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Controlling the dynamics of the plasmonic field in the nano-femtosecond scale by chirped femtosecond laser pulse

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Abstract

Arbitrary control of the electromagnetic field in femto-nano scale has attracted significant research attention in nano-photonics. Although the electromagnetic field controlled in femto-nano scale could be realized by illuminating metallic nanoparticles with femtosecond chirped laser pulses, the quantitative relation of the laser chirp and the temporal evolution of the plasmonic field hasn’t yet been fully revealed. Here, active control of the localized plasmonic field is demonstrated by a chirped femtosecond laser pulse in an asymmetric Au nano-cross system within nm-fs scale using the finite differential time domain method. The transferring of the plasmonic field between the two poles of the nanocross is determined by the laser chirp and exhibits linear dependence on the time interval between the corresponding plasmonic resonant frequencies dispersed in the chirped laser pulse. The arrival time and amplitude of the peak field from the plasmonic hot spot are determined by the superposition of the induced field excited by the on-resonant and off-resonant frequency components distributed in the chirped laser pulse. The peak field would arrive behind the resonant frequency component for sufficient oscillation of the localized field. This relative delay between the resonant frequency and field peak is influenced by the temporal distribution of the resonant frequency in the chirped pulse and the response of localized field interpreted by the damped harmonic oscillator model. This result demonstrates that larger near-field enhancement is determined by not only the temporal sequence of the frequency component modulated by chirp but also the temporal distribution of the resonant frequency.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

It’s strongly desired to control the electromagnetic field in extremely confined spatiotemporal region for a variety of ambitious researches ranging from ultrafast optical switching to attosecond electron streaking [14]. However, the spatiotemporal scale of electromagnetic field is limited by optical diffraction and pulse duration. With the development of plasmonics, localized field could be confined beyond the optical diffraction limitation with strong enhancement in metallic nanoparticle. Moreover, metallic nanoparticle provides geometry and resonance degree of freedom for further controlling the spatiotemporal evolution of localized field [512], e.g., ultrafast switching of localized field with nanometric and sub-femtosecond temporal precision by coherent control of Localized Surface Plasmons (LSPs) in Au bowtie by the orthogonally polarized two laser pulses pair, active control of the near-field distribution of Ag island plasmon through adaptive laser pulse shaping technology [13,14]. Among these schemes, control of the plasmonic field is achieved either by the interference of plasmonic field excited by the two incident laser pulses, or single laser pulse with designed spatial distribution or polarization evolution with the degradation of temporal manipulation [1520].

In order to achieve active control of electromagnetic energy in real nano-femto scale, chirped laser pulse is proposed to illuminate the composite metallic nanostructure. Stockman et al. has firstly investigated the effect of chirp on the dynamic of electric field in the metal structure. Transformation of localized field between vertices in V-shaped nanostructure was achieved by the illumination of chirped laser pulse [21]. For composite nanostructure with multi plasmonic modes, the plasmonic field could be selectively excited by changing the frequency of the incident laser pulse. Lévêque G et al. has realized selective excitation of single plasmonic mode in xylophone by chirped laser pulse with thin Au film underneath, providing laser chirp as another degree of freedom for controlling the near-field of LSPs [22]. Moreover, tighter concentration of electromagnetic field could be achieved with negatively chirped pulse, which allows to obtain the best hyper focus of femtosecond plasmons with frequency modulation [23,24]. Although the localized field could be switching by chirped laser pulse, the influence of the laser chirp on the dynamics of the near-field has yet to be elucidated. The underlying mechanism of the temporal evolution of the electric field modulated by the chirped laser pulse needs to be furtherly revealed.

In this paper, dynamics of plasmonic field influenced by the laser chirp in asymmetric gold nanocross is investigated by Finite Domain Time Differential (FDTD) method. Transformation of the localized plasmonic field in asymmetric gold nano-cross within nm-fs scale is achieved under the illumination of chirped laser pulse. The relationship of the nanoscale field transferring speed and the laser chirp is investigated, i.e., the quantitative relation of time interval for field transferring and the dispersion of the corresponding resonant frequencies. The delayed appearance of the peak field with respect to the arrival of the resonant frequency is interpreted by the superimposed oscillation of localized field excited by the frequency components of the chirped laser pulse. In addition, the influence of laser chirp on the field amplitude is investigated for some canonical nanostructures, and theoretically interpreted by the damped harmonic oscillator model.

2. Models and methods

As shown in Fig. 1(a), Au nanocross is consisted of two orthogonal Au nanorods in x-y plane with poles from A1 to A4 with the width of 30nm and a thickness of 30nm in z direction. The longitudinal nanorod of Au nanocross in y axis is divided into two asymmetrical nanoarms with the length of 80nm (with the pole of A1 in the + y direction) and 50nm (with the pole of A3 in the -y direction) by the transverse nanorod, and the transverse nanorod is divided into two symmetric nanoarms with the equivalent length of 90nm (with the poles of A2, A4 in the -, +x direction, respectively) by the longitudinal nanorod. The pole of the nanorod is composed of semi-cylinder with the curvature radius of 15nm in x-y plane. The optical response of Au nano-cross structure is simulated by commercial FDTD solution software. In order to obtain the extinction spectra of nanostructure, total field scattered-field (TFSF) is employed to illuminate Au nanocross. Au nanocross is illuminated along the z-axis with the polarization along y-axis as shown in Fig. 1(a). The medium surrounding nanostructure is set as a vacuum environment of index n=1 in the simulation domain. Multilayers of perfect matching boundary is employed for prevent the simulation result from disturbed by the reflective radiation around FDTD region.

 figure: Fig. 1.

Fig. 1. (a) Schematic diagram of asymmetric Au nano cross structure: A1 = 80nm, A3 = 50nm, A2=A4 = 90nm, arm width 30nm, height 30nm. The optical source is incident from the positive direction of Z axis and polarized along Y axis. (b) Extinction spectrum of nanostructures. Field profile of Au nanocross at 718nm (c) and 852nm (d).

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The illuminated laser pulse is set as Gaussian pulse: [25,26]

$$E(t) = A(t)\cos ({w_0}t + \varphi (t)) = {A_0}{e^{ - {{(\frac{{t - {t_{offset}}}}{{{\tau _G}}})}^2}}}\cos ({w_0}(t - {t_{offtset}}) + \varphi (t - {t_{offtset}}))$$
where ${\omega _0}$ is the center angular frequency, ${t_{offtset}}$ is the offset of the center of incident laser, A(t) is the Gaussian envelope, A0 is the unit coefficient, ${\tau _G} = {\tau _P}\sqrt {2\ln 2}$ with ${\mathrm{\tau }_\textrm{P}}$ the duration of the incident pulse. Chirp of the incident laser pulse is controlled by temporal phase of $\varphi (t)$ [27]:
$$\varphi (t - {t_{offtset}}) = \frac{{\alpha {\omega _0}{{(t - {t_{offset}})}^2}}}{{{\tau _P}}}$$
where α is the dimensionless chirp coefficient of the incident laser pulse.

