1. Introduction

The localized surface plasmon (LSP) of metal nanoparticles is the result of a collective oscillation of the interaction between the conductive electrons and the incident light [1]. The plasmon dephasing process [2,3] is closely related to its practical application. Accurate measurement, manipulation, and, ultimately, prolongation of the dephasing time are the prerequisites to realize active control of photocatalytic efficiency [4] and thereby greatly benefit emerging sensor sensitivity conversion technologies [5].

In recent years, researchers have begun to manipulate the plasmon dephasing time by adjusting the spacing of coupled particles [6], the size of the stacked structure [7] or the period of the array structure [8], which is attributed to the change in coupling strength between two LSPs or between an LSP and a surface plasmon polariton. All of the aforementioned approaches of manipulating the dephasing time have a common feature in that dephasing time depends on complex structures and it cannot be dynamically reconfigured flexibly, i.e., active control of the dephasing time cannot be achieved, which limits plasmonic engineering applications. In addition, the dephasing time measured using the array structure includes the effect of inhomogeneous broadening [9], and averaging effects from the different sizes and shapes present in the samples cannot be removed [10]. The overall effect involved in the dephasing time measurement masks the nature of the individual plasmonic hotspot. Different plasmonic hotspots in a single structure can differ in their properties because of deviations in the local morphology of the structure [11]. Therefore, the high spatial study of different hot spots under a single structure will pave the way to a deeper understanding of the properties of plasmons and thereby enable their further exploitation.

In this paper, the plasmon dephasing time at different hot spots in single bowtie nanostructure is studied using interferometric time-resolved techniques combined with photoemission electron microscopy (ITR-PEEM) [12,13]. We found that the dephasing time can be strongly modified by plasmon mode variation induced by simply changing the polarization direction of the femtosecond laser, which provides an easy-to-operate method to flexibly control the dephasing time. In contrast to those previous global-parameter descriptions, we here report the experimental observation of apparently spatially diverse plasmon dynamic characteristics and spatially different dephasing time within a plasmonic bowtie. Experimentally, by adjusting the laser polarization direction, the minimum dephasing time of 7 fs and the maximum dephasing time of 17 fs are obtained, exhibiting a large range of dephasing time manipulation. In addition, the dephasing time of plasmons with and without defects is compared. Assisted with the finite-difference time-domain (FDTD) simulation, we proved that the small structural protuberant defect induces a local mode with long dephasing that hybridizes with the shorter-lived mode of the hotspot and extend the dephasing time of the hotspot where there is with an extra small protrusion.

2. Experimental details

A photoemission electron microscope (IS PEEM, Focus GmbH) was used in this study. PEEM enables high-spatial-resolution imaging with the ability to accurately locate near-field characteristics of plasmon modes. As an excitation source, we used either a mercury lamp or a Ti: sapphire laser excitation source with a single pulse energy of 4 nJ, a repetition rate of 75 MHz, a center wavelength of 800 nm, and a spectral bandwidth from 600 to 900 nm (FEMTOLASERS; Rainbow). At the sample position, the pulse duration was measured to be 9 fs. In ITR-PEEM measurements, chirp mirror pairs and wedge pairs are used to compensate for dispersion to achieve the shortest possible pulse duration in the PEEM chamber. The experimental setup is shown in Fig. 1(a). Throughout the paper, the femtosecond laser pulses illuminate the sample along the x-axis direction at an incidence angle of 65° with respect to the surface normal from the right side, and PEEM is used to collect the emitted electrons for imaging. The polarization direction of light along the x-axis is defined as the 0° polarization angle. The combination of PEEM and pump–probe techniques specifically, time-resolved PEEM was established to investigate the dynamics of LSPR and thus study plasmon dephasing time. The interference time resolution device consists of a Mach–Zehnder interferometer. The details of the experimental setup have been described in our earlier report [14]. Notably, we took advantage of the wide spectrum of the laser pulse and PEEM image to determine the zero time: after obtaining a rough position of the zero time (within −π to π), we further determined the zero-time delay between two separated pulses (with an error less than π/8) by finding the strongest photoemission intensity from a series of PEEM images.

