Ultrafast Plasmon Propagation in Nanowires Characterized by Far

Letter pubs.acs.org/NanoLett

Ultrafast Plasmon Propagation in Nanowires Characterized by FarField Spectral Interferometry Christian Rewitz,† Thomas Keitzl,† Philip Tuchscherer,† Jer-Shing Huang,‡,# Peter Geisler,§ Gary Razinskas,§ Bert Hecht,*,§,∥ and Tobias Brixner*,†,∥ †

Institut für Physikalische und Theoretische Chemie, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany Department of Chemistry, National Tsing Hua University, Hsinchu 30013, Taiwan # Frontier Research Center on Fundamental and Applied Sciences of Matters, National Tsing Hua University, Hsinchu 30013, Taiwan § Nano-Optics and Biophotonics Group, Experimentelle Physik 5, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany ∥ Röntgen Center for Complex Material Systems (RCCM), Am Hubland, 97074 Würzburg, Germany ‡

ABSTRACT: Spectral interferometry is employed to fully characterize amplitude and phase of propagating plasmons that are transmitted through silver nanowires in the form of ultrashort pulses. For nanowire diameters below 100 nm, the plasmon group velocity is found to decrease drastically in accordance with the theory of adiabatic focusing. Furthermore, the dependence of the plasmon group velocity on the local nanowire environment is demonstrated. Our findings are of relevance for the design and implementation of nanoplasmonic signal processing and in view of coherent control applications.

KEYWORDS: Plasmon propagation, plasmon group velocity, silver nanowires, plasmonic waveguides, ultrafast spectroscopy, spectral interferometry

M

blocks of future plasmonic nanocircuits, they have been studied extensively in this context16,22−25 and in the context of controlling plasmon propagation.26,27 They also have been used to study fundamental properties of plasmons.28,29 Furthermore, the group velocity of plasmons on nanowires was measured exploiting their low-Q resonator properties.30 In this Letter, we demonstrate that far-field spectral interferometry can be employed to fully characterize ultrafast plasmon pulse propagation on silver nanowires. For this purpose, we carry out a rigorous size-dependent universal characterization of light that is emitted at one nanowire end due to the radiative decay of propagating plasmons, which have been excited by a laser pulse at the other nanowire end. We find that for nanowire diameters below 100 nm the plasmon group velocity decreases drastically and that the dispersion upon plasmon propagation is small. In addition, we show the dependence of the plasmon group velocity on the local nanowire environment. The method allows us to determine the spectral transfer function of complete plasmonic systems including plasmon launching, propagation, and emission. Applications are expected in nanoplasmonic signal process-

iniaturization and packaging density of integrated optics based on dielectrics is limited by the wavelength-scale modal profiles of conventionally guided modes.1 In contrast, plasmonic modes supported by noble-metal nanostructures offer strong subwavelength confinement2−6 and therefore promise the realization of nanometer-scale integrated optical circuits with well-defined functionality.7−13 In view of applications in the field of optical communication, the propagation of ultrashort pulses representing bits of information is of fundamental importance and needs to be characterized in detail. Of particular interest in this context is the speed of propagation, i.e., the plasmon group velocity, and the dispersion. The plasmon group velocity for nanowires, i.e., the slope of the plasmon dispersion relation, is expected to depend strongly on the wire geometry.2,3 This encompasses peculiar effects such as the vanishing group velocity in adiabatic focusing.14,15 Similar behavior is not known for electronic integrated circuits and can lead to characteristic signal delays in information processing systems. Near-field optical microscopy has been successfully applied to study plasmon propagation effects via steady-state mode patterns that build up due to the formation of standing waves in isolated plasmonic nanowires16,17 and tapered transmission lines.18 Furthermore, ultrashort pulse propagation on dielectric photonic waveguides19,20 and plasmonic waveguides has been visualized.21 As silver nanowires can be considered building © 2011 American Chemical Society

Received: August 18, 2011 Revised: November 11, 2011 Published: December 20, 2011 45

dx.doi.org/10.1021/nl202864n | Nano Lett. 2012, 12, 45−49

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Figure 1. (a) Sketch of the experimental setup. A propagating plasmon pulse is excited with an x polarized femtosecond laser pulse at one end of a silver nanowire (input). The nanowire is oriented to include a 45° angle with the x axis. After propagating along the nanowire, the plasmon pulse is radiated into a free-space propagating pulse at the other end of the nanowire (output). An analyzer (yellow disk) selects the y component of the emission signal and blocks the reflected light. The emission signal is then superimposed with a reference beam, and the resulting interferometric signal is detected by a spectrometer. The λ/2 plate (green disk) rotates the polarization of the reference parallel to the analyzer axis. (b) SEM image of a representative silver nanowire with diameter d = 115 nm and length l = 4.5 μm.