3. Results and discussion

Figure 1(b) shows the extinction spectrum of the nanocross. Multiply plasmonic modes can be sustained by the asymmetric Au nanocross as the separate peaks is observed in this spectrum. These spectrally separated two plasmonic modes originate from the electric field in longitudinal nanorod interacting with the transverse nanorod in asymmetric nano-cross, i.e., the oscillating of collective free electrons in one side of longitudinal nanorod can induce polarized charge stored in the orthogonal nanorods through the intersection of nanocross, diminishing the coupling with the other side of the same nanorod [15]. Therefore, the asymmetric geometry of the nano-cross forms discrete LSPR modes corresponding to the excitation of upper and lower arms at A1 and A3 in this case. Electric field is dramatically enhanced around one of the poles of longitudinal nanorods, with slightly concentration at other poles of the nanocross as shown in Fig. 1(c) and 1(d). These two plasmonic modes originate from the asymmetric splitting of the longitudinal nanorod of Au nanocross in this configuration.

For investigating the response of Au nanocross, Fourier transform limited (FTL) pulse is employed to illuminate Au nanocross with the center wavelength of 800nm, FWHM of 644–1064nm, time offset of 7.5fs and carrier envelope phase of φ(t) = 0 as shown in Fig. 2(a). Dynamics of localized field in asymmetric nanocross is investigated by monitoring temporal evolution of near field around the poles of nanoarms of A1 and A3. Localized electric fields of the A1 and A3 almost oscillate in the same phase within the incident pulse until 13fs, and then separates with an increasing phase delay due to the instinct plasmonic resonant frequencies of different hot spots as shown in Fig. 2(b). For both hot spots, localized field can be excited almost simultaneously due to the damping of LSPs, e.g., the localized fields from A1 and A3 reach their maximum at almost the same moment of 10.67fs as shown in Fig. 2(c).

 figure: Fig. 2.

Fig. 2. (a) Temporal evolution of the electric field of transform-limited pulse with the center wavelength=800nm and the spectral range from 644 to 1064nm. (b) Localized electric field versus time around the poles of nanoarms of A1 (blue) and A3 (green). (c) Field profile of asymmetric Au nano-cross structure at 10.67fs

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In order to control the localized electric field in fs-nm scale, chirp is introduced as the nonzero quantity of α in the second order phase of the incident laser pulse in Eq. (2). Frequency component would spread with the derivative of temporal phase and monotonously increase or decrease within the duration of chirped laser pulse. Due to resonant effect, localized field is sensitive to the instantaneous frequency of the incident laser pulse. As a result, temporal evolution of near field from nanoarms of A1 and A3 would be influenced by chirp of the incident light as shown in Fig. 3.

 figure: Fig. 3.

Fig. 3. spatiotemporal evolution of asymmetric Au nano-cross under the illumination of chirped laser pulse. Temporal evolution of the poles of longitudinal nanoarms of A1 (blue) and A3 (green) under the illumination of 40fs chirped laser pulse of α=−0.17 (a) and +0.17 (b), respectively. Time interval for ultrafast energy transferring between two poles of longitudinal nanoarms of A1 and A3 with temporal separation between resonant frequencies in the negative (c) and positive (d) chirped pulses.

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Figure 3(a) shows the temporal evolution of the electric field around the poles of nanoarms of A1 and A3 under the illumination of negatively chirped-pulse with the pulse duration ${\tau _P} = 40fs$ and chirp coefficient $\alpha ={-} 0.17$ for keeping the same FWHM of 644–1064nm and the center wavelength of 800nm with the FTL pulse. Under the illumination of negatively chirped laser pulse, localized field at A1 and A3 no longer oscillate simultaneously to reach the maximum of the field density. As shown in Fig. 3(a), electric field is concentrated around A3 at ∼100fs and then transfer to A1 after ∼20fs as the switching of peak electric field induced by the dispersion of the corresponding resonant frequencies in the chirped laser pulse. Within the pulse duration, instantaneous frequency monotonically decreases due to the negative chirp of the incident laser pulse, resulting to the resonant excitation of localized surface plasmons for hot spots from A3 to A1, following the sequence of the corresponding resonant frequencies dispersed in the incident chirped laser pulse. Under the illumination of positively chirped laser, electric field is transferring from A1 to A3 as shown in Fig. 3(b), also consistent with the distribution of the corresponding resonant frequencies. In both cases, localized field is transferred between A1 and A3 in both femtosecond and nanometric scale, demonstrating the validity of the coherent control for the localized electric field by chirped laser pulse.

For clarifying the switching speed of plasmonic field controlled by the chirp, it is necessary to ascertain the relation of time interval for field transferring with the separation of the corresponding resonant frequencies in the chirped laser pulse. Under the illumination of negatively chirped laser pulse of α=−0.17, the resonant wavelengths of 718nm and 852nm are dispersed to t1=86.6fs and t2=107.3fs obtained by the instantaneous frequency of ${\omega _{ins}} = {\omega _0} + {{2\alpha {\omega _0}(t - {t_{offset}})} / {{\tau _P}}}$ according to Eq. (2), and peaks of the electric field appear at 99.6fs and 117.3fs for A3 and A1 as shown in Fig. 3(a). In this case, peaks of electric field for both A1 and A3 can’t immediately follow the corresponding resonant frequencies and the relative temporal delays are 13fs for A3 and 10fs for A1, respectively. When tuning to positively chirped laser pulse with α=+0.17, the peak electric field appears at 102.1fs for A1, about 9.5fs after the arrival of the corresponding resonant wavelength of 852nm at 92.7fs. And for A3 it appears at 117fs, slightly delay to the arrival of the resonant wavelength of 718nm at 113.4fs as shown in Fig. 3(b).

It is necessary to reveal the relation of the time interval for field transferring and the dispersion of the two resonant frequencies spread by the chirp of the incident laser pulse. The time for field transferring from A3 to A1 is changing with the dispersion of resonant frequencies spread from 20fs to 80fs by tuning the quantity of chirp in the incident laser pulse as shown in Fig. 3(c). The result shows the transferring time is linear dependent on the separation of the resonant frequencies with the slope about k-=0.96, indicating it takes about the equivalent time interval for the switching of electric field compared to the dispersion of the corresponding resonant frequencies in the negatively chirped pulse. When changing to the positively chirped laser pulse, linear relation for the field transferring from A1 to A3 can also be obtained with the linear slope of k+=0.90 as shown in Fig. 3(d).

