## Abstract

We demonstrate a two-handed metamaterial (THM), composed of highly symmetric three-layered structures operated at normal incidence. Not only does the THM exhibit two distinct allowed bands with right-handed and left-handed electromagnetic responses, but posses a further advantage of being independent to the polarizations of external excitations. In addition, the THM automatically matches the wave impedance in free space, leading to maximum transmittances about 0.8 dB in the left-handed band and almost 0 dB in the right-handed band, respectively. Such a THM can be employed for diverse electromagnetic devices including dual-band bandpass filters, ultra-wide bandpass filters and superlenses.

© 2008 Optical Society of America

## 1. Introduction

It is an interesting observation that the right-handed systems appear to prevail in nature- for example, the major population of right-handed people, the right-handed helix of deoxyribonucleic acids (DNA) traced by the sugar-phosphate backbone [1] and certainly, electromagnetic (EM) responses of materials in which electric field **E**, magnetic field **H**, and wave vector **k** form a right-handed triplet of vectors. Although rare, the left-handed systems do exist in nature such as left-handed people and left-handed helical DNAs [2], the lefthanded EM response in naturally occurring materials remains missing. Recently, a new class of artificially constructed sub-wavelength structures termed as metamaterials [3], possesses unprecedented EM properties to revise new chapters in electromagnetics. One revolutionary example is a negative-refractive-index medium [4–7], whose electric permittivity and magnetic permeability are negative simultaneously so that the relationship among **E**, **H** and **k** turns to be left-handed, leading to striking EM behaviors like inverse Snell’s law [7, 8], inverse Doppler shift [9], inverse Cerenkov effect [10], and superlensing effect [11, 12]. More interestingly, naturally occurring systems in fact allow the co-existence of both right-handed and left-handed sets (e.g., clearly observed in human beings and DNAs). As a consequence, to further enrich the possible EM properties of materials, in this letter we present a highly symmetric two-handed metamaterial (THM) to exhibit two distinct sets of EM responses. The designed THM and its corresponding geometric parameters are detailed in Fig. 1, presenting a four-fold symmetric periodic array composed of two metal discs sandwiching a dielectric layer to eventually form a continuous structure connected by very narrow metal “necks” with one another.

In accordance with the dynamic Maxwell’s equations, as applying external excitations normal to the THM (i.e., along z-axis), the time-varying magnetic flux oscillating along the yaxis introduces antiparallel surface currents vertically (along the x-axis) within the two metal plates against the changing magnetic flux [13] and then results in artificial magnetic dipole moments oscillating along the y-axis. Established from the induced antiparallel surface currents, an *L-C* resonance occurs where the capacitance comes from the opposite charges in these two insulated metal plates and the inductance comes from the entire metals themselves, giving rise to a negative effective permeability (*µ _{eff}*) when such a magnetic response turns to be out-of-phase at frequencies just above the resonant frequency. Meanwhile, the metal stripes along E-field also contribute an additional shunt inductance, providing a negative effective permittivity (

*ε*) in the THM [14]. As a result, the THM exhibits both negative

_{eff}*µ*and

_{eff}*ε*at the same time to introduce the left-handed response (e.g., negative refraction) [3, 6]. On the other hand, once this sandwiched structure is at its off-resonance frequency, it exhibits a positive refractive index to behave the conventional right-handed response.

_{eff}## 2. The measurement and simulation

The designed THM was fabricated into a 44×28 unit cell sample (457 mm×305 mm×0.79 mm) by means of commercial printed-circuit-board technology with 17-µm-thick copper plates and a Rogers TMM4 board with a relative dielectric constant of 4.5. Besides, the fabricated samples were characterized by using an *E8363B PNA* series network analyzer connecting with an *HP 8349B* amplifier and standard gain horns to measure both the transmitted magnitude (i.e., S21 parameter) and the phase of transmittance at normal incidence scanning from 8 to 18 GHz. As shown in Fig. 2(a), there appear two profound allowed bands to evidence the two-handed electromagnetic responses as expected from the above discussion– the left-handed EM one is sharp with a minimum loss of 0.5 dB at 11.2 GHz due to the intrinsic loss at resonance, the right-handed other appears broad with nearly no loss at 15.7 GHz, and both the measurements are numerically verified by a commercial electromagnetic solver (*CST Microwave studio*) presented in black solid/dash lines (Fig. 2(a)). Furthermore, we conduct a series of transmittance measurements under normal incidence by rotating the THM from 0 to 90 degrees with the increment of 15 degrees with respect to the electric field. All the spectra at four distinct angles in Fig. 2 reveal similar behaviors, indicating that our designed four-fold symmetric THM is independent from all linear polarizations of incident electromagnetic waves. These characteristics of normal-incidence and polarization-independence operations are very encouraging for the future applications compared with other metamaterials that prefer grazing-angle and/or other polarized excitations [6, 15–19], particularly for higher frequency applications beyond infrared regions in which typically the size of structure is submicron-scale not to allow large incident angles.

Remind that the key to cultivate the left-handed response is the induced antiparallel surface currents within two insulated copper plates aforementioned [13]. To verify this point a controlled sample was fabricated by removing a single layer of copper plates from the original THM. Figure 2(b) shows both the measured results and the numerical simulations of the single-layer system about two polarizations at 0 and 45 degrees, respectively. Without the antiparallel surface currents in the case of a single-plate sample, it is rational to observe the survival of the right-handed peak alone, but the left-handed response disappears because neither artificial magnetic dipole nor *L-C* resonance is created. Consequently, we further measure the phase changes during the transmittance measurements. As shown in Fig. 2(c), for the sharp peak at 11 GHz a significant phase change occurs due to the *L-C* resonance, for all polarizations. In contrast to the sharp peak, however, there is no sudden phase change for the broad allowed band centered at 15.7 GHz in Fig. 2(c). Finally, the measured phase change of the single-metal-layer structure displays no sudden phase change either within the entire scanning range as plotted by two dash lines as shown in Fig. 2(c).

