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We theoretically demonstrate spatiotemporal control of local plasmon distribution on Au nanocrosses, which have different aspect ratios, by chirped ultra-broadband femtosecond laser pulses. We also demonstrate selective excitation of fluorescence proteins using this spatiotemporal local plasmon control technique for applications to two-photon excited fluorescence microscopy.
©2011 Optical Society of America
1. Introduction
Plasmon photonics in the nanometer region beyond the diffraction-limit of light has rapidly developed in recent years. One topic that deserves special attention is localized plasmon resonance on metal nanostructures. This plasmon resonance leads to the excitation of localized light fields at a specific wavelength in the nanoscale [1–8]. The plasmon resonance wavelength depends on the shape and the size of the nanostructures [9], and the resonance enhancement factor of the plasmon field varies by incident light polarization.
In addition, spatiotemporal control has been achieved over localized plasmons in regularly arranged nanostructures using a polarization pulse-shaping technique developed for femtosecond lasers [10–12]. 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 [10]. Stockman et al. showed that arbitrarily shaped laser pulses can vary the plasmon-polariton field distribution at a V-shaped nanostructure [12]. Therefore, the spectral phase and the temporal polarization of 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 [13–15] developed to realize optimum ultrafast interaction between ultrashort laser pulses and matter are suitable to realize spatiotemporal control over localized plasmons in nanostructures. Currently, various arbitrary polarization pulse-shaping apparatus are available [16–18].
Although this adaptive pulse-shaping scheme is applicable to the spatiotemporal control of the localized plasmon distribution at any nanostructures, when we design them, more straightforward control of plasmon distribution can be obtained by ultrashort laser pulses shaped in their temporal frequency and polarization. Lévêque has theoretically demonstrated that spatiotemporal control of local plasmon can be achieved by combination of frequency chirped femtosecond excitation laser pulses and arrangement of metal nanorods [19]. The sign of the chirp controls the excitation sequence of the nanorods with great flexibility. When expanding their scheme into asymmetric two-dimensional nanostructures and combining polarization switching with the frequency chirp design, more flexible control can be obtained in the local plasmon excitation sequence.
In this paper, using a finite-difference time-domain (FDTD) numerical model, we theoretically demonstrate spatiotemporal control of localized plasmon distribution on Au nanocrosses that have different aspect ratios in the nanoregions irradiated by chirped ultra-broadband femtosecond laser pulses. We also show that this scheme is applicable to selectively excite different fluorescence proteins by two-photon absorption processes.
2. Spatiotemporal control
The local plasmon spectrum at an isolated nanostructure can simply be described as a product of irradiated light spectrum and plasmon response function:
where and are the spectral amplitude and the spectral phase, respectively. In principle, since the dipole moment of noble metals can instantaneously respond to the incident light field, when an ultrabroad laser pulse with a certain frequency chirp is irradiated on an isolated nanostructure, the localized plasmon is enhanced only when the instantaneous laser frequency matches the plasmon resonance frequency. Therefore, for example, when we arrange various shaped nanorods on a substrate plane, each nanorod exhibits the plasmon enhancement at a different time.
Figure 1(a) shows a calculation model to demonstrate the spatiotemporal control of local plasmon using an FDTD method [20–26]. The computation space size is 600 x 600 x 200 nm3 with 2-nm grid sizes. Time step Δt of 3.85 attosecond is used to satisfy the Courant-Friedrich-Levy (CFL) stabilization condition defined by Eq. (2) [27]:
Fig. 1 (a) Simulation model: Au nanocrosses consisting with two rods having the same cross-section and different aspect ratios are arranged on SiO2, and a chirped ultra-broadband femtosecond laser pulse with x- or y-polarization is launched from + z direction; (b) time history of irradiation pulse with a second-order dispersion of 86 fs2 : ; and (c) corresponding spectrum of (b)
where ν denotes the velocity of the electro-magnetic wave in a medium.
The boundary condition proposed by Mur is employed as an absolute boundary condition in every boundary surface [26]. In Fig. 1(a), various Au nanocrosses are arranged using two Au nanorods which have a common 20 nm x 20 nm cross-section and different aspect ratios (4–15). Combinations of the aspect ratios (x, y) used for four nanocrosses are (15, 4), (4, 15), (6, 8) and (8, 6), which are denoted as a rod A, B, C, and D and are placed on an SiO2 substrate with a sufficient interval of ~300 nm as shown in Fig. 1(a). The complex refractive index of Au nanorods is defined over a wide spectrum range by the Drude model. We obtained the plasmon resonance wavelength peak for those nanorods with different aspect ratios by separate FDTD simulation runs. The calculated resonance peak locates as 1180, 880, 760 and 650 nm for the nanorod with the aspect ratio of 15, 8, 6, and 4, respectively. The plasmon resonance is not so sharp. The resonance bandwidth is typically 125 nm (FWHM) for these rods. Therefore, in order to clearly distinguish the plasmon resonance in time and space, the plasmon resonance wavelength at each nanostructure must be designed with sufficient wavelength separations from that of the other nanostructures.
