Nanocircuit Elements Research Articles

Third-order nanocircuit elements for neuromorphic engineering.

Current hardware approaches to biomimetic or neuromorphic artificial intelligence rely on elaborate transistor circuits to simulate biological functions. However, these can instead be more faithfully emulated by higher-order circuit elements that naturally express neuromorphic nonlinear dynamics1-4. Generating neuromorphic action potentials in a circuit element theoretically requires a minimum of third-order complexity (for example, three dynamical electrophysical processes)5, but there have been few examples of second-order neuromorphic elements, and no previous demonstration of any isolated third-order element6-8. Using both experiments and modelling, here we show how multiple electrophysical processes-including Mott transition dynamics-form a nanoscale third-order circuit element. We demonstrate simple transistorless networks of third-order elements that perform Boolean operations and find analogue solutions to a computationally hard graph-partitioning problem. This work paves a way towards very compact and densely functional neuromorphic computing primitives, and energy-efficient validation of neuroscientific models.

Coexistence of two graphene-induced modulation effects on surface plasmons in hybrid graphene plasmonic nanostructures.

Integrating gate-tunable graphene with plasmonic nanostructures or metamaterials offers a great potential in achieving dynamic control of plasmonic response. While remarkable progress has been made in realizing efficient graphene-induced modulations of plasmon resonances, a full picture of graphene-plasmon interactions and the consequent deep understanding on graphene-enabled tuning mechanism remain largely unexplored. Here, we theoretically identify, for the first time, two distinct modulation effects that can coexist in graphene-based plasmonic nanostructure: graphene can influence the plasmon resonances by either acting as equivalent nanocircuit elements or effectively altering their excitation environment, leading to totally different tuning behaviors. A general dependency of tuning features on the graphene-induced impedance, irrespective of structure geometries, is established when graphene serves as nanocircuit elements. We demonstrate that these two modulation effects can be dynamically controlled by appropriately integrating graphene with plasmonic nanostructures, which provide an active window for efficient modulation of surface plasmons. Our findings may pave the way towards realizing dynamic control of plasmonic response, which holds great potential applications in graphene-based active nanoplasmonic devices.

Nonlinear nanocircuitry based on quantum tunneling effects

Abstract

Quantum Nonreciprocity of Nanoscale Antenna Arrays in Timed Dicke States

We predict a linear nonreciprocal effect that is based on the timed Dicke states in an ensemble of dipole-dipole coupled oscillators. This effect is examined on a nanoscale antenna array comprising two-level identical emitters. The studied nonreciprocity, which has no analogs in classical antennas, manifests itself in strong characteristic asymmetry of the radiation pattern, even for a single-photon laser pumping. Promising applications of our results for remotely tunable nanoantennas and nanocircuit elements are discussed.

New Models Designed for Nanocircuit Elements for Nanotransmission Line

New Models Designed for Nanocircuit Elements for Nanotransmission Line

Tunable circuit elements at optical frequencies using gyroelectric nanoparticles

This paper addresses the possibility of realizing fixed as well as variable electric circuit elements at infrared and visible frequencies using a gyroelectric nanosphere biased with a static magnetic field. With a proper choice of port designation, one might exercise field control over the impedance offered by the nanoparticle. It is shown that although the driving-point impedance looking into a pair of terminals chosen in some directions remains fixed, it can vary significantly in other directions with respect to the magnetic field biasing the particle. When combined with other isotropic nanocircuit elements, more complex tunable nanocircuits can be designed. This paves the way for adaptive nanosystems for smarter applications.

Nanocircuit Loading of Plasmonic Waveguides

We apply the optical nanocircuit concepts to model and design optical nanofilters in realistic plasmonic waveguides of different nature, including strips and groove waveguides. The nanocircuit elements are designed to fit the waveguide geometry, and its equivalent impedance is analytically calculated by substituting the role of the conduction current with displacement current. The effect of plasmonic waveguide walls is rigorously modeled in terms of an extra nanocircuit loading that is included in our model. We show via numerical results that the nanocircuit approach may be effectively applied to the design of nanofilters, analogous to familiar concepts at radio-frequencies.

From RF Circuits to Optical Nanocircuits

This article presents a brief review of the concept of optical metatronics, i.e., the metamaterial-inspired optical nanocircuitry that my group has introduced and developed in recent years. In this paradigm, deeply subwavelength nanostructures, when judiciously designed and properly arranged, may act as optical lumped nanocircuit elements, thus extending the concept of circuit elements from the RF and microwave into the optical frequencies. Collections of such optical lumped elements provide functionalities that resemble their RF circuit counterparts while operating with light. Such metatronic circuitry has the potential to provide a new platform for optical information processing at the nanoscale, with ultrafast, low-power, high-bandwidth, and deeply miniaturized operation.

