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The development of new substrates for surface-enhanced spectroscopy is primarily motivated by the ability to design such substrates to provide the maximum signal enhancement. In this paper, we theoretically design and investigate a crisscross dimer array as a plasmonic substrate for enhancing coherent anti-Stokes Raman scattering (CARS). The plasmonic film-crisscross dimer array system can excite multiple resonances at optical frequencies. By properly designing structure parameters, three plasmon resonances with large field enhancements and same spatial hot spot regions can spectrally match with the pump, Stokes and anti-Stokes beams, respectively. The CARS signals are strongly enhanced by multi-resonance plasmon field enhancements. The estimated CARS factor can reach as high order as ~1016 over conventional CARS without the plasmonic substrate.
© 2017 Optical Society of America
1. Introduction
The CARS is a third-order optical process that couples Stokes Raman and anti-Stokes Raman processes within a coherent four-wave mixing mechanism [1] and is performed by simultaneously mixing three distinct photons at two different frequencies ωP and ωS in the media. A coherent excitation is generated in the probed regions at the frequency of ωP-ωS while the pump beam ωP and the Stokes beam ωS interact with media. If the excited frequency matches Raman active molecular vibration, the Stokes emission interacts coherently with the pump beam to drive the resonant oscillators at the anti-Stokes frequency ωAS = 2ωP − ωS. This leads to the emission of the CARS photon at the anti-Stokes frequency. The intensity of the CARS signal is given as follows [2]
where is the third-order nonlinear dielectric susceptibility, and IP and IS are the intensity of pump and Stokes light, respectively. Because the process is coherent, the CARS magnitude is stronger than spontaneous Raman scattering. The CARS signal of a molecule provides a characteristic vibrational spectrum fingerprint for detection. This spectral fingerprint can be exploited as a chemically selective “label free” contrast mechanism for 3-D imaging [3,4].Detecting molecular complexes at nanoscale presents a challenge for current state-of-the-art spectroscopy due to weak signals from small amounts of material, spectral congestion from complex mixtures and background from solvents, substrates or the molecules themselves. Two of the most commonly used techniques, which provide species-specific spectroscopic signals in the form of vibrational fingerprints, are surface-enhanced Raman scattering (SERS) [5] and the CARS [6] spectroscopies. The SERS benefits from a signal increase of the order of ~103~1010 primarily because of the electromagnetic (EM) field enhancements associated with surface plasmon resonance at the proximity of the metallic nanostructure [7]. The surface enhancement effect is available not only for spontaneous Raman spectroscopy but also for non-linear spectroscopy that is expected to be applicable to new fields of spectroscopic analysis of molecules. In analogy to the SERS effect, the nonlinear optical processes can also be efficiently strengthened by employing the plasmon resonances on rough metallic nanostructures. If the input (ωP, ωS) or output (ωAS) beam in the CARS resonates with surface plasmon coupled modes, the surface-enhanced CARS (SECARS) signal from the probed molecules around the hot spot regions will be greatly enhanced by the local fields of the excited plasmon resonances. The EM filed enhancement factor (EF) in the SECARS is estimated as follows
which implies the product of the local EM fields enhancement at three characteristic frequencies. It is a well-known fact that, the SERS EFs can reach to order of ~103~1010 due to surface plasmon resonances [8]. The coherent nonlinear optical signals have a higher-order dependence on the incident electric fields, and can have larger EFs than the linear signals. Therefore, one can expect ~106~1020 EFs from the local fields of plasmonic nanostructures compared to the conventional CARS [9]. However, EFs with several orders of magnitude smaller than those expected for the SECARS have been observed so far. Chew et al. firstly predicted that the maximum surface enhancement of the CARS for silver nanospheres is about 1012 over the conventional CARS signals [10]; however, only ~10~103 EFs were observed in the subsequent experiments [11–13]. In addition, other enhanced structures such as self-assembly multilayer gold nanoparticles arrays [14], aggregated gold nanoparticles [15], nanovoid gold substrates and commercially Klarite chips [16], and carbon nanostructures [17] have achieved higher sensitivity with overall enhancement of ~105~1010 over the conventional Raman spectroscopy, which are also smaller than the expected.Due to the complex coherent nonlinear optical possesses and nonresonant background, and there are few works in the SECARS with large EFs in the previous works. Recently, He et al. theoretically provided an efficient method for generating the “mixed frequency coherent mode” by using the plasmonic trimer assembly supporting double Fano resonances [18], and the theoretically calculated CARS EF can reach ~1013 in specially designed plasmonic substrates. Following this idea and according to the formula (2), we theoretically design and investigate a multi-resonance plasmonic substrate to enhance the CARS signal in this work. Three excited plasmon resonance modes with large field enhancements have the same hot spots and spectrally match with the pump, Stokes, and anti-Stokes beams, respectively. The theoretically estimated maximum SECARS EF can reach as high order as ~1016.
