1. Introduction

Surface plasmon polaritons (SPPs) are propagating electromagnetic waves at the metal-dielectric interface, which has great potential as next-generation information carriers for highly integrated nanophotonic devices [1–3]. Accurate acquisition of the spatiotemporal characteristics of SPPs is an important prerequisite for realizing SPP as information carriers [4]. However, due to the nanoscopic and dissipative nature of SPPs, microscopy with the high spatial and temporal resolution is required for detailed characterization. As one of the outstanding microscopic techniques, multi-photon photoemission electron-based femtosecond interferometric time-resolved photoemission electron microscopy (ITR-PEEM), combining the merits of high temporal and spatial resolution with highly parallel data acquisition, is suited for studying spatiotemporal imaging of ultrafast SPPs [5–7].

PEEM images SPPs field by collecting the electrons emitted from the sample surface based on the photoelectric effect, where the electrons emitted process is typically a multiphoton photoemission (MPPE) processes [8,9]. Although most existing techniques used to visualize SPPs utilize single-color PEEM, the melting and sample restructuring can easily occur of such measurements since the high local field on sample surface is required to obtain nonlinear signal that meets the needs of the probe at a distance from the nanostructure [10]. To avoid the above limitations, it is usually to reduce the nonlinear order of MPPE processes to enable the sense of SPPs, a deposition of a thin layer of alkali metal (e.g. cesium) on the surface of the structure to reduce work function of the sample surface was previously employed [11–13]. The method was proved effective in visualizing the SPPs field. However, it is difficult to be practical due to the high reactivity of the alkali metal and inevitably affects the plasmon field [14,15]. Very recently, two-color PEEM imaging of the localized and propagating surface plasmon has been performed to obtain distinct localized plasmon or SPPs with a degenerated local field [16,17]. The advantage of such measurements is that it can achieve better imaging sensitivity by enhancing photoelectron yields and achieve imaging of the plasmon field below the sample damage threshold. Alan G. Joly et al. reported to use 800nm and 400nm spatially-overlapped femtosecond pulses for imaging the SPP and with the assistance of numerical analysis to determine the group velocity of SPPs excited by 400nm pulses [10]. However, in their scheme, although the high local field like the monochromatic case was avoided to get a PEEM image, rather complex entangled interference fringes had appeared due to the overlapping of fringes formed by 800nm and 400nm light respectively, which seriously diluted the information of SPPs obtained via the interference fringes. Thus amplitude and absolute phase, as well as other useful information on the traveling SPPs are difficult to recover from the SPP trajectories because of the entanglement of interference fringe between the SPPs and probe pulse induced by 800nm and 400nm light pulses respectively. Moreover, the mechanism of electron emission during the SPPs spatiotemporal imaging process optimized for two-color PEEM is simply attributed to the interaction between different fields [10]. A further quantum explanation of the mechanism of photoelectron emission in the two-color scheme has not been revealed, which is helpful to understand the quantum properties of SPPs and expand the field of the two-color scheme, such as to the imaging SPPs in the communication wave band.

In this paper, we achieved distinct spatiotemporal imaging of femtosecond SPPs with 400nm-assisted near IR femtosecond laser interferometric time-resolved PEEM imaging technology. The scheme consists of two spatially-separated near-infrared (∼800 nm) as the pump-probe setup to avoid the entanglement of interference fringe. Here a weak probe pulse is intentionally employed to remove the risk of sample damage. Additionally, a 400nm (the second harmonic from femtosecond laser) pulses is used to open the two-color quantum pathway and enhance the quantum pathway interference effect for improving the visualization of interference fringe stemming from SPPs and pump-probe pulse. Two-color quantum pathway refers to electron emission by absorption of non-degenerate photons in multiphoton photoemission. Here, two-color quantum pathway is employed as it can lead to a dramatic reduction of the nonlinear order of the plasmon-assisted photoelectrons (compared to the 800 nm near-infrared only induced photoemission process) due to the participation of 400 nm photon, and results in a huge increment of the photoemission yields. It is found that the contrast of the SPPs dynamic interference fringes is significantly enhanced by the participation two-color quantum pathway. Thanks to distinct spatiotemporal imaging of non-entangled interference fringe of the dynamic SPPs, the carrier wavelength (785nm), group velocity (0.94c) and phase velocity (0.98c) are obtained. To the best of our knowledge, the quantum pathway interference model was employed for the first time to fit the experimental results of SPPs images, and this enables us to obtain the probabilities of electrons emission in different quantum channels quantitatively. It is suggested that the two-color scheme can be used in the imaging of SPPs in the communication wave band.