Experimental realization of optical lumped nanocircuits at infrared wavelengths

The integration of radiofrequency electronic methodologies on micro- as well as nanoscale platforms is crucial for information processing and data-storage technologies. In electronics, radiofrequency signals are controlled and manipulated by 'lumped' circuit elements, such as resistors, inductors and capacitors. In earlier work, 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 Si3N4 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.

Optical Metamaterials Based on Optical Nanocircuits

Here we review the application of the optical nanocircuit paradigm to design and characterize metamaterials with exotic optical properties. The interaction of small nanoparticles with light is equivalently described in terms of optical lumped circuit elements, which relate the equivalent optical voltage across the particles and the optical displacement field current circulating through them. This equivalence goes beyond a simple description of the interaction of an individual nanoparticle with the impinging optical signal, as collections of closely spaced particles may be tailored as complex nanocircuit connections with specific optical response. Inspired by the fascinating concept and potentials of transmission-line metamaterials at microwaves, in which networks of lumped radio-frequency (RF) and microwave circuit elements may provide exotic metamaterial properties, in this paper, we review and discuss how analogous concepts may be translated to optical frequencies at the nanoscale, by applying the nanocircuit paradigm. We present several designs of 0-D, 1-D, 2-D, and 3-D arrays of nanoparticles supporting subwavelength resonances, negative-index propagation, and other exotic optical effects, achieved by suitably combining and connecting nanoparticles operating as optical lumped nanocircuit elements. Fascinating applications of these concepts are proposed in a variety of optical scenarios, considering the influence of natural material dispersion and loss in optical materials.

All Optical Metamaterial Circuit Board at the Nanoscale

Optical nanocircuits may pave the way to transformative advancements in nanoscale communications. We introduce here the concept of an optical nanocircuit board, constituted of a layered metamaterial structure with low effective permittivity, over which specific traces that channel the optical displacement current may be carved out, allowing the optical "local connection" among "nonlocal" distant nanocircuit elements. This may provide "printed" nanocircuits, realizing an all-optical nanocircuit board over which specific grooves may be nanoimprinted within the realms of current nanotechnology.

Input Impedance, Nanocircuit Loading, and Radiation Tuning of Optical Nanoantennas

Here we explore the radiation features of optical nanoantennas, analyzing the concepts of optical input impedance, optical radiation resistance, impedance matching, and loading of plasmonic nanodipoles. We discuss how the concept of antenna impedance may be applied to optical frequencies and how its quantity may be properly defined and evaluated. We exploit these concepts in the optimization of nanoantenna loading by optical nanocircuit elements, extending classic concepts of radio-frequency antenna theory to the visible regime for the proper design and matching of plasmonic nanoantennas.

Tuning the scattering response of optical nanoantennas with nanocircuit loads

Optical nanodipoles made of plasmonic elongated nanoparticles have been theoretically and experimentally characterized by various groups in recent studies1,2,3,4,5,6,7,8,9,10. However, compared with their radiofrequency counterparts, less attention has so far been paid to systematic design methodology for these nanoantennas, and in particular to the possibility of optimizing their radiation and scattering properties and tuning their frequency response by using proper ‘loading’ techniques. By interpreting nanoparticles' interaction with light as lumped nanocircuit elements11,12, we show how the concepts of antenna loading may be fully introduced in plasmonic nanoantenna design. In particular, we show how nanocircuit elements, and in general more complex nanofilters, designed within the framework of nanocircuit theory11 and used as nanoloads, may allow tuning of the frequency response of scattering from these nanoantennas at will. Series and parallel combinations of these nanoloads are also considered to add further degrees of freedom in the design. Optical-frequency antennas efficiently couple light into very small volumes. Introducing an important concept from radiofrequency antenna design, that of loading with so-called lumped circuit elements, may provide a way of tuning the frequency response of optical nanoantennas.

