Subwavelength imaging and control of ultrafast optical near-field under resonant- and off-resonant excitation of bowtie nanostructures

We demonstrate subwavelength imaging and control of localized near-field distribution under resonant and off-resonant excitation of identical gold bowtie nanostructures through photoemission electron microscopy. Control of the near-field distribution was realized by polarization rotation of single femtosecond laser pulse and variation of the phase delay of two orthogonally polarized femtosecond laser pulses. We show that the localized optical near-field distribution can be well controlled either among the corners of the nano-prisms in the bowtie for resonant excitation or the edges for off-resonant excitation. A better visualization of the PEEM image is achieved for resonant excitation than in the case of off-resonant excitation. The experimental results of the optical near-field distribution control are well reproduced by finite-difference time-domain simulations and understood by linear combination of electric charge distribution of the bowtie by s- and p- polarized light illumination. In addition, a shift of the near-field excitation position with inverted or unchanged phase, alternatively an un-shift of the excitation position but only with inverted phase of the near-field, can be realized by rotating the polarization angle of a single pulse and coherent control of two orthogonally polarized fs laser pulses.


Introduction
Localized surface plasmons (LSPs) are coherent collective oscillations of charge carriers inside a metal nanostructure that result in the confinement of the electromagnetic field below the diffraction limit of traditional optics and have attracted considerable research interest for a broad range of applications in sensing [1,2], imaging [3][4][5], solar cell [6] and so on. Special attention has been given to the active control of LSPs in the vicinity of noble metal nanostructures which offers a way to manipulate light on the nanoscale [7]. Such control has a great potential in many fields, such as information technology and biomedicine, and it has great promise to improve the development of nano-optics.
Near-field control plays an important role in the research field of plasmonics [8][9][10]. Active near-field control in the vicinity of nanostructures can be realized in many ways. For example, phase modulation of one ultrashort pulse (i.e. modulating the chip of pulse) [11], adaptive near-field control related to multi-parameter pulse shaping with a learning algorithm [12,13], polarization rotation of a single linearly polarized pulse [14][15][16][17] and relative phase delay modulation of two orthogonally polarized laser pulses (hereby named as 'coherent control') [14,18]. Among these techniques, polarization rotation and coherent control are two widely used control schemes because they avoid the use of complex closed-loop learning algorithms and are easily achievable by a convenient experimental set up [14].
Effort has been made to pursue maximal field enhancement in the research of excitation and control of LSPs, and this has been realized by tuning illumination wavelength to the resonant peak of a nanostructure [19]. This is vital to some applications such as single molecule sensing, detecting, high harmonic generation and surface enhanced Raman scattering (SERS) in which a maximal LSP enhancement is desired [7,[20][21][22]. Meanwhile, with a broadening application of LSP effect, researchers have found that excitation of LSP with illumination wavelength tuning off the resonant peak often becomes important, i.e. employing LSP effects under off-resonant conditions. For example, off-resonant excitation of LSPs in nanostructure is found to have great potential applications in the field of biomedicine, in which the generation of nanobubbles and simultaneously avoiding the melting of nanoparticles under resonant excitation that could bring toxicity issues is required in this application [23]. Hence, in addition to the resonant excitation, study of near-field control under off-resonant excitation in nanostructures is of importance. Up to now, a full and direct study to the optically induced nearfield control within single nanoparticles both under resonant and off-resonant excitation is still absent. Besides this point, the dependence of the relative phase status of near-field upon the excitation scheme is an interesting and unexplored topic.
