Results and Discussion

A fundamental antenna geometry that has been tested and analyzed particularly rigorously is that of single- and coupled-bar antennas (15, 21, 30⇓⇓⇓–34) (Fig. 1, Inset). Thus, in a first experiment, we focus on the bar antenna as building block and determine the complex spectrum in the near-field hotspots on bars of varying lengths. Fig. 2A presents the antenna signatures of single-bar antennas with increasing lengths from 480 to 640 nm, recorded with Fourier limited laser pulses of 15 fs width (corresponding to a spectral bandwidth of 120 nm at 776 nm; Fig. 1A and Materials and Methods). The parameters for the cosinusoidal phase are and . An intuitive understanding of these data can be gained by considering that the highest TPPL signal occurs when the shifting cosinusoidal phase compensates for the spectral phase of the antenna resonance best. The particular shape of the band of maximum intensity that starts at rad for 480-nm rods and curves toward for longer rods (Fig. 2A) can thus be interpreted as the phase jump that the excitation light at carrier wavelength 776 nm experiences when it drives the antenna above or below the resonance frequency.

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Fig. 2.

Coherent ultrafast dynamics of single nanoantenna hotspots. (A) Antenna signatures of gold nano-antennas of increasing lengths. The signatures measure the spectral phase and, therefore, through the Fourier transform, the ultrafast dynamics of the hotspot. Recording the signature between and allows differentiating between the effect the antenna has on the spectral amplitude and on the spectral phase of the field; this can clearly be seen in, for instance, the case of a 560-nm antenna: When δ is ∼π/2 the cosine function compensates best for the dispersion of the antenna, and the combination with a good overlap of the excitation spectrum with the resonance of the antenna provides for a high two-photon signal. In contrast, when δ is ∼3π/2, the overlap between the excitation spectrum and the antenna resonance is equally good but the cosine function adds to the antenna dispersion, and the two-photon signal is very low. (B) Corresponding signatures calculated for Lorentzian resonances at different wavelengths with a width of 0.13 ± 0.02 rad⋅fs⁻¹ (41 ± 6 nm at 776 nm).

To retrieve the spectral resonance profiles of the antennas, the measured signatures are compared with fits based on Lorentzian resonances that are given by . Here, ω_cent is the central frequency of the resonance, 2γ is the FWHM of the imaginary (i.e., absorptive) part of the resonance, and the antenna phase is defined as . The best fits (Fig. 2B) are obtained if the width of the Lorentzian is kept at 2γ = 0.13 ± 0.02 rad⋅fs⁻¹ (corresponding to Δλ= 41 ± 6 nm at 776 nm central wavelength) while the resonance wavelength is varied from 640 nm for antennas of 480-nm length to 940 nm for antennas of 640-nm length (corresponding, respectively, to ω_cent = 2.95 rad⋅fs⁻¹ and 2 rad⋅fs⁻¹).

The measurement depicted in Fig. 2 is a systematic exploration of the complex spectral modulation that calibrated nano-antennas impose on an impinging ultrafast pulse. This realization now allows us to create plasmonic structures with tailored and predetermined ultrafast responses by coupling antennas. The field in each hotspot in such a system is influenced by the resonances of the building blocks, modified by the dispersion and absorption of the coupled system. One feasible application is a subwavelength resolution phase modulator: a plasmonic structure that imparts a predefined spectral phase on the field in a hotspot for use in high-resolution, small-volume nonlinear experiments.

This concept of engineering ultrafast nanophotonic systems is demonstrated in Fig. 3, in which we present the measured and fitted TPPL signature and the retrieved amplitude-phase modulation added to a hotspot by a single-bar antenna of 530-nm (Fig. 3A) and 620-nm length (Fig. 3B), as well as to the hotspot on the 530-nm (Fig. 3C) and 620-nm side (Fig. 3D) respectively, by a coupled antenna with a gap of ∼30 nm. The best fits for the signatures were obtained by significantly broadening the single-antenna resonances from 0.13 ± 0.02 rad⋅fs⁻¹ to 0.26 ± 0.06 rad⋅fs⁻¹ for coupled antennas, indicating that the total dispersion of the combined antenna determines the width of the resonances in each profile. The losses in the metal, giving rise to the broadening, are a vital property of the design, because they in part determine the range of the spatial mode associated with the resonance and therefore its strength in a particular hotspot. The spectral phase modulation the antenna imprints on the hotspot-sized field can directly be controlled by adapting the strength and separability of the resonances of the constituent antennas in the hotspot of interest through a wide range of readily accessible parameters (i.e., antenna dimensions, material, geometry, and gap widths).

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Fig. 3.

Shaping the phase in hotspot on a plasmonic structure using the resonances of the constituent antennas. (A) Antenna signature measured in a hotpot on a 530-nm single antenna (Left) and the resonance profile retrieved from the fit (Right). (B–D) Corresponding signatures (Left) and resonance profiles (Right) for a 620-nm single antenna and different positions on a coupled 530- to 620-nm asymmetric antenna, demonstrating the engineering of spectral phase in antenna hotspots by mixing resonances with different strengths.

