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Abstract
For sensing and imaging applications of surface-enhanced Raman scattering (SERS), one needs a substrate with the capability of generating a consistent and uniform response and increased signal enhancement. To this goal, we propose a photonic-crystal (PC) structure capable of supporting large field enhancement due to its high quality-factor resonance. Moreover, we demonstrate that the interaction of two modes of this all-dielectric PC can provide an almost uniform field enhancement across the unit cell of the PC. This is of practical importance for SERS applications. The designed structure can support a maximum field enhancement of 70 and 97 percent of uniformity.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The extremely small cross-section levels of Raman scattering (10−24−10−30cm2/sr) render its measurement challenging. Introduction of surface-enhanced Raman scattering (SERS) techniques improves this measurement and paves the way for further applications of Raman scattering. The earliest SERS technique was based on roughened metallic surfaces and reached its highest level of enhancement by utilizing metallic nanoparticles [1]. Metallic nanoparticles as SERS agents can support enhancement factors above 108 [2,3], which is adequate for detection of low-concentration analytes down to a single-molecule level [4,5]. Despite this achievement, there are a number of limitations. Nanoparticle-assisted SERS commonly operates through generations of svtrong local electromagnetic field enhancements (called “hot spots”) within nano-gaps [6–8]. Reduced gap size between adjacent metal nanostructures generates the highest enhancement factor [9,10]. However, it has been recently shown that quantum mechanical effects such as nonlocality and electron tunneling stop the hot spot intensity from further increasing monotonically [11,12]. For a high level of enhancement, ultra-small nano-gaps (in the order of 1nm) have been investigated [13–15]. Obviously, fabrication of such nano-gaps faces various limitations which restrict the reproducibility of the structure. Furthermore, large biological molecules such as proteins or nucleic acids, no longer fit into the hot spot volume. Also, embedding the small analyte molecules inside the hot spot is another challenge. When the field enhancement is restricted only to the hot spots, the emitted Raman wave will be non-uniform depending on whether the molecules are settled inside or outside the hot spot.
Because of the aforementioned limitations, higher signal amplification with higher uniformity and reproducibility is the objective of the current SERS studies. Here, the goal is to increase the volume fraction of the hot spots, which is generally difficult to achieve or even to predict reliably. Some research projects focus on this topic [16–20]. However, ohmic losses may put an upper limit on those SERS techniques which are based on metallic structures [21,22]. Also the strong tendency of many metals to oxidation at room temperature (except for gold) may force another limitation on their performance [23]. Alternatively, dielectric structures can compensate losses and oxidations of metallic structures at the expense of lower field enhancement. Dielectric SERS substrates with improved stability and biocompatibility compared to their metallic counterparts are designed based on Fabry-Pérot (FP) resonance [24,25], field enhancement by dielectric nanoparticles [26–28], and photonic-crystal (PC) resonance [29,30].
Among the investigated dielectric structures, PCs with the capability to support a high-quality-factor guided mode resonance (GMR) enable the required resonance for achieving large enhancement factors [31]. These narrow Fano resonances are realized by inserting one or two-dimensionally periodic index contrast into a high-index dielectric slab to form a one-dimensional (1D) or a two-dimensional (2D) PC. Each resonance corresponds to a particular field distribution which intensifies the electric field at certain locations of the PC for SERS applications. Both 1D and 2D PCs can be designed to provide the required resonances for SERS [32]. An Au-coated 2D PC in [33] provides a SERS enhancement factor of 104. A 1D dielectric PC with nanostructures made of noble metals is introduced in [34,35] for SERS application. Although different PC structures have been investigated for field enhancement so far, less effort has been made to achieve a uniform field enhancement using an all-dielectric structure.
In this research, we demonstrate a 2D PC showing a hybrid mode composed of two Fano resonances. At the resonance frequency of this hybrid mode, a reproducible and uniform field enhancement is achievable. Consequently, the enhanced electric field regions are not restricted only to the hot spots, but they are distributed in a larger area in favor of SERS application. The interaction of Fano resonances for 3D structure consisting of a vertical asymmetric SRR and planar air hole array has been discussed in [36]. We investigate here the Fano resonance interaction of a simple 2D PC with its applicability in SERS. The design procedure and the obtained results are presented in the following sections.
2. Device structure and simulation parameters
While the PCs have been designed in a variety of configurations, the focus of our discussion is on designing a reproducible SERS substrate with uniform enhancement for biosensing application. Our starting point is the 2D square-lattice PC structure shown in Fig. 1. It consists of an arrangement of identical holes introduced into a dielectric titanium dioxide (TiO2) substrate. The structure is an improvement for ease of fabrication to the 1D-PC presented in [34], and almost the same material parameters have been utilized for modeling. However, unlike [34], we design and engineer the suspended PC which the process flow to its generation is discussed in [37]. According to [38], using a 2D phase mask facilitates fabrication of the proposed 2D grating by means of a production-friendly single-step exposure over a relatively large area. Thus, the structure can be fabricated uniformly with reliable reproducibility. In order to realize a trade-off between the fluorescence suppression and much weaker Raman scattering at near-IR, the period of the unit cell is designed to move the resonances to the wavelength range of 590-660nm. The exact values of the hole radius $R$, and the PC periods ${P_x}$ and ${P_y}$ are determined in the following sections. The PC covered by water medium. The fixed refractive index value of n=1.33 is used for water while the wavelength-dependent dielectric constant for the PC is extracted from the refractive index database in [39]. The Finite-Difference Time-Domain (FDTD) technique was used for electromagnetic simulation of the device. The unit cell of the structure inside a periodic boundary condition is illuminated by an x-polarized normally-incident plane wave along the z-direction. The enhancement of the electric field in magnitude is calculated relative to the illuminating electric field intensity of ${E_0} = 1$ V/m.