In this paper, by tuning the output laser wavelength, we control the distribution of near-field in bowtie structure under resonant (850 nm) and off-resonant (700 nm) conditions with the schemes of polarization rotation of single laser pulses and variation of relative phase delays of orthogonally polarized two femtosecond laser pulses. In the mean time, we investigated the dependence of the relative phase status upon the two excitation schemes. The control of LSP processes in bowtie nanostructure is imaged with a photoemission electron microscope (PEEM), which provides a non-invasive probe of optical near-field by imaging fieldinduced photoemission electrons with high spatial resolution. The technology has been widely used to study the dynamics of surface plasmon evolution [24][25][26][27]. Experimental results show that, under resonant wavelength excitation, enhancement of the near-field mainly locates at the corners of the nano-prisms and can be controlled by rotating polarization of a single laser pulse or by varying the relative phase delay of orthogonally polarized two femtosecond laser pulses. Under the off-resonant wavelength excitation, the enhanced near-field mainly locates at the edge regions of the nano-prism, and the near-field shows a relatively less prominent visualization compared with the resonant case. Furthermore, a linear combination of the simulated charge distribution in sand ppolarized cases could be used to better understand near-field control behavior, and the simulation results are in good agreement with the results of the PEEM measurement. To the best of our knowledge, this is the first engaged discussion on the dependence of the relative phase status upon the excitation scheme and also near-field distribution difference within a nanostructure between resonant and off-resonant excitations. Figure 1 shows the experimental set up. PEEM (FOCUS, IS-PEEM) with 30 nm spatial resolution was used to image the optical near-field of a bowtie nanostructure. Two excitation sources were used, one was an unpolarized Hg lamp (one photon energy less than 5.2 eV, to contour the bowtie antenna) and the other was a femtosecond Ti-Sapphire laser oscillator (Coherent, Mira 900), delivering pulses with a duration of 200 fs, tunable output wavelength (from 680 nm to 900 nm), single pulse energy of 13 nJ and a repetition rate of 76 MHz. The laser power at the sample surface was estimated to be about 1.0×10 8 W cm −2 and 4.5×10 8 W cm −2 for resonant and off-resonant excitations, respectively. Under the above laser power, we did not observe any sign of sample damage in the PEEM experiment. The sample was illuminated at a 65°angle to the normal of the substrate with excitation light sources. The polarization direction of the femtosecond laser pulse was varied using a broadband half-wave plate. A Mach-Zehnder interferometer was used to make two orthogonally polarized laser pulse separate with several tenths of attoseconds, in which two half wavelength plates were used, one of which is to polarize the laser pulse and the other is to compensate the pulse width of the other arm (see figure 1(a)). The phase stability of the Mach-Zehnder interferometer over 1 min of the accumulation time of the PEEM image in the current experiment has been found to be better than π/10, which is much smaller than the phase delay step (π/2) used in the PEEM experiment. Moreover, before taking each PEEM image, we re-calibrated the temporal overlap of the two pulses of the Mach-Zehnder interferometer system to ensure reliability of the phase delay that was employed in the PEEM image results. Photon energies of the laser pulse are 1.45 eV(850 nm) and 1.77 eV(700 nm), respectively, for resonant and off-resonant excitations of the bowtie structure, both of them are below the work function of gold (∼4.5 eV), indicating that the absorption of at least 3 photons is required for each emitted electron, so the photoelectron yield is proportional to the 6th power of |E z | amplitude of the local electric field (near-field). Fabrication of the gold bowtie nanoantenna was realized via collaboration with the Suzhou Institute of Nano-tech and Nano-bionics, Chinese Academy of Sciences. The sample preparation procedure was as follows. An indium tin oxide (ITO) coated glass was used as a substrate. On top of the ITO layer resist was coated. After the procedure of etching and resist development, nano-prisms were formed. Then a layer of gold with thickness of 40 nm was sputtered on the developed sample, and finally after the lift-off process, the sample preparation was done. The antenna consists of two triangular nano-prisms with a thickness of 40 nm and equilateral sides with a length of 350 nm and a gap distance of 100 nm. The scanning electron microscopy image of the bowtie is shown in figure 1(b). The onephoton photoemission image with mercury lamp illumination is shown in figure 1(c), which shows homogeneous electron emission and generates a high contrast to the ITO substrate. The schematic of the bowtie structure is shown in figure 1

Experimental and simulation setup
The simulation of near-field distribution control was performed with commercial software FDTD solutions (Lumerical, Ltd) based on the finite-difference time domain method (FDTD) [28,29]. The structural parameters taken were the same as the experimental ones. The dielectric properties of gold were fitted to experimental data from Johnson and Christy [30]. The real and imaginary part of the refractive index of ITO was set as 1.95 and 0.1 [31]. We used a total field scattering field (TFSF) source with 1 V m −1 of electric amplitude in the case of polarization rotation control and two TFSF sources for the case of coherent control to illuminate the sample with an angle of incidence of 65°to the surface normal to mimic the experiment. The mesh size nearby the sample was 1.6 nm×1.6 nm×2 nm and the total simulation area was blocked by perfectly matched layers (PMLs) to reduce artificial reflections from the boundaries. A convergence study had performed and the error was within acceptable limit.