2. System description
The theoretical model of designed plasmonic system was verified by using a time domain solver of a commercial finite-integration technique package (CST Microwave Studio), where the computational domain is truncated by the perfectly matched layers in the z-direction and the periodic boundary conditions are used to truncate the unit cell in the x-y plane. In the calculation, a good convergence on the calculated results can be obtained by utilizing adaptive meshing technique to handle the structure boundaries and geometries that require large aspect ratios of meshes.
Figures 1(a) and 1(b) show a typically periodical array of designed plasmonic system and a sketch of a unit cell with relevant geometric parameters, respectively. The metallic crisscross dimer consists of two identical and symmetrical sub-arrangements with a narrow gap d = 14 nm. The crisscrosses have two arm lengths a and b in the x- and y-directions, respectively, and the same arm width w = 35 nm and height h = 40 nm. The crisscross dimer arrays are periodically arranged in the x- and y-directions with the same lattice constant P, and mounted on the metallic substrate (110 nm thickness) separated by a SiO2 spacer with a thickness of 30 nm. A plane wave propagates along the z-direction with the electric and magnetic field polarization along the x- and y-directions, respectively. The metallic elements were numerically treated as silver, and the dielectric constants of silver measured by Palik were used to model the crisscrosses and metallic substrate [19]. The dielectric spacer is SiO2 with the relative dielectric constant of 2.07. The whole structure was surrounded by dielectric environment of vacuum.
Fig. 1 (a) Principal sketch of the designed plasmonic coupled system consisting of two identical metallic crisscrosses arrays and supported by a 30 nm thickness of SiO2 spacer and a 110 nm thickness of silver substrate. The SiO2 and silver regions are colored in grey and purple, respectively. (b) Definition of the geometrical parameters in the elementary unit cell with a square lattice and a pair of crisscrosses. The propagation direction of the incident light wave is along the z-axis, with the electric and magnetic fields along the x- and y-axes, respectively. The orange spot in the gap center of crisscross dimer indicates the probing location of electric field.
3. Results and discussions
The localized field enhancement caused by plasmon resonance opens up a new opportunity to study the light-matter interactions at the nanoscale, especially when probed molecules are located in regions where the fields are both enhanced and focused to the sub-wavelength scale. The near field enhancement can be realized by either the excited plasmon resonances in single metallic nanoparticles [20], nanoparticle pairs or arrays [21], and Fano-like nanostructures [22,23] or the coupling of localized surface plasmon resonances (LSPR) with propagating surface plasmon polaritons (PSPP) [24,25]. The LSPR-PSPP coupled system shows significantly increased EM wave absorption and near field localization.
The periodic array arrangement of crisscross dimers provides the additional momentum to excite the PSPP modes due to the changed wave vector of incident radiation by adding an integer multiple of the grating wave vector. The momentum conservation condition is satisfied in the propagation direction of PSPP wave by the grating coupling as described by the following equation:
whereis the PSPP wave vector, is the in-plane wave vector component of incident light wave, and are the reciprocal lattice vectors (), and i and j are integers and represent the grating diffractive orders. For a square array at the normal incidence, it can be shown that the resonance positions are then given below with the first-order approximation:whereand are the dielectric constants of the metal and the dielectric media, respectively.The calculated absorption spectra and probed electric field enhancements for different lattice periods are plotted in Figs. 2(a) and 2(b), respectively. According to the magnitudes of S11 and S21 parameters from the simulation results, we can achieve the absorbance A = 1-|S11|2-|S21|2 in Fig. 2(a). Four distinct absorption bands (dashed line, denoted as L, A, S1, and S2, respectively) can be observed for the designed plasmonic system as the lattice period changes from 490 nm to 1141 nm. The S1 and S2 modes move to the long-wavelength region and exhibit approximately linear trend with different slopes as the lattice period becomes large, and can be attributed to the first order (i = 1, j = 0) and second order (i = 1, j = 1) PSPP modes at the silver-dielectric interface, respectively, according to the formula (4). On the other hand, both L and A modes represent a weak dependence with the lattice period beyond the coupling regions. Three pronounced anti-crossing regions are observed in the absorption mapping, which originate from the plasmon coupling of the L-S1, A-S1, and A-S2 modes, respectively, and suggest the strong interactions of the LSPR and PSPP modes with the large near-field enhancement. Figure 2(b) shows the corresponding probed electric field enhancement (|Ex/E0|) with different lattice periods. The L mode reveals a stronger electric field concentration than the A mode, and the maximum electric field enhancement about 250 appears at the anti-crossing coupling regions of the L and S1 modes.