Fig. 1. Schematic of the 2D PC surrounded by water media under the illumination of an x-polarized normally incident plane wave.
3. Design principle
To meet the requirements for maximum field enhancement and to keep the design procedure simple, it will be shown in what follows that the radius of the nano-holes in Fig. 1 can be 20nm. The slab has a thickness of 107.6nm and a periodicity of 400nm in both the x and y-directions. The PC works under GMR and supports two sharp Fano resonances in the wavelength range of 590-660nm as shown in Fig. 2.
Fig. 2. Reflectance of the 2D PC for a normal x-polarized plane wave with the structural parameters of $R = 20nm$, and ${P_x} = {P_y} = 400nm$.
The resonances are prominent at the wavelengths of 598.79nm and 646.66nm. The electric field distribution within the structure at two resonances is shown in Fig. 3. The electric field pattern at the resonance wavelengths points to two distinct modes which are studied as follows. The electric field distribution pattern at a wavelength of 646.66nm, represented in Fig. 3(b), corresponds to the electric field pattern of a 1D PC similar to what can be seen in [34]. Figure 4 compares the 1D resonance demonstrated in [34] with that of this work. As a result, we can conclude that this resonance is generated through the refractive index contrast of the structure along the x-direction. This resonance can be categorized as 1D resonance due to its resemblance with that reported in [34]. As illustrated in Fig. 3(b), this mode is a bulk mode, which mostly confines in water on top of the PC rather than on its surface. Also, the electric field at this mode has a minimum value inside the holes.
Fig. 3. Electric field distribution inside the 2D PC at the wavelengths of (a) 598.79 nm, and (b) 646.66 nm. The bottom figures are the cross section along the dash-dot line on the surface. Four unit cells are included in this representation.
Fig. 4. Electric field distribution in the structure of (a) 1D corrugated PC and (b) the 1D resonance of 2D PC. Four unit cells of the structures can be seen in this figure. As can be inferred from the figure (b), the electric field pattern of the proposed structure within a period has slight variation along the y-direction while it fluctuates along the x-direction. This is comparable to the field variation in the one-dimensional grating structure of (a).
The electric field distribution at 598.79nm stems from the 2D nature of the PC. Dimensions of the unit cell both in the x and y-direction affect this resonance, so it can be sorted as a 2D resonance. As illustrated in Fig. 3(a), the generated hot spots at this resonance can provide significant advantages for Raman spectroscopy and sensing. A biomolecule placed inside the hot spot can generate a strong Raman signal. Obviously, the electric field intensity inside a given hot spot can be affected by the hole-diameter. The effect of changing the hole-radius on both the 1D and 2D resonances and on the electric-field enhancement factor inside the holes is investigated in Fig. 5.
Fig. 5. Hole radius effect on the (a) resonances and (b) maximum enhancement factor of the electric field inside the hot spots.
Figure 5(a) shows that the hole-radius considerably affects the 2D resonance. The resonance wavelength of 1D mode mostly depends on the period of the holes in the x-direction, so the 1D resonance does not show a remarkable shift when compared to the wavelength shift of the 2D resonance. The field enhancement of the two modes inside the holes is illustrated in Fig. 5(b). As can be inferred from this figure, the 1D resonance does not cause any field-enhancement inside the holes. Moreover, the plot indicates that a larger hole increases the scattering from the PC and consequently results in a lower quality factor and lower field enhancement inside the holes in resonance wavelength of 2D mode.
Although the structure can provide a great field enhancement inside the hot spots at 2D resonance, practically the attached molecules are not necessarily trapped inside the hot spots. Hence, it is desirable that the field enhancement is not restricted only to hot spots.
By considering the electric field distribution at two resonances of the PC in Fig. 3, it is shown that the 1D and 2D resonances confine the electric field mostly at the surface and inside the hole of the PC, respectively. If the two modes could be excited simultaneously, field enhancement and uniformity can be achieved simultaneously. As a result, the modes integration can eliminate most of the electric field nulls at the surface of the substrate of the 2D mode and inside the hole of the 1D mode. In what follows, we investigate the possibility of mode integration to have a more uniform field enhancement across the SERS substrate. Although the small radius has the maximum filed enhancement, for the ease of the design process, we continue with the hole radius $R = 20nm$.
