Dual-tip-enhanced ultrafast CARS nanoscopy

Coherent anti-Stokes Raman scattering (CARS) and, in particular, femtosecond adaptive spectroscopic techniques (FAST CARS) have been successfully used for molecular spectroscopy and microscopic imaging. Recent progress in ultrafast nanooptics provides flexibility in generation and control of optical near fields, and holds promise to extend CARS techniques to the nanoscale. In this theoretical study, we demonstrate ultrafast subwavelentgh control of coherent Raman spectra of molecules in the vicinity of a plasmonic nanostructure excited by ultrashort laser pulses. The simulated nanostructure design provides localized excitation sources for CARS by focusing incident laser pulses into subwavelength hot spots via two self-similar nanolens antennas connected by a waveguide. Hot-spot-selective dual-tip-enhanced CARS (2TECARS) nanospectra of DNA nucleobases are obtained by simulating optimized pump, Stokes and probe near fields using tips, laser polarization- and pulse-shaping. This technique may be used to explore ultrafast energy and electron transfer dynamics in real space with nanometre resolution and to develop novel approaches to DNA sequencing.

The sphere sizes were chosen according to the design of the self-similar nanolens [36]. The sphere radii satisfy R i+1 = R i 3 . The distance between the surfaces of the consecutive spheres is d i,i+1 = 0.3 R i+1 . The near-field response of the nanostructure was calculated using the multiple elastic scattering of multipole expansions (MESME) approach [38,39] in the range from 200 to 700 nm with x-polarized incident plane waves for all tip 2 positions. Each incident field E(ω) was multiplied by a response function F m (ω), where m corresponds to a particular tensor component. E local = E(ω)F m (ω) was used in the tip-enhanced CARS simulations. The Gaussian pump/Stokes pulses were ∼ 6 fs in duration corresponding to ∼ 2400 cm −1 bandwidth. The Gaussian probe pulse had a bandwidth of 3 cm −1 . Pulse durations were held constant during the scan of the center frequency, with the bandwidth changing accordingly. Gaussian laser pulse shapes E k (ω) = Exp[−2ln(2) ω−ω ko ∆ω k 2 ], (k = 1, 2) were used to induce the CARS signals, where k = 1, 2 stands for pump and Stokes, respectively.
The picosecond probe pulse was modelled by E pr (ω) = 1, if |ω − ω pr | ≤ 1.5 cm −1 α, and 0 otherwise, where α = 2πc, c is the speed of light in vacuum, ω ko is the center frequency of the k'th pulse, and ∆ω k is the corresponding bandwidth. The Raman data for linewidths, cross sections, and resonance frequencies was obtained for DNA nucleobases from [40]. The dielectric function of silver was taken from [41]. Vacuum permittivity was used to describe the surrounding dielectric medium. Additional  simulations were performed in air, but did not show significant differences. Another set of simulations was also performed using gold instead of silver. Reduced surface enhancement factors were obtained, but the CARS spectra did not show significant changes. The simulations were performed in Mathematica R 8.
In figure 1b, four hot spots in the gaps between the 50 and 150 nm spheres are labeled 1-4 and highlighted by red, green, blue, and purple stars, respectively. Tip 1 is fixed and forms the receiving antenna for x-polarized light localized at spot 1. The x-polarized spectral response of this nanostructure without tip 2 at spot 1 is shown in figure 2a (black solid line), in which several resonances are observed with the strongest peak at 440 nm. The corresponding temporal near-field profile at spot 1 due to the excitation by x-polarized 6 fs incident laser pulses centered at 440 nm is shown in figure 2b (black line), while this response is compared to the response of a nanostructure without tips at spot 1 (red line) and to the original incident laser pulse (blue line) which shows that there is a factor of 8 enhancement of the electric field amplitude of the nanostructure without tips compared to the incident laser pulse and an additional enhancement due to the presence of tip 1. This order of magnitude field enhancement results in several orders of magnitude enhancement in the nonlinear optical signals such as CARS. The enhancement may be further improved by optimizing the nanostructure design, e.g. decreasing the gap size.
Spatiotemporal control of the near-filed response will allow localizing and controlling CARS signals. Therefore, we next investigate the temporal near field pulse shapes from other hot spots. The temporal near field amplitude profiles due to the excitation by x-polarized 6 fs Gaussian laser pulses centered at 440 nm from hot spots 1-4 without tip 2 (a,b), and with tip 2 at −60 • (c,d) and −90 • (e,f) positions are shown in figure 3. The corresponding nanostructure geometries are sketched in the left column. The x-(Ex) and y-polarized (Ey) field profiles are shown in the middle pulse shaping. This provides several control parameters for manipulating CARS signals. We first use these parameters to isolate CARS nanospectra of DNA nucleobases. In our work, the third-order nonlinear polarization is modelled by where χ R , the resonant third-order nonlinear susceptibility, is given by and S 12 is A k is a constant related to the Raman cross-section, Γ k gives the Raman line halfwidth, and Ω Rk gives the k'th vibrational frequency. In calculations with single broadband pump/Stokes laser pulses, we set E 1 = E 2 = E, with E sufficiently broad to excite the desired vibrations. The non-resonant background was not included in this work. Interference between signal and background is common, but many methods have been developed to minimize the non-resonant background. Our tr-CARS approach is especially useful for background suppression [30,31]. The CARS signal is given by Figure 4d shows CARS spectra of cytosine (red), thymine (green), adenine (blue) and guanine (purple) obtained using x-polarized Gaussian 6 fs pump/Stokes (440 nm) and picosecond probe (480 nm) laser pulses without a nanostructure. All the spectra were normalized to the maximum of the strongest guanine peak at 942 cm −1 . Figures  4a-4c show CARS spectra of nucleobases placed in the hot spots of the nanostructure described above. Cytosine, thymine, adenine, and guanine were placed in spots 1, 2, 3, and 4, respectively. Figure 4a shows the x-polarized CARS spectra from the nanostructure without tip 2. CARS signal of cytosine in spot 1 dominates (red). In figure 4b, for tip 2 at −60 • , the y-polarized CARS spectra of cytosine and thymine are suppressed and spectra of adenine (blue) and guanine (purple) dominate, with adenine making the largest contribution. In figure 4c for tip 2 at −90 • , adenine (blue) dominates (y-polarized). These spectra illustrate the use of tip 2 as a nanocontrol parameter.