 

Fig. 1. (a) Schematic of the ITR-PEEM experiment with p-polarized laser pulses at a 65° incident angle off the normal of the sample. (b) Scanning electron microscopy (SEM) image of the bowtie nanoparticle (upper); PEEM image of the structure illuminated by a mercury lamp source (one-photon photoemission) (bottom).

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The sample we used is a gold bowtie structure, which was prepared by electron-beam lithography. The sample preparation procedure was as follows. Glass coated with indium tin oxide (ITO) was used as the substrate. The top of the ITO layer was coated with a resist. The nanometer prism was formed after etching and resist development. A gold layer with a thickness of 40 nm was then sputtered onto the developed samples. Finally, after the lift-off process, sample preparation was completed. Figure 1(b) shows a typical scanning electron microscopy (SEM) image of the bowtie structure. The bowtie structure is composed of an equilateral triangle with two sides 357 nm in length, and the gap between the two triangles is 105 nm. The bottom image in Fig. 1(b) shows the PEEM image under a mercury lamp. The cut-off photon energy of a mercury lamp is 4.9 eV, and the typical gold material has a work function of approximately 4.5 eV. The one-photon PEEM image obtained under Hg light excitation was a direct observation of the morphologies of the bowtie structure and served as a reference to determine the localized photoemission induced by the femtosecond laser pulses.

The near-field distribution and charge distribution of the bowtie structure were simulated using the finite-difference time-domain (FDTD) method. FDTD modeling was performed using the FDTD Solutions software (Lumerical, Inc.). The optical properties of Au were obtained using data from Johnson and Christy [15]. The calculations were performed for a cubic grid under perfect matched layer boundary conditions with a discrete step size of 2 nm.

3. Results and discussion

Interferometric time-resolved PEEM was used to measure the plasmon dephasing time (T2) at different polarizations. Figure 2(a), (b), and (c) display the function of the measured photoelectron (PE) yield of H1 with the time delay between the pump pulse and the probe pulse under 150°, 135°, and 120° polarization angles. The upper insets of Fig. 2(a), (b), and (c) are the PEEM images with polarization directions of 150°, 135°, and 120°, respectively. The PEEM images clearly show that the photoelectron yield of H1 varies with the polarization angle, which is consistent with our PEEM images simulated under the corresponding polarization using FDTD software, as shown in the left insets of Fig. 2(a), (b), and (c). Note that the hot spot appears mainly at the H1 position. Numerical calculations of the time-resolved nonlinear photoemission signal were performed using a plasmon oscillator model with an exponential damping term [16], and laser power-dependence versus electron yield measurements showed a three-photon emission process, as described previously for gold bowtie structures under 800 nm femtosecond excitation [17]. The simulated curves shown in Fig. 2 yielded the best-fitted dephasing times of 11, 8.5, and 7 fs at 150°, 135°, and 120° laser polarization directions, respectively. The PE autocorrelation curve for the 150° case was selected as a typical result, and the errors for the extracted dephasing times was obtained by trying different dephasing times in the model to fit the PE curves, which gives an estimated error of ± 0.5fs. The right insets of Fig. 2(a), (b), and (c) show the charge distribution at the resonant wavelengths of 850 nm for 150°, 135°, and 120° polarizations, respectively. The charge distribution diagrams show that, at 120° and 135° polarization, the plasmon modes are both quadrupole modes with two nodes in the left triangle. Although they are all quadrupole modes, their charge distribution and density differ, indicating that the corresponding plasmons should have different properties. For comparison, under 150° polarization, the plasmon mode has three nodes, corresponding to the octupole mode. The different modes are responsible for the measured variation in dephasing time. The longer dephasing time at 150° polarization is due to the lower damping rate of the higher-order octupole mode than that of quadrupole mode at the other two polarization angles [18,19].

 

Fig. 2. PEEM signal and numerically simulated photoemission intensity by plasmon oscillator model for the hot spot H1 as a function of the delay time between pump and probe pulses for (a) 150°, (b) 135°, and (c) 120° polarization directions of the excited femtosecond laser. The insets show the corresponding PEEM images, simulated PEEM images by calculation $\smallint {|{\vec{E}({\vec{r},t} )} |^6}dt$ in the plane of incidence, and the FDTD simulated charge distribution under the corresponding laser polarization directions. (d) Normalized spectrum obtained by fast Fourier transform (FFT) of the electric-field time response of hot spot H1 under 150°, 135°, and 120° polarization directions, as obtained using an FDTD simulation.