Figure 2. Plasmon propagation experiment and data evaluation. (a) Representative map of sample emission upon excitation of plasmons in a silver nanowire with the reflection of the excitation spot at the input of the nanowire (“Refl.”, black circle) and the emission at the output end of the nanowire (“Em.”, red circle). Inset: The linear excitation polarization (green arrow) includes roughly a 45° angle with the nanowire’s long axis and is perpendicular to the detection polarization (red/black arrow). (b) Spectral interferograms detected by overlapping the signals in the diffraction-limitsized circles of (a) at the reflection position (black line) and the emission position (red line) with the reference pulse. (c) Reconstructed temporal positions with respect to the reference pulse of the reflection (black line) and the emission (red line) using the interferograms of (b).

ing7−13 and in the coherent control of plasmonic systems.26,27,31−34 The experimental setup is sketched in Figure 1a. A linearly x polarized femtosecond laser pulse [peak wavelength λ0 = 800 nm, spectral full width at half-maximum (fwhm) = 46 nm] excites a plasmon at one end of a silver nanowire. The plasmon pulse propagates with a certain group velocity vg along the nanowire and is re-emitted as a free-space propagating pulse at the other end of the nanowire. In order to characterize amplitude and phase of the emitted field, spectral interferometry35 is realized by collinear superposition of the emitted signal with a reference pulse at a fixed time delay τ. The resulting heterodyne interferometric signal is spectrally dispersed and recorded by a charge-coupled device (CCD). Applying a fast Fourier transform to this spectral interferogram allows us to separate the oscillatory from the non-oscillatory part. The oscillatory part is then isolated using a Fourier window, and the

inverse fast Fourier transform is applied. This yields a complex valued spectrum from which the spectral intensity and phase of the emitted signal can be deduced, if the amplitude and phase of the reference pulse are known.35 Optimal excitation of plasmons in silver nanowires is typically obtained for a polarization parallel to the nanowire.36 In our setup, we deliberately introduce a ca. 45° and −45° angle with respect to the nanowire’s long axis for excitation and detection polarization, respectively, to realize a crossed-polarizer scheme (see Figure 1a). This configuration yields a total angle of 90° between excitation and emission polarization, allowing for efficient suppression of reflected light without severe loss of signal strength. We use the same immersion-oil objective (Nikon Plan Apo, 100×/1.40) to focus the excitation pulse down to a diffraction-limited spot and to collect signals from the overall image plane. For the selective detection of particular emission spots, independent of the excitation position, a piezo 46


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scanning mirror in conjunction with a lens ( f = 200 mm) and a pinhole with a diameter of 30 μm are used. Our sample consists of chemically grown silver nanowires obtained from PlasmaChem GmbH (Berlin, Germany) that have been drop-casted on indium tin oxide (ITO)-coated microscope coverslips. After evaporation of the solvent (H2O), the nanowires, adsorbed to the surface, were embedded in index-matching oil (type B, Cargille-Sacher Laboratories Inc., NJ). The geometric dimensions were obtained from scanning electron microscope (SEM) images prior to optical experiments. The range of investigated nanowire diameters is d = 70− 260 nm, whereas the lengths vary from l = 1.9 to 6.2 μm. Figure 1b shows a representative SEM image of such a nanowire. In order to investigate the propagation of a plasmon pulse, we first locate a suitably oriented nanowire by means of a reflection-mode confocal scan image, in which silver nanowires appear as bright elongated structures. In a second step, the input end of the nanowire is placed at the position of the excitation focus. While keeping the excitation position fixed, we then scan the piezo mirror in the detection path to obtain a spatially resolved map of the sample emission, as shown in Figure 2a. This map is dominated by the direct reflection of the excitation spot (“Refl.”, black circle in the upper right corner). For sufficiently long nanowires, the radiative decay of plasmons at the output end is observed as a bright spot, which is well separated from the reflection spot. This emission can be seen in the lower part of Figure 2a (“Em.”, red circle). The remaining visibility of the direct-reflection spot in the crossed-polarizer scheme is due to high numerical aperture (NA) depolarization effects37 and is used to obtain the reference starting time of the plasmon pulse, as indicated in Figure 2c. To perform spectral interferometry of both the reflected and emitted pulse after propagation, the signal in each circle of Figure 2a is overlapped individually with the reference pulse. The resulting spectral interferograms are shown in Figure 2b, where the black line represents the interferometric signal of the reflection and the red line the interferometric signal of the emission. As can be inferred from the modulation of the red line over the complete spectrum, the whole laser pulse spectrum is transmitted through the nanowire. From the interferograms, the spectral intensity Ii(ω) and phase φi(ω) of both signals (reflection i = 1, and emission i = 2) can be reconstructed if the amplitude and phase of the reference pulse are known. 35 For the determination of the plasmon group velocity, however, knowledge of the reference pulse phase φref(ω) is not required. To determine the group velocity, it is sufficient to reconstruct Ii(ω) and the difference phase of each signal with respect to the reference: φdiff,i(ω) = φi(ω) − φref(ω). Since the reference pulse is dispersion compensated (by traversing an equal amount of glass as the reflected pulse), this difference phase is mainly linear for the reflection. The dispersion upon plasmon pulse propagation, which is visible in the emission phase, is discussed later. Using Ii(ω) and φdiff,i(ω) of the reflection and the emission, we employ a fast Fourier transformation to obtain the temporal envelopes shown in Figure 2c. We then deduce the plasmon propagation time from the separation between the maxima of the emission (red) and the reflection (black) temporal signals. In the case of multiple reflections of the propagating plasmon wave inside the nanowire, multiple signal pulses are expected. These signals will show up as additional (though much lower) peaks in the temporal envelopes and will not affect the data evaluation because here only the global maximum is evaluated. The thus obtained time difference Δt