In this case, the electric field originates from the integral of the localized field excited by the frequency component of the incident chirped laser pulse. The peak electric field would follow behind the instantaneous resonant frequency since the early arrived plasmonic on-resonant mode could sufficiently superpose with the subsequently appeared off-resonant mode to obtain the strongest field enhancement. Therefore, the appearance of the maximum field is delayed with respect to the arrival of the corresponding resonant frequency for both A1 and A3 under the illumination of positively and negatively chirped laser pulse. In both cases, the peak of electric field is determined by the superposition of the induced field by resonant and off-resonant frequency component. The separation between the peak field from the plasmonic hot spot and the corresponding resonant frequency is also influenced by the dispersion of the chirped laser pulse. It could be seen that the relative delay is decreasing from 13fs for A3 to 10fs for A1 between the peak field and the corresponding resonant frequency as shown in Fig. 3(a). For positively chirped laser pulse, this decreasing of the relatively delay is more evidently from 9.5fs for A1 to 3fs for A3. As these results shows the relative delay between the resonant frequency and the peak field would be reduced when the resonant frequency is lying in the back side of the incident chirped laser pulse. The peak electric field is inevitably tending to arrive earlier since the main part of laser spectrum is in front of the resonant frequency in this case. The relative delay is different for positively and negatively chirped laser pulse due to the imbalance of the plasmonic field response to the off-resonant frequency component around the resonant frequency with the damped harmonic oscillator model as discussed later. These results prove that the chirp can be used as a reversible knob for quantitatively controlling the localized electric field in fs-nm scale, and ultrafast switching of the localized field can be achieved within 20fs in this configuration.

It is noted that not only the appearance time as shown in the temporal evolution of the localized electric field (Figs. 3(a-b)), but also the amplitude of the peak field would be influenced by the chirp of the incident laser pulse due to the plasmonic effect. Figure 4(a) and (b) show the electric field around the poles of A1 and A3 under the illumination of positively(blue) and negatively(green) chirped pulses. The amplitudes of localized electric field around A1 and A3 are 18 V/m and 16.5 V/m under the illumination of positively chirped laser pulse, respectively. Meanwhile, both of them can reach 20 V/m for negatively chirped laser pulse. Therefore, larger field enhancement can be achieved under the illumination of negatively chirped-pulse compared to positively chirped pulse for both A1 and A3 in this configuration. And also, we have calculated electric field from the poles of nanoarms of A1 and A3 under the excitation of positively and negatively chirped pulses with the chirp coefficient of α=−0.17 and ±0.17 for the pulse durations of 40, 70, 100 and 150fs, and extracted the temporal evolution of the localized field ( Fig. S1 in the Supplement 1). These results show that the localized peak field of A1 would appear before that of A3 for positively chirped laser pulse, and vice versa for negatively chirped laser pulse. Meanwhile, it is found that even if the pulse duration is adjusted from 40 to 150fs, larger field enhancement can always be achieved under the illumination of negatively chirped-pulse compared to positively chirped pulse for both A1 and A3, and the switching time of localized field between A1 and A3 become larger due to the slow changing rate for the instantaneous frequency in the extended pulse duration (Fig. S1 and Table S1 in Supplement 1). Moreover, it is found that localized amplitudes become larger with the increasing pulse duration from 40 to 150 fs for both A1 and A3 (See Fig. S1 and Table S1 in Supplement 1). And this relation holds for various types of nanoparticles (nanobar, nanocross and nano triangle). In addition, the simulated field amplitudes under different laser chirp amount show that the amplitudes depend on the chirping properties. See Supplement 1 (Fig. S2, Table S2 and Table S3).

 figure: Fig. 4.

Fig. 4. Electric field from the poles of nanoarms of A1(a) and A3(b) under the excitation of positively (blue) and negatively (green) chirped pulses with pulse duration ${\tau _P} = 40fs$

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For further revealing the characters of localized field modulated by the chirp of the laser pulse, the amplitudes of the electric field from plasmonic hot spot are retrieved for three canonical metallic nanostructures under the illumination of positively and negatively chirped laser pulse. Table 1 shows the amplitudes in different nanostructures with the resonant frequency around the blue boundary, center and red boundary of spectra of the incident chirped pulse. It can be seen that the maximum electric field is not only determined by the sign of the chirp, but also the distribution of the resonant wavelength in the spectrum of the incident pulse. The amplitude is larger under the illumination of positively than negatively chirped laser pulse for the resonant wavelength around the red boundary of the spectrum of the chirped pulse, and vice verse for LSPR wavelength around the blue boundary. In both cases, larger amplitude could be excited when the resonant plasmonic field was distributed to the beginning of the incident chirped laser pulse, i.e., the resonant mode is firstly excited at the oscillation of the plasmonic field. Meanwhile, when the resonant frequency is lying in the center of the spectra, larger field enhancement can be achieved under the illumination of negatively than positively chirped laser pulse. These results indicate the evolution of plasmonic field is sensitive to the temporal consequence of the frequency component of the incident laser pulse.

Tables Icon

Table 1. The amplitudes of electric field in different nanostructures with the illumination of chirped laser pulse (RW, the resonance wavelength)

To get insight into the influence of chirp on the oscillation of plasmonic field, damped harmonic oscillator model is employed to describe the response of near field to the incident chirped laser pulse in metallic nanostructure. Localized surface plasmons can be retreated as the collective oscillation of free electrons suffering from the restoring force of center ion with the decay channel stemming from radiation, intraband and interband transition [28]. As a result, the response function R(ω) of LSP in frequency domain is [29]:

$$R(\omega ) = \frac{1}{{\omega _r^2 + 2\gamma i\omega - {\omega ^2}}} = \frac{{\omega _r^2 - 2\gamma i\omega - {\omega ^2}}}{{{{(\omega _r^2 - {\omega ^2})}^2} + 4{\gamma ^2}{\omega ^2}}}$$
where ${\omega _r}$ the resonance frequency, γ the damping constant of the nanostructure. The response of the plasmonic field to different frequency components can be obtained by this model, e.g., for two frequency components of ${\omega _1} < {\omega _r} < {\omega _2}$ with equivalent distance to the resonant frequency, the response of the localized electric field is $|{R({\omega_1})} |> |{R({\omega_2})} |$ from Eq. (3). Larger field amplitude can be excited by red off-resonant than blue off-resonant laser pulse with identical detuning amount to the resonant frequency. The instantaneous electric field of LSPs can be obtained by Fourier Transform of the response function with the excitation source as [30]:
$${E_{pl}}(t) \propto \int_{ - \infty }^t {\frac{1}{{{\omega _r}}}} {E_{laser}}({t^\ast }){e^{ - \gamma (t - {t^\ast })}}\sin [{\omega _r}(t - {t^\ast })]d{t^\ast }$$
where ${E_{laser}}(t\ast )$ is the electric field of the incident laser pulse. The oscillation of electric field is determined by the integral of the electric field excited by the frequency component of the incident laser pulse with the exponential decay term of ${e^{ - \gamma (t - {t^\ast })}}$ from -∞ to t as Eq. (4), instead of that solely induced by the instantaneous frequency component. Therefore, the oscillation of plasmonic field could be sensitive to the dispersion of frequency component modulated by chirp of the incident laser pulse.