## 3. The nature of the THM

The nature of these two allowed bands in Fig. 2 can be further elucidated. Firstly we numerically simulate the s-parameters of both reflectance (S11) and transmittance (S21), then calculate the refractive index and the wave impedance of the metamaterial from the simulated s-parameters, and eventually retrieve *µ _{eff}* (

*ω*) (blue curve) and

*ε*(

_{eff}*ω*) (red curve) as plotted in Fig. 3. Be specific, for the left-handed allowed band the resonating behaviors of both

*µ*(

_{eff}*ω*) and

*ε*(

_{eff}*ω*) in the THM can be expressed in the following equations [20–23],

where *ω _{M0}* represents the resonant frequencies of the magnetic dipole and

*ω*’

_{P}are the new effective plasma frequencies [23–25] of the metallic structures, Γ

_{M}and Γ

_{E}the resistive losses in the resonating structures, respectively. These two equations depict the artificial magnetic dipoles stemming from the induced antiparallel surface currents within the paired circular metal discs, functioning as Lorentz oscillators to own negative values of

*µ*(

_{eff}*ω*) between

*ω*and

_{M0}*ω*. Furthermore, in the THM the dielectric apertures adjacent to the copper plates exactly form slot arrays, serving as a typical frequency-selective-surface [26] that can be excited by the magnetic field of incident EM waves to exhibit the right-handed allowed band as shown in Fig. 2(a).

_{MP}As a result, in the region between *ω _{M0}* and

*ω*, the coexistence of the double negative

_{MP}*µ*(

_{eff}*ω*) and

*ε*(

_{eff}*ω*) indicates that the THM embraces the extraordinary property of negative refractive indices (i.e., left-handed response) to allow a passband. Note that the retrieved effective refractive index shown in the inset of Fig. 3(a) does evidence profound negative valus in such high frequencies. In contrast, in the region between

*ω*’

_{P}and

*ω*, the values of the

_{E0}*µ*(

_{eff}*ω*) and

*ε*(

_{eff}*ω*) now become both positive at their off-resonance frequencies, so that the refractive indices turn to a real positive number to permit the other passband with the righthanded response. Similarly, we also calculate the material parameters of the controlled singlelayered structures. As shown in Fig. 3(b), there appears only one allowed band for which all

*µ*(

_{eff}*ω*),

*ε*(

_{eff}*ω*), and

*n*(

*ω*) are positive to present a conventional right-handed response.

## 4. Spontaneous match of wave impedance

Another noticeable property from the THM is that it can spontaneously match the wave impedance, *$\tilde{\eta}$*=*η*′+*iη*″(*η*′ and *η*″ are real and imaginary parts of complex wave impedance *$\tilde{\eta}$*, respectivley), in free space in both the left- and right-handed allowed bands. In order to match the wave impedance, both the real and immaginary parts of permeability and permittivity should be considered together. In Fig. 3(a), the two crossovers indicated by the black arrows reveal the same values between the real parts of *µ _{eff}*(

*ω*) and

*ε*(

_{eff}*ω*) from the THM and meanwhile the imaginary parts approximate zeros at these two corresponding frequencies, leading to a unity of

*η*′ and a negligible

*η*″. Therefore, as EM-waves propagate across the interface between free space and the THM, a quasi wave impedance match occurs and further diminishes the reflectance,

*R(ω)*, referring to the Fresnel equation [27] in normal incidence as below,

where *η _{0}* and

*$\tilde{\eta}$*denote the wave impedance in free space and the THM, respectively. Once the reflectance is eliminated, the transmittance,

_{THM}*T(ω)*, across the interface between the THM and air can be maximized and only determined by the absorbance,

*A(ω)*, of the THM, according to the following relation [28],

As a result, by matching the wave impedance, the THM can be employed to considerably depress the unwanted reflectance loss, resulting in higher transmission efficiency. For example, the maximum transmittance is about -0.5 dB at 11.2 GHz in the left-handed band and almost 0 dB at 15.8 GHz in the right-handed band, respectively.

Actually the transmittance from the THM in the left-handed allowed band originated from the resonance is slightly lower than that in the right-handed allowed band. It is due to the larger values of imaginary parts in the left-handed band rather than the right-handed. Besides, there are other crosssovers not indicated by arrows in Fig. 3(a), where the imaginary parts of *µ _{eff}*(

*ω*) and

*ε*(

_{eff}*ω*) are much different with each other at these frequencies, eventually causing the impedance mismatch between vacuum and the THM regardless of the same values between.the real parts.

## 5. Conclusion

This work provides a highly symmetric THM to exhibit two distinct sets of left-handed and right-handed electromagnetic responses, showing two highly transparent bands in microwave frequencies proved by both experimental measurements and numerical simulations. The THM can be operated under normal-incidence excitations, its operation frequencies are scalable, its fabrication only requires a single lithographic step, and all these beneficial characteristics aforementioned are in particular critical for photonic devices. In addition, the THM responds independently to all polarizations, and spontaneously matches the surface impedance to accomplish excellent transmission properties, promising its ready and steady implementation for diverse electromagnetic devices, including dual-band pass filters, ultra-wide bandpass filters and superlenses.

## Acknowledgments

The authors gratefully acknowledge the financial support from National Science Council (NSC 95-2112-M-007 -048 MY3) and the National Nano Device Laboratories (NDL-94SC142) for this study.

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