has to be corrected for time delays due to geometrical path differences that are acquired in the microscope setup because of the different detection positions in the sample plane. This correction is possible with an accuracy of about 1 fs using a straightforward geometric model for the path lengths together with an experimental calibration. The plasmon group velocity can then be calculated by dividing the nanowire length by the corrected plasmon propagation time. The reflection signal is due to a nonresonant scattering process at the input end of the silver nanowire. Within the laser pulse spectrum the complex valued reflection coefficient is quasi constant. Therefore, since the relative change between reflection and emission signals is measured, no additional phase or amplitude effects (e.g., of the setup), apart from the geometrical correction, have to be considered separately in the evaluation. Finally, possible phase offsets (i.e., zero-order Taylor coefficients) that may occur upon reflection at the nanowire input end do not matter for the determination of the plasmon group velocity or the dispersion of the plasmon mode upon propagation. We have applied the outlined method to investigate a set of nanowires with various lengths and diameters determined by SEM. As expected, the plasmon group velocity shows no systematic dependence on the nanowire length. However, since our data set spans a large range of diameters from d = 70 to 260 nm, we observe a pronounced dependence of the plasmon group velocity on the nanowire diameter as indicated by the blue crosses in Figure 3. In particular, we observe a drastic

Figure 3. Plasmon group velocity as a function of the total nanowire diameter. Blue crosses indicate experimental results. Simulation results are represented by diamonds connected by lines. Results of simulations without a corrosion layer, a 5 nm, and a 10 nm corrosion layer of silver sulfide are indicated with red dotted and black and green dashed lines, respectively. Inset: Two-dimensional near-field intensity distribution of the fundamental plasmon mode for a silver nanowire immersed in index-matched oil (noil = 1.5071) on a 200 nm thick ITO layer (nITO = 1.8)38 on top of glass (nglass = 1.51). The nanowire diameter is d = 100 nm including a 10 nm silver sulfide corrosion layer (nAg2S = 2.9).39 Optical properties of silver were modeled according to experimental data.40

decrease of the group velocity for nanowire diameters below d = 100 nm, while it saturates for larger diameters. In the presented data, the velocity varies from 44% (for the largest diameter) to 22% (for the smallest diameter) of the velocity of light in vacuum. Not all nanowires show good transmission of plasmons in our experiments even though SEM images provide 47


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1 fs, i.e., no linear spectral phase effects due to insertion or extraction at the nanowire ends have to be considered separately. In addition to measuring the group velocity, which is connected to the first-order Taylor coefficient of the spectral phase, we also analyzed higher-order phase terms, i.e., the dispersion of propagating plasmon pulses. In the case of silver nanowires, the dispersion is very low, i.e., the plasmon pulse is not significantly broadened in the time domain while it propagates along the nanowire. An upper limit of the experimentally determined group delay dispersion per propagation length is 50 fs2 rad−1 μm−1 for all investigated nanowires, being in good agreement with values obtained from the second derivative of the simulated dispersion relation. We also investigated the dependence of the plasmon group velocity on the local nanowire environment. For this purpose, we measured the plasmon group velocity of a nanowire with a nominal diameter of d = 100 nm in two different environments: before and after adding the index-matched oil. In contrast to the previous experiments, the microscope coverslip used for this sample was not covered with an ITO layer. Therefore, we assumed for the simulations a homogeneous local environment with the refractive index of glass for the case with oil immersion, while for the case without oil, we assumed air (refractive index equal to one) in the upper half space. The results are shown in Table 1. Experimental and simulated values