To illustrate the response of plasmonic field to the excitation pulse, temporal evolutions of localized field from plasmonic hot spot on the nano-cross with the resonance wavelength of 702nm are retrieved under the illumination of blue off-resonant (486–524m), on-resonance (667–740nm) and red off-resonant (896–1032nm) FTL pulse as shown in Fig. 5(a-c), respectively. Plasmonic field could oscillate with a larger field enhancement(∼30V/m) and longer lifetime(∼20fs) when it is excited by the resonant frequency component due to the resonant effect (Fig.6(b)), and for off-resonant excitation it would oscillate with a decreased amplitude(∼2.5 V/m for (a) and ∼10 V/m for (c)) and quickly vanish(∼12fs for (a) and (c)) due to the dephasing stemming from the detuning of the resonant frequency of plasmonic field with the driven frequency of the incident pulse (Fig. 5(a) and Fig. 5(y)(c)). As discussed above, the amplitude of plasmonic field is the maximum of the integral of the localized field excited by all the frequency component of the incident laser pulse, mainly determined by the superposition of that excited by the plasmonic on- and off- resonant frequency components. The chirp of laser pulse will spread the frequency component within the pulse to modulate the dynamics of localized field for plasmonic hot spot. For the canonical metallic nanostructures as listed in Table1, when the resonant frequency is around the red boundary of the spectrum of the incident positively-chirped laser pulse, the on-resonant plasmonic mode would be excited at first and then decay exponentially before its superposition with that excited by off-resonant mode, and the consequence of the excitation would be reverse for negatively chirped laser pulse. The off-resonant mode would suffer greater loss compared to on-resonant mode when it was firstly excited due to fast dephasing process. The amplitude of the plasmonic field would be smaller for negatively chirped laser pulse due to the insufficient superposition of the localized field. Similarly, when the resonant frequency was around the blue boundary of the spectrum of the incident chirped laser pulse, a larger field amplitude could be achieved with the negatively chirped laser pulse. This relation is valid for various types of nanoparticles, such as Au nanobar, Au nanocross and Au nanotriangle as shown in Table 1, and this validity can be hold for the same nanostructures consisted of noble metals, such as Au and Ag.

 figure: Fig. 5.

Fig. 5. Temporal evolution of electric field from plasmonic hot spot in symmetric Au nano-cross structure excited by (a) blue off-resonant, (b) on-resonant and (c) red off-resonant FTL pulse with duration of 10fs.

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Meanwhile, the amplitude of electric field is determined by the superposition of induced field excited by the resonant, blue- and red- off-resonant frequency components of the chirped laser pulse for the resonant frequency around the center of laser spectrum. The instantaneous frequency monotonously increases or decreases for positively and negatively chirped laser pulse, respectively, resulting that the off-resonant modes around the resonant frequency are excited at the beginning and ending of the incident chirped laser pulse. Due to the stronger response of the plasmonic field to red than blue off-resonant frequency component, larger field amplitude can be achieved for sufficient superposition of induced field excited by resonant with red off-resonant frequency components. Meanwhile, this imbalanced response indicates the more importance of red off-resonant frequency components. As a result, the field peak would tend to arrive closely to the red off-resonant frequency component of the chirped laser pulse. It is evident for the relative delay between the resonant frequency and field peak transferring from 13fs at A3(negatively chirped) to 9.4fs at A1(positively chirped) for the resonant frequency in the front side of the incident laser pulse, and 10fs at A1(negatively chirped) to 3.6fs (positively chirped) for the resonant frequency lying in the back side. In both cases, the incident laser pulse is changing from negatively chirped to positively chirped, with the accompanying red off-resonant frequency component transferring from the behind to the in-front of the resonant frequency of the incident laser pulse. This result shows the relative delay is influenced by the distribution of off-resonant frequency components in the incident chirped laser pulse.

As discussed above, the field amplitude is mainly determined by the superposition of localized field induced by resonant and red off- resonant frequency component of the incident laser pulse. Significant loss can be avoided when the red off-resonant mode is excited behind the resonant mode with a longer lifetime, a larger field amplitude can be achieved for negatively chirped laser pulse due to the sufficient superposition of both modes. On the other hand, an insufficient superposition of resonant mode with red- off-resonant mode occurs for positively chirped laser pulse due to the early excitation and subsequent fast dephasing process of the red off-resonant frequency component. the resulting amplitude would be smaller than that excited by negatively chirped laser pulse as shown in Fig. 4(a, b). The relation of the amplitudes excited by the chirped laser pulse could be kept for the canonical metallic nanostructures as shown in Table 1, demonstrating the validity of this interpretation for the influence of laser chirp on the temporal evolution of the plasmonic field.

4. Conclusions

In this paper, the influence of chirp in ultrafast laser pulse on the dynamic of plasmonic field in asymmetric Au nano-cross structure is investigated by FDTD algorithm. Under the illumination of chirped laser pulse, the spatiotemporal evolution of the plasmonic field can be manipulated by chirped laser pulse in nanometer-femtosecond scale. Localized field can be transferring with the time interval linearly dependence on the dispersion of the corresponding resonant frequency in the chirped laser pulse. The peak field would appear behind the resonant frequency component for sufficient oscillation of the plasmonic on-resonant mode, and the relative delay between the resonant frequency and the amplitude is influenced by the weighing of off-resonant frequency component in the incident laser pulse and the response of the plasmonic field. Due to the longer lifetime, larger amplitude can be achieved if the resonant mode was excited at the beginning of the oscillation of localized electric field for the resonant frequency around the boundary of the spectrum of incident laser pulse. Due to less decay of the early excited off resonant mode, the amplitude is mainly determined by that superposition with the resonant mode for the resonant frequency around the center spectrum. As a result, larger field amplitude can be obtained for negatively than positively chirped laser pulse since the more importance of the induced field excited by red off-resonant frequency component was later excited to sufficient superposition with the resonance mode in this configuration. These results show the plasmonic field can be dramatically influenced by chirped laser pulse, providing an effective degree of freedom for coherently control the dynamics of localized field of LSP in femto-nano spatiotemporal scale.