2. Experimental details

The rectangular 10×1µm² trench coupling structures are milled into a ∼100 nm thicknesses silver film on a clean Si substrate using focused ion beam (FIB) lithography. Figure 1 shows the schematic diagram of experimental setup. A commercial Ti: sapphire laser at a central wavelength of 800nm with a spectral bandwidth extending from 600∼900nm (FEMTOLASERS; Rainbow, 76MHz repetition, 7fs pulse width) is utilized for the excitation of SPPs. Chirp mirrors pairs are used in the beam path to compensate for the optical dispersion for obtaining the minimal pulse duration at the sample position. A beam-splitting mirror (BS1) is used to divide the laser pulse into two paths with equal intensity. One path entered the Mach–Zehnder type interferometer to generate two pulses pair with the same fundamental frequency of 800nm, while the other path is employed for a second harmonic generation (SHG) by a β-BaBO3 (BBO) crystal. The intensities of these three laser pulses can be adjusted independently by neutral density filter wheels. Moreover, the polarization direction of the three beams is P polarization. The incident laser are focused onto the sample surface at an incident angle of 65° respect to the surface normal. The spot sizes of the separate beams are adjusted such that the red pulse spot size is roughly 50% smaller than the blue pulse spot size at the sample position. A typical spot size for the red laser is 70µm×120µm at the sample. A typical work function of silver, depending on the crystal orientation and morphology of nanostructure, is around 4.26 eV. In our experiment, the power range of the two fundamental frequency pulse is 25∼60mW (pump light) and 15∼40mW (probe light) respectively, while the power of the second harmonic pulse is fixed at 1mW. To achieve better interference between SPP and probe pulse in the probe pulse area, the power of the probe pulse is slightly lower than the power of the pump pulse.

 

Fig. 1. Experimental set up of the two-color three beams scheme. The laser pulse is compensated for dispersion by a group of chirped mirrors and then split by BS1 after passing through silver reflective mirrors M0-M4. Part of the light generated by the beam splitting enters the Mach-Zehnder interferometer. BS2 is a beam splitter, BS3 is a combiner, and M5-M8 are silver mirrors. The partial beam passing through the BS1 is converted into SHG by a β-BaBO3 (BBO) crystal. L1 and L2 are convex lenses with a focal length of 200 mm and 125 mm, respectively. After that, the two silver mirrors M9-M10 are used to combine with the 800 nm pulse through the combiner BS4. Finally, it enters PEEM via the off-axis parabolic mirror L3.

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3. Results and discussion

Figure 2 shows our experimental sketch and PEEM images recorded following (i) Near-infrared femtosecond laser interference time-resolved scheme (NIR pump-probe) (ii) 400nm-assisted near IR femtosecond laser interferometric time-resolved scheme (400nm-assisted NIR pump-probe). To avoid the entanglement of the static interference fringe formed by the interference between SPPs wave packet and the laser pulse responsible for its excitation (termed the “pump” pulse from hereon) and the dynamic interference fringe formed by the interference between second laser pulse (termed the “probe” pulse from hereon) and the SPP wave packet excited by the pump pulse, a spatial separation of these two pulses was proposed. Excitation of the trench structure with ultrafast pump laser pulses launches surface plasmon wave packet propagating in the Y-direction. Figures 2(b) and 2(c) displays ITR-PEEM images recorded at different pump-probe delay time for the two schemes respectively (we vary the time delay ${\Delta {\textrm{t}}}$ between pump and probe pulses, and both pulses are at the wavelength of 800 nm). We define Δt = 0 when the SPPs and probe pulses are overlapped in time. Figure 2(b) shows that, under one color scheme, static interference fringes induced from the interference of SPPs and the 800 nm excitation field can be observed near the trench and the blurred SPPs dynamic fringes generated by SPPs with probe pulse are hardly visible in the probe zone.

 

Fig. 2. (a) Sketch map of our experiments: the pump pulse and probe pulse are spatially separated. The SPPs generated by the pump pulse is detected by the probe pulse at more than one hundred microns away from the plasmonic trench structure. The second harmonic pulse irradiates the entire field of view. (b)Photoemission interference patterns acquired by a NIR pump-probe scheme at different relative delays of pump and probe pulse. The right side yellow dash line ellipses mark the probe zone. (c) Photoemission interference pattern in a UV-assisted NIR pump-probe scheme obtained by maintaining the same experimental conditions as the NIR pump-probe scheme except for introducing a second harmonic pulse at 400nm. The yellow dotted ellipse on the left and right sides in (b) and (c) represent the zones irradiated by the pump pulse (left side) and the probe pulse (right side). The out- ring blue dotted ellipse in (c) represents the regions where the second harmonic pulse irradiates. The small white dash squares represent the trench position. The green dotted arrow in (c) marks the SPP propagation at different delays. Pump and probe pulses are polarized with the electric vector parallel to the out-of-plane axis (p-polarization). Laser pulses propagate from the left to the right in b−c.

