1. Introduction

Surface-enhanced Raman Spectroscopy (SERS) is widely used to sensitively detect molecules or markers for numerous applications [1–5], such as pharmacology [4], biology [3, 5], etc. In many applications, the detections are implemented in a free space configuration, leading to quite bulky and costly systems [6]. Some SERS detections of molecule analysis are completed in close-circuits such as microfluidic systems [7, 8], with a reproducible quantification. However this approach still suffers from long integration time, mechanical instability, and need of some other macro-components, such as objectives to collect Raman scattering signals. Meanwhile, the advent of integrated optics has facilitated a number of micro-based sensors or optical components on optical-circuits chips [9, 10]. This provides a possible approach to miniaturize SERS machines into microscale devices. Some research has successfully validated that integrated optical components could be used in Raman spectroscopy [11–13] such as micro-spectrometers.

We investigate the possibility to fabricate a full SERS nanosensor on a chip with optical circuits, which can be linked to a micro-laser and a micro-spectrometer to constitute a fully integrated SERS detection system. In a free space configuration, Raman spectrometers can collect Raman scattering signals by a microscope objective with a high numerical aperture. However, extracting Raman signals by an optical circuit on a photonic chip can prove to be very difficult, which is the major challenge in miniaturizing the Raman instrumentation. To solve this problem, we chose in our work a structure (a hybrid waveguide) made of a metallic slot and a dielectric strip. Some previous researches showed that the dipole radiation from a single emitter, which is embedded into metal-air-metal slot structures, will be preferentially coupled into plasmon guided modes of metallic slot waveguides [14, 15]. The coupling of light from metallic slot/dielectric strip waveguides to dielectric strip/metallic slot waveguides has been demonstrated by the works on the couplers between electronic and photonic devices [16, 17]. As shown in this work, an efficient and stable SERS nanosensor on a microchip can be achieved by the sensor design in which a dielectric strip lies inside the substrate while a metallic slot, where analytes are dripped, lies vertically above it.

Gold and silicon nitride (Si₃N₄) are specially chosen as the materials to design the SERS sensor here. Gold is one of the most promising metals for plasmonics in the red and near-infrared range with a better chemical stability than silver [18]. Silicon nitride is almost non-lossy in the visible and near IR range with a high dielectric constant $\epsilon =4$, which ensures a good confinement of light fields. Considering the mainstream CMOS technologies, silicon nitride circuits can be achieved on a silicon-on-insulator chip easily. Also, these technologies offer a very flexible route to attach solid-state emitters and micro-spectrometers, such as micro-lasers consisting of quantum dots embedded in SiN_x strip waveguides [19, 20] and integrated circuits used to disperse spectra [21], to realize a fully integrated SERS micro-system.

The system under study is based on a hybrid waveguide, the frame of which is that a metallic slot is located in the silica substrate while a dielectric strip is embedded below vertically (Fig. 1). For simplicity, the shapes of the slot and strip waveguides are kept as square in our investigations. S_m and S_D are the side lengths of the square cross sections of the slot and the strip respectively. Dis is the edge-edge distance between the slot and the strip. In experiments, analytes would be dripped into the gold slot where enhanced Raman scatterings occur. Here water is taken as the superstrate material, assuming that the analyte has a refractive index similar to water ε = 1.33. The illumination is injected into the Si₃N₄ strip at z = 0 nm. The light propagating in the Si₃N₄ strip will couple into the Au slot and excites the intense plasmonic local fields. The local field will induce the Raman dipoles of molecules present in the slot, which will couple back to the plasmon guided modes of the slot, and then couple into the Si₃N₄ strip, which is connected to dispersive elements. According to the properties of surface plasmons, only the TE mode (E_x >> E_y, E_z) of the strip can be coupled into the metallic slot. In this work, the results are obtained with the software FDTD Solutions from Lumerical Solutions, Inc. It is based on the finite-difference time–domain method, which is a powerful numerical tool for theoretical studies of the SERS electromagnetic enhancement mechanisms [22–24].

 

Fig. 1 Layout of the SERS sensor: (a) Cross section of the hybrid waveguide, where a square-section Si₃N₄ strip of side S_D is located at a distance Dis under a square-section gold slot of side S_m deposited on the silica substrate. (b) Sensor frame, where the L-length gold slot is laid above the embedded Si₃N₄ strip.

Download Full Size | PDF

2. Field beating in the hybrid waveguide

We will first have a glance at the beating pattern of the energy coupling between the Au slot and the Si₃N₄ strip to demonstrate how electromagnetic field behaves in the hybrid waveguide. The coupling between the metallic slot and the dielectric strip is one of the most important concepts in this sensor, which bridges the plasmon mode and the photonic mode of light.

