Communication: Toward ultrafast, reconfigurable logic in the nanoscale

We propose and illustrate numerically a class of nanoscale, ultrafast logic gates with the further advantage of reconfigurability. Underlying the operation of the gates and their versatility is the concept of polarization control of the electromagnetic energy propagating via metal nanoparticle arrays. Specifically, a set of different logic gates is shown to obtain from a single metal nanoparticle junction by modification of the polarization properties of the input light sources. Implications and extensions of the gates are discussed.

High-speed, all-optical logic gates are key elements in all-optical signal processing, including all-optical switching, encryption, and data encoding.^1–3 Extensive efforts have been directed in recent years toward the application of optical fibers,⁴ semiconductor optical amplifiers,^5–9 waveguides,^10,11 and integrated silicon-on-insulator¹² junctions to that end. Likewise exciting are logic gates based on the temporal evolution of optically tailored wavepackets in atomic or molecular media.^13–15 Inspired by this previous research and intrigued by the range of potential applications, we propose, in the present communication, a new paradigm for logic gates with the advantages of ultrafast, nanoscale, reconfigurable operation and the potential to large-scale parallelization.

Our approach is based on the already demonstrated ability of metal particle arrays, metal nanorods, and metal films to guide electromagnetic energy at sub-diffraction lengthscales. Although radiation losses prevent guiding over long distances, at least in the case of nanoparticle arrays, relatively small (vide infra) constructs are able to guide, reroute, and bend^16–28 the electromagnetic (EM) energy trajectories at sub-diffraction lengthscales with minimal losses. In particular, Ref. 20 proposes and illustrates numerically the possibility of routing EM energy propagating down the leg of a T-junction exclusively into one or the other of the symmetry equivalent arms of the junction by choice of the two parameters that characterize the polarization of the spatially localized, elliptically polarized excitation pulse. The elliptical polarization crafts a superposition of longitudinal and transverse plasmon modes that allows the EM energy to bend at the T-junction intersection. The phase between the two field components breaks the symmetry of the junction and allows selective routing of the energy into a desired one of the arms. A first experimental realization of the approach of Ref. 20 was very recently reported.²⁴ A thorough analysis of the polarization control concept proposed in Ref. 20, in the context of routing of energy via a T-junction, is presented in Ref. 25.

Our focus in the present work is the extension of phase and polarization control^20–22 to produce logic elements. To that end, we consider excitation of the junction with two sources, denoted A and B, where each source α, α = A, B, takes the general form,

where E₀ is a constant and ω is the central frequency of a laser pulse with pulse envelope

$sin2πtτ$⁠. The parameter ξ_α determines the relative amplitudes of the electric field components which, in conjunction with the phase, ϕ_α, determines the polarization of the source and hence, as shown below, also the function of the construct.

The interaction of the electromagnetic field with the silver nanoparticle array is simulated using the finite-difference time-domain method of solving Maxwell's equations within the Yee algorithm.²⁹ Due to the cylindrical symmetry of the problem, we focus on the TE_z mode, which is capable of supporting surface modes, such as surface plasmons. This reduces the 3D problem to a 2D one, where the field components are given by²⁰ 

In Eqs. (2)–(4), ε_eff = ε₀ in vacuum, and approaches ε₀ε(ω → 0) in the metal regions. In vacuum, the electric current components J_x and J_y are identically zero, whereas in the metallic region they are given by

The constants α and β are described within the Drude Model,³⁰ where α accounts for electron relaxation processes and β is related to the bulk plasmon frequency. These two parameters, in conjunction with the dielectric constant for the metal, describe the relevant physics in the metallic medium.

The radius of the metal nanoparticles composing the T-shaped structure (inset of Fig. 1(a)) is 25 nm and the center-to-center distance is 60 nm. The structure is embedded in vacuum in a simulation box of dimensions 1020 nm × 1020 nm, with spatial step-size of 1 nm in both the X- and the Y-direction. The pulse duration of the input excitation field, τ, is chosen to be 15 fs, with a wavelength of λ = 360 nm. The simulation is performed for a total of 30 fs in time steps of 0.001 fs.