As stated previously, the index contrast along the x-axis is the origin of the 1D resonance. Therefore, a small change in the unit cell dimension in the y-direction along with keeping the x-polarized incident wave will not shift the 1D resonance remarkably since this resonance is not seriously affected by this parameter. However, it shifts the 2D resonance significantly. As the resonances behave independently, while keeping the first one fixed, the wavelength of the second resonance can be changed. The resonance wavelengths as a function of the unit cell dimension are depicted in the reflectance spectrum of Fig. 6. As it is evident from the figure, the 1D resonance is fixed at 646.66nm, while the 2D resonance is shifting towards it.
Fig. 6. Effect of ${P_y}$ variation on the PC resonances. It changes only the 2D resonance position.
The desired hybrid mode can be achieved when the 2D resonance approaches the 1D one. In a perfect interaction of the resonances, no clear and sensible resonance is observable in the reflectance spectrum. Indeed, the energy couples to higher-order modes. Yet, the perfect interaction of two modes which leads to a hybrid mode is detectable by observing the magnitude of the electric field at three different points in the structure. The chosen points (a,b,c) illustrated in Fig. 7 provide checkpoints. In other words, once the electric field reaches its maximum value at all of these three points, a complete mode interaction is achieved. According to Fig. 7, a value of ${P_y} = 508.04nm$ corresponds to the electric field maximum at three points a, b, and c.
4. Results and discussion
The resulting electric field pattern of the hybrid mode is represented in Fig. 8. As can be seen from the figure, the electric field minima of the 1D and 2D modes are eliminated at this mode, so the mode can provide a more uniform Raman signal for adsorbed molecules. The structure has minimum enhancement factor of 20 fold which has increased four times when compared to the same value in 2D resonance.
Fig. 8. Electric field distribution on the surface of the PC. The bottom figure is the cross section along the dash-dot line on the surface. Four unit cells are included in this illustration.
Figure 8 shows the magnitude of electric field averaged over all phase angles on the surface of the structure. Figure 9 represents the instantaneous electric field pattern at some constitutive phases in which the pattern of 1D and 2D modes can be distinguished, which insures that the hybrid mode consists of 1D and 2D mode interactions. As can be seen in Fig. 9, two modes can be recognized in alternating phases, i.e., $\varphi = 70$ and $\varphi = 160$..
Fig. 9. Instantaneous electric field distribution on the surface of the PC at various phases. The associated parameters are ${P_x} = 400nm$, ${P_y} = 508.04nm$, and $R = 20nm$. The PC is illuminated by an x-polarized normally incident plane wave.
For further investigation, we can define a uniformity factor as $UF = {P_{dc}}/{P_{tot}}$, which shows the ratio of the DC to the total power. By using the Fourier transform, the numerator is equal to the square of the zeroth order Fourier coefficient ${|{{c_{00}}} |^2}$, and the denominator is equal to $\sum\limits_m {\sum\limits_n {{{|{{c_{mn}}} |}^2}} }$ where ${c_{mn}}$ are Fourier coefficients. The relations can be substituted from the Fourier coefficient formula, and Parseval's theorem as follows:
For a uniform electric field distribution, $UF = 1$. By applying Eq. (1) to the structures of 2D and hybrid modes, we obtain $UF = 0.9$ for 2D mode and $UF = 0.97$ for hybrid mode which shows increased uniformity for hybrid mode. For the hybrid mode, maximum field enhancement of 70 fold is achieved on the surface of the substrate which is greater than the local enhancement factor reported for the dielectric-based structures [21,40,41].
The SERS enhancement factor can be calculated according to
Fig. 10. Typical local field enhancement on the surface of the structure for ${P_x} = 400nm$, and ${P_y} = 508.04nm$.
On the other hand, note that the uniformity of the enhancement across a unit cell of the structure maximizes the contribution of several molecules in comparison to hot-spot based SERS spectroscopy techniques. This explains one of the major advantages of the present research.
5. Conclusion
In this paper, interaction of two guided-mode resonances in an all-dielectric PC has been investigated for uniform and reproducible SERS, which is in favor of realizing an ideal Raman spectroscopy. Toward an ideal SERS, one needs to discuss further considerations in addition to making a strong field enhancement. Conventional metallic structures concentrated mostly on this aspect which makes the probe molecule difficult to locate inside the hot spots. Moreover, the fabrication of the mentioned hot spots is challenging. Our purposed structure consists of a rectangular array of identical holes in a dielectric substrate which can create hot spots inside the holes as well as on the surface of the substrate through the interaction of two Fano resonances. Furthermore, due to its all-dielectric nature, it is biocompatible and does not suffer from the typical limitations of metallic structures, including the ohmoic loss and oxidation. The proposed substrate has reproducibility in fabricating uniform SERS active sites which can be realized by a simple fabrication method and does not need the sophisticated procedures of realizing the closely spaced metallic nanoparticle dimers.
Acknowledgments
The first author would like to thank Professor Brian T. Cunningham for his supervision during her research stay at the University of Illinois at Urbana-Champaign for his contribution to the study of the 1D corrugated PCs.
Disclosures
The authors declare no conflicts of interest.
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