To investigate the origin of the spatial dependencies of 2TECARS signals in figure  4, we performed similar simulations on pyridine molecules located at every hot spot with the pump, Stokes and probe pulses having the same parameters as in figure 4. Similar effects of tip position seen for the nucleobases were also observed for pyridine. Therefore, the effects are not simply due to different molecular responses, but are predominantly due to the structure response.
Next, we simulate spectral control of 2TECARS signals by laser polarization-and pulse-shaping. Laser pulse shaping provides additional "knobs" for controlling ratios of spectral peaks. We achieved spectral control of CARS signals by varying the center wavelengths of the incident laser pulses in figure 5. Ratios of the y-polarized CARS signals of adenine to guanine, and of thymine to other nucleobases are maximized in figures 5a and 5b, respectively, by varying both the pump/Stokes and the probe center wavelengths. The y-polarized spectrum of guanine (purple) is amplified using the same strategy in figure 5c. For analysis, these results can be understood by examining the near field pulse shapes and overlaps via S 12 cross-correlation in (3). Figure 6 shows the pump/Stokes pulse S 12 (1050 cm −1 ) autocorrelation plots as a function of the center wavelength for the nanostructure without tip 2 (6a), and for tip 2 positions at −30 • (6b), −60 • (6c) and −90 • (6d) from different spots in the nanostructure. The average value 1050 cm −1 was chosen to simplify the analysis. Figure 6 reveals the optimal spectral range of the response for controlling CARS spectra by varying the pump/Stokes pulse center wavelength. For example, Figure 6c can be used to select the suitable wavelength range of the pump/Stokes pulses in order to achieve switching between adenine (figure 5a) and guanine (figure 5c) signals with tip 2 at −60 • . Figure 6c shows that the intensity (autocorrelation) of the pump/Stokes pulse is larger at spot 3 (adenine) for most of the spectral range, except in the region around 500 nm. Therefore, 332 nm and 550 nm center wavelengths were chosen to achieve the switching. Another control parameter is given by the probe pulse center wavelength and is directly proportional to the nanostructure response. Analysis of these plots allows optimizing parameters to control nanoscopic CARS signals and gives a clear understanding of the control mechanisms. The proposed nanostructure provides a nanosphere analogue of the dual-antenna plasmonic circuit [34,35] as an example of a controllable plasmonic system for spacetime-resolved ultrafast nanoscopy. These and other geometries based on optical nanoantennas have been experimentally realized [42,43,44,45,46]. We note that the self-similar nanolens antenna has another resonance in the gap between the 17 and 50 nm spheres which has a larger enhancement [42]. However, we assume that there are no molecules in that hot spot. Experimentally this may be achieved, for example, by coating only the large sphere with molecules. The nanostructure design may be further improved by using these stronger hot spots. Also, Fano resonances may provide advantages in light focusing and control [47,48].
Using two scanning tips and pulse shaping, the CARS signal enhancement factors (EFs) of up to 10 7 were obtained (figure 5b). This corresponds to the expectations based on the ∼ 10 1 near field enhancement in the hot spots using (1)- (3). In this letter, we focus on separating CARS signals from different hot spots and on increasing the contrast rather that optimizing EFs. In principle, the EF for TECARS can reach ∼ 10 18 for the strongest hot spots with the near fields enhanced by ∼ 10 3 in the self-similar nanolens antenna [36]. CARS signals may be further increased by coupling two nanolens antennas. For example, we obtain an order of magnitude increase in EF by adding the second tip ( figure 5b compared to figure 4a). In addition, the results presented here can be generalized to remove one or both tips by building the nanostructures with the small spheres on the substrate, with all different arrangements manufactured on one surface. Coherent control [49,50] by phase-and amplitude-laser pulse shaping [51] may be used to control spatiotemporal plasmon dynamics in nanostructures [52,53,54,55,56] and may further improve the EFs and performance of ultrafast nanoscopic spacetime-resolved spectroscopy [57]. This approach may be applied to other nonlinear optical techniques [58] such as surface-enhanced four-wave mixing [59], and coherent twodimensional nanoscopy [60]. Thus, multiparameter optimization may improve EFs and contrast of nonlinear signals, and will be considered in future work.
In conclusion, we propose a new approach to probing ultrafast nanoscale phenomena using ultrafast 2TECARS nanoscopy. Dual-tip-enhanced coherent Raman spectra of DNA nucleobases separated on a nanometre scale are obtained using a combination of two scanning tips and laser pulse shaping. This technique provides useful control knobs for manipulating CARS nanospectra and will further advance the field of nanobiophotonics.