Fig. 2 The simulated absorption spectra (a) and corresponding E field enhancement (b) mapping for different lattice periods and fixed a = 100 nm and b = 280 nm. The E field enhancement is the absolute value ratio of the x component of electric field to the incident electric field (i.e. |Ex/E0|). E0 is the incident electric field with the linear polarization in the x-direction. The probing location of electric field locates in the gap center of crisscross dimer shown in Fig. 1(b) (orange spot).
In order to gain insight into physical origin of different LSPR modes, we investigate the electric field and current distributions of the A and L modes on the metallic surface in the x-y plane for P = 540 nm, respectively, as shown in Fig. 3. In this case, the S1, A, and L resonance peaks separately appear at 622 nm, 795 nm, and 1001 nm, respectively. Therefore, the modes coupling interaction can be neglected. In Figs. 3(a) and (b), both A and L modes concentrate the near field energy in the central gap of crisscross dimer, and they have the same hot spot regions. However, the in-phase current of the A mode mainly locates at the two arms in the horizontal direction, and the crisscross dimer at the A mode can be simplified as an end-to-end nanorod dimer served as an optical dipole antenna oscillation. As for the L mode, the anti-parallel current loops appear at top and down parts of crisscross dimer as indicated in Figs. 3(b) and 3(d), and two LC resonances with the same resonance frequencies and magnetic dipoles with the out-of-phase oscillation can be excited in the crisscross dimer. Therefore, we can only consider the LC resonance for the crisscross dimer at the L mode.
Fig. 3 The electric field (a, b) and current (c, d) distributions for the A (a, c) and L (b, d) plasmon modes in the x-y plane while the lattice period is fixed to be 540 nm. The dashed lines in (a) and (b) indicate the directions of current flow induced by metal crisscross dimer at different resonance modes. Scale bar, 100 nm.
Figure 4 show the effect of arm length in the y-direction on the absorption spectra and electric field enhancements. As the arm length b increases, the L mode linearly shifts to the long-wavelength direction, and both A and S1 modes remain almost unchanged. The L mode is related to the LC resonance caused by oscillating currents loops and charge accumulation at the middle gap. The arm length b is only related to the mutual inductance of the crisscross dimer, and the resonant frequency depends on the resonator path length and is proportional to 1/b [27]. The L and A modes also present anti-crossing spectra with different b, and the plasmon hybridization and modes coupling will lead to the large localized field concentration.
Fig. 4 The simulated absorption spectra (a) and corresponding E field enhancements (b) mapping for different arm length b of crisscross dimer. The other parameters: P = 530 nm, a = 100 nm, and d = 14 nm. The E field enhancement is the absolute value ratio of the x component of electric field to the incident electric field (i.e. |Ex/E0|). E0 is the incident electric field with the linear polarization in the x-direction. The probing location of electric field locates in the gap center of crisscross dimer shown in Fig. 1(b) (orange spot).
