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Spectral interferometry combined with near-field scanning optical microscopy is applied in the spatiotemporal characterization of femtosecond plasmon localized at gold nanostructures and surface plasmon polariton in an air-gap waveguide. Based on the plasmon response function in both the amplitude and the phase obtained from the measurements, we deterministically tailored the femtosecond plasmon pulse by shaping the femtosecond excitation laser pulses.
© 2013 Optical Society of America
1. Introduction
Localized plasmon resonance at noble metal nanostructures has been receiving much attention for producing a nanometer-sized platform for the interaction between light and matter or for developing sub-micrometer-sized optical circuits. The plasmon resonance wavelength depends on the shape and the size of the nanostructure materials, and the resonance enhancement factor of the plasmon field varies by incident light polarization. When noble metal nanostructures are properly designed, spatial and temporal plasmon distribution can be controlled by ultrashort laser pulses shaped in their instantaneous frequencies. Lévêque theoretically demonstrated that the spatiotemporal control of local plasmon can be achieved by combining frequency chirped femtosecond excitation laser pulses and the arrangement of metal nanorods [1]. The sign of the chirp controls the excitation sequence of the nanorods with great flexibility.
Ultrashort laser pulses excite the optical near-field on the nanostructure over a range of frequencies, and the superposition of these plasmon field distributions with different frequencies determines the actual localized plasmon field evolution. Stockman et al. showed that arbitrarily shaped laser pulses can vary the surface plasmon-polariton field distribution at a V-shaped nanostructure [2]. Therefore, the spectral phase and the temporal polarization of the incident laser pulses affect the instantaneous plasmon distribution in the vicinity of the nanostructure. In such a case, the self-learning adaptive pulse-shaping schemes [3,4] developed to realize optimum ultrafast interaction between ultrashort laser pulses and matter are suitable to realize spatiotemporal control over localized plasmons in nanostructures. In fact, spatiotemporal control over localized plasmon was experimentally demonstrated using a vector pulse shaping technique for femtosecond excitation laser pulses [5].
Although this adaptive pulse-shaping scheme is applicable to the spatiotemporal control of the localized plasmon distribution at any nanostructures, we can deterministically achieve spatiotemporal control if the plasmon response functions can be obtained. Huang et al. used the finite-difference time domain ΠFDTD) method to simulate the near-field impulse response of a nanostructure [6]. Using this impulse response, the near-field responses to any desired pulse shape can be obtained by multiplication in the spectral domain. By applying pulses with an opposite phase with respect to the impulse response, they showed that optimal temporal compression is achieved in asymmetric rods. Harada et al. applied this control scheme for nanometer-sized selective two-photon excitation [7]. They predicted the two-photon fluorescent rates at various fluorophores at nanostructures using plasmon SHG spectra calculated by the plasmon response function and the shaped laser pulses, and the two-photon fluorescence excitation spectra of fluorophores.
To control the spatial plasmon distribution, Volpe et al. demonstrated a deterministic control scheme [8] called a deterministic optical inversion (DOPTI) algorithm that can obtain the desired near-field pattern and the closest physical solution for the incident field, expressed based on focused Hermite-Gaussian (HG) beams.
These deterministic plasmon control schemes are very useful to achieve spatiotemporally localized excitation in sub-wavelength scales. However, in reality, since even nanostructures fabricated with e-beam or ion-beam lithography deviate from the design, the plasmon response function at the actual nanostructures must be measured. So far, various diagnostics have been applied for ultrafast plasmon pulse measurements, such as fringe-resolved autocorrelation [9] and frequency-resolved optical gating (FROG) [10]. Since the spatial resolution is limited by optical diffraction, these conventional ultrafast optical measurements are applicable only to well isolated nanostructures.
In this paper, we employed a new diagnostics: spectral interferometer (SI) that was combined with near-field scanning optical microscopy (NSOM) to characterize the local plasmons excited by ultrashort laser pulses at gold nanostructures. We can deduce a bandwidth-limited plasmon response function from the Fourier analysis of heterodyne SI. Then, based on the response function, we arbitrarily tailored the local plasmon pulse by shaping the excitation femtosecond laser pulses. Because of the different plasmon response functions at different local positions, the intense Fourier transform limited plasmon pulse can be concentrated on a certain point in the vicinity of the nanostructures. We also applied this deterministic plasmon pulse control scheme to surface plasmon-polariton in an air-gap plasmon waveguide, which corresponds experimental verification of Huang’s theoretical prediction [6].
2. Heterodyne spectral interferometry to deduce plasmon response functions
To measure the temporal characteristics in both the amplitude and the phase of the localized plasmon excited by ultrafast laser pulses, we used SI measurement for the plasmon pulses collected by a NSOM fiber probe. Heterodyne SI is a linear optical technique that temporally overlaps the unknown pulse with a reference pulse to measure for the pulses that are potentially complicated in time or frequency. Fiber optics is used to introduce the beams into the device, which simplifies alignment.