Coupled plasmonic nanoantennas can be used in this way as a subwavelength resolution phase modulator, as shown in Fig. 3 C and D, Right); the reconstructed modulation functions in the hotspots give insight into the role of the spatial range of resonant antenna modes. This allows controlled realization of another anticipated application of ultrafast plasmonics: hotspot switching. This can be achieved by addressing localized resonances at different times in an excitation pulse through application of a spectral chirp (e.g., by adding dielectric material in the beam path). To demonstrate this concept, we engineer an asymmetric coupled antenna to function as a sub-100-fs spatial hotspot switch.

Antennas with 530-nm and 620-nm lengths are chosen as suitable building blocks owing to their resonances at the high- and low-frequency ends, respectively, of the excitation spectrum. The coupled antenna is excited with a −500-fs² chirped pulse. The dynamics of the field is resolved in a pump-probe experiment (Fig. 4A and Materials and Methods). The ratio between the TPPL intensity from the outermost hotspots on the constituent bar antennas is depicted in Fig. 4B (Right, gray points) as a function of pump-probe delay. The spatial asymmetry in the resonances (Fig. 3 C and D, Right) makes the hotspot intensity switch from the short antenna bar to the long antenna bar between τ = −50 fs and τ = +35 fs with contrast ∼2.8. Comparison between experiment and theory based on the resonance structure of the hotspots and the chirp in the excitation pulse (Fig. 4B, Right, solid black line) shows a good agreement between the actual hotspot switching of the antenna and the theoretical behavior for which the antenna was designed. The ultrafast switching can directly be visualized by imaging the antennas with fixed pump-probe delay at −50 fs (Fig. 4B, Upper Left) and 35 fs, respectively (Fig. 4B, Lower Left). This demonstrates the utility of a coupled plasmonic antenna as an ultrafast hotspot switch.

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Fig. 4.

A sub-100-fs plasmonic switch. (A) The dynamics of the hotspots are resolved in a pump-probe experiment. (B) Between a pump-probe delay of −50 fs and 35 fs the luminescence intensity switches from the 530-nm antenna bar to the 620-nm antenna bar with a contrast ratio ∼2.8 (Right). Imaging the antenna with these delays fixed demonstrates the sub-100-fs plasmonic switching (Left).

In an intricate plasmonic structure, the local field potential is determined by the eigenmodes of the structure and the dielectric constants of the materials involved (4). In other words, the local spectral amplitude and phase in a hotspot on a plasmonic system are determined by the amplitude and phase profiles of the resonant modes contributing to the hotspot. These modes and the timing with which they are addressed then control the dynamics of the field in the hotspot. Hence, local complex spectra can be readily interpreted by decomposition of the structure into constituent antenna building blocks with specific resonances and coupling constants; consequently, local spectra can be designed in a bottom-up approach by coupling antennas with well-defined resonances. This also implies that, although the control of the dynamics of the near-field ultrafast pulse is based on resonances, an arbitrary shape can be imposed upon the field in a particular hotspot by picking the right combination of structure shapes and material for the constituent antennas.

There are several limitations to this approach. A plasmonic structure does not allow transformation of one arbitrary pulse shape into another arbitrary pulse shape. This means we are designing a particular structure to imprint one particular pulse shape on an impinging, Fourier limited pulse in a particular hotspot (i.e., currently this would be a static “pulse shaper”). The occurrence of absorption in plasmonic structures means that there is a limit on the applicability of time reversal, meaning that there are in fact limitations on the pulse shapes that can be created in a predefined hotspot, starting from, for instance, a Fourier limited pulse.

However, here we have concerned ourselves with the simplest possible incarnations of coupled plasmonic structures and show that the simplest possible designs (single- and double-bar antennas) already lead to a wide variety of possible phase shapes and high-fidelity control over nanoscale field dynamics, using Fourier limited or linearly chirped pulses. With this, we aim to simplify ultrafast plasmonics enough for it to make the transition to a useful research tool for nanometric and femtosecond physics. Investigations at these ultrafast timescales and ultrasmall length scales are rapidly being embraced in fields as diverse as material science, cell biology, and quantum optics. What unites these areas is the transition from research on phenomena in isolated or uniform systems (molecular jets, ultracold atoms, and bulk materials) to nanoscale components interconnected in larger systems (nanostructured surfaces, supramolecular complexes, cells, and nitrogen-vacancy center networks). The concept of plasmonic antennas as elements in near-field femtosecond pulse shapers feeds this paradigm shift with its potential for, for example, nanoscopic coherent control, spatially selective ultrafast spectroscopy, quantum information in complex systems, pulse-shaped scanning probe microscopy, and the possibility of integration in chip-based constructs. For successful transition into these regimes, femtosecond time resolution needs to be combined with high spatial selectivity and complete control of the time evolution of fields with nanometer precision, as we have demonstrated here.