1. Introduction

Surface plasmon polaritons (SPP), propagating electromagnetic modes that are bound to a metal-dielectric interface, are considered as one of the key ingredients of next-generation nano-photonic devices [1]. This promising perspective is one of the driving forces for the multitude of current research activities in the field of plasmonics [2]. With regard to high-speed applications well-founded means for the development of SPP-based devices rely on a comprehensive knowledge of the spatio-temporal characteristics of ultrashort SPP pulses and their modifications during formation and propagation. Optical pump-probe schemes in combination with near-field microscopy [3] and photoemission electron microscopy (PEEM) [4] techniques provide experimental means to track and visualize the two-dimensional SPP propagation in space and time at sub-µm lateral and femtosecond temporal resolution. The potential of both approaches in tracking the ultrafast SPP dynamics has been demonstrated in numerous works in the recent past [5–9].

For these types of experiments the PEEM technique is operated in an interferometric time-resolved mode (ITR-PEEM), and usually the properties of the SPP are probed via spatio-temporal interference while SPP wave packet and the probing laser pulse are co-propagating, as illustrated in Fig. 1(a) . The entanglement of different contributions to the PEEM signal in this detection scheme implicates, however, a rather indirect data interpretation. In this work we demonstrate experimentally that a counter-propagating PEEM detection mode, as illustrated in Fig. 1(b), provides a much more intuitive access to the SPP wave packet propagation. Particularly the group velocity and the phase velocity of the SPP can be deduced from these data in a very direct manner.

 

Fig. 1 Comparison of co-propagation (left) and counter-propagation (right) PEEM detection of SPP wave packet propagation; (a),(b) scheme of the co-propagation (counter-propagation) detection mode: SPP and probing laser pulse are propagating in the same (opposite) direction; (c) co-propagation PEEM data of SPP propagation along a planar gold surface for temporal excitation-probe delays of 0 fs and 40 fs; (d) corresponding data for the counter-propagating PEEM imaging mode; (e), (f) scheme of the gold structures as used for the PEEM experiments shown in (c) and (d);

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2. Experimental

The ITR-PEEM experiments were performed with a photoemission electron microscope (IS PEEM, Focus GmbH) [10] mounted in an ultrahigh vacuum µ-metal chamber (base pressure 1$\times$10⁻¹⁰ mbar) and providing a lateral resolution of better than 40 nm. The interferometer is an actively stabilized Mach-Zehnder interferometer following a design described in detail in reference [11]. The stability of the interferometer allows us to adjust the temporal delay between the two excitation laser pulses with a timing accuracy of better than 30 attoseconds. The interferometer is also used for characterization of the laser pulse profile via second harmonic generation interferometric autocorrelation measurements. These measurements are performed in parallel to the ITR-PEEM experiments. Laser pulses are delivered by a commercial Ti:Sapphire laser system providing 15 fs pulses at 816 nm and a pulse energy of 6 nJ. The laser pulses are p-polarized and hit the sample at an angle θ = 65° with respect to the sample surface normal. More details of the experimental setup are described in [12].

For the experiments in the counter-propagating scheme we used 60 nm thick gold films evaporated onto a silicon substrate (see Fig. 1(f)). A 2.25 µm wide and 140 nm high gold bar was fabricated on top of the gold film by means of electron beam lithography, gold deposition via evaporation, and lift-off. The two edges of the gold bar can provide the wave vector required to overcome the wave vector mismatch between laser field and SPP [13] and are used in the experiment as defined and localized sources for SPP wave packet emission. For some of the experiments a 45 nm thick film of para-Hexaphenylene (p6P) molecules was evaporated onto the gold film. Reference measurements in the co-propagating scheme were performed at a flat rectangular gold pattern on silicon (see Fig. 1(e)). In this case, the wave vector required for SPP excitation was provided by an edge of the gold pattern.

Prior to the PEEM measurements, the sample was covered under UHV conditions with a small amount of Cesium (coverage << 1 monolayer) from a well degassed resistively heated SAES getter source. This treatment is required to lower the work function of the gold surface from a value of about 5.5 eV to about 3 eV to facilitate a two-photon photoemission process with the 816 nm light pulses.