Figure 1 illustrates the origin of polarization control, which underlies the concept of nanoscale, ultrafast logic gates. The inset of Fig. 1(a) depicts schematically the junction envisioned, whereas the main panels of Figs. 1(a) and 1(b) illustrate snapshots of the time-evolving EM energy via the T-shaped nanoparticle array for two choices of the sources polarization. The supplementary material shows movies of the time evolution via the junction for the two source polarizations and provide better insight into the wave dynamics.³³ The choice ξ_A = ξ_B = 0 (Fig. 1(a) and movie 1(a)) guides the EM energy to the detector, whereas the choice ξ_A = ξ_B = π/2 (Fig. 1(b) and movie 1(b)) blocks the light propagation. Below it is shown that, with the choice ξ_α = 0, α = A, B, each of the individual sources likewise lights the detector, hence making the OR logic gate, corresponding to the truth table of Table I(a).

The ability of the same junction to support several other gates, and hence the reconfigurability of the gates, is illustrated in Fig. 2, which also examines in more detail the quality of the gates. Fig. 2(b) shows the energy enhancement factor, defined as

$∣E⃗∣2$ at the detector, as a function of ξ_A and ξ_B, whereas Fig. 2(a) shows the same quantity for excitation with a single source vs ξ_α. As with other electronic and optical logic gates, reading the results requires that we define a threshold enhancement factor, above which the detector is considered to be turned on, and here we choose the threshold to be I_TH = 1500. The OR gate discussed above is seen, Fig. 2, to obtain for ξ_A = ξ_B = 0. Similarly, the choice ξ_A = ξ_B = π/4 provides the AND gate, with the truth table given by Table I(b). The INHIBIT A gate, with the truth table of Table I(c), is seen in Fig. 2 to obtain for ξ_A = π/2 and ξ_B = 0, whereas the INHIBIT B gate obtains for the reverse choice of ξ_A and ξ_B. Finally, to generate the logical NOT gate, see the truth table of Table I(d), we consider a single source, input A with ξ_A = π/2 and apply a modulation input with ξ_M = π/8 in lieu of input B. As seen in Fig. 2, turning input A on switches the EM energy at the detector off, thus generating the NOT gate.

We remark that the same functions illustrated here can be achieved with smaller junctions (scaling all dimensions of a given construct leaves the dynamics invariant in the domain of interest, where the wavelength is much larger than the junction lengthscales), and current fabrication techniques allow the fabrication of constructs of the type considered here for a wide range of sizes. Whereas the junctions considered here consist of perfectly ordered nanoparticles with uniform sizes, in experiments, although the fabrication technology is very advanced, irregularities are inevitable. It is, therefore, important to note that while the details of the EM energy propagation via the junction, and the time averaged energy at the detectors are sensitive to the size and shape of the particles, the qualitative effects described here are entirely robust. Thus, for the case of the T-junction of Fig. 1(a)(inset), the introduction of random variations in size, shape, and relative arrangements were shown to leave invariant the control mechanism and its consequences.²⁰ The concept exhibited in Fig. 2 is not unique to the T-junction; we have devised the same and other logic gates also based on a Y-shaped and an X-shaped plasmonic junction.

Plasmon-based logic gates offer potentially a variety of attractive features. (1) Metal nanoparticle arrays are compatible with molecules, thus providing a useful approach to integrate logic gates for more complex operations in the nanoscale. (2) Means of writing the input and reading the output in the nanoscale are experimentally established.^23,31,32 (3) The entirely classical operation implies that creation and maintenance of entanglement are not necessary. (4) Metal nanoparticle can be prepared in large arrays in a controllable fashion.

In summary, we proposed the application of metal nanoparticle arrays to generate ultrafast, reconfigurable logic in the nanoscale and numerically explored several designs, leading to the NOT, OR, AND, and INHIBIT logic gates. One of our objectives in future research would be to numerically interconnect such gates to achieve the functionalities of a half and a full adder.

We gratefully acknowledge the support of the National Science Foundation (Award No. CHEM-1012207), the Department of Energy (Award No. DE-FG02-09ER16l 09), and the National Science Foundation through the Northwestern Material Research Science and Engineering Center (Award No. DMR-0520513).