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Abstract
The development of surface enhanced infrared absorption has been constrained by the limited field enhancement and narrow-band resonance of commonly used metal resonators. In this theoretical work, the design of a crescent resonator (CR) combined with graphene-enabled plasmon tuning is proposed to settle the drawbacks. The CR is similar to a split ring resonator (SRR), but exhibits a much improved field enhancement. The influence of graphene on the field enhancement of the CR has been systematically investigated. Coupling from localized plasmon of CR to propagating plasmon of graphene has been observed, and the constructive interference of the plasmon wave has led to not only better enhancement inside the gap but also usable enhancements all over the graphene film, which go beyond the localized nature of metal plasmons.
© 2017 Optical Society of America
1. Introduction
In molecular vibrational spectroscopy, energy transitions can be probed by either Raman scatting or infrared absorption. Since the two techniques are complementary with each other, both of them are widely used to identify chemical composition of an analyte [1-2]. However, infrared absorption does provide some notable advantages over Raman scatting, including consistent absorption cross section of different compounds and no fluorescence interference. The main shortcoming of infrared absorption is the relatively low detection sensitivity. While ultrasensitive Raman detection of single molecule has been realized through surface enhanced Raman scatting (SERS) [3], the application of infrared absorption is mostly constrained to film analyzing [4–6]. Similar to SERS technique, the infrared absorption can be dramatically improved while the molecule is placed within the strongly enhanced electric field, which arises from the excitation of surface plasmon resonance (SPR) [7–9]. However, in contrast to its successful implementation in SERS, normal surface plasmon resonators (e.g., nanorod and nanosphere) cannot fully fulfill the enhancement requirement of infrared absorption spectroscopy because of two reasons. Firstly, the electric field confinement of metal SPR in infrared range is weaker than that in visible range. Secondly, the resonance peak of metal SPR is narrow and lack of tunability, which fails to cover the broad molecular fingerprint range.
The design of metal resonator is the fundamental for high performance surface-enhanced infrared absorption (SEIRA) substrate. Lots of work has been devoted to the design of surface plasmon resonators to improve the field enhancement. In middle-infrared range, nanorod resonator has attracted most attention due to its simple configuration [8-9]. The φ resonator, as a modification of nanorod, is also applied for SEIRA with a higher sensitivity [7,10]. But it is worth noting that the higher enhancement of φ resonator compared with nanorod comes at the expense of less ‘hot spots’ in resonator arrays. Split ring resonator (SRR), with compact geometry and natural gap, is found to be promising for SEIRA application and monolayer molecule detection has already been achieved [11]. To date, the exact dependence and optimization of SRR geometry parameters on field enhancement has not yet been investigated.
On the other hand, the plasmon tuning of metal SPR still sticks to change the resonator’s size [9, 12–15], which makes the practical application sophisticated and costly. Compared with metals, the plasmon resonance of graphene, a representative two-dimensional semi-metal, can be easily tuned by changing the Fermi level and with stronger field confinement in infrared regime [16–19]. Intensive research has been paid on the SPR properties of nanostructured graphene. D. Rodrigo et.al. used gate voltage to dynamically tune the resonance wavelength of graphene nanoribbon, and by using this method, broadband infrared absorption enhancement of protein molecule was accomplished [20]. In the following report, calcium fluoride was used as substrate material to replace silicon dioxide, the decreasing of field enhancement induced by phonon-plasmon interaction can then be avoided [21]. D. B. Farmer et.al. successfully tuned the plasmon resonance wavelength of graphene nanoribbon by both size adjustment and chemical deoxidization [22]. Our previous work also introduced a facile production strategy of graphene nanodots and demonstrated its practical use in broadband plasmon-enhanced infrared spectroscopy for sensitive detections [23]. However, the reported infrared absorption enhancement in these approaches (less than 10-fold) was limited by the low carrier concentration of graphene, and hence contributes much lower enhancement than metal resonators. A reliable field enhancement coupled with dynamic tuning characteristic of SPR is indeed necessary for the practical applications of SEIRA. Recently, research on light modulator with hybrid structure of SPR and graphene illustrates that resonance wavelength of metal resonator can be dynamically tuned by coupling SPR near field to graphene [24–30], which also indicates the potential of these hybrid devices in SEIRA application with its field enhancement in a broad spectral range.
In this work, the hybrid structure of crescent resonator (CR) and graphene is proposed as excellent substrate for SEIRA as shown by Fig. 1, with both high field enhancement and dynamic plasmon tuning ability. With optimized feature geometry and a design of metal reflection layer, the CR gives both a well-improved field enhancement rather than that of normal SRR and a broad plasmon tuning range combined with graphene [25]. The influence of graphene loading on the field enhancement of CR is also investigated. It is surprising to find out that the field enhancement at the “hot spot” (gap area) can be improved by loading graphene, and this is attributed to the constructive interference of graphene plasmon. Moreover, this graphene plasmon interference also enables a usable field enhancement on the whole graphene film, which may be beneficial for improving the infrared signal intensity from molecules located outside the “hot spot”.