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Moreover, the spectrum obtained by Fourier transform of the electric-field time response of hot spot H1 was obtained by FDTD simulation (Fig. 2(d)). According to the figure, the line width corresponding to the 150° polarization angle is less than those corresponding to the 135° and 120° polarization angles. The widest line width was observed for the polarization angle of 120°, which indicates that the case at this polarization angle has larger damping and corresponds to the smallest dephasing time. The experimental results in Fig. 2 show that, as a result of the mode variation caused by laser excitation at different polarization directions, the dephasing time of plasmons can be changed by adjusting the laser polarization direction. Furthermore, the polarization-dependent dephasing time can be understood by the superposition of different plasmonic modes as it has been demonstrated for example by Melchior et al. [20] i.e., light with different polarization can be decomposed into different plasmonic modes superposition, corresponding to the varied dephasing times.

Figure 3 shows the interferometric time-resolved photoemission signals at point H2 under different polarization directions. As shown in the upper insets of Fig. 3(a) and (b), when the polarization direction is further reduced to 90° and 68°, the hot spot changes to the H2 position. In particular, we observed that, at 90° polarization, the photoelectron yield of H2 is unexpectedly much higher than that of H1, which is inconsistent with the simulated PEEM image in the lower inset of Fig. 3(a), which shows that H2 and H1 should have the same intensity for a 90° laser polarization direction. The unusually high photoelectron emission of H2 is generally accepted as being caused by structural defects because the appearance of small structural defects in nanostructures (such as the tip of the nanosized bowtie) is a common phenomenon and because such defects greatly increase the photoelectron yield [21,22]. As shown in Figs. 3(a) and 3(b), the plasmon dephasing time of H2 is 17 fs and 12 fs at 90° and 68° polarization, respectively. Compared with the case of hot spot H1 at 120°, 135°, and 150° laser polarization angles, the dephasing time is further extended. The spectra of the two laser polarization angle cases shown in the inset of Fig. 3(b) indicate that the line width in the 68° case is less than that in the 90° case, indicating that the dephasing time at a 90° polarization angle should be smaller. However, this prediction is not consistent with the experimental results indicating that the 90° polarization angle case is unexpected, with a longer dephasing time. This result indicates that the dephasing time of the H2 plasmon is influenced by other factors in addition to the mode. As previously noted, the defect can be inferred as the influencing factor in the dephasing time of the plasmonic H2 in our case. The inhomogeneity of the shape or size of the structure will lead to different responses of the plasmons in the same structure with varied laser polarization angles [23].

 

Fig. 3. PEEM signal and numerically simulated photoemission intensity by plasmon oscillator model for hot spot H2 as a function of the delay time between pump and probe pulses for the (a) 90° and (b) 68° laser polarization directions. The illustrations show the PEEM images obtained by experiment and simulation. The normalized spectrum obtained by FFT of the electric-field time response of hot spot H2 under 90° and 68° polarization using FDTD simulation is given in the inset of Fig. 3(b).

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It should be pointed out that asymmetric broadening in the FDTD based spectra (Fig. 2(d) and 3(b) insets) may result from the coupling of multiple plasmonic modes. However, we believe that the coupling of multiple plasmonic modes can be negligible in our case. The reasons are as follows. Previous researches show that a PE curve with multimode coupling effect is typically characterized by either beating phenomenon or a slow decline in intensity [24]. However, the PE curves in our case do not show those obvious characteristics that owned by the coupling of multiple plasmonic modes, which indicates that the coupling effect of the involved plasmonic modes is very weak if there is any. Besides, the fittings of PE curves using the single harmonic oscillator model is generally acceptable in the current work. The noticeable deviation in the fitting dephasing time in our work, for instance in Fig. 2(c) and 3(a) is speculated to be caused by the beam drift or power fluctuation of the few-cycle lasers [11]. The power fluctuation and deviation in fitting dephasing time with few-cycle lasers has been commonly observed in previous studies as well [10,17]. The small deviation in the fitting should have a marginal effect on the measurement of dephasing time. Hence, it is reasonable to believe that the single harmonic oscillator model is still applicable in our case.