3. Results and discussion

Figures 1(c) and 1(d) compare ITR-PEEM data of SPP wave packet propagation in co-propagating and counter-propagating PEEM detection mode for two different temporal delays τ between the applied laser pulses. The characteristic beating pattern and its modulation as function of delay observed in the co-propagation mode results from the superposition of SPP induced polarization field and laser pulse and agrees qualitatively well with data reported for silver films by other groups before [7, 9]. The periodicity of the beating pattern (7.25 ± 0.15 µm) is given by the wave vector mismatch between laser field and SPP and, therefore, allows determination of the wave vector k_SPP and the phase velocity v_p,SPP of the SPP. Two different contributions in the imaged superposition field have to be distinguished: A dominating static (delay-independent) term that starts right at the excitation edge of the gold film and that is damped in the direction of SPP propagation. It is formed by the interference between SPP wave packet and the laser pulse responsible for its excitation. Additionally, in the very vicinity of the edge, this signal may also be affected or even dominated by contributions from the excitation of so-called quasi-cylindrical waves (cw waves) [14]. An estimation based on Eq. (20) given in reference [14] yields a maximum distance of ≈3.5 µm at which the amplitude of the cw wave should dominate the SPP field. Indications for the presence of cw contributions in the PEEM signal for plasmon excitation at a metallic edge have been reported in reference [15].

It can be shown that the detected amplitude decay of the superposition field is governed by the damping length of the SPP and, furthermore, by the mismatch in the group velocity between SPP and laser pulse: As the laser pulse passes the SPP wave packet the intensity of the probed superposition field gradually decreases.

The other contribution to the co-propagation PEEM signal arises from the interference between second laser pulse and the SPP wave packet excited by the first laser pulse. It consequently exhibits a distinct dependence on the temporal delay τ between the laser pulses, which is adjusted by the interferometer. This signal is the actual probe of the SPP propagation in this experimental scheme. The most distinct feature that can be associated with this contribution is the increase in relative photoemission intensity at large distances from the excitation edge as can be seen in Fig. 1(c) in the comparison of the data recorded at τ = 40 fs with the data recorded at time-zero: for large delays τ the second laser pulse probes the propagating SPP wave packet at later times, i.e. more distant from the SPP excitation edge. It is rather evident that the entanglement of the co-propagation signal and the dominating static background in these data makes a quantitative analysis with respect to the SPP propagation dynamics difficult.

In the counter-propagating SPP imaging mode the propagation signal is much less affected by the static background as demonstrated in Fig. 1(d). Now, the laser field is incident from the right and probes the SPP wave packet propagating in opposite direction. The most distinct difference in comparison to Fig. 1(c) is the significantly shorter decay length of the static superposition background (note the different length scales in Fig. 1(c) and Fig. 1(d)). This is a direct consequence of the propagation of laser field and SPP wave packet in opposite directions which guarantees that both fields overlap for a very short time, only, virtually given by the temporal width of the excitation laser pulse. One observes, furthermore, a reduction in the period of the beating pattern to a value of 423 nm ± 10 nm as the relative orientation of the interacting wave vectors is changed. We would like to note that interference patterns arising from the counter-propagation of the excitation laser field and the SPP wave have been observed before for instance in a study on a 100 nm thick gold film using scanning near-field optical microscopy [16]. Furthermore, recent FDTD simulations on the SPP excitation at defined nanometer-scaled slits in a silver film provided also evidence for the existence of such a signature in ITR-PEEM experiments [15].

The efficient suppression of the static background signal in this imaging mode as observed in our study enables one to obtain a much more distinct view onto the propagation of the SPP wave packet. As seen in the image recorded at τ = 40 fs, the signal arising from the interference between second laser pulse and propagating SPP wave packet excited by the first laser pulse is now well separated from the static background and clearly resolved. Note that the identical temporal delay applied to the two detection modes does not correspond to the same SPP propagation distance. Counter-propagation snapshots recorded at varying temporal delays τ between the two laser pulses allow one to directly follow the propagation of the SPP wave packet. The results of such a pump-probe scan are summarized in Fig. 2(a) in terms of a delay-path diagram. For this depiction photoemission intensity line profiles were deduced for each delay τ by integration along the vertical axis of the PEEM image. In addition, the displayed data are background corrected by subtraction of reference data recorded at τ = 0 fs and each line profile is normalized to its maximum. At small propagation distances some residuals of the static superposition background are still visible because of a non-perfect background correction. Furthermore, at these distances the signal may also be affected by the presence of cw waves.

 

Fig. 2 (a) Delay-path diagram of SPP propagating at the gold-vacuum interface deduced from the ITR-PEEM measurements, (b) corresponding delay-path diagram as deduced from an analytic simulation (c) delay-path diagram of SPP propagating at the gold-p6P interface; note that in the latter case the second SPP wave packet excited at the left hand edge of the gold bar is not observable; the green dashed line in the graph marks a trace along an interference maximum; the red dashed line follows the envelope maximum of the SPP-laser superposition signal.