Funding

National Natural Science Foundation of China (12004052, 61775021, 62005022, 91850109); Education Department of Jilin Province (JJKH20190555KJ); Department of Science and Technology of Jilin Province (20200201268JC, 20200401052GX); 111 Project (D17017); China Postdoctoral Science Foundation (2019M661183).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Supplemental document

See Supplement 1 for supporting content.

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16. F. Zhou, Z. Y. Li, Y. Liu, and Y. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008). [CrossRef]  

17. C. Awada, T. Popescu, L. Douillard, F. Charra, and R. Bachelot, “Selective excitation of plasmon resonances of single Au triangles by polarization-dependent light excitation,” J. Phys. Chem. C 116(27), 14591–14598 (2012). [CrossRef]  

18. E. Mrsell, R. Svrd, M. Miranda, C. Guo, and A. Losquin, “Direct subwavelength imaging and control of near-field localization in individual silver nanocubes,” Appl. Phys. Lett. 107(20), 201111 (2015). [CrossRef]  

19. C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11(2), 402–407 (2011). [CrossRef]  

20. M. Rycenga, C. M. Cobley, J. Zeng, W. Li, C. H. Moran, Q. Zhang, D. Qin, and Y. Xia, “Controlling the synthesis and assembly of silver nanostructures for plasmonic applications,” Chem. Rev. 111(6), 3669–3712 (2011). [CrossRef]  

21. M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. 88(6), 067402 (2002). [CrossRef]  

22. G. Lévêque and O. J. F. Martin, “Narrow-band multiresonant plasmon nanostructure for the coherent control of light: an optical analog of the xylophone,” Phys. Rev. Lett. 100(11), 117402 (2008). [CrossRef]  

23. E. S. Manuilovich, V. A. Astapenko, and P. A. Golovinskii, “Superfocusing of an ultrashort plasmon pulse by a conducting cone,” Quantum Electron. 46(1), 50–56 (2016). [CrossRef]  

24. M. I. Stockman, D. J. Bergman, and T. Kobayashi, “Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems,” Phys. Rev. B 69(5), 054202 (2004). [CrossRef]  

25. A. N. Koya, B. Ji, Z. Hao, and J. Lin, “Coherent control of gap plasmons of a complex nanosystem by shaping driving femtosecond pulses,” Plasmonics 12(6), 1693–1699 (2017). [CrossRef]  

26. J. Liu, “Study on the regulation of surface plasmon interaction between light and metal micro-nanostructure,” Chinese Academy of Sciences, 2016.

27. T. W. Lee and S. K. Gray, “Controlled spatiotemporal excitation of metal nanoparticles with picosecond optical pulses,” Phys. Rev. B 71(3), 035423 (2005). [CrossRef]  

28. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002). [CrossRef]  

29. M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016. [CrossRef]  

30. B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83(21), 4421–4424 (1999). [CrossRef]  

References

  • View by:

  1. M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B: At. Mol. Opt. Phys. 45(7), 074006 (2012).
    [Crossref]
  2. S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
    [Crossref]
  3. P. Hommelhoff and M. Kling, Attosecond Nanophysics: From Basic Science to Applications (Wiley, 2015).
  4. G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
    [Crossref]
  5. N. N. Jiang, X. L. Zhuo, and J. F. Wang, “Active plasmonics: principles, structures, and applications,” Chem. Rev. 118(6), 3054–3099 (2018).
    [Crossref]
  6. A. G. Joly, P. Z. EL-Khoury, and W. P. Hess, “Spatiotemporal imaging of surface plasmons using two-color photoemission electron microscopy,” J. Phys. Chem. C 122(36), 20981–20988 (2018).
    [Crossref]
  7. A. G. Joly, Y. Gong, P. Z. El-Khoury, and W. P. Hess, “Surface plasmon-based pulse splitter and polarization multiplexer,” J. Phys. Chem. Lett. 9(21), 6164–6168 (2018).
    [Crossref]
  8. S. Kim, J. Jin, Y.J. Kim, I.Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
    [Crossref]
  9. M. Abb, Y. Wang, C. H. De Groot, and O. L. Muskens, “Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas,” Nat. Commun. 5(1), 4869 (2014).
    [Crossref]
  10. P. Dombi, A. Hrl, P. Racz, I. Marton, and U. Hohenester, “Ultrafast strong-field photoemission from plasmonic nanoparticles,” Nano Lett. 13(2), 674–678 (2013).
    [Crossref]
  11. M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, and W. Bao, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene re-vealed by infrared pump–probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
    [Crossref]
  12. X. Fang, L. T. Ming, J. Y. Ou, K. F. Macdonald, D. P. Tsai, and N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial ab-sorption,” Appl. Phys. Lett. 104(14), 141102 (2014).
    [Crossref]
  13. B. Y. Ji, J. Qin, H. Y. Tao, Z. Q. Hao, and J. Q. Lin, “Subwavelength imaging and control of ultrafast optical near-field under resonant-and off-resonant excitation of bowtie nanostructures,” New J. Phys. 18(9), 093046 (2016).
    [Crossref]
  14. M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
    [Crossref]
  15. B. Ji, J. Qin, Z. Hao, and J. Lin, “Features of local electric field excitation in asymmetric nanocross illuminated by ultrafast laser pulse,” Plasmonics 10(6), 1573–1580 (2015).
    [Crossref]
  16. F. Zhou, Z. Y. Li, Y. Liu, and Y. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
    [Crossref]
  17. C. Awada, T. Popescu, L. Douillard, F. Charra, and R. Bachelot, “Selective excitation of plasmon resonances of single Au triangles by polarization-dependent light excitation,” J. Phys. Chem. C 116(27), 14591–14598 (2012).
    [Crossref]
  18. E. Mrsell, R. Svrd, M. Miranda, C. Guo, and A. Losquin, “Direct subwavelength imaging and control of near-field localization in individual silver nanocubes,” Appl. Phys. Lett. 107(20), 201111 (2015).
    [Crossref]
  19. C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11(2), 402–407 (2011).
    [Crossref]
  20. M. Rycenga, C. M. Cobley, J. Zeng, W. Li, C. H. Moran, Q. Zhang, D. Qin, and Y. Xia, “Controlling the synthesis and assembly of silver nanostructures for plasmonic applications,” Chem. Rev. 111(6), 3669–3712 (2011).
    [Crossref]
  21. M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. 88(6), 067402 (2002).
    [Crossref]
  22. G. Lévêque and O. J. F. Martin, “Narrow-band multiresonant plasmon nanostructure for the coherent control of light: an optical analog of the xylophone,” Phys. Rev. Lett. 100(11), 117402 (2008).
    [Crossref]
  23. E. S. Manuilovich, V. A. Astapenko, and P. A. Golovinskii, “Superfocusing of an ultrashort plasmon pulse by a conducting cone,” Quantum Electron. 46(1), 50–56 (2016).
    [Crossref]
  24. M. I. Stockman, D. J. Bergman, and T. Kobayashi, “Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems,” Phys. Rev. B 69(5), 054202 (2004).
    [Crossref]
  25. A. N. Koya, B. Ji, Z. Hao, and J. Lin, “Coherent control of gap plasmons of a complex nanosystem by shaping driving femtosecond pulses,” Plasmonics 12(6), 1693–1699 (2017).
    [Crossref]
  26. J. Liu, “Study on the regulation of surface plasmon interaction between light and metal micro-nanostructure,” Chinese Academy of Sciences, 2016.
  27. T. W. Lee and S. K. Gray, “Controlled spatiotemporal excitation of metal nanoparticles with picosecond optical pulses,” Phys. Rev. B 71(3), 035423 (2005).
    [Crossref]
  28. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
    [Crossref]
  29. M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
    [Crossref]
  30. B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83(21), 4421–4424 (1999).
    [Crossref]