Complex electric-field cross-correlation , which can be obtained from SI measurements, is described using the following complex electric-field response function of the localized plasmon:
where , , and are the complex electric-field of a localized plasmon, a reference pulse, and a pump pulse, respectively. According to Eq. (1), is obtained from the cross-correlation and the reference spectrum amplitude as follows when :Therefore, complex localized plasmon waveform can be molded by shaped complex laser pulse as follows:In these procedures, however, must be specified by such diagnostics as FROG. When we measure cross-correlation function at a plane point where no nanostructure exists, reference cross-correlation can be described as follows:Here is the near-field at a plane point, which corresponds to . Therefore,We do not need to separately specify the reference pulse. Moreover, we do not need to specify the dispersion at the signal and the reference arms of the optics.3. Experimental setup
In our experimental setup of SI-NSOM (Fig. 1) we used an ultra-broadband femtosecond laser (VENTEON Laser Technologies GmbH: 600~1000 nm, repetition frequency of 150 MHz) as an excitation laser source (Fig. 2(c)). Its spectral width was limited to 630~970 nm after passing through a spatial light modulator (SLM) in a 4-f pulse shaper. Our homemade NSOM employs an Au-coated fiber probe (opening size: 50 nm), whose position is precisely controlled by the share-force detected by a quartz tuning fork. The femtosecond laser beam was split into two beams before the pulse shaper. One beam was irradiated nanostructures in an evanescent mode through a prism attached to the back of the SiO2 substrate. The other beam was delivered with a single-mode fiber identical to that used for the NSOM fiber probe and overlapped the signal beam in a spectrometer. We measured the spectral interference by an electrically cooled CCD camera. The dispersion of the optical arms of the pumping pulse and the residual dispersion of the laser oscillator beam were measured and compensated by the pulse shaper. After the response function was obtained by the SI-NSOM followed by the numerical procedure described in Section 2, we arbitrarily shaped the plasmon pulse using the excitation laser pulse shaped by the pulse shaper. The spectral phase for pulse shaping is simply added to the spectral phase necessary for dispersion compensation.
Fig. 2 (a) Designed Au nanocrosses, (b) SEM pictures of fabricated Au nanocrosses, (c) plasmon response functions of nanorods calculated by a FDTD numerical model for various aspect ratios R, and (d) plasmon resonance function predicted by FDTD calculation for an Au nanocross consisting of a longer arm with R = 3 and a shorter arm with R = 2.5. Spectrum of our excitation laser pulse is shown in Fig. 2(c).
We used Au nanocrosses fabricated by e-beam lithography as a nanostructure sample (Fig. 2(a)). An aspect ratio R (ratio of length to width) of the Au rods in the crosses was 2.5 or 3. Figure 2(c) shows the intensity of the plasmon response function predicted by a FDTD numerical model for the Au nanorods with various aspect ratios. The plasmon resonance of a nanorod with R = 2.5 or 3 exists within the spectrum of our laser source. Figure 2(d) shows the intensity of the plasmon resonance functions predicted by FDTD calculation for an Au nanocross consisting of a longer arm with R = 3 and a shorter arm with R = 2.5. The excitation laser polarization is set parallel to the one of two arms indicated in Fig. 2(d). The plasmon resonance of the nanocross still exists within the spectrum of our laser source. However, since the manufacturing accuracy of manufacturing is not so high as shown in the SEM picture of Fig. 2 (b), the actual plasmon response function will vary.
We fabricated also an air-gap plasmon waveguide as shown in Fig. 3. The width of the air gap and the gold rods are 50 nm and 100 nm, respectively. The thickness is 30 nm. At the end of the waveguide, three exits were fabricated, where we measured plasmon response functions. The excitation laser was coupled to the waveguide by simply irradiating the input edge of the waveguide in an evanescent mode through a prism attached to the back of the SiO2 substrate. The excitation beam spot size is ~1 μm dia. A 50-μm long straight waveguide brings the plasmon pulse to the output branches so that the influence of scattered excitation light which would be background noise at NSOM measurements was minimized. An inset in Fig. 3 is the distribution of plasmon pulse intensity during propagation calculated by a FDTD numerical model. Thus, this air-gap waveguide can guide surface plasmon polariton excited by 800-nm laser pulses. We set a reference point at 50-μm from the input edge to define of Eq. (4) for the series of response function measurements.
Fig. 3 An air-gap surface plasmon-polariton waveguide designed for experiment. An inset is a FDTD prediction on surface plasmon-polariton propagation in this waveguide. The SEM picture of fabricated waveguide is shown in the bottom.
