PHYSICAL REVIEW B 84, 075140 (2011) Redshifting extraordinary transmission by simple inductance addition M. Beruete, 1,* M. Navarro-C´ ıa, 2 V. Torres, 1 and M. Sorolla 1 1 Millimeter and Terahertz Waves Laboratory, Universidad P´ ublica de Navarra, 31006 Pamplona, Spain 2 Experimental Solid State Group, Department of Physics, Imperial College London, London SW7 2AZ, UK (Received 7 April 2011; revised manuscript received 10 July 2011; published 12 August 2011) By interpreting the extraordinary transmission phenomenon on the basis of induced surface currents, the potential of engineering Rayleigh-Wood anomalies is shown, or more specifically, moving down the resonant peak away from the Rayleigh-Wood’s anomaly. The strategy presented here relies simply on enlarging the path explored by the induced-surface current so as to increase the inductance of the structure, shifting consequently the resonant peak to lower frequencies because of the 1/L 1/2 dependence. This brings about two important consequences: The aperture is more subwavelength, which opens novel possibilities for realistic metamaterials, and the phenomenon emerges away from the onset of higher-order modes. Numerical as well as experimental results are given at the millimeter-wave regime supporting the initial assumptions. DOI: 10.1103/PhysRevB.84.075140 PACS number(s): 42.79.Dj, 42.25.Fx, 84.30.Bv I. INTRODUCTION Extraordinary optical transmission is considered one of the milestones that have made the field of plasmonics take off in the 21st century. 1 The phenomenon of transmission through arrays of subwavelength apertures was briefly reported by Lewis and coworkers in the 1980s while working on the development of the near-field scanning optical miscrocopy. 2,3 However, it did not find notoriety, and the topic laid dormant for about 10 years, when Ebbessen et al. studied it thoroughly, emphasizing the enormous relevance of the periodic structure in the phenomenon of subwavelength transmission, coining the term Extraordinary Optical Transmission and contributing crucially to the development of plasmonics. 4 Within the past years an unexpected theoretical development as well as experimental efforts have helped to strengthen the evidence that the enhanced transmission observed in those two first experiments indeed has a resonant character, and it is founded on a first approach on a complex surface wave 5–7 (i.e., a leaky wave) excited at the interface of the metal and coupled evanescently through the hole to the output face. 8 In passing, this complex surface wave interacting with the periodic structure (by Bloch model) can be identified as the resonant discrete state in the Fano picture. 9 Because of its strong correlation with diffraction (it appears in nearby Rayleigh- Wood anomalies, and it can indeed be demonstrated that it is governed by the diffraction order (0, ±1) of the complex surface wave 6,7 ), it is extremely dispersive with the angle of incidence. 4,10–12 In order to overcome this aspect, researchers have proposed enhanced transmission by localized modes like longitudinal Fabry-Perot waveguide resonances. 13,14 However, this leads to thick metal layers. Other approaches rely on the excitation of transversal Fabry-Perot resonances (i.e., classical slot resonances 15,16 ) and observe a peak of transmission below Rayleigh-Wood’s anomaly. 17–20 Nevertheless, strictly speaking, such transversal-slot resonance cannot be rightfully considered subwavelength transmission, as it happens at exactly the waveguide cutoff, i.e., when the slot side is half-wavelength. 15,16 Since the experimental demonstration of the phenomenon at millimeter wavelengths where no plasmon effect can be claimed, 21 extraordinary transmission has been revisited via equivalent circuit models using lumped resistors, inductors, and capacitors, which is bringing about a powerful tool for analysis and design. 22,23 The electromagnetism of circuits discussed in Ref. 24, and more recently Ref. 25, provides electrical circuit descriptions for bulk plasmons, single-surface plasmons, and parallel-plate plasmons. Indeed, reinspection of the extraordinary transmission phenomenon from this well-developed electrical engineering perspective and the grating theory 26,27 allows us to propose an alternative route to overcome all the previously mentioned problems. The strategy shown here depends at heart on the understanding of the induced-surface current along the structure and displacement current, which constitute the ultimate origin of the induc- tance and capacitance composing the LC circuit modeling the enhanced transmission. 22,28 The induced-surface current propagates parallel to the incident electric field around the middle line of the unit cell in the metal region, and it goes round the aperture. The circuit is closed through displacement current lines connecting the upper- and lower-metal strips, giving rise to the capacitance. The path travelled by the surface current is directly linked to the inductance in such a way that the larger the path, the higher the inductance. 24,29 This quasiestatic interpretation allows us to foresee that circular apertures should exhibit the resonance peak at higher frequencies than rectangular apertures with the same height but different width. We exploit here up to the extreme this interpretation by creating a meander channel for the surface current in order to increase its travelled path, and thus, the inductance of the structure, pushing down the resonant peak, see Fig. 1(b). Similar approaches can be found in metamaterials to make the split-ring resonator exceptionally subwavelength. 30 II. EQUIVALENT CIRCUIT ANALYSIS The study begins with a theoretical analysis of the structure based on the equivalent circuit of Ref. 22. With this approach the periodic screen is reduced to a unit cell inside an artificial waveguide of electric and magnetic walls. 22,28 The excitation is done with a vertically polarized plane wave, which is related to the fundamental transversal electromagnetic mode of the waveguide. The response is obtained in terms of the aperture 075140-1 1098-0121/2011/84(7)/075140(5) ©2011 American Physical Society