2019 (1)

S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
[Crossref]

2018 (3)

N. N. Jiang, X. L. Zhuo, and J. F. Wang, “Active plasmonics: principles, structures, and applications,” Chem. Rev. 118(6), 3054–3099 (2018).
[Crossref]

A. G. Joly, P. Z. EL-Khoury, and W. P. Hess, “Spatiotemporal imaging of surface plasmons using two-color photoemission electron microscopy,” J. Phys. Chem. C 122(36), 20981–20988 (2018).
[Crossref]

A. G. Joly, Y. Gong, P. Z. El-Khoury, and W. P. Hess, “Surface plasmon-based pulse splitter and polarization multiplexer,” J. Phys. Chem. Lett. 9(21), 6164–6168 (2018).
[Crossref]

2017 (1)

A. N. Koya, B. Ji, Z. Hao, and J. Lin, “Coherent control of gap plasmons of a complex nanosystem by shaping driving femtosecond pulses,” Plasmonics 12(6), 1693–1699 (2017).
[Crossref]

2016 (3)

E. S. Manuilovich, V. A. Astapenko, and P. A. Golovinskii, “Superfocusing of an ultrashort plasmon pulse by a conducting cone,” Quantum Electron. 46(1), 50–56 (2016).
[Crossref]

M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
[Crossref]

B. Y. Ji, J. Qin, H. Y. Tao, Z. Q. Hao, and J. Q. Lin, “Subwavelength imaging and control of ultrafast optical near-field under resonant-and off-resonant excitation of bowtie nanostructures,” New J. Phys. 18(9), 093046 (2016).
[Crossref]

2015 (2)

B. Ji, J. Qin, Z. Hao, and J. Lin, “Features of local electric field excitation in asymmetric nanocross illuminated by ultrafast laser pulse,” Plasmonics 10(6), 1573–1580 (2015).
[Crossref]

E. Mrsell, R. Svrd, M. Miranda, C. Guo, and A. Losquin, “Direct subwavelength imaging and control of near-field localization in individual silver nanocubes,” Appl. Phys. Lett. 107(20), 201111 (2015).
[Crossref]

2014 (3)

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, and W. Bao, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene re-vealed by infrared pump–probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref]

X. Fang, L. T. Ming, J. Y. Ou, K. F. Macdonald, D. P. Tsai, and N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial ab-sorption,” Appl. Phys. Lett. 104(14), 141102 (2014).
[Crossref]

M. Abb, Y. Wang, C. H. De Groot, and O. L. Muskens, “Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas,” Nat. Commun. 5(1), 4869 (2014).
[Crossref]

2013 (1)

P. Dombi, A. Hrl, P. Racz, I. Marton, and U. Hohenester, “Ultrafast strong-field photoemission from plasmonic nanoparticles,” Nano Lett. 13(2), 674–678 (2013).
[Crossref]

2012 (2)

M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B: At. Mol. Opt. Phys. 45(7), 074006 (2012).
[Crossref]

C. Awada, T. Popescu, L. Douillard, F. Charra, and R. Bachelot, “Selective excitation of plasmon resonances of single Au triangles by polarization-dependent light excitation,” J. Phys. Chem. C 116(27), 14591–14598 (2012).
[Crossref]

2011 (3)

G. A. Wurtz, R. Pollard, W. Hendren, G. P. Wiederrecht, D. J. Gosztola, V. A. Podolskiy, and A. V. Zayats, “Designed ultrafast optical nonlinearity in a plasmonic nanorod metamaterial enhanced by nonlocality,” Nat. Nanotechnol. 6(2), 107–111 (2011).
[Crossref]

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11(2), 402–407 (2011).
[Crossref]

M. Rycenga, C. M. Cobley, J. Zeng, W. Li, C. H. Moran, Q. Zhang, D. Qin, and Y. Xia, “Controlling the synthesis and assembly of silver nanostructures for plasmonic applications,” Chem. Rev. 111(6), 3669–3712 (2011).
[Crossref]

2008 (3)

G. Lévêque and O. J. F. Martin, “Narrow-band multiresonant plasmon nanostructure for the coherent control of light: an optical analog of the xylophone,” Phys. Rev. Lett. 100(11), 117402 (2008).
[Crossref]

S. Kim, J. Jin, Y.J. Kim, I.Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[Crossref]

F. Zhou, Z. Y. Li, Y. Liu, and Y. Xia, “Quantitative analysis of dipole and quadrupole excitation in the surface plasmon resonance of metal nanoparticles,” J. Phys. Chem. C 112(51), 20233–20240 (2008).
[Crossref]

2007 (1)

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
[Crossref]

2005 (1)

T. W. Lee and S. K. Gray, “Controlled spatiotemporal excitation of metal nanoparticles with picosecond optical pulses,” Phys. Rev. B 71(3), 035423 (2005).
[Crossref]

2004 (1)

M. I. Stockman, D. J. Bergman, and T. Kobayashi, “Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems,” Phys. Rev. B 69(5), 054202 (2004).
[Crossref]

2002 (2)

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[Crossref]

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. 88(6), 067402 (2002).
[Crossref]

1999 (1)

B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83(21), 4421–4424 (1999).
[Crossref]

Abb, M.

M. Abb, Y. Wang, C. H. De Groot, and O. L. Muskens, “Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas,” Nat. Commun. 5(1), 4869 (2014).
[Crossref]

Aeschlimann, M.