A chirped femtosecond laser pulse with polarization parallel to the x- or y-axis is launched from the z-direction. The spectrum width of the laser pulse is set to 400 nm (FWHM) with a center wavelength of 800 nm. Thus, the four plasmon resonance peaks of the nanorods A-D can be covered by this excitation laser pulse. The second-order dispersion of + 86 fs2 is added to the laser pulse resulting in a pulse width of 150 fs (FWHM). The electric field is calculated at the edge of each Au nanorod.
Figure 2 (a) shows the time histories of the electric field obtained at the edge of the Au nanorod parallel to the x-axis for various Au nanocrosses excited by the ultra-broadband chirped femtosecond laser pulse with x-polarization. A clear temporal peak shift is observed depending on the aspect ratio of the Au nanorods. Sequential enhancement occurs in an order of the crosses A, D, C and B. Au nanorods with larger aspect ratios exhibit plasmon resonant enhancement at longer wavelengths. Consequently, because of the up-chirped laser pulse, they exhibit an earlier pulse peak. Figure 2 (b) shows images of localized plasmon field amplitude at different delays. Similar sequential enhancement but in an opposite order of B, C, D, and A is observed for the Au nanorods parallel to the y-axis with the y-polarization pulse as shown in Fig. 3 .
Fig. 2 (a) Time histories of electric field at the edge of rod parallel to the x-axis for various Au nanocrosses irradiated by x-polarization pulse; and (b) screenshots of plasmon field amplitude corresponding to Fig. 2 (a) at four different delays
Fig. 3 (a) Time histories of electric field at the edge of rod parallel to the y-axis for various Au nanocrosses irradiated by y-polarization pulse; and (b) screenshots of the plasmon field amplitude corresponding to Fig. 3 (a) at four different delays
The effect of an irradiation pulse with third-order dispersion was also investigated. Figures 4 (a) and (b) show the time history and the spectrum of the irradiation pulse with a third-order dispersion of −50 fs3. The spectral amplitude of the laser pulse is same as Fig. 1(c). As shown in Figs. 4 (c) and (d) only plasmon resonance of the rod A is excited at 470 fs, whereas plasmon resonances of the others are simultaneously excited at 510 fs. In the femtosecond laser pulse with a third-order dispersion, the group delay is in a quadratic function. At the third-order dispersion of −50 fs3, the spectral component at ~1180 nm that causes the plasmon resonance peak at the cross A with the x-polarization has a substantial negative group delay (arriving earlier), whereas the other three plasmon resonance wavelengths ranging in 650-880 nm for the nanocrosses B-D arrive at the almost same time at ~510 fs. Therefore, more flexible spatiotemporal control of plasmon resonance can be achieved by employing higher-order dispersion of the excitation pulse. Moreover, since different excitation sequences are obtained just by switching the polarization, polarization shaped femtosecond laser pulses will further increase the flexibility of plasmon excitation sequence.
Fig. 4 (a) Time history of the excitation pulse with dispersion of −50 fs3: ; (b) corresponding spectrum of (a); (c) time histories of electric field at various Au nanocrosses irradiated by x-polarization pulse; and (d) screenshots of the plasmon field amplitude corresponding to (c).
We will be able to extend this plasmon control scheme using excitation laser pulse shaping toward the control of surface plasmon-polariton propagation in nanostructure waveguide circuits. We can also apply this spatiotemporal control of localized plasmon for a novel two-photon excitation scheme. Second-order nonlinear excitation schemes such as two-photon excitation with ultra-broadband laser pulses can be controlled by shaping the second-harmonic (SH) spectrum of excitation pulses, which is varied by temporal pulse shaping. When the temporal sequence of the instantaneous frequency (frequency chirp) of the plasmon fields at different nanostructures is controlled in the order of ~5 fs (it is different from the control in the temporal sequence of plasmon field amplitude as demonstrated in Figs. 2 and 3), selective two-photon excitation in nanostructures could be achieved. We will show our numerical model calculations for selective two-photon excitation at nanostructures in the following section.