To analyze how the defect affects the dephasing time, the influence of the mode on the dephasing time should be eliminated by keeping the hot spot in the same mode. Although the plasmons of H1 and H2 are in the same mode at a 90° polarization angle, the photoelectron yield of H1 is particularly small and difficult to extract. The photoelectron yield of hot spots is difficult to extract in some cases, or the hot spots are not very isolated in other cases; consequently, finding a particularly good symmetric polarization (with respect to the x-axis) to study H1 and H2 in the same mode under this geometry is difficult. To remove the problem of incomparable photoemission yields from H1 and H2 at the aforementioned illumination geometry, we rotated the structure clockwise by 90°, in which case polarization angles of 50° and 132° were chosen to excite the bowtie nanostructure. The insets on the left side of Fig. 4(a) and (b) show that hot spots appear at H3 at 50° polarization and at H2 at 132° polarization. Notably, the hot spots appear only on the left side of the bowtie structure (away from the light source) because of the retardation effect [25]. We observed that the photoelectron emission of H2 (with a defect in the position) is higher than that of H3 (without defect at this position).

 

Fig. 4. PEEM measured and numerically simulated photoemission intensities for hot spot H2 as a function of the delay time between pump and probe pulses for (a) 50° and (b) 132° laser polarization directions. The insets show the corresponding PEEM images and charge distribution maps. (c) FDTD simulation results showing the z-component of the electric field at H2 with and without defects, lying in the plane of incidence, as a function of time. (d) Normalized near-field autocorrelation traces calculated from the fields in (c).

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The numerical fitting experimental PE curve is shown in Fig. 4(a) and (b). Under 50° polarization, the plasmon dephasing time at H3 is 10 fs, which is less than the dephasing time of 14 fs for the defective H2 at 132° polarization. The insets in Fig. 4(a) and b also give the charge distribution for the cases of the two laser polarization angles, showing that the charge distribution and intensity at H2 and H3 are consistent except for the opposite polarity. The plasmon modes should be the same according to the simulation in both cases because the two polarizations are symmetric. Therefore, in this case H2 and H3 should correspond to the same values of the plasmon dephasing time. However, the measured dephasing time of H2 is longer, indicating that the defect leads to an extension of the dephasing time. We deduced that the defect is not a lattice defect [22] because a lattice defect will promote the interband transition and increase damping, thereby decreasing the dephasing time. Meanwhile, it is most likely a structural defect; tiny structural defects are likely to occur during electron-beam lithography in the fabrication of nanostructures. The strong coupling between the plasmon field of the structural defect and the plasmon field supported by the bowtie structure can result in a high absorption efficiency, leading to a decrease in the damping rate and a greater near-field enhancement [26, 27].

The inference that a structural defect extends dephasing time was further verified from the simulation described as follows. We selected a typical structural defect in the simulation to mimic experimental conditions; a semi-ellipsoidal particle with a length of 3 nm, width of 3 nm, and height of 7 nm was used as the defect at the H2 position, and the light polarization was set to 132°. We extracted the time-domain electric field at H2 with and without the defect from the FDTD simulations (Fig. 4(c)). Figure 4(c) reveals that the structural defect induces a large near-field enhancement compared to the case of no defect, corresponding to a longer oscillation decay time [28]. According to the electric field autocorrelation equation $\smallint {|{{\vec{\textrm {E}}}({{\vec{\textrm {r}}},\textrm{t}} )+ {\vec{\textrm {E}}}({{\vec{\textrm {r}}},\textrm{t} + {\tau }} )} |^6}\textrm{dt}$ [29], the third-order interferometric autocorrelation traces can be calculated from the simulated fields (Fig. 4(d)). The plasmon oscillation frequency with structural defects is slightly larger than the one without structural defects, but the autocorrelation curve is higher, i.e. the plasmon decay is slow, corresponding to a larger the dephasing time [17]. The simulation results support that the plasmon with a structural defect has a longer dephasing time.