Results and discussion
We first clarify the resonant wavelength for the fabricated bowtie structure. The wavelength-dependent nearfield property of G 1 of the bowtie (marked in figure 1(d)) by PEEM measurement as well as by FDTD simulation, and also absorption spectrum of the bowtie structure by FDTD simulation are given in figure 2. To present curves of similar physical significances, the cube root of the photoemission electron yield was displayed [32]. From the wavelength-dependent PEEM signal as well as the FDTD simulated near-field intensity curve in figure 2, we found that resonance of the structure was obtained at a wavelength near 850 nm. The simulated absorption curve in figure 2 shows a resonant peak appearing at wavelengths of 836 nm. Difference in resonant wavelengths between the absorption and maximum electric intensity at the surface had already been reported by several other groups [33][34][35]. Based on the laser spectral tunable range (from 680 to 900 nm, shadow area in figure 2), 850 nm is used as resonant excitation wavelength and 700 nm is selected as off-resonant excitation for the nanostructure in the current research.
Near-field distribution control under femtosecond resonant wavelength excitation was investigated. Figure 3(a) shows the PEEM images by rotating polarization direction of the femtosecond laser pulse for 850 nm resonant modes. Comparing with the one photon PEEM image with Hg lamp illumination as shown in figure 1(c), PEEM images obtained with a femtosecond laser pulse show that near-field distribution is not uniform on the nano-prisms surface anymore but mainly is located at corners of the structure as hotspots in the PEEM images. It is seen that hotspot distributions depend on the angle θ as polarization direction deviates (in the anti-clockwise direction) from p-polarization of the incident light (0°). Figure 3(a) shows that near-field is mainly enhanced at G 1 position for p-polarization cases. As the polarization angle θ of a laser pulse tunes to θ=45°, the local field at G 1 position becomes weak and strong near-field starts to emerge at C 2 position. As the polarization θ increase to 90°(s-polarization), the photoemission electron signal induced by local field at the G 1 position becomes invisible, excitation of C 1 and C 2 are clearly visible as well. With the further increase of polarization angle θ to 135°, the hotspot at G 1 position reappears and the strong near-field enhancement shifts to C 1 from the C 2 position that is symmetrical to the case of 45°. The results clearly show that strong near-field distribution can be controlled among the corners of the bowtie nanostructure by tuning the polarization angle of the excitation laser pulse. In the experiment, we have also performed control of local field distributions by using a pair of orthogonally polarized laser pulses; the corresponding PEEM images are displayed in figure 3(c). Similar to the results obtained by rotating the polarization direction of single laser pulses, strong local field enhancement at C 1 and C 2 positions can also be selectively achieved by varying relative phase delay ΔΦ of the two pulses. As shown in figure 3(c), strong near-field can be shifted from the C 2 to C 1 positions by changing the phase delay from ΔΦ=0 to ΔΦ=π. It should be noted that the near-field distribution control under the latter scheme has been realized at nanometer spatial resolution and attosecond temporal precision (ΔΦ=π/2, corresponding to the time delay of Δt=708 attoseconds between the two pulses). We should mention that the coherent control method we used here is actually also a polarization control, however, it is switched from  It is interesting to note that a common feature of the near-field pattern of the PEEM images in figure 3 is that only the farther side of individual nano-prisms in the bowtie (referring to C 1 and C 2 corners of the left side nanoprism, and G 1 corner of the right side nano-prism, respectively) get stronger enhancement rather than the nearer side (referring to G 2 corner on the left side nano-prism and C 3 , C 4 corners on the right side nano-prism). This characteristic regarding to local field distribution in the bowtie may be attributed to a retardation effect that occurs when the structural size under study is in the order of the wavelength of the oblique incident of the excitation light pulse [18], or to interference between bright-and dark-modes that are supported by a bowtie structure [36]. It is noted that the design of the antenna is actually just two rather independent nano-prisms. The difference in response between both nano-prisms arises because of the different orientation with respect to the incident beam. There is no strong coupling between the nano-prisms, which is different from the case of a real bowtie antenna structure.