3. Selective excitation of fluorescent proteins with spatiotemporally controlled plasmon
Two-photon excited fluorescence microscopy has become a powerful tool for investigating biological phenomena [28–37]. This technique requires distinctive excitation modes in which various fluorophores are excited either selectively or simultaneously. Isobe et al., who demonstrated that selective excitation of fluorescent proteins can be attained using a femtosecond pulse-shaping technique [35], designed the SH spectrum of pumping laser pulses by spectral phase modulation so that only one of two fluorescent proteins is two-photon excited. By combining this selective two-photon excitation technique with our spatiotemporal plasmon control scheme, we can achieve selective two-photon excitation at nanometer scale resolution.
The luminescence intensity of the fluorescence protein under two-photon excitation is described in Eq. (3) [35]:
where is the two-photon excitation spectrum expressed against the half excitation wavelength and is the SH spectrum of the plasmon field.
We assume two fluorescent proteins of Venus and CFP (cyan-emitting fluorescent proteins) [36], which have commonly been used for fluorescence resonance energy transfer (FRET) microscopy. The two-photon absorption spectra of these fluorescence proteins are shown in Fig. 5(a) [36]. Note that in order to compare the two-photon absorption spectra with SH spectra of shaped laser pulses, the two-photon spectra were plotted against the half excitation wavelength. Their main two-photon absorption peaks exist at the 2x500- and 2x425-nm bands, respectively. Therefore, the aspect ratio of the Au nanorods must be adjusted so that plasmon resonance occurs at the wavelength of the two-photon absorption peak. Figure 5(b) shows the SH spectra of the plasmon calculated for aspect ratios of 4 and 6 in an H2O solvent environment. The spectrum width of the excitation laser pulse is set to 400 nm (FWHM) with a center wavelength of 800 nm. For these calculations the Fourier transform limited (FTL) x-polarization laser pulse is assumed. From the spectra, Venus is efficiently two-photon excited by the plasmon resonance at the Au nanorod with an aspect ratio of 6. On the other hand, CFP is efficiently two-photon excited by that with an aspect ratio of 4.
Fig. 5 (a) Two-photon excitation spectra plotted against the half of the excitation wavelength for these fluorescence proteins. (b) SH spectra of Au nanorods calculated for the aspect ratios of 4 and 6.
Since the actual excitation rates are proportional to their local protein concentrations, the fluorescence distinguish ratio changes as their concentrations change. In the following calculation, we calculated the two-photon excitation rates for CFP and Venus using their normalized two-photon absorption spectra, and the same protein concentrations are assumed.
If two-photon excitation spectra of two fluorescent proteins are well separated, one may be able to selectively excite the proteins using different plasmon resonance exhibited by two proper nanorods without any laser pulse shaping. In the case of this example with CFP and Venus proteins, both SHG spectra partially overlap with the other excitation spectrum. Therefore, significant cross-talk is observed at two-photon excitation. The calculated distinguish ratios are CFP:Venus = 100:20.7, and 1.9:13.9 for the nanorods with the aspect ratio of 4 and 6, respectively (see the summary in Table 1 ).
Table 1. Summary of selective excitation of CFP and Venus proteins at the nanorod with an aspect ratio of 4 or 6 by various excitation pulsesa
We shape the excitation laser pulses to concentrate the SHG power of the plasmon field into the spectrum region matched to specified two-photon excitation. Two pulse shaping schemes are available to concentrate the SHG power into desired spectral region: one is spectral amplitude shaping and the other is spectral phase shaping.
We assumed that two Au nanocrosses with two arms at different aspect ratios of 4 and 6 are arranged on a SiO2 substrate. One is rotated at 90° to the other. Thus, these nanocrosses exhibit the opposite plasmon resonance at the orthogonal polarization excitation. These nanocrosses are assumed to be immersed in a solution containing two fluorescence proteins, Venus and CFP. First, the excitation femtosecond laser pulse is shaped by spectral amplitude modulation so that one of the two plasmon resonances is excited.
Figure 6 shows the fluorescence images obtained by the model calculations. Shaped laser spectra and the SHG spectra calculated for the local plasmon generated at both nanocrosses are also shown. We simply eliminate the spectral component, which induces the excitation cross-talk among CFP and Venus proteins.