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Figure 2(c) displays the time-resolved PEEM images recorded following the 400nm-assisted scheme with the various time delay between pump and probe pulses (both at 800nm). The experimental conditions for Fig. 2(c) are the same as that of Fig. 2(b) except for introducing a second harmonic-400nm pulse. The time delay between 800nm pump pulse and 400nm pulses is fixed at which maximum photoemission was obtained in the cross-correlation photoemission curve. It shows that, after introducing the 400nm pulse, the brightness of static stripes formed by 800 nm pump pulse near the trench is increased (nearly 6 times higher than that of the NIR pump-probe scheme). Importantly, the Fig. 2(c) exhibits additional distinct interference fringes appearing in the 800nm laser probe zone in the PEEM images and newly-emerged interference fringes shift along the Y-direction when the delay is increased as shown in the middle and lower panels of Fig. 2(c). The shift of fringe indicates dynamic SPPs propagation. For a guide of eyes, a green dotted arrow is used in Fig. 2(c) to mark the propagation of SPPs along the Y-direction at different delay times. The dynamic interference fringes of SPPs, which are absent in the NIR interferometric time-resolved scheme, are clearly distinguished with the assistance of 400nm laser pulse. The dynamic interference fringes propagate along Y direction at different delay times in Fig. 2(c) suggest the temporal evolution of SPPs emanating from the trench.

According to the fringe shift of SPP in Fig. 2(c), the group and phase velocities of the SPPs are calculated to be 0.94c and 0.98c respectively, and they are consistent with previous literature [18]. Besides, a periodicity of 7.1µm of the beating pattern formed by the superposition of the probe pulse and the SPPs is also obtained. Accordingly, SPPs carrier wavelength is measured to be 785 nm. Thanks to the assistance with 400 nm femtosecond laser pulse in the PEEM imaging, a distinct spatiotemporal visualization of SPP propagation can be realized, enabling quantitative analysis of the dynamics of SPPs.

Please note that in the current scheme a weak 400 nm (the second harmonic from femtosecond laser) femtosecond pulse is used to open the two-color quantum pathway for improving the visualization of interference fringe stemming from SPPs and pump/probe pulse formed by 800 nm light rather than used to generate interference fringes stemming from SPPs and pump/probe pulse formed by 400 nm as Alan G. Joly et al. performed [10]. Thus the interference fringes we observed are only induced by 800 nm light pulse and the rather complex entangled interference fringes caused by 400 nm and 800 nm light are avoided. As a result, the group and phase velocities of the SPPs induced by 800 nm are easily obtained.

To reveal the underlying physics responsible for realizing distinct spatiotemporal visualization of the SPPs field with a 400nm-assisted scheme in PEEM, we measured the power dependence of the NIR femtosecond ITR scheme and the 400nm-assisted ITR scheme, respectively, and the results are shown in Fig. 3. Figure 3(a) displays the 800nm laser power dependence of the normalized photoemission yield under the NIR interference time-resolved scheme. It is found that the value of the slope is 2.82, indicating at least three 800nm photons are required for photoemission from this silver surface. Thus, a 3-photon photoemission process has been confirmed to be the dominant mechanism. Figure 3(b) displays the total power (pump + probe) dependence of the 800nm pulses with the presence of 1mW 400nm laser power. The yellow dotted circles in the inset of Fig. 3(b) label the detected zone. It shows a slope value of 1.17 and indicates a variation of the photoemission nonlinear order from three-photon to two-photon (one 400nm and one 800nm photon), which can be attributed to that the two-color quantum channel for photoemission has been effectively opened.

 

Fig. 3. (a) Power dependence of the total photoelectron yield of 800 nm laser pulse in the NIR pump-probe scheme. (b)Power dependence of the total photoelectron yield of the 800 nm laser pulse after applying the second harmonic pulse. The yellow dotted line circles in the inset PEEM images mark the measurement position of the power dependence. The other two insets in figure a and b show the corresponding dominant electron emission mechanism. (c-d) The power dependence of the probe pulse and the pump pulse in the UV-assisted NIR pump-probe scheme. In all power-dependence measurements involving the second harmonic pulse, the power of it is 1 mW. For the three beams power-dependent measurements, the background signal induced by the non-varied laser is subtracted.