In this work, off-resonant mode near-field control is also investigated with the two control schemes as introduced in the resonant wavelength excitation case. Figure 4 shows the PEEM images obtained by rotating the polarization direction and varying the phase delay of two laser pulses for the 700 nm off-resonant mode. Different from the near-field distribution under resonant wavelength excitation, a prominent feature of the figure 4 is that the enhanced near-field regions distribute along edges of the nano-prisms. As shown in figures 4(a) and (c), the local field distributions show noticeably controllable modulation when the polarization angle and relative phase delay are changed. It is seen that near-field in figure 4(a) mainly locates in two edges M 3 and M 4 (labeled by red dot) of the right prism at 0°, and then the field focus on the M 4 as the polarization angle tunes to 45°. The field shifts to M 3 as the angle further tunes to 135°. For the case of the two laser pulses scheme, the fields mainly locate in the lower edge M 4 of the right nano-prism for the relative phase delay ΔΦ=0, and the near fields shift to the upper edge M 3 of the right nano-prism as the relative phase delay is changed to π. Finally, the field returns to M 4 again as the relative phase tunes to ΔΦ=2π. These results demonstrate that active control of near-field at edge of the nano-prism can be achieved by rotating polarization of single pulse and changing relative phase delay of the two laser pulses. In addition, it is seen that near-field on the vertical edge of the left nano-prism shows high intensity in the case of the off-resonant excitation.
Obviously, visualization of the near-field distribution control is less prominent for the off-resonant excitation compared to the resonant case. And also, for the off-resonant excitation case it shows that the nearfield enhancement distributes along edges of the two nano-prisms, which is totally different from the near-field enhancement pattern observed for the case of resonant wavelength excitation in that strong near-field enhancement focuses on corners of the nano-prism and meanwhile locates at the farther side away from the excitation source. It has to be noted that the investigated bowtie nanostructure exhibits dipole mode at resonant peak of 1300 nm, and quadrupole mode resonance at 850 nm. The different signature that the enhanced nearfield distribution on the corners for resonant illumination at 850 nm while along the edges for off-resonant at 700 nm is ascribed to that a higher order excitation of the bowtie structure occurs as the excitation light is blueshifted to the off-resonant wavelength at 700 nm.
Less prominently visualized images under off-resonant excitation than that for resonant excitation could be attributed to the following reasons. Weak plasmon excitation at 700 nm laser wavelength illumination determines that a much strong local field enhancement can not be expected under this circumstance. Also, since the local field position of off-resonant mode is mainly on the edge of nano-prisms, lightning rod effect, which reinforces local field enhancement for the case of sharp corner of the nano-prism under resonant wavelength excitation, can not be expected either. In addition, the excitation of possible imperfection that introduced from the electron beam lithography process could occur [37]. The appearance of imperfection can enlarge the nearfield intensity from several to more than a dozen times [38,39] and makes it comparable to the field enhancement of the off-resonant excitation. Thus the imperfection induced near-field could show up and affect the visualization effect under off-resonant illumination. As a result, degraded visualization of PEEM images are observed in the case of the off-resonant illumination. It has to be noted that even though visualization of the images for off resonant illumination is lower than the resonant case, the degree of control is still high for off resonant case. A rather high degree of the field control achieved in the off-resonant case is attributed to the fact that the relative strength of the local field induced by both incident polarizations is similar.
The simulated |E z | 6 images of polarization rotation control and coherent control from FDTD simulations supports the measured PEEM images. These images were eventually convolved by a Gaussian filter to account for the finite resolution of the PEEM [17]. As one can see that figures 3(b) and (d) are in excellent agreement with experimental multiphoton PEEM images in figures 3(a) and (c). And also, as shown in figure 4, the simulated results for off-resonant excitation well correspond to the PEEM measurement, the small discrepancy between the simulated and experimental results in figure 4 could be attributed to weak excitation under off-resonant illumination and the excitation of possible imperfection in the nanostructure induced during the lithography process as those discussed in the above.