Nanoinsulators and nanoconnectors for optical nanocircuits

Following our recent idea of using plasmonic and nonplasmonic nanoparticles as nanoinductors and nanocapacitors in the infrared and optical domains [N. Engheta et al., Phys. Rev. Letts. 95, 095504 (2005)], in this work we analyze in detail some complex circuit configurations involving series and parallel combinations of these lumped nanocircuit elements at optical frequencies. Using numerical simulations, it is demonstrated that, after a proper design, the behavior of these nanoelements may closely mimic that of their lower-frequency [i.e., radio frequency (rf) and microwave] counterparts, even in relatively complex configurations. In addition, we analyze here in detail the concepts of nanoinsulators and nanoconnectors in the optical domain, demonstrating how these components may be crucial in minimizing the coupling between adjacent optical nanocircuit elements and in properly connecting different branches of the nanocircuit. The unit nanomodules for lumped nanoelements are introduced as building blocks for more complex nanocircuits at optical frequencies. Numerical simulations of some complex circuit scenarios considering the frequency response of these nanocircuits are presented and discussed in detail, showing how practical applications of such optical nanocircuit concepts may indeed be feasible within the current limits of nanotechnology.

Parallel, series, and intermediate interconnections of optical nanocircuit elements 2 Nanocircuit and physical interpretation

Applying the analytical closed-form solutions of the quasi-static potential distribution around two conjoined resonant half-cylinders with different permittivities, reported in the first part of this manuscript, here we interpret these results in terms of our nanocircuit paradigm applicable to nanoparticles at infrared and optical frequencies [Phys. Rev. Lett.95, 095504 (2005)]. We investigate the possibility of connecting in series and parallel configurations plasmonic and/or dielectric nanoparticles acting as nanocircuit elements, with a goal for the design of a more-complex nanocircuit system with the desired response. The present analysis fully validates the heuristic predictions regarding the parallel and series combination of a pair of nanocircuit elements depending on their relative orientation with respect to the field polarization. Moreover, the geometries under analysis present interesting peculiar features in their wave interaction, such as an intermediate stage between the parallel and series configurations, which may be of interest for certain applications. In particular, the resonant nanocircuit configuration analyzed here may dramatically change, in a continuous way, its effective total impedance by simply rotating its orientation with respect to the polarization of the impressed optical electric field, providing a novel optical nanodevice that may alter its function by rotation with respect to the impressed optical local field.

Parallel, series, and intermediate interconnections of optical nanocircuit elements 1 Analytical solution

Following our recent development of a paradigm for extending the classic concepts of circuit elements to the infrared and optical frequencies [Phys. Rev. Lett.95, 095504 (2005)], in this paper we investigate the possibility of connecting nanoparticles in series and in parallel configurations, acting as nanocircuit elements. In particular, here we analyze a pair of conjoined half-cylinders whose relatively simple geometry may be studied and analyzed analytically. In this first part of this work, we derive a novel closed-form quasi-static analytical solution of the boundary-value problem associated with this geometry, which will be applied in Part 2 for a nanocircuit and physical interpretation of these results.

Circuits with Light at Nanoscales: Optical Nanocircuits Inspired by Metamaterials

A form of optical circuitry is overviewed in which a tapestry of subwavelength nanometer-scale metamaterial structures and nanoparticles may provide a mechanism for tailoring, patterning, and manipulating local optical electric fields and electric displacement vectors in a subwavelength domain, leading to the possibility of optical information processing at the nanometer scale. By exploiting the optical properties of metamaterials, these nanoparticles may play the role of "lumped" nanocircuit elements such as nanoinductors, nanocapacitors, and nanoresistors, analogous to microelectronics. I show that this concept of metamaterial-inspired nanoelectronics ("metactronics") can bring the tools and mathematical machinery of the circuit theory into optics, may link the fields of optics, electronics, plasmonics, and metamaterials, and may provide road maps to future innovations in nanoscale optical devices, components, and more intricate nanoscale metamaterials.

Coupling of optical lumped nanocircuit elements and effects of substrates

We present here an analytical quasi-static circuit model for the coupling among small nanoparticles excited by an optical electric field in the framework of the optical lumped nanocircuit theory [N. Engheta, A. Salandrino, and A. Alù, Phys. Rev. Lett. 95, 095504 (2005)]. We derive how coupling effects may affect the corresponding nanocircuit model by adding lumped controlled sources that depend on the optical voltages applied on the coupled particles as coupled lumped elements. With the same technique, we may model the presence of a substrate located underneath the nanocircuit elements, relating its presence to the coupling with a properly modeled image nanoparticle. These results are of importance in the understanding and the design of complex optical nanocircuits at infrared and optical frequencies.

Optical ‘Shorting Wires’

Connecting lumped circuit elements in a conventional circuit is usually accomplished by conducting wires that act as conduits for the conduction currents with negligible potential drops. More challenging, however, is to extend these concepts to optical nanocircuit elements. Here, following our recent development of optical lumped circuit elements, we show how a special class of nanowaveguides formed by a thin core with relatively large (positive or negative) permittivity surrounded by a thin concentric shell with low permittivity may provide the required analogy to 'wires' for optical nano-circuits.