Fig. 6 Shaped laser pulses and fluorescence images obtained with the shaped pumping pulses: (a) pumping pulse shaped to selectively excite Venus proteins; (b) selective two photon excitation images for Venus proteins; (c) SH spectra of plasmon excited by the pulse of (a) for the nanorod with an aspect ratio of 4; (d) SH spectra of plasmon excited by the pulse of (a) for the nanorod with an aspect ratio of 6; (e) pumping pulse shaped to selectively excite CFP proteins; (f) selective two photon excitation images for CFP proteins; (g) SH spectra of plasmon excited by the pulse of (e) for the nanorod with an aspect ratio of 4; and (h) SH spectra of plasmon excited by the pulse of (e) for the nanorod with an aspect ratio of 6.
When pulse of Fig. (a) is applied, mainly fluorescence from Venus is observed at the arm with an aspect ratio of 6 (Fig. 6(b) left). The luminescence can be switched between the two orthogonally placed nanocrosses by changing the polarization (Fig. 6(b) right). On the other hand, mainly fluorescence from CFP is observed at the arm with an aspect ratio of 4 by pumping pulse shown in Fig. 6(e) (Fig. 6(f) right). The calculated distinguish ratios are CFP:Venus = 100: 1.7, and 1.8:100 for the nanorods with the aspect ratio of 4 and 6, respectively (see the summary in Table 1). Therefore, cross-talk in the two-photon excitation is significantly improved compared with those obtained by the FTL pulse excitation. However, since the Venus protein is also two-photon excited by the spectrum ranging in 800-900 nm of pulse (e), as shown in the absorption spectrum in Fig. 5(c), the fluorescence of Venus is still slightly visible (~1.7% of CFP fluorescence emission) in Fig. 6(f). The distinguished ratio will be improved with a more properly shaped SH spectrum.
Next, the excitation femtosecond laser pulse is shaped by spectral phase modulation so that mainly one of the two plasmon resonances is excited. Various spectral phase profiles suitable for selective two-photon excitation have been previously demonstrated [35,37–39]. We use here third-order spectral phase [38,39]. Spectral phase masks and corresponding SHG spectra calculated for local plasmon fields on the nanorods with the aspect ratio of 4 and 6 are shown in Fig. 7 . We leave the linear phase at the spectrum region where two-photon excitation is allowed, while the third-order dispersion functions with the same sign are set for the outside of the allowed spectral region. For an example, the flat dispersion was set between ω 1( = 2.22x1015 rad/s: λ 1 = 850 nm) and ω 2( = 2.51x1015 rad/s: λ 2 = 750 nm) to excite CFP protein and prevent excitation of Venus (Fig. 7 (d)). We set the third-order dispersion with ϕ 2(ω) = 1/6x1.0x10−43(ω-ω 2)3 and ϕ 1(ω) = 1/6x1.0x10−43(ω-ω 1)3 for ω >ω2, and ω <ω 1, respectively. The resulting SHG spectrum generated by sum frequency mixing between the spectrum components with the same group delay at ω > ω 2 and ω < ω 1 is centered at the frequency ω 1 + ω 2. The calculated distinguish ratios are CFP:Venus = 100: 1.6, and 0.6:100 for the nanorods with the aspect ratio of 4 and 6, respectively (see the summary in Table 1).
Fig. 7 Shaped laser pulses and corresponding SH spectra at the nanorods with an aspect ratio of 4 or 6: (a) spectral amplitude and phase of the pumping pulse shaped to selectively excite Venus proteins; (b) corresponding temporal pulse; (c) SH spectrum of plasmon excited by the pulse of (a) for the nanorod with an aspect ratio of 4; (d) SH spectrum of plasmon excited by the pulse of (a) for the nanorod with an aspect ratio of 6; (e) spectral amplitude and phase of the pumping pulse shaped to selectively excite CFP proteins; (f) corresponding temporal pulse; (g)SH spectrum of plasmon excited by the pulse of (e) for the nanorod with an aspect ratio of 4; and (h) SH spectrum of plasmon excited by the pulse of (e) for the nanorod with an aspect ratio of 6.
4. Conclusions
We demonstrated that the excitation sequence of local plasmon enhancement on Au nanocrosses with different aspect ratios can be controlled by chirped ultra-broad femtosecond laser pulses and their polarization. This is a straightforward scheme to control the spatiotemporal distribution of near-field in nanometer sizes using isolated nanostructures, whereas a self-learning close-loop control is necessary for control in the near-field in the vicinity of high density nanostructures. This technique can be used as a template for selective two-photon excited fluorescence microscopy. To experimentally demonstrate our idea, a practical diagnostics is required to obtain the characteristics of localized plasmon in femtosecond and nanometer resolutions.
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.
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