The experimentally demonstrated control of the near-field localization can be further understood as linear combinations of near-field excited by sand ppolarized light, respectively. Under the excitation of single laser pulse the local electric field can be expressed as [17]: For the case of coherent control by two orthogonally polarized laser pulses, the local field response can be expressed as [13]: the amplitudes A describe the extent to which the two far-field polarization propagation, ΔΦ=j s -j p corresponds to the relative phase delay of two orthogonal pulses, G i (r) determines the local near-field response of the structure with the illumination of two far-field polarization components, i=s and p. The term in brace reflects a period modulation to the near-field response. If we assume optical path of E p is constant and of E s is changed, term j p is constant, while, the second term in the brace will change relative to ΔΦ. Ultimately, the near-field of superposition region between E p and E s can add constructively or destructively corresponding to ΔΦ. For fixed illumination layout, the term of exp [ij p ] will not affect the local near-field distribution anymore. The experimental results in figure 3 show that near-field enhancement as well as its control mainly locate on corners of the nano-prisms for resonant wavelength excitation, while in figure 4 at the edges of the prisms for off-resonant case. To qualitatively demonstrate characteristics of the near-field enhancement and control for both the resonant and off-resonant cases, we firstly plotted the simulated |E z | image of the bowtie illuminated by 850 nm resonant and 700 nm off-resonant of pand s-polarized light, respectively, in figure 5. Figures 5(a) and (c) show that the strongly excited near-field mainly locates at the corners of prisms under the illumination of 850 nm, i.e. the near-field distribution is dominated by G 1 position, meanwhile with much strong field in C 1 and C 2 points for p-polarization laser illumination. The corresponding field focuses at C 1 and C 2 positions for spolarization excitation. The near-field distribution in sand p-polarization excitation under the 850 nm resonant wavelength implies that near-field distribution and its control on corners of C 1 , C 2 and G 1 of the nanoprism are expected in the experiment. On the other side, the near fields in edge region of the prism dominate for 700 nm excitation for both pand s-polarization cases, therefore, the near-field enhancement and its control mainly locate at edges of the prism for off-resonant case. Moreover, it is noticeable that the plasmon-enhanced near-field of 700 nm mode is much weaker due to the off-resonant nature of the nano-prism at this wavelength.
Furthermore, experimental results of the near-field distribution control can be understood by linear combinations of charge distribution in the nanostructure, as charge is responsible for the near-field generation. The 850 nm resonant mode is considered as an example for better visuals, while the general principle holds regardless of modes. Figure 6(I) shows the case of polarization rotation from θ=45°to θ=315°by a step of 90°, in which the left two images represent the 850 nm mode for s and p-polarization, and the images on the right side of figure 6(I) originates from a linear combination of the two images on the left side according to equation (1). For θ=45°, the result in this figure (represented by (a+b) in figure 6(I)) shows that charges add constructively in C 2 position due to the same sign for sand p-polarization, whereas they add destructively in C 1 position due to the inverse sign of charges there. As a result, the PEEM images in figure 3(a) show a large photoemission electron yield originating from an enhanced field at C 2 position, and correspondingly no photoelectron emission due to the cancelling of field intensity at the C 1 position. Similarly, a sketch of charge corresponding to a polarization of θ=135°is also shown in figure 6(I) (represented by (a-b) in figure 6(I)), which results in an enhanced field at C 1 instead of C 2 position due to the sign change of the p-polarized component. In addition to shift of the excitation point from C 2 to C 1 , the phase of point C 1 for θ=135°is inverted compared with the point of C 2 for θ=45°. If we further increase the angle to θ=225°(represented by (-a-b) in figure 6(I)), the excitation point returns to C 2 , but with an inverted phase compared to the case of θ=45°. If the polarization angle is increased to θ=315°(represented by (b-a) in figure 6(I)), the excitation point shifts to C 1 again while keeping the same phase with C 2 of the case θ=45°. Note that phase of the points can only be revealed by the charge distribution and not by PEEM image in our case. To summarize if we take C 2 point as example point for reference (the case of θ=45°, i.e., (a+b)), the enhanced near-field can be shifted to point C 1 with inverted phase (the case of (a-b)) or unchanged phase (the case of (b-a)). Alternatively, un-shift of the enhanced field position but only with inverted phase (the case of (-a-b)). Therefore, a control of near-field distribution or phase of the interest points in the bowtie nanostructure can be realized by rotating the polarization direction of the laser pulse.