The plasmonic system with three separate resonances in this work can be used to achieve the strong field enhancements at multi-frequency bands for the SECARS probing. Thereby, we appropriately adjust plasmon resonance frequencies to match the input and output beams. Figure 5 shows calculated the reflective spectrum (black curve) and corresponding E field enhancement spectrum (red curve) for P = 640 nm, a = 102 nm, b = 258 nm, and d = 14 nm. Three reflective bands with the strong field enhancements appear at λ1 = 687 nm, λ2 = 800 nm, and λ3 = 957 nm, which correspond to the (1,0) PSPP mode, end-to-end coupled nanoantennas mode, and LC resonance mode, respectively. The probed near field enhancements in the central gap of crisscross dimer for three plasmon resonances are g1 = 100, g2 = 115, and g3 = 210, respectively. The electric field distributions for three plasmon resonances are shown in Fig. 6, and they have the same spatial hot spots at the central gap of crisscross dimes in the x-y plane as shown in Figs. 6(a)~(c). Figures 6 (d)~(f) show the z component of near field enhancement in the x-z plane at different resonance wavelengths. The plasmon resonances at both λ1 = 687 nm and λ2 = 800 nm exhibit the enhanced near fields in the vicinity of the crisscross dimer, but with the additional extended evanescent field above the silver film, which is the typical character of the PSPP. These results indicate that the two resonances for the coupling case carry both the characters of LSPR and PSPP [26]. The coupling strength can be adjusted by the lattice periods.
Fig. 5 The simulated reflective spectra (black curve) and corresponding E field enhancement (red curve) for P = 640 nm, a = 102 nm, b = 258 nm, and d = 14 nm. E0 is the incident electric field with the linear polarization in the x-direction. Ex is the x component of near field probed in the gap center of crisscross dimer in the x-y plane.
Fig. 6 The Ex (a~c) and Ez (d~f) field enhancement distributions at the resonance wavelengths of λ1 = 687 nm (a, d), λ2 = 800 nm (b, e), and λ3 = 957 nm (c, f). The near field Ex and Ez are evaluated in the x-y and x-z planes, respectively. Scale bar, 100 nm.
These simultaneous resonances in the same spatial location result in a “mixed frequency coherent mode” previously described on more complex plasmonic clusters, and lead to the large enhancement of nonlinear optical signal. To evaluate the CARS enhancement of the plasmonic substrate, we next calculate magnitude of the SECARS EF for a Raman mode at 2050 cm−1. Using an 800 nm wavelength pumping laser, the corresponding Stokes and anti-Stokes wavelengths are 957 nm and 687 nm, respectively. According to formula (2) and probed E field enhancement curve in Fig. 5 (red curve), we can calculate the corresponding SECARS EF in the central gap region, which is significantly larger than the previous works [16,18]. This implies that the multi-resonance plasmonic substrate maybe provide a more promising choice for the SECARS due to its stronger light harvesting abilities.
While the pump light is selected as 800 nm, we can obtain the different anti-Stokes light output by adjusting the wavelength of the Stokes light. As for our designed plasmonic substrate, the Stokes and the anti-Stokes wavelengths can match with the plasmon resonances of the L and S1 modes, respectively, and the L and S1 modes can be tuned by changing the lattice period P and crisscross dimer arm b, respectively. Figure 7 shows the calculated reflective spectra with the different configuration parameters. The plasmon resonance at 800 nm remains unchanged, and the L mode moves to the short-wavelength direction and the S1 mode moves to the long-wavelength direction with the increasing of the lattice period P and the decreasing of the crisscross dimer arm b. Moreover, the three plasmon resonance frequencies in all reflective spectra satisfy ωS1 = 2ωA-ωL. Subsequently, we evaluate the SECARS EF with the multi-resonance plasmonic substrate for the different configuration parameters (I~VII), as shown in Table 1. While the Stokes light shift towards the pump laser, the large SECARS EF with the order of ~8 × 1016 can be achieved due to the coupling enhancements among the different plasmon resonance modes. However, the SECARS EF gradually becomes smaller as the Stokes light moves closer to the pump photon, which is attributed to the weakened field enhancement in the central gap region at pump wavelength. We plot the near field and current distributions at 800 nm as the Stokes light is close to the pump laser (not shown here). The new plasmon resonance mode with the different current pattern appears at 800 nm due to the decrease of the length ratio of two arms of the crisscross (i.e. b/a), and the hot spot regions have been transferred to the two ends of the nanorod dimer in the x-direction. Therefore, the divergence of the spatial hot spot positions finally leads to the weakened SECARS signals.