Fig. 1 Proposed crescent resonator (a) on dielectric substrate and (b) with metal-insulator-metal configuration. (c) graphene loading for dynamic plasmon tuning and better field enhancement. These three structures are numerically analyzed in sequence.
2. Resonance modes of the split ring resonator
Figure 2(a) shows the absorption spectra of SRR in mid-infrared regime with two peaks. The outer radius, line width, thickness, and gap size of SRR is 340nm, 30nm, 50nm and 30nm respectively. The dielectric constant of underlying substrate is ε = 2. According to the charge density distributions given by Fig. 2(b) and 2(c), the resonance mode at 7.7μm is a dipole resonance mode and the other one at 2.5μm is a quadrupole resonance mode. It is obvious that with more free electrons gathered at the gap area, the dipole mode would provide a better field enhancement than the quadrupole mode. In this paper, we focus on the structure design of SRR for better enhancement with the dipole mode. Two ways are often used for optimizing field enhancement, one is to sharpen the tip to increase the charge density and the other is reduce the gap size to strengthen the coupling effect in adjacent structures. Anyway, these two methods are highly dependent on the fabrication resolution. Without changing the size of gap area, it is proposed in the following part that charge density at the tip can be effectively increased by using a gradual change gold ligament.
Fig. 2 (a) Absorption spectra of SRR. Charge density distribution of (b) dipole resonance mode at 7.7μm and (c) quadrupole resonance mode at 2.5μm.
3. Design of the crescent resonator
Figure 3(a) shows the schematic structure of the proposed CR, which is similar to normal SRR but with a gradual change gold ligament. The gap size and resonance wavelength are kept unchanged in order to compare the field enhancement with different outer/inner radius. The size of the gap is set as h = w = 30nm considering the limitation of practical fabrication and the thickness of the resonator is 50nm. With the fixed gap size, the black line in Fig. 3(b) shows the relationship between outer radius R and inner radius r at resonance wavelength of 7.7μm, where r increases with increasing R and reaches saturation at 425nm. The first data point (R, r) = (340nm, 310nm) corresponds to the normal SRR. The reason why the resonance wavelength is not sensitive to R with r = 425nm is due to that the current is mostly confined in the inner side of the ring and the increment of R has little influence on the current distribution after r reaches saturation, and this is proved by the comparison between Fig. 3(e) and 3(f) that the variation of current density distribution is not significant and the only obvious change is the larger blue area, which corresponds to small current density. The resonance wavelengths are determined by the absorption of resonators, which can be calculated using Lumerical FDTD Solutions. The period of the resonator array is P = 2R + 200nm.
Fig. 3 (a) CR unit cell on a dielectric substrate. (b) Dependences of inner radius and field enhancement on the outer radius with fixed gap size of h = w = 30nm and resonance wavelength of 7.7μm. (c) Two dimensional field enhancement distribution of CR with (R, r) = (620nm, 425nm). (d) Field enhancement of CR at the center of the gap (on resonator-substrate interface) increases with increasing R. Current density distribution of CR with (e) (R, r) = (580nm, 425nm) and (f) (R, r) = (620nm, 425nm).
Figure 3(c) is the field enhancement distribution of CR and most energy of the resonance mode is concentrated in the gap area, which is known as the “hot spot”. It is shown by Fig. 3(d) that, by using the design of CR, the field enhancement at the center of the gap (on the surface of dielectric substrate) increases with increasing R (the gray square represents for the gap area and the black line corresponds to normal SRR). The broader gold ligament of CR is expected to act as charge reservoir and provide more free electrons, and therefore a higher field enhancement can be obtained in the gap. It is a useful strategy to obtain large field enhancement by increasing outer radius with SRR geometry, but it is worth pointing out that the increment gets smaller with large R as illustrated by the blue line in Fig. 3(b). This can also be explained by Fig. 3(e) and 3(f) that, after r reaches saturation, the current at the outer side of the ring is small and the free electrons provided by this part is limited, and therefore very large R is not preferred.
The direct evidence for more free electrons can be collected at the gap area by the design of CR is given by Fig. 4, which shows the charge density gets larger with increasing R. It is very clear that with the unchanged CR tip size, it is the free carriers provided by the broader gold ligament that improves the field enhancement, and this mechanism is totally different from either sharpening the resonator’s tips or strengthening the coupling effect between the two tips, which requires higher fabrication resolution to obtain better enhancement.
Fig. 4 Charge density of CR at gap area increases with increasing outer radius R. (a) (R, r) = (460nm, 390nm), (b) (R, r) = (540nm, 415nm), (c) (R, r) = (620nm, 425nm).