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The relevant signature in the delay-path diagram arises from the superposition signal between first SPP and second laser pulse. It exhibits a linear slope which is governed by the phase and the group velocity of the SPP. In more detail, the depiction shows that the superposition signal contains two distinct contributions (see blue arrows), a dominating leading beating pattern, followed by a weaker second beating pattern. We will see later that the two signals arise from different SPP excitation processes at the gold bar. For now, we will concentrate on the analysis of the dominant leading part of the cross-correlation signal. The slope τ / x_p of the straight line defined by an individual beating maximum resulting from constructive interference (see for instance green dashed line in Fig. 2(a)) is governed by the phase velocity of SPP and laser pulse. It can easily be shown that

Correspondingly, the slope of the envelope maximum of the beating signal, τ / x_g (see red dashed line in Fig. 2(a)), is related to the group velocity v_g,SPP of the SPP wave packet:

 

Fig. 3 (a) signal envelope of the laser-SPP superposition pattern for different temporal delays between 65 fs and 120 fs; for better illustration, the signals have been normalized to the envelope maxima; the full lines show Gaussian fits to the data to determine the position x_g of the envelope maxima; (b) shows a plot of x_g versus τ inclusive linear fit.

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Above, it has been mentioned that the second laser-SPP superposition signal following the main peak in Fig. 2(a) at significantly reduced amplitude can be associated with a second SPP wave packet that has been excited at the gold bar. A quantitative analysis of the pulse envelope of this wave packet signature shows that it follows the main peak at a distance of 4.5 µm, which exactly corresponds to twice the width of the gold bar. We suggest that we observe here a SPP wave packet that was excited at the gold bar in co-propagating direction and that was then back-reflected at the left hand edge of the gold bar. A corresponding beating pattern is indeed observed on top of the gold, as seen for instance in Fig. 1(d). The reduced amplitude of the signal in comparison to the preceding wave packet is associated with a finite reflectivity of the left hand edge and a finite transmission probability as the pulse penetrates the right hand edge of the gold bar.

To further support our data interpretation we performed analytic model simulations of ITR-PEEM data under consideration of the relevant parameters used in the experiment, such as sample geometry, excitation and probing geometry, and laser pulse width and wave length. To account for the propagation properties of the SPP wave packet dielectric data tabulated in [18] were used. The results of the simulation are summarized in the delay-path diagram in Fig. 2(b). A comparison with Fig. 2(a) clearly shows that the relevant signatures considered in this work are quantitatively well reproduced. The analysis of the simulated data yields correct values for group and phase velocity and also the two-peak structure in the delay-path diagram agrees with the experimental data.

For illustration of the sensitivity of the counter-propagating PEEM mode to changes in the propagation properties of the SPP, Fig. 2(c) shows data recorded for a gold film covered with a 45 nm thick p6P film. The dielectric response of the organic overlayer acts dispersive onto the SPP wave packet propagation and consequently modifies v_p,SPP and v_g,SPP. The distinct changes in the slopes of the phase trace (dashed green line) and the envelope maximum trace (dashed red line) in comparison to the results for the gold-vacuum interface (Fig. 2 (a)) are characteristic for these modifications. The quantitative analysis of the p6P data yield v_p,SPP = (0.88 ± 0.04)⋅c_Vac and v_p,SPP = (0.60 ± 0.04)⋅c_Vac and indicates the enhanced dispersive character of this interface in comparison to the gold-vacuum interface. Note that for the p6P sample a second SPP pulse is not resolved in the data. A likely explanation is a reduction in reflectivity and/or transmission of the gold edges by the presence of the p6P film.

4. Conclusion

The spatio-temporal characterization of propagating surface plasmon polaritons becomes important as potential applications rely more and more on SPP pulse profiles in the low femtosecond time regime. In this work a PEEM-based scheme has been presented that provides an efficient experimental access to the characterization of relevant propagation properties of SPP wave packets. The present experimental configuration is particularly suitable for the study of two-dimensional systems such as for instance multilayer systems, where the interaction of SPP modes located at different interfaces becomes relevant. A further aspect that was not addressed in this study is the effect of SPP pulse broadening in a strongly dispersing environment. The signal probed in the counter-propagating PEEM scheme is essentially a cross correlation signal so that a data analysis should in principle also provide information of SPP pulse broadening effects. Even more, the phase sensitivity of the used interferometric approach could in future experiments allow for quantitative insights into the phase modulation of the SPP wave packet.