The corresponding electric charge schematic illustrations based on equation (3) are shown in figure 6(II). For the case of j p =0, when the relative phase delay of the two orthogonally polarized laser pulses is set to ΔΦ=0 (equivalent to diagonally linear polarization under 45°), the resulting net electric charge add constructively at C 2 and destructively in C 1 position (the case of (b+a)). It is seen that, as the phase delay is changed to ΔΦ=π (to diagonally linear polarization under 315°), the charge add constructively in C 1 and destructively in C 2 position (the case of (b-a)). For the phase offset j p turns to π and with phase delay of ΔΦ=0 (to diagonally linear polarization under 225°), the resulting net electric charge add constructively at C 2 and destructively in C 1 position (the case of (-a-b)). If we set ΔΦ=π (to diagonally linear polarization under 135°), the charge add constructively in C 1 and destructively in C 2 position (the case of (a-b)). It is seen that the phase of the excitation point keeps unchanged when the positions shift both for the cases of j p =0 and j p =π. Note that figure 6 shows that the near-field distribution is the same but just with 180°phase shift between the case of θ=45°and θ=225°(or between the case of θ=135°and θ=315°) for polarization control, and also the same but just with 180°phase shift between the case of j p =0, ΔΦ=0 and j p =π, ΔΦ=0 (or between the case of j p =0, ΔΦ=π and j p =π, ΔΦ=π) for coherent control. Similar to the case of the control by rotating the polarization angle of single pulse, we can realize the near-field excitation position shift with the inverted phase or unchanged phase. Alternatively, we can invert the phase of the near-field excitation points while keeping its position unchanged. Furthermore, it is seen from figure 6(II) that the phase and position of the excitation points are controlled by j p and ΔΦ, respectively.
On the other hand, the phase relation of the excitation points can be revealed from the temporal evolution of the electric field on corners of the bowtie structure. Figure 7 shows phase relation among the near-field excitation points corresponding to the results in figure 6. Figure 7(a) shows that the near-field at points of C 1 and C 2 under the polarization rotation scheme is with inverted phase between θ=45°(θ=315°) and θ=135°or θ=225°, while keeps in phase between θ=45°(θ=135°) and θ=315°(θ=225°). Similar results can be obtained from the dynamic evolution of the near-field with coherent control scheme as shown in figure 7(b). Figure 7 intuitively gives phase relations among the near-field points shown in the figure 6.

Conclusions
Subwavelength imaging and control of localized near-field distribution under resonant and off-resonant excitation within identical gold bowtie structures were demonstrated for the first time. The near-field control was established by two ways, i.e. polarization rotation of single fs laser pulse and coherent control of two orthogonally polarized fs laser pulses. We found that the modulation result to the hotspot under resonant wavelength illumination shows a better visualization in the PEEM image than the case under off-resonant wavelength illumination. The observed photoemission electron pattern in the PEEM images with both control for ΔΦ=0 or ΔΦ=π (corresponding to diagonally linear polarization under 45°or 315°(−45°)) with j p =0. Lower right two pictures corresponding to ΔΦ=0 or ΔΦ=π (corresponding to diagonally linear polarization under θ=225°or θ=135°) with j p =π. For both of the pictures, the constants before p and s components are omitted for simplicity. The direction of the incoming light is at grazing incidence from right side of the sample, which is shown by the pink arrow. The polarization direction is shown by blue double arrow. schemes are well reproduced using finite-difference time-domain simulation. The results of electric near-field distributions for rotation of polarization direction and relative phase delay are explained by using a linear combination of the simulated charge distribution by pand s-polarized excitations. The demonstrated near-field control has a spatial resolution of nanometer and temporal precision of attosecond. In addition, we can realize the near-field excitation position shift with the inverted phase or unchanged phase. Alternatively we can invert the phase of the near-field excitation points while keeping its position unchanged by rotating the polarization angle of single pulse and coherent control of two orthogonally polarized fs laser pulses, respectively. Our finding for the near-field control of the identical nanostructure under resonant and off-resonant excitation and the phase modulation of the excitation points will pave the way for applications such as sensing, SERS, biomedicine and plasmonic devices.