no clear evidence for the presence of defects. We discarded nanowires for which the ratio of emission intensity and reference intensity was below a threshold of 3 × 10−3. This typically happened for nanowires that showed strongly distorted emission spots and unexpectedly low emission intensities. For comparison, we simulated the system’s dispersion relation by the two-dimensional, full-vectorial finite-difference frequency-domain (FDFD) method41 (MODE Solutions, version 4.0.4, Lumerical Solutions Inc., Vancouver, Canada). Due to the well-known reactivity of silver at ambient conditions,42 we included the possibility of corrosion, which was modeled by replacing a thin outer shell of the nanowire by silver sulfide or silver oxide. The inset of Figure 3 shows the simulated geometry and the near-field intensity distribution of the fundamental plasmon mode. A uniform mesh with discretization of 0.5 nm in each direction covered the complete nanowire and its close surrounding. To avoid spurious absorption of the nanowire’s near fields, all boundaries of the simulation box were set to be at least 800 nm away from the structure. The plasmon group velocity was obtained as the slope of the simulated dispersion relation of the fundamental mode at the laser pulse center wavelength of 800 nm. The fundamental quasi TM mode is usually the only mode with a sufficient propagation length to reach the output end of a nanowire. For sufficiently small nanowire diameters, all other higher-order modes are damped out very quickly upon propagation. The red dotted line in Figure 3 indicates the simulated group velocities for pure silver nanowires, i.e., without a corrosion layer. The trend of the experimental results (blue crosses) is confirmed: Below d = 100 nm, the plasmon velocity decreases strongly. However, the experimental data seem to systematically deviate toward lower group velocities. We attribute this behavior to the influence of a thin silver sulfide corrosion layer as depicted in Figure 3: The shaded area covers changes in the group velocity for up to 10 nm thick corrosion layers. The black and dashed green lines indicate simulated group velocities for 5 and 10 nm thick silver sulfide shells, respectively. A silver oxide shell has a similar although slightly less pronounced effect due to its lower refractive index. Further careful analysis of the influence of geometrical aberrations, such as ellipticity or a (more realistic) pentagonal cross section of the nanowire, ITO layer thickness, and refractive index as well as uncertainties in the dielectric function of silver43 (data not shown), shows that a shell with a high refractive index (nAg2S = 2.9 or nAg2O = 2.25)39,44 is the only simulation parameter that yields good agreement of the simulation and the experimental data. Note that for large nanowire diameters (d ≥ 200 nm), simulations indicate the occurrence of a second mode with an even slightly higher group velocity and a larger propagation length than the fundamental mode. Such a mode with the intensity mostly localized at the upper side of the nanowire has been observed by others as well45 and might explain the shift to higher propagation velocities of the experimental data point at d = 263 nm. We verified that the group velocities determined by our twodimensional simulations agree very well with much more costly full three-dimensional simulations of pulse propagation in silver nanowires that include the excitation geometry (polarization and spotsize). In these simulations we also confirmed that, as expected, any photon−plasmon conversion time is shorter than

Table 1. Dependence of the Plasmon Group Velocity on the Local Nanowire Environmenta experiment simulation

vair [108 m/s]

voil [108 m/s]

1.42 ± 0.03 1.45

1.14 ± 0.02 1.00

a

The upper half space filled with air or index-matched oil. The nominal diameter of the nanowire according to the manufacturer was d = 100 nm. The simulation geometry models the same diameter including a 5 nm silver sulfide corrosion layer. Note that the simulated value for voil differs from the one in Figure 3 since no ITO layer is present.

agree reasonably well and emphasize the strong dependence of the plasmon group velocity on the local nanowire environment. The plasmon propagation is approximately 25% faster if the upper half space consists of air compared to the case of indexmatched oil. The structure- and environment-dependent group velocity and dispersion are of high relevance for the design and implementation of signal processing in plasmonic nanocircuits. The spectral interferometry method is not limited to nanowires and can be applied to a large variety of nanostructures that support propagating plasmons and provide input and output antennas.12,13 In fact, the concept of using far-field microscopy to investigate plasmonic structures models the scenario of optically integrated plasmonic circuits: A far-field light source excites plasmon pulses that are processed in the near field and are converted back to far-field detectable signals. Since our method provides the full amplitude and phase information of the propagated signal, the spatial/spectral transfer function of plasmonic functional elements, such as splitters, multiplexers, switches, or logic gates, can be determined. Applications are also expected in the field of coherent control of optical excitations in nanostructures where the far-field laser pulse can 48


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be shaped in order to focus the plasmonic energy in space and time.26,27,31−34

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; [email protected].

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ACKNOWLEDGMENTS

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REFERENCES

This work was supported by the DFG within the priority program “Ultrafast Nanooptics” (SPP 1391). C.R. thanks J. Kern for help with the sample preparation and early SEM images. J.-S.H. gratefully acknowledges the support from National Science Council of Taiwan (Grant NSC 99-2113-M007-020-MY2).

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Ultrafast Plasmon Propagation in Nanowires Characterized by Far

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