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Figures 3(c) and 3(d) display the dependence of the normalized photoemission yield upon the probe pulse only (Fig. 3(c)) and the pump pulse only (Fig. 3(d)) at the same position under 400nm-assisted scheme, respectively. During the measurement, the power of the 400 nm pulse and the pump laser (in Fig. 3(c)) or probe laser (in Fig. 3(d)) were kept unchanged. Figure 3(c) and 3(d) show that the slope of the probe pulse and pump pulse power dependence are measured to be 0.57 and 0.61. Note that multiphoton photoemission corresponds to a quantum process. The results in Fig. 3 show the multiphoton photoemission is realized through contributions from surface plasmon and probing photon in our two-color scheme. Therefore, our experimental results suggest the quasiparticle property of SPP [19]. The results suggest that the energy for one electron overcoming the material work function is partly supplied by adsorbing one 400 nm photon, and the rest part is supplied by 800 nm photon that jointly contributed by pump pulse that induces SPPs and from probe pulse, in which the pump and probe pulse supply with 50% probability respectively. It is worth pointing out that the experimental results reflect the absorption probabilities for the SPPs and probe pulse in this configuration.

To gain further insight into the underlying process of distinct visualization of dynamics SPPs, a comparison of the interference fringes with and without the 400 nm pulse is performed. Herein, we employ a typical dynamic interference pattern as shown in Fig. 4(a) to perform the analysis. The PEEM image is obtained by the 400nm-assisted scheme when the relative time delay between the pump pulse and the probe pulse is 8.01fs. The line profile of photoelectron under the different exciting condition at the position (marked by the yellow rectangular dashed box in Fig. 4(a)) is extracted, as shown in Fig. 4(b).

 

Fig. 4. (a) PEEM image with 800 nm pulses delay of 8.01fs in the UV-assisted NIR pump-probe scheme. The blue and white dash squares in the figure were used to mark the sources of photoemission at the bright and dark stripes, respectively. The extraction location of the SPPs line was performed in the yellow rectangular dashed box in the image. (b) The profile lines in red, blue and black represent the cases of the NIR pump-probe scheme, 400 nm(1 mW) pulse alone, and the UV-assisted NIR pump-probe scheme, respectively. The average photoemission intensity from the dark fringe is labeled by a green dot line. The photoemission at the position of the dynamic fringe of the SPPs is mainly provided by the interaction of pump pulse(R), probe pulse(R) and blue pulse (B).

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Figure 4(b) displays that line profile of the photoelectron from the interference fringe induced by SPPs with the probe laser pulse (black and red lines cases) and local photoemission from only 400 nm irradiation (blue line). It can be seen that clear fringe with a 400nm-assisted scheme (black line) has been obtained compared to the case without 400 nm irradiation (red line) in which the fringe is hardly visible. The greatly improved visibility of the fringe in the PEEM image while observed with the assistance of 400 nm femtosecond laser pulse results from the new opening of the two-color quantum pathway, which is achieved by electron absorption of one 400 nm photon and an 800 nm photon supplied by either SPPs or probe pulse. The quantum pathway at the bright fringes induced by the constructive interference between the SPPs and the probe pulse is mainly composed of three components: the electron interacts with 800 nm or 400 nm photons only, or particularly with both [16]. Among these pathways, it is inferred that the photoemission process through the two-color pathway dominates as depicted in the inset of Fig. 3(b) in the probe region in the 400nm-assisted NIR pump-probe scheme as it can greatly enhance the photoemission in contrast to the case excited with the monochromatic photon. As a result, the electron emission at the bright fringes further increases due to nonlinear order reduction in the multiphoton process. On the other hand, only the 400 nm laser beam contributes to the photoemission in the dark fringes formed by the destructive interference between SPPs and probe pulse, and conditions for the effective opening of the two-color pathway can't be reached. Therefore, a distinct visualization of SPPs (interference fringe) is attributed to the participation of two-color quantum pathways in the probe zone.