It is interesting to note that the agreement between FDTD calculations and experiment is shown as in Fig. 2, and there the influence of a defect to the H1 is trivial. We simulated and compared the field enhancement and temporal response of electric field in hot spot H1 and H2 under the conditions of with or without defect (size and shape of a defect taken the same as used in Fig. 4) at hotspot H2 of bowtie under 90° polarization to furtherly mimic our experiment. As expected, the near-field spectral and temporal response of the electric field in hotspots H1 and 2 without defect are the same (not shown) because the two hot spots are symmetric to 90° polarization. On the other side, Fig. 5(a) and (b) show that the near-field spectral and temporal response of the electric field in hot spot H2 when there is the defect introduced to the position under 90° polarization. It can be seen that the resonance frequency of hotspot 2 is basically unchanged, but an introduction of the defect leads to huge local field enhancement. Interestingly, the near-field spectral and temporal response of the electric field of hotspot H1 are not affected, as shown in Fig. 5(c) and (d), even though a defect is introduced to the position of H2.

 

Fig. 5. The spectra obtained by FFT of the electric-field time response of hot spots under 90° in bowtie with and without defect(a and c). FDTD simulation results showing the z-component of the electric field at H2 and H1 in bowtie with and without defect (b and d). The FDTD simulated charge distribution of the bowtie without (e) and with the defect (f).

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Furthermore, the simulated the charge distribution with or without defects, as shown in Fig. 5(f) and (e), which intuitively validates our claim that an introduction of the tiny defect in the position H2 of the nanoprism has almost no influence on the whole plasmonic mode of the structure. It clearly shows the charge distribution on the whole is basically the same in both cases, but with a limited local influence near corner H2 where a defect is sitting. Still, the charge distribution in the H1 position as well as the whole structure keep unaffected no matter there is a defect in H2 or not. The charge distribution of the structure indicates that a tiny defect has not affected the other hotspot of the nanoprism as well as the whole plasmonic mode, but only the local position in our case. The simulations suggest a small defect does not affect the whole mode of the bowtie, particularly, the other corner. Hence, it is deduced that the actual lateral size of the defect on our sample is small, and thus exhibits the characteristics as we observed in the experiment.

To glimpse physical picture of the dephasing time extension by the structural defect, the normalized spectrum obtained by fast Fourier transform (FFT) of the electric-field time response of the defect, bowtie, and bowtie with defect under 90° polarization are displayed in Fig. 6. In order to compare the line widths of the three spectra more conveniently, the spectra are normalized and the frequencies are shifted. Figure 6 shows that the individual small protrusion has the narrowest line width while the bow-tie corresponds to the widest one, and line width for the protrusion-bowtie coupling locates in the between. The results drive us to conceive how the defect influences the dephasing time of the hotspots in the bowtie. The small protrusion induces a local mode with long dephasing that hybridizes with the shorter-lived mode of the hotspots in bowtie, and the coupling of protrusion and hotspot in the bowtie extend the dephasing time of the hotspot where an extra small protrusion is sitting. The extension of dephasing time is attributed to that the coupling of small protrusions and bowtie enhances the absorption efficiency of local hot spots and reduces radiation damping.

 

Fig. 6. Normalized spectrum obtained by fast Fourier transform (FFT) of the electric-field time response of hot spot H2 under single defect, bowtie, and bowtie with a defect. In order to compare the line widths more conveniently, the spectra are normalized and the frequencies are shifted. (It needs to be mentioned that the resonance wavelength of the single protrusion is 580 nm. When it is placed at the H2 position of the bowtie, its overall resonance wavelength is basically consistent with that of the bowtie structure at 850nm.)

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4. Conclusions

In summary, we used ITR-PEEM to study the control of the dephasing time of different plasmonic hotspots in a single gold bowtie nanostructure. The experimental results showed a strong dependence of the dephasing time on the plasmon mode, which could be manipulated by adjusting the polarization direction of the excitation laser. A two-fold dephasing time of 7 to 17 fs was demonstrated in our experiment. The experimental results show that the nature of different plasmon hotspots in a single structure differs because of the deviation of the local morphology of the structure, thereby demonstrating the importance of detecting different hotspots. In addition, we found that a structural defect can greatly extend the dephasing time. The findings in this work provide a path to engineering control of the dephasing time.