A highly symmetric two-handed metamaterial spontaneously matching the wave impedance Yi- Ju Chiang1 and Ta-Jen Yen1,2† 1 Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan, R.O.C. 2 Institute of NanoEngineering and MicroSystems, National Tsing Hua University, 101, Section 2, Kuang Fu Road, Hsinchu 30013, Taiwan, R.O.C. † E-mail: [email protected]; Tel: 886-3-5742174; Fax: 886-3-5722366 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. 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Although rare, the left-handed systems do exist in nature such as left-handed people and left-handed helical DNAs [2], the left- handed 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 y- axis 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 (μeff) when such a magnetic response turns to be out-of-phase at frequencies just above the resonant frequency. Meanwhile, the metal stripes #97050 - $15.00 USD Received 5 Jun 2008; revised 17 Jul 2008; accepted 19 Jul 2008; published 7 Aug 2008 (C) 2008 OSA 18 August 2008 / Vol. 16, No. 17 / OPTICS EXPRESS 12765 Fig. 1. The fabricated THM (right panel) and the perspective view of a unit cell (left panel). The THM shows a four-fold symmetric sandwiched structure, composed of 17-m-thick copper plates and a Rogers TMM4 board with the relative dielectric constant of 4.5. The geometric parameters of the THM are as following: ax=ay=9.8 mm, r=4.75 mm, d= 0.7874 mm, h=0.30 mm, and w=0.28 mm. along E-field also contribute an additional shunt inductance, providing a negative effective permittivity (εeff) in the THM [14]. As a result, the THM exhibits both negative μeff and εeff 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.