The obtained distinct dynamic fringes of SPP can be further analyzed by the quantum pathway interference model. Particularly, the contribution to electron emission through one-color as well as two-color quantum pathways in the 400nm-assisted scheme can be quantitatively obtained by fitting the experiment results with the quantum pathway interference [20]. According to the previous research of the quantum pathway for MPPE, emission can be achieved by either absorption of 2 photons from SHG or one photon from fundamental laser pulse and SHG [21,22]. As a result, the possible quantum pathways for electron emission is schematically shown in Fig. 5(a):

 

Fig. 5. (a) The illustration of the multiphoton photoemission process from six quantum pathways ${\textrm{A}_0}$ to ${\textrm{A}_5}$. Since the quantum channel of 400 nm two photons contributes very little to the overall electron yield in the experiment, the contribution of this quantum channel electron yield is neglected. The black arrow, red arrow and blue arrow represent the photon absorbed from the pump, probe and second harmonics pulses by electron, respectively. FL and VL represent Fermi level and vacuum level; E, energy. Numerical fitting of experiment results in the same relative time delay by quantum pathway interference model for the NIR pump-probe scheme (b) and UV-assisted NIR pump-probe scheme(c).(d) The probability of photoemission from different quantum pathways. It is noted that the abscissa represents the relative position in (b) and (c).

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Thus, the photoelectron yield $Y(\tau )$ can be obtained as

We first use the single-color quantum channel model to numerically fit the experimental results in the NIR interference scheme and obtain the fitting coefficients α and β of the pump pulse and the probe pulse, respectively. Since the experimental conditions of the 400nm-assisted interference scheme are the same as those of the single-color scheme, the ratio of $\mathrm{\alpha}/\mathrm{\beta}$ is fixed for both the experimental result due to the same ability of electron interacting with SPP and probe pulse. Based on it, the experimental results of the 400nm-assisted scheme were further numerically fit according to the fitting coefficient obtained in the single-color scheme, and obtain the fitting coefficient of the second harmonics pulse. θ. The fitting coefficients $\mathrm{\alpha}$, $\mathrm{\beta},$ and θ are 0.1011,0.099 and 2.323, respectively. According to the fitting coefficients $\mathrm{\alpha}$, $\mathrm{\beta}$, and θ, we can obtain the probability of electron emission through different quantum pathways by ${|{{A_n}} |^2}$ from Eqs. (1) and (2) in the 400nm-assisted scheme, and the obtained probability of electron emission are displayed in Fig. 5(d). The figure shows that electron is mainly emitted (86%) through a two-color quantum pathway (${A_4},{A_5}$) and only a few electrons (14%) can be emitted through the single-color quantum channel. Specifically, for the single color channel, electron emitted from the pathways of ${\; \; }{A_0}{\; },{\; \; }{A_1},{\; }{A_2}$ and ${A_3}$ are with probabilities of 3%, 1%, 6% and 4%, respectively. Moreover, it is noted that the probability for electrons emitting from the two-color quantum pathways ${A_4}\;\textrm{and}\;{A_5}$ is very close, indicating that electron is emitted with similar probability for the absorption of pump and probe pulse, and this is consistent with the photoemission order we obtained from the power dependence of the probe pulse and the pump pulse in the 400nm-assisted scheme as shown in Figs. 3(c) and 3(d). The probability that electrons emitted through the quantum pathway model allows us to quantitatively analyze the contribution to electron emission from the two-color quantum channel as well as the single-color channel formed by SPPs pulse, NIR probe pulse or both in the SPP dynamic fringe zone respectively in the PEEM images.

4. Conclusions

In summary, we have utilized the 400nm-assisted NIR interferometric time-resolved PEEM for imaging the spatiotemporal evolution of femtosecond SPPs. The advantages of non-entangled interference fringe (between the SPP and probe pulse), avoidance of high-intensity one-color light field but with huge photoemission and effective opening of the two-color quantum pathway have been combined in this scheme. Our results show that a clear visualization of SPPs in the metal film has been realized in the weak probe pulse mode with the assistance of 400nm laser pulse in the NIR interference time-resolved experiment. The successful imaging of the dynamic SPPs with a weak probe pulse is attributed to the effective opening of the two-color quantum pathway under the 400nm-assisted spatially-separated pump-probe NIR time-resolved experiment that significantly reduces the nonlinear order for the photoemission process, and consequently, greatly increase the photoemission at interference constructive fringe. The opening of quantum pathways by the 400nm pulse improves the contrast of the SPP interference fringe, allowing us to characterize the spatiotemporal imaging process of the femtosecond SPP and accurately determine its wavelength, group velocity, and phase velocity information. Moreover, the probability of electrons emission from different pathways is determined by fitting the quantum pathway model to the profile of the distinct SPPs image. Using 400nm-assisted NIR time-resolved scheme to detect SPPs is expected to provide a flexible way for controlling the nonlinear order of photoemission as well as the photoelectron yield, which is a benefit for expanding the imaging of plasmonic field from visible, near-infrared to optical communication waveband.