LETTERS PUBLISHED ONLINE: 29 JANUARY 2012 | DOI: 10.1038/NMAT3230 Experimental realization of optical lumped nanocircuits at infrared wavelengths Yong Sun 1 , Brian Edwards 1 , Andrea Alù 1,2 and Nader Engheta 1 * The integration of radiofrequency electronic methodologies on micro- as well as nanoscale platforms is crucial for information processing and data-storage technologies 1–3 . In electronics, radiofrequency signals are controlled and manipulated by ‘lumped’ circuit elements, such as resistors, inductors and capacitors. In earlier work 4,5 , we theoretically proposed that optical nanostructures, when properly designed and judiciously arranged, could behave as nanoscale lumped circuit elements—but at optical frequencies. Here, for the first time we experimentally demonstrate a two-dimensional optical nanocircuit at mid-infrared wavelengths. With the guidance of circuit theory, we design and fabricate arrays of Si 3 N 4 nanorods with specific deep subwavelength cross- sections, quantitatively evaluate their equivalent impedance as lumped circuit elements in the mid-infrared regime, and by Fourier transform infrared spectroscopy show that these nanostructures can indeed function as two-dimensional optical lumped circuit elements. We further show that the connections among nanocircuit elements, in particular whether they are in series or in parallel combination, can be controlled by the polarization of impinging optical signals, realizing the notion of ‘stereo-circuitry’ in metatronics—metamaterials- inspired optical circuitry. One of the main factors behind the success of electronics is our ability to control and tailor, both temporally and spatially, the motion of charged particles in electronic circuits using electric and/or magnetic fields. Moreover, the notion of lumped elements, such as resistors, capacitors, inductors and so on, and the concept of a circuit as a collection of properly arranged and suitably connected lumped elements in radiofrequency, has facilitated the modelling and enabled modularity in designing complex circuit architectures with unprecedented functionalities. In our previous work, we have extended and applied the concept of lumped circuit elements and its corresponding mathematical tools to higher frequencies, for example terahertz, infrared and visible frequencies 4,5 . More specifically, we have proposed nanostructures exposed to optical signals to function as lumped circuit elements. Historically, the basic ‘alphabets’ of nano-optics and nanophotonics have been considered to be waveguides, gratings and diffractive elements 6 . However, our theoretical works have predicted an entirely new set of ‘alphabets’ for the field. We have put forward a circuit paradigm at optical frequencies, based primarily on the use of optical displacement field current ∂ D/∂ t , instead of conduction current J , and have theoretically shown that nanoparticles, when designed properly, would indeed act as lumped circuit elements in an optical field 4,5,7–10 . This is consistent with the dispersion properties of plasmonic materials 11 and surface plasmon polaritons at optical frequencies 12 . A collection of such nanoparticles may then form a ‘circuit of light’, which, 1 Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA, 2 Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, Texas 78712, USA. *e-mail:engheta@ee.upenn.edu. when excited by an optical signal, shows local electric fields and displacement currents analogous to voltage and current distributions in conventional radiofrequency circuits 5,7–10 . We have named the new circuit paradigm ‘metatronics’, as metamaterial- inspired optical circuitry 13 . In this work, we report the first experimental realization of a two-dimensional optical circuit at infrared wavelengths. As our theoretical study has shown, a nanostructure may function as a lumped circuit element, such as a nanocapacitor, a nanoinductor or a nanoresistor, provided that its permittivity satisfies Re(ε) > 0, Re(ε) < 0 or Im(ε)  = 0, respectively. A careful design of nanostruc- tures, as shown in Fig. 1, would then be ideal for verifying the optical circuit concept. In this figure, the optical circuit consists of an array of deeply subwavelength dielectric nanorods, completely suspended in air. Here, the air gaps (Re(ε) > 0, Im(ε) = 0) between neighbour- ing nanorods may be considered as lossless nanocapacitors, whereas the nanorods with permittivity Re(ε) < 0, Im(ε) = 0 in a certain wavelength regime (and Re(ε) > 0, Im(ε) = 0 at other wavelengths) as nanoinductors in parallel with nanoresistors (and nanocapacitors in parallel with nanoresistors). Within this design, all basic lumped circuit elements are presented, and the optical circuit concept may be tested in one single experimental effort. It must be emphasized that our goal here is not to merely model nanostructures as circuit elements, which has been done before 14–18 . Instead, we are more interested in realizing optical nanocircuits with desired functionalities by tailoring nanoparticles and their relative arrangement, as we would do in a low-frequency electronic circuit. Although only a few nanoparticles connected to one another may provide a more general platform to illustrate the optical circuit concept, the experimental realization of such three-dimensional arrangements is challenging at present. For this reason, we focus here on a periodic array of dielectric nanorods— the two-dimensional version of such an optical circuit. This makes the fabrication and characterization of such a device achievable, yet retains all the relevant physics. The permittivity requirements for dielectric nanorods in Fig. 1 have led us to employ low-stress silicon nitride (LS Si 3 N 4 ) grown by the low-pressure chemical vapour deposition method. LS Si 3 N 4 has long been studied for a variety of applications 19 and it exhibits an intrinsic resonance near 12 μm (refs 20,21). It is interesting to note that, in most metamaterial-related applications where negative real part of permittivity is required 22 , extremely low material losses are desirable to achieve metamaterial effects such as superlensing 23 or extreme field concentration 24 . Here, however, our goal is to experimentally verify the optical circuit concept, so the presence of material losses is not a concern as long as the permittivity of the nanorods satisfies Re(ε) < 0, Im(ε) = 0 in a certain wavelength regime, and Re(ε) > 0, Im(ε) = 0 at other wavelengths. The losses of LS Si 3 N 4 can be simply associated with nanoresistors. 208 NATURE MATERIALS | VOL 11 | MARCH 2012 | www.nature.com/naturematerials © 2012 Macmillan Publishers Limited. All rights reserved