M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
[Crossref]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
[Crossref]

Astapenko, V. A.

E. S. Manuilovich, V. A. Astapenko, and P. A. Golovinskii, “Superfocusing of an ultrashort plasmon pulse by a conducting cone,” Quantum Electron. 46(1), 50–56 (2016).
[Crossref]

Aussenegg, F. R.

B. Lamprecht, J. R. Krenn, A. Leitner, and F. R. Aussenegg, “Resonant and off-resonant light-driven plasmons in metal nanoparticles studied by femtosecond-resolution third-harmonic generation,” Phys. Rev. Lett. 83(21), 4421–4424 (1999).
[Crossref]

Awada, C.

C. Awada, T. Popescu, L. Douillard, F. Charra, and R. Bachelot, “Selective excitation of plasmon resonances of single Au triangles by polarization-dependent light excitation,” J. Phys. Chem. C 116(27), 14591–14598 (2012).
[Crossref]

Bachelot, R.

C. Awada, T. Popescu, L. Douillard, F. Charra, and R. Bachelot, “Selective excitation of plasmon resonances of single Au triangles by polarization-dependent light excitation,” J. Phys. Chem. C 116(27), 14591–14598 (2012).
[Crossref]

Baierl, S.

S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
[Crossref]

Bao, W.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, and W. Bao, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene re-vealed by infrared pump–probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref]

Bauer, M.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
[Crossref]

Bayer, D.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
[Crossref]

Bergman, D. J.

M. I. Stockman, D. J. Bergman, and T. Kobayashi, “Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems,” Phys. Rev. B 69(5), 054202 (2004).
[Crossref]

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. 88(6), 067402 (2002).
[Crossref]

Brixner, T.

M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
[Crossref]

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
[Crossref]

Charra, F.

C. Awada, T. Popescu, L. Douillard, F. Charra, and R. Bachelot, “Selective excitation of plasmon resonances of single Au triangles by polarization-dependent light excitation,” J. Phys. Chem. C 116(27), 14591–14598 (2012).
[Crossref]

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11(2), 402–407 (2011).
[Crossref]

Cobley, C. M.

M. Rycenga, C. M. Cobley, J. Zeng, W. Li, C. H. Moran, Q. Zhang, D. Qin, and Y. Xia, “Controlling the synthesis and assembly of silver nanostructures for plasmonic applications,” Chem. Rev. 111(6), 3669–3712 (2011).
[Crossref]

De Groot, C. H.

M. Abb, Y. Wang, C. H. De Groot, and O. L. Muskens, “Hotspot-mediated ultrafast nonlinear control of multifrequency plasmonic nanoantennas,” Nat. Commun. 5(1), 4869 (2014).
[Crossref]

Dombi, P.

P. Dombi, A. Hrl, P. Racz, I. Marton, and U. Hohenester, “Ultrafast strong-field photoemission from plasmonic nanoparticles,” Nano Lett. 13(2), 674–678 (2013).
[Crossref]

Douillard, L.

C. Awada, T. Popescu, L. Douillard, F. Charra, and R. Bachelot, “Selective excitation of plasmon resonances of single Au triangles by polarization-dependent light excitation,” J. Phys. Chem. C 116(27), 14591–14598 (2012).
[Crossref]

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11(2), 402–407 (2011).
[Crossref]

Ebnet, T.

S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
[Crossref]

El-Khoury, P. Z.

A. G. Joly, Y. Gong, P. Z. El-Khoury, and W. P. Hess, “Surface plasmon-based pulse splitter and polarization multiplexer,” J. Phys. Chem. Lett. 9(21), 6164–6168 (2018).
[Crossref]

A. G. Joly, P. Z. EL-Khoury, and W. P. Hess, “Spatiotemporal imaging of surface plasmons using two-color photoemission electron microscopy,” J. Phys. Chem. C 122(36), 20981–20988 (2018).
[Crossref]

Faleev, S. V.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. 88(6), 067402 (2002).
[Crossref]

Fang, X.

X. Fang, L. T. Ming, J. Y. Ou, K. F. Macdonald, D. P. Tsai, and N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial ab-sorption,” Appl. Phys. Lett. 104(14), 141102 (2014).
[Crossref]

Fei, Z.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, and W. Bao, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene re-vealed by infrared pump–probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref]

Feldmann, J.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[Crossref]

Fischer, A.

M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
[Crossref]

Förster, M.

M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B: At. Mol. Opt. Phys. 45(7), 074006 (2012).
[Crossref]

Franzl, T.

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A. G. Joly, Y. Gong, P. Z. El-Khoury, and W. P. Hess, “Surface plasmon-based pulse splitter and polarization multiplexer,” J. Phys. Chem. Lett. 9(21), 6164–6168 (2018).
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A. G. Joly, P. Z. EL-Khoury, and W. P. Hess, “Spatiotemporal imaging of surface plasmons using two-color photoemission electron microscopy,” J. Phys. Chem. C 122(36), 20981–20988 (2018).
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E. S. Manuilovich, V. A. Astapenko, and P. A. Golovinskii, “Superfocusing of an ultrashort plasmon pulse by a conducting cone,” Quantum Electron. 46(1), 50–56 (2016).
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G. Lévêque and O. J. F. Martin, “Narrow-band multiresonant plasmon nanostructure for the coherent control of light: an optical analog of the xylophone,” Phys. Rev. Lett. 100(11), 117402 (2008).
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M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, and W. Bao, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene re-vealed by infrared pump–probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
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S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
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E. Mrsell, R. Svrd, M. Miranda, C. Guo, and A. Losquin, “Direct subwavelength imaging and control of near-field localization in individual silver nanocubes,” Appl. Phys. Lett. 107(20), 201111 (2015).
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M. Rycenga, C. M. Cobley, J. Zeng, W. Li, C. H. Moran, Q. Zhang, D. Qin, and Y. Xia, “Controlling the synthesis and assembly of silver nanostructures for plasmonic applications,” Chem. Rev. 111(6), 3669–3712 (2011).
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E. Mrsell, R. Svrd, M. Miranda, C. Guo, and A. Losquin, “Direct subwavelength imaging and control of near-field localization in individual silver nanocubes,” Appl. Phys. Lett. 107(20), 201111 (2015).
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C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
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S. Kim, J. Jin, Y.J. Kim, I.Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
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M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
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M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
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M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
[Crossref]

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Qin, J.