Since our fiber probe is Au-coated (Fig. 4(a)), it may influence the plasmon field generated around the Au nanocrosses. We calculated the plasmon spectra on a 120 x 40 nm Au nanorod with and without the Au-coated fiber probe. The aperture size is 50-nm dia. similar to that used in our experiments. The probe end was placed 10 nm above the nanorod. Even at the fiber probe’s opening where no Au coating existed, the plasmon field was substantially modified by the fiber probe (Fig. 4(b)). In this case, the plasmon enhancement peak shifted to a longer wavelength and reduced the enhancement. Even if the opening size is increased to 160 nm, the probe effect is almost the same. On the other hand, regarding the intensity distribution along the 120-nm-long nanorod measured by scanning the probe, the probe does not change the original plasmon distribution (Fig. 4(c)). The influence of the probe can be reduced when the probe position is moved more than 30 nm above the nanorod (Fig. 4(d)).These numerical analyses show that our method is not a perfectly non-demolition measurement of the localized plasmon at the nanostructures. Therefore, strictly speaking, our experiment corresponds to the measurement of response functions and the localized plasmon control at nanostructures unified with the probe. The plasmon response function of the nanostructure alone will vary. However, this situation remains useful since we intend to specify the plasmon field at a certain nanostructure to selectively excite two-photon pumping and measure fluorescence with NSOM. Selective CARS excitation and probing are also attainable. We also calculate the influence of NSOM probes coated with Ag and Al (Fig. 4(b)). Ag coating varies the plasmon spectrum more, but Al coating’s influence is slightly less. To avoid the influence of the NSOM probe on the local plasmon, a bare fiber probe must be used, even though it degrades the spatial resolution.
Fig. 4 Numerically predicted influence of Au-coated fiber probe on plasmon distribution: (a) Schematic cross-section and SEM picture of our NSOM fiber probe (although this picture is a fiber probe with 100-nm aperture, our measurements and FDTD calculations were done by the fiber probe with 50-nm aperture), (b) plasmon intensity spectrum of a 120 x 40 nm Au nanorod at center of NSOM probe apex with that without fiber probe, (c) plasmon intensity distribution for a 120 x 40 nm Au nanorod with and without an Au-coated NSOM probe, and (d) change in plasmon intensity spectrum at center of NSOM probe apex for various heights.
Dark-field microscopy, where a scattered plasmon field is measured in the far-field, can measure the plasmon response functions when we also combine SI schemes [11, 12]. In this method, the plasmon field is not affected by the measurement. However, the spatial resolution is limited by optical diffraction.
4. Results and discussion
4.1 Localized plasmon control on nanocrosses
Figure 5 shows the plasmon spectrum intensity and phase measured at a longer arm of the Au nanocross with R = 3. The position of the fiber probe was set at the center of the arm based on its topography image. The excitation laser pulse incident from the back of the substrate is in the TM mode. Therefore, E-field is parallel to the R = 3 arm of the Au nanocross, and the plasmon intensity is enhanced at 750-900 nm. Since the cutoff wavelength of the single-mode fiber probe is 750 nm, coupling efficiency shorter than 730 nm was enhanced. The intensity ratio between the measured and reference intensity corresponds to the intensity response function. The difference in the spectral phase between the measured and reference phases in Fig. 5(b) corresponds to the response function phase. The second-order spectral dispersion indicates the dispersion in the reference arms since we used the Fourier transform limited femtosecond laser pulse for excitation. When switching the excitation laser from TM to TE, plasmon polarization is perpendicular to the substrate; no plasmon enhancement was observed.
Fig. 5 Plasmon spectral intensity (a) and plasmon spectral phase (b) at an R = 3 longer arm of the nanocross and at a plane reference point on the substrate. Plasmon response function can be obtained by ratio between two intensity spectra and difference between two phase spectra.
Figures 6 and 7 summarize the spectral plasmon response functions and the plasmon time histories at excitation by a Fourier transform limited (FTL) laser pulse of our laser oscillator predicted using the response function. In Fig. 6 an R = 3 longer arm of the nanocross was aligned parallel to the excitation pulse polarization, but an R = 2.5 shorter arm was aligned parallel to the polarization in Fig. 7. The linear component of the spectral phase in Fig. 6 corresponds to the delay time caused by the distance between the nanocrosses and the reference point.
Fig. 6 (a) Spectral plasmon response functions deduced from SI-NSOM measurement for R = 3. (b) Plasmon time history at excitation by Fourier transform limited laser pulse predicted using response function.
Fig. 7 (a) Spectral plasmon response functions deduced from SI-NSOM measurement for R = 2.5. (b) Plasmon time history at excitation by Fourier transform limited laser pulse predicted using response function.
