transmittance, the frequencies a little lower than the resonance frequency are considered, where the magnetic resonance is still strong enough to align the TM wave, and allow a relatively large transmittance. Figure 5 shows the H field distribution of the system at the frequency of 13.8 GHz. This simulation results is almost the same with that at the resonance frequency.
Fig. 5 H field distribution at resonance frequency of 13.8 GHz with different rotation angles of the SRR. This result is similar to that at the resonance frequency. The unit of the scale is A/m.
To investigate the feasibility and performance on guiding a beam, we design a waveguide with an inner radius of 20 mm, as shown in Fig. 6(a) . The waveguide is composed by 13 concentric semicircular SRR arrays with the same size of the SRR in Fig. 2. The distance between two SRRs arrays is 1.5 mm, which is short enough to cause a coupling effect in each two SRRs and then enhance the magnetic resonance. An EM wave was first fed into a planar waveguide then came into our waveguide, in order to achieve a mode equivalent to a plane wave. The transmission property can be obtained by computing the transmittance of Port 2. We also computed the transmittance of a rectangular SRR arrays with same parameters in the semicircular waveguide to determine the resonance region, which is corresponding to a bandstop due to the negative permeability. Both transmittance spectra are computed by commercial software of HFSS 11 based on finite element method, and the results are illustrated in Fig. 6(b). The bandstop of the two spectra is not identical due to the lattice difference brought by the arc-shape. According to Fig. 6(b), the frequency point (11.6GHz) where transmittance is highest is chosen to be the operating frequency. Moreover, the operating frequency 11.6 GHz is just the falling edge of the bandstop of the blue curve in Fig. 6(b), at which the SRRs keep rotating H field ability and ensure a high transmittance.
Fig. 6 (a) The layout of the performance test for the semicircle waveguide. An EM wave with E field polarized along z axis is fed into a planar waveguide with absorbers along two sides first to form a TM with single mode. Then, TM wave transmits through the semicircle waveguide consisted of SRRs arrays (the yellow section) and is collected by port 2 after 180 degrees’ bending. (b) The transmission spectrum for the, rectangular SRRs arrays (blue curve) and bent waveguide (red curve).
The simulation result of the magnitude of E field vector distribution at 11.6 GHz is illustrated in Fig. 7(a) . The beam is deflecting with the rotation of SRR and propagating in the semicircle waveguide consciously. The wave front is parallel to the tangential direction along the whole arc-shaped propagation route. There is no reflection occurs between the interface of metamaterial and the air, which can avoid the bending loss. Figure 7(b) shows the H vector of the semicircular waveguide. The direction of the H vector is rotating with the SRR, keeping perpendicular to the SRR at any segment of the waveguide, as shown in the inset of the Fig. 7(b). Thus, the wave vector is rectified by the SRR to the tangent of the semicircular all the time and the control of the wave propagation is realized. Accordingly, we can make a wave propagate in an arbitrary trajectory by design a SRR arrays with a special shape. The arc-shape, however, may bring a little variance on the resonance frequency of SRRs at different radius, which may depress the guiding performance. A more rational disposal of the SRR in the arc-shape based on precise computation may reduce the loss and improve the transmittance furthermore.
Fig. 7 (a) The magnitude of E field distribution for the semicircle waveguide at the frequency of 11.6 GHz. (b) the H vector distribution in the waveguide. The inset in Fig. 7(b) shows a magnification of the H vector around two SRRs. The H field lays normal to the SRR plane and the wave vector k is along the SRR plane.
4. Conclusion
In conclusion, propagation direction of a TM wave can be controlled by the orientation of a SRR when the beam passes through the SRR. Strong magnetic resonance excited in SRR aligns the H field to the normal of the SRR plane and then change the direction of the wave vector. Thus, we can make a wave propagate in an arbitrary trajectory. Waveguide consisted of SRRs arrays can realize a 180 degrees’ bending by this theory at certain frequency. This approach provides an alternative and feasible way for constructing bent waveguide with low loss and other potential applications in microwave devices.
Acknowledgements
This work is supported by the National Science Foundation of China under Grant Nos. 90922025, 50632030, 50921061, and 10774087.
References and links
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