In the previous SEIRA applications, nanorod resonator is commonly used because of its simple configuration [8-9]. However, as shown by Fig. 5(a), the performance of nanorod highly depends on its length/width ratio (large length for mid-infrared resonance and small width for better field enhancement), which has been constrained by fabrication process. To enable 7.7μm resonance, the length, thickness, gap size and periods in both directions of the nanorods are set to be 2100nm, 50nm, 30nm and 2130nm, respectively. The influence of nanorod width (90nm, 150nm, 210nm) on resonance wavelength has been neglected because it is very small compared with mid-infrared wavelength. CR is an ideal choice to replace nanorod due to its compact geometry and better performance. The field enhancements of both nanorod and CR are demonstrated here for comparison. The width of nanorod used here is 30nm, which is the same size with tip of CR. According to Fig. 2(b), the size of CR is chosen as (R, r) = (965nm, 425nm) in order to share the same periods with nanorod. Figure 5(b) shows the field enhancement of CR is about 40% higher than that of nanorod, which corresponds to about two-fold infrared absorption enhancement.
Fig. 5 (a) The field enhancement of nanorod resonator highly depends on its width with fixed length, which makes nanorod long and thin in infrared wavelength, and therefore the performance improvement has been constrained by fabrication process. (b) The field enhancement of CR is 40% higher than that of nanorod resonator, which has a length/width ratio of 70:1.
To further improve the field enhancement, the design of perfect absorber (PA) based on CR is introduced. Due to the radiative decay, only part of the incident power can be absorbed by the resonator with only dielectric substrate underlying. By introducing metal reflection layer into the substrate, the interaction between light and resonator can be much enhanced according to Fig. 6(a), where absorption of the resonator is enhanced from less than 40% to near unity by the design of PA. The PA proposed here is consisted of CR, dielectric layer (ε = 2, 470nm thick) and metal reflection layer (metal boundary condition in FDTD Solutions). With 7.7μm resonance wavelength, the size of the CR used in PA, (R, r) = (470nm, 370nm), does not fit the relationship given in Fig. 3(b). This is because of the blue shift of resonance wavelength induced by the near field coupling between the resonator and metal reflection layer. According to Fig. 6(b), the field enhancement of PA is larger than that of CR without metal reflection layer even though the latter possesses a larger size ((R, r) = (500nm, 405nm)), which proves the validity of PA design for field enhancement.
Fig. 6 (a) Absorption spectra and (b) field enhancement of PA ((R, r) = (470nm, 370nm)), and CR without metal reflection layer ((R, r) = (500nm, 405nm)).
For infrared absorption enhancement, the localized nature of metal plasmons has the limitation that molecule needs to be located in the gap to be efficiently excited according to Fig. 3(c), which is also a problem for other surface enhanced spectroscopies, for example, SERS. In the following parts, CR-based PA (the same parameters used in last paragraph) with graphene loading will be proposed for not only broadband dynamic plasmon tuning, but also better enhancement both inside and outside the gap area.
4. Dynamic plasmon tuning of the crescent resonator enabled by graphene
The excitation of SPR enables the confinement of incident light into subwavelength volume, which makes the resonance wavelength extremely sensitive to the dielectric constant of surrounding environment. The dynamic plasmon tuning ability of metal resonator enabled by graphene is based on this principle, where graphene due to its intrinsic linear dispersion band structure provides a freely tunable Fermi level. Graphene can be modeled as either bulk material with finite thickness or an infinitesimally thin surface characterized by a surface conductivity. In the first approach, the thickness of graphene needs to be sufficiently small (typically 1nm), which requires a fine mesh size and thus adds computational complexity [26]. Therefore, the surface conductivity model is chosen here because it is much more efficient. The conductivity of graphene can be represented as σ (ω, μc, τ, T), where ω is radian frequency, μc/Ef is chemical potential or Fermi level, τ is scatting rate and T is temperature [31]. Both intra- and inter-band transitions have been considered, and the temperature and scatting rate are kept constantly at 300K and 0.01ev, respectively, for simplicity [32]. With increasing graphene Fermi level, Fig. 7(a) shows the blue shift of resonance wavelength of CR/graphene hybrid structure, in which graphene is sandwiched between CR and dielectric layer. The decreasing absorption is due to the increasing impedance mismatch between this hybrid structure and free space. The tuning range can be as large as 1.6μm, which is about 20% of the initial resonance wavelength. The tuning efficiency of the hybrid structure depends on the coupling between the SPR near field of metal resonator and graphene, therefore both the field enhancement and dynamic tuning efficiency can be improved by reducing the gap size [20–22]. Also, the tuning efficiency of the hybrid structure can be improved by enhance the interaction between SPR near field and graphene, and the simplest way is to use multilayer graphene film. Figure 7(b) shows that higher tuning efficiencies can be obtained in this way. Two reasons may be responsible for the high tuning efficiency. First, the conductivity variation of graphene is proportional to its layer number. Second, the increasing thickness of graphene is beneficial for enhancing the interaction with CR. However, the second point has not been taken into consideration here because the surface conductivity model has been used. On the other hand, utilization of multilayer graphene may weaken the field enhancement of this hybrid structure, which will be revealed by the next section.