Fig. 7 The simulated reflective spectra with the different configuration parameters. The transverse arm length of the crisscross is fixed to be a = 102 nm, and the other configuration parameters are listed in the following Table.
Table 1. Evaluation of the SECARS EF with the different configuration parametersa
aHere, the spectra refer to the different reflective curves shown in Fig. 7. The pump, Stokes and anti-Stokes lights spectrally overlap with the A, L and S1 modes in Fig. 7, respectively. The gP, gS and gA are the enhancements of the x components of the localized electric fields (i. e. |Ex/E0|) at the pump, Stokes and anti-Stokes wavelengths, respectively. The monitored position of the electric field enhancements is located in the central gap region of the crisscross dimer in the x-y plane. The SECARS EF (GSECARS) is calculated by formula (2).
In most SECARS applications, the visible region is of great interest. Therefore, we can use a short wavelength laser to pump the substrate and materials. Figure 8(a) shows the reflective spectrum (black curve) and the corresponding E field enhancement spectrum (red curve) for P = 530 nm, a = 76 nm, b = 212 nm, and d = 14 nm. Three plasmon resonance dips with large near field enchantments appear at the visible regions, and resonance frequencies satisfy ω1 = 2ω2-ω3. Furthermore, we plot the electric field enhancement patterns in the x-y plane at three resonance wavelengths (i. e. λ1 = 579 nm, λ2 = 661 nm, and λ3 = 769 nm) as shown in Fig. 8(b). It is obvious from Fig. 8(b) that they have the same hot spot in the central gap. When the pump and Stokes lights overlap with the plasmon resonances at λ2 = 661 nm, and λ3 = 769 nm, respectively, the strong spatial localization at all three frequencies leads to a tightly confined SECARS hot spot in the center of crisscross dimer. In this region, the calculated SECARS reaches to the order of ~3.03 × 1015 (GSECARS = g12g24g32 = 732 × 754 × 1342 ≈3.03 × 1015). By optimizing the crisscross dimer sizes and array periods, we can tune the plasmonic substrate geometry so that its multiple resonances correspond to the frequencies of the pump, Stokes, and anti-Stokes lights in the visible and near infrared spectral range.
Fig. 8 (a) The simulated reflective spectra (black curve) and corresponding E field enhancement (|Ex/E0|, red curve) for P = 530 nm, a = 76 nm, b = 212 nm, and d = 14 nm. E0 is the incident light with the linear polarization in the x-direction, and Ex is the x component of near field probed in the gap center of crisscross dimer in the x-y plane. (b) Corresponding E field patterns in the x-y plane at the three resonance frequencies: λ1 = 579 nm, λ2 = 661 nm, and λ3 = 769 nm. Scale bar, 100 nm.
4. Conclusions
In this work, we have theoretically investigated a multi-resonance plasmonic substrate consisting of crisscross dimer elements. The periodic arrangement combining with special metallic nanostructure provides a framework for plasmon mode generation and coupling. Three plasmon resonance modes can be excited, and the large field enhancements can be realized by coupling between different plasmon modes. We can tune the plasmonic substrate geometry so that its multiple resonances correspond to the frequencies of the pump, Stokes, and anti-Stokes lights in the visible and near infrared spectral range. The CARS signal can be greatly magnified by using the designed plasmonic substrate, and the SECARS EFs can reach to order of ~1015~1016. There are three mainly factors to support the maximum SECARS signals in this work: (1) the excitation of multiple plasmon resonances with the strong spatial localization at different frequencies, (2) the spectral overlap between plasmon resonances and input beams or output beams, and (3) the same spatial hot spot position at different plasmon resonances. The multi-resonance plasmonic substrate developed here holds promise for applications such as design of optical chips with enhanced nonlinear spectroscopy and multiphoton imaging.
Funding
National Natural Science Foundation of China (NSFC) (11504333, 61505178, 11404290, and 11404291); Basic and Frontier Technology Research Program of Henan Province (142300410365); Program for Science & Technology Innovation Talents in Universities of Henan Province (17HASTIT016); Natural Science Foundation of Henan Educational Committee (17A140002); Outstanding Young Talent Research Fund of Zhengzhou University (1521317007).
Acknowledgments
We would like to thank Prof. Wenhua Yu for his careful reading and editing of the manuscript.
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