After the response function is obtained, we can shape the plasmon pulse based on Eq. (3). We applied the reverse spectral phase of the response function at the pulse shaper of the excitation laser pulse to generate a Fourier limited plasmon pulse. Figure 8 shows the measured plasmon pulse at R = 3 and 2.5, and Fig. 9 shows the corresponding numerically predicted plasmon pulses using the experimentally obtained response functions. Figures 8(a) and 9(a) show the plasmon time histories when the excitation laser pulse was shaped to compensate for the spectral phase of the response function to generate a FTL pulse at a longer arm with R = 3. Figures 8(b) and 9(b) show the plasmon time histories at a shorter arm with R = 2.5 for the excitation at (a). Since the plasmon functions are different at R = 3 and 2.5, the plasmon pulse at R = 2.5 is temporally broadened. Compared with the numerical prediction, temporal confinement was not ideal in our experiment. Figures 8(d) and 9(d) show the plasmon time histories when the excitation laser pulse was shaped to compensate for the spectral phase of the response function to generate a FTL pulse at an R = 2.5 shorter arm. Figures 8(c) and 9(c) show the plasmon time histories at an R = 3 longer arm for the excitation at (d). Thus, we can selectively generate intense plasmons among nanostructures that exhibit specific responses.
Fig. 8 Measured plasmon pulses on a longer arm with R = 3 ((a)&(c)) and a shorter arm with R = 2.5 ((b)&(d)) excited by femtosecond laser pulse shaped to generate FTL pulse on a longer arm R = 3 ((a)&(b)) and a shorter arm with R = 2.5 ((c)&(d))
Fig. 9 Numerically predicted plasmon pulses using experimentally obtained response functions on a longer arm with R = 3 ((a)&(c)) and a shorter arm with R = 2.5 ((b)&(d)) excited by femtosecond laser pulse shaped to generate a FTL pulse on a longer arm with R = 3 ((a)&(b)) and a shorter arm with R = 2.5 ((c)&(d))
4.2 Surface plasmon polariton control in the air-gap waveguide
In the SPP control experiment using the air-gap waveguide, we measured the cross-correlation SI at three exit points and one reference point. Alignment of the excitation laser beam at the coupling to the waveguide was adjusted so that the highest power transmission to the reference point was achieved.
Figures 10(a)-10(c) show the response functions measured at three exits. Since these measurements were done at separate laser pulse excitations, correlation in the amplitude among three points may not so accurate. It should be noted that these response functions corresponds propagation from the reference point to each the exit. The plasmon propagation characteristics from the input to the reference point is not included.
Fig. 10 Response functions measured at three exits of the surface plasmon-polariton waveguide shown in Fig. 3: (a) Exit 1, (b) Exit 2, and (3) Exit 3.
Significant amplitude attenuation from the reference point is evident at three exits especially for longer wavelengths. The spectral phases show similar shape at three exits but indicate phase delay relative to the reference point. Based on these response functions, we shaped the excitation laser pulse by adding the inverse spectral phase of one of the response functions at the pulse shaper so that the Fourier transform limited pulse with highest peak power can reach at the corresponding exit. The experimentally measured plasmon pulses at the exits are shown in Fig. 11. At three experiments, the output pulses at the specified exit show higher peak power than those without phase compensation. Because of the some difference in the spectral phase among three exits, the output plasmon pulses at unspecified exits show lower peak power. Therefore, when we design a surface plasmon-polariton waveguide more carefully, we may be able to realize a surface plasmon-polariton switching with input laser pulse shape encoding.
Fig. 11 Time histories of surface plasmon-polariton pulses measured at the three exits of the waveguide in Fig. 3. The excitation laser pulse was shaped so that the Fourier transform limited plasmon appears at (a) Exit 1, (b) Exit 2, and (3) Exit 3, respectively, based on the obtained plasmon response functions (Fig. 10).
5. Conclusion
We employed a new diagnostics using an SI combined with near-field scanning optical microscope to characterize the local plasmon excited by ultrashort laser pulses at gold nanostructures. We deduced the bandwidth-limited plasmon response functions from the Fourier analysis of cross-correlation SI. Then, a simple multiplication of a new excitation laser pulse and the response function in the spectral domain followed by an inverse Fourier transformation can predict the plasmon pulse. The validity of this approach was demonstrated by deterministic shaping of the source spectral phase thus enhancing the peak intensities at the structure. This deterministic control scheme was applicable also for propagation of surface plasmon-polariton in a plasmon waveguide.
Acknowledgments
This research was supported by a Grant-in-aid from the Ministry of Education, Culture, Sports, Science, and Technology, Japan for the Photon Frontier Network Program and by JSPS KAKENHI Grant Number 23360036.
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