B. Y. Ji, J. Qin, H. Y. Tao, Z. Q. Hao, and J. Q. Lin, “Subwavelength imaging and control of ultrafast optical near-field under resonant-and off-resonant excitation of bowtie nanostructures,” New J. Phys. 18(9), 093046 (2016).
[Crossref]

B. Ji, J. Qin, Z. Hao, and J. Lin, “Features of local electric field excitation in asymmetric nanocross illuminated by ultrafast laser pulse,” Plasmonics 10(6), 1573–1580 (2015).
[Crossref]

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P. Dombi, A. Hrl, P. Racz, I. Marton, and U. Hohenester, “Ultrafast strong-field photoemission from plasmonic nanoparticles,” Nano Lett. 13(2), 674–678 (2013).
[Crossref]

Rodin, A. S.

M. Wagner, Z. Fei, A. S. McLeod, A. S. Rodin, and W. Bao, “Ultrafast and nanoscale plasmonic phenomena in exfoliated graphene re-vealed by infrared pump–probe nanoscopy,” Nano Lett. 14(2), 894–900 (2014).
[Crossref]

Rogach, A. L.

C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11(2), 402–407 (2011).
[Crossref]

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M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
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M. Rycenga, C. M. Cobley, J. Zeng, W. Li, C. H. Moran, Q. Zhang, D. Qin, and Y. Xia, “Controlling the synthesis and assembly of silver nanostructures for plasmonic applications,” Chem. Rev. 111(6), 3669–3712 (2011).
[Crossref]

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C. Hrelescu, T. K. Sau, A. L. Rogach, F. Jäckel, G. Laurent, L. Douillard, and F. Charra, “Selective excitation of individual plasmonic hotspots at the tips of single gold nanostars,” Nano Lett. 11(2), 402–407 (2011).
[Crossref]

Schenk, M.

M. Krüger, M. Schenk, M. Förster, and P. Hommelhoff, “Attosecond physics in photoemission from a metal nanotip,” J. Phys. B: At. Mol. Opt. Phys. 45(7), 074006 (2012).
[Crossref]

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S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
[Crossref]

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S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
[Crossref]

Sönnichsen, C.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[Crossref]

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M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
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Steeb, F.

M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F. J. G. de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, and F. Steeb, “Adaptive subwavelength control of nano-optical fields,” Nature 446(7133), 301–304 (2007).
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M. I. Stockman, D. J. Bergman, and T. Kobayashi, “Coherent control of nanoscale localization of ultrafast optical excitation in nanosystems,” Phys. Rev. B 69(5), 054202 (2004).
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M. I. Stockman, S. V. Faleev, and D. J. Bergman, “Coherent control of femtosecond energy localization in nanosystems,” Phys. Rev. Lett. 88(6), 067402 (2002).
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E. Mrsell, R. Svrd, M. Miranda, C. Guo, and A. Losquin, “Direct subwavelength imaging and control of near-field localization in individual silver nanocubes,” Appl. Phys. Lett. 107(20), 201111 (2015).
[Crossref]

Tao, H. Y.

B. Y. Ji, J. Qin, H. Y. Tao, Z. Q. Hao, and J. Q. Lin, “Subwavelength imaging and control of ultrafast optical near-field under resonant-and off-resonant excitation of bowtie nanostructures,” New J. Phys. 18(9), 093046 (2016).
[Crossref]

Thielen, P.

M. Aeschlimann, T. Brixner, A. Fischer, M. Hensen, B. Huber, D. Kilbane, C. Kramer, W. Pfeiffer, M. Piecuch, and P. Thielen, “Determination of local optical response functions of nanostructures with increasing complexity by using single and coupled Lorentzian oscillator models,” Applied Physics B Lasers & Optics 122, 1992016.
[Crossref]

Tsai, D. P.

X. Fang, L. T. Ming, J. Y. Ou, K. F. Macdonald, D. P. Tsai, and N. I. Zheludev, “Ultrafast all-optical switching via coherent modulation of metamaterial ab-sorption,” Appl. Phys. Lett. 104(14), 141102 (2014).
[Crossref]

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S. Schlauderer, C. Lange, S. Baierl, T. Ebnet, C.P. Schmid, D.C. Valovcin, A.K. Zvezdin, A.V. Kimel, and R.V. Mikhaylovskiy, “Temporal and spectral fingerprints of ultrafast all-coherent spin switching,” Nature 569(7756), 383–387 (2019).
[Crossref]

von Plessen, G.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
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Supplementary Material (1)

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Supplement 1       Supplementary Information

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic diagram of asymmetric Au nano cross structure: A1 = 80nm, A3 = 50nm, A2=A4 = 90nm, arm width 30nm, height 30nm. The optical source is incident from the positive direction of Z axis and polarized along Y axis. (b) Extinction spectrum of nanostructures. Field profile of Au nanocross at 718nm (c) and 852nm (d).
Fig. 2.
Fig. 2. (a) Temporal evolution of the electric field of transform-limited pulse with the center wavelength=800nm and the spectral range from 644 to 1064nm. (b) Localized electric field versus time around the poles of nanoarms of A1 (blue) and A3 (green). (c) Field profile of asymmetric Au nano-cross structure at 10.67fs
Fig. 3.
Fig. 3. spatiotemporal evolution of asymmetric Au nano-cross under the illumination of chirped laser pulse. Temporal evolution of the poles of longitudinal nanoarms of A1 (blue) and A3 (green) under the illumination of 40fs chirped laser pulse of α=−0.17 (a) and +0.17 (b), respectively. Time interval for ultrafast energy transferring between two poles of longitudinal nanoarms of A1 and A3 with temporal separation between resonant frequencies in the negative (c) and positive (d) chirped pulses.
Fig. 4.
Fig. 4. Electric field from the poles of nanoarms of A1(a) and A3(b) under the excitation of positively (blue) and negatively (green) chirped pulses with pulse duration ${\tau _P} = 40fs$
Fig. 5.
Fig. 5. Temporal evolution of electric field from plasmonic hot spot in symmetric Au nano-cross structure excited by (a) blue off-resonant, (b) on-resonant and (c) red off-resonant FTL pulse with duration of 10fs.

Tables (1)

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Table 1. The amplitudes of electric field in different nanostructures with the illumination of chirped laser pulse (RW, the resonance wavelength)

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

E ( t ) = A ( t ) cos ( w 0 t + φ ( t ) ) = A 0 e ( t t o f f s e t τ G ) 2 cos ( w 0 ( t t o f f t s e t ) + φ ( t t o f f t s e t ) )
φ ( t t o f f t s e t ) = α ω 0 ( t t o f f s e t ) 2 τ P
R ( ω ) = 1 ω r 2 + 2 γ i ω ω 2 = ω r 2 2 γ i ω ω 2 ( ω r 2 ω 2 ) 2 + 4 γ 2 ω 2
E p l ( t ) t 1 ω r E l a s e r ( t ) e γ ( t t ) sin [ ω r ( t t ) ] d t

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