Fig. 7 (a) The resonance peak of CR/graphene hybrid structure blue shifts with increasing graphene Fermi level. (b) Dependence of hybrid structure resonance wavelength on the Fermi level of graphene with different layer number.
5. The influence of graphene on the field enhancement of the crescent resonator
For SEIRA application, it is necessary to investigate the influence of graphene loading on the field enhancement of CR. According to Fig. 8(a), the plasmon coupling from localized surface plasmon of CR to propagating surface plasmon of graphene film is proved by the interference pattern (annular standing wave inside the resonator) of graphene plasmon, which cannot be directly excited without metal resonator as coupler due to wave vector mismatch between plasmon wave and propagating light in free space. The constructive graphene plasmon interference provides two great advantages for SEIRA detection.
Fig. 8 (a) Two-dimensional field enhancement distribution in CR/graphene hybrid structure with graphene Fermi level of 0.2ev. (b) Usable field enhancements can be obtained both inside and outside the gap area (~11 fold with monolayer graphene) and the enhancement decreases with increasing graphene layer number. (c) CR/graphene hybrid structure exhibits 25% percent higher field enhancement at the gap area than CR without graphene. (d) The field enhancement of the hybrid structure decreases with increasing Fermi level, and is higher than that of bare CR in the range below 0.3ev.
Firstly, it enables usable field enhancements outside the gap area, which is beneficial for enhancing the signal intensity from molecules located outside the “hot spot”. According to Fig. 8(b), the maximum field enhancement outside the gap, with resonance wavelength of 6.5μm, is about 11-fold, corresponding to about 120-fold infrared absorption enhancement. Considering the large area occupies by this standing wave, this enhancement is non-negligible.
Secondly, graphene can also improve the “hot spot” intensity. With Fermi level of 0.2ev, the field enhancement of CR/graphene hybrid structure is 25% percent higher than CR without graphene as shown by Fig. 8(c) (The resonance wavelengths are 7.1μm and 7.7μm, respectively). This is attributed to the constructive interference of graphene plasmon in the gap of CR. The two dips, on the other hand, is because of destructive interference. The interference effect gets weaker with increasing graphene Fermi level since the loss of graphene plasmon is getting larger. Figure 8(d) shows that the enhancement at the gap of the hybrid structure decreases with increasing Fermi level, and the hybrid structure possesses a better enhancement than bare CR with Fermi level smaller than 0.3ev by comparing with the black ling in Fig. 8(c). Figure 9 shows the two-dimensional field enhancement distributions with different graphene Fermi levels, which reveals that this graphene plasmon interference enabled large area enhancement exists in the whole plasmon tuning range. It is revealed by Fig. 7(b) that the plasmon tuning efficiency can be improved by using multilayer graphene, but it is worth to be noted that, more graphene layers will lead to larger loss and, consequently, weakened field enhancement as shown by Fig. 8(b). The resonance wavelength is fixed at 6.5μm here and the applicable Fermi levels for monolayer, bilayer and trilayer graphene are 0.44ev, 0.26ev and 0.20ev, respectively. It means that, in the practical application of this hybrid structure, the tuning efficiency and field enhancement need to be balanced.
Fig. 9 Two-dimensional field enhancement distributions in CR/graphene hybrid structure with different graphene Fermi levels of (a) 0.3ev, (b) 0.4ev, and (c) 0.5ev.
6. Conclusion
In summary, the hybrid structure of CR and graphene is proposed for broadband and large-area plasmon enhanced infrared spectroscopy. The CR exhibits higher field enhancement than normal SRR and the metal reflection layer underneath is utilized to enhance the interaction between incident light and the resonator, which further improves the performance. By loading graphene to the CR, dynamic plasmon resonance wavelength tuning can be obtained and the tuning efficiency is determined by the coupling between the SPR near field and graphene, which can be enhanced by using multilayer graphene film. However, the implementation of multilayer graphene leads to a decreasing field enhancement. Plasmon coupling has been observed in this hybrid structure and it provides a higher enhancement at both the gap area and other part of graphene film, which is beneficial for large-area infrared detection enhancement. This work not only provides a promise route for large-area SEIRA substrate, but also can be useful for the development of middle-infrared light modulator and photon detection as well.
Funding
Hundred Talent Program of Chinese Academy of Sciences; National Natural Science Foundation of China (11574349); Natural Science Foundation of Jiangsu province (BK20150365, BK20170424).
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