The energy coupling between the Au slot and the Si₃N₄ strip is illustrated in Fig. 2. The hybrid waveguide can support a pair of fundamental supermodes (E_x >>E_y, E_z): pseudo even and pseudo odd [16], as shown in Figs. 2(a) and 2(b). For example, the two modes have different signs of the real part of E_x in the dielectric strip waveguide while the same sign in the metallic slot. The inserts at the top-right corners of Figs. 2(a) and 2(b) show that the even and odd modes have respectively a symmetric and an anti-symmetric phase profile in the vertical direction, i.e. with respect to the slot and the strip. The interference between two field modes of same amplitude but slightly different wave vectors (k₁, k₂) propagating in the z direction leads to a total amplitude A = cos(k₁z) + cos(k₂z) = 2cos[0.5(k₁ - k₂)Z]cos[0.5(k₁ + k₂)Z], leading to a beating phenomenon, perceived as a periodic variation in amplitude whose rate is 0.5(k₁ - k₂). In Fig. 2(c) the energy is coupled into each single waveguide which thus propagates with a beating pattern. Considering that Real(k₁ - k₂)L_Beating = 2π and k_{1, 2} = (2π/ λ)ERI_{even, odd}, the beating length can be expressed as:

 

Fig. 2 Diagrams of coupling in the hybrid waveguide with S_m = 40 nm, Dis = 20 nm, S_D = 200 nm and λ = 720 nm: (a) Even mode shown with real part of E_x with REI = 2.584 + 0.0755i and (b) Odd mode shown with real part of E_x with REI = 1.381 + 0.00195i. The inserts present their phase profiles, respectively symmetric and anti-symmetric. (c) Beating of |E_x| (normalized to the source) in a y-z cross section with x = 20 nm.

Download Full Size | PDF

3. SERS processes: excitation and radiation

The working procedure of the sensor is directly related to the two basic SERS processes: excitation of in-slot plasmon and radiation of induced Raman dipoles; the two corresponding enhancement effects are the two main enhancement mechanisms in SERS. Thus, the global enhancement factor can be expressed as EF = EF_Loc(ω_L)EF_Rad(ω_R), where EF_Loc is the local field enhancement in the excitation process due to plasmon, EF_Rad is the radiation enhancement in the radiation process of induced Raman dipoles, and ω_L and ω_R are the frequencies of the excitation incident and the Raman scattering light respectively. In this section, we will show the validity of the |E|⁴-approximation, which is extensively utilized in our work.

The two simulations of the excitation of in-slot plasmon and the radiation of induced Raman dipoles are presented in Fig. 3. The gold slot is 0.61 μm in length, which is the length of one coupling beating in the hybrid waveguide with λ = 720 nm. In the excitation process, an impulse of the fundamental TE mode (the insert in Fig. 3(a)) is injected into the Si₃N₄ strip at z = 0 nm. This calculation, based on FDTD, can cover a wide range of wavelengths with a single simulation of the sensor, due to its time-domain advantage. The distribution of |E| in the excitation process is presented in Fig. 3(c) with λ = 778 nm. It is seen that the electric field of surface plasmon is excited in the slot particularly near the four corners. If the analyte is located in the slot, the intense local field could induce Raman dipoles in these detected molecules with an enhancement factor EF_Loc. The EF_Loc of the specific point (23 nm, 22 nm, 0.805 μm), at mid-length of the gold slot in the excitation process, is plotted with a blue line in Fig. 3(e). Its highest peak appears at λ = 778 nm and not at λ = 720 nm. This effect occurs because a wavelength λ ≠ 720 nm has a shorter or longer field beating than 0.61μm of λ = 720 nm, which means that the non-zero in-slot field at the slot end would be reflected back, resulting in an interference of the incoming and reflecting fields in the slot. Besides, the propagation loss also changes the beating shape in the slot. In the radiation simulation, a single induced Raman dipole is located at the point (23 nm, 22 nm, 0.805 μm) and its orientation is marked by the red arrow as shown in Fig. 3(b). This point is chosen because it corresponds to the peak position of the energy beating in the slot where a maximum of energy is coupled from the strip into the slot and it is in the middle of the y direction, which is the position where the molecule undergoes an average enhancement. However if a molecule is in the corners we can have stronger enhancements, it is close to the slot wall and molecules are likely to be adsorbed onto gold. Similarly, the simulation can give out the electromagnetic fields with a wide band of wavelengths at the x-y output plane with z = 1.3 μm. As shown in Fig. 3(d), the field profile can be decomposed into some orthogonal modes but only the fundamental TE mode of the strip is coupled into the dielectric strip to be detected. The EF_Rad of the radiation process is plotted with a black line in Fig. 3(e), and the global enhancement factor EF is with a red line.

 

Fig. 3 Simulations of the basic SERS processes: excitation and radiation with S_m = 48 nm, Dis = 10 nm, S_D = 200 nm and L = 0.61 μm: (a) Side view of the sensor, where the insert shows the incident light field i.e. the fundamental TE mode of the Si₃N₄ strip in the excitation simulation. (b) Front view of the sensor, where one induced Raman dipole is located at (23 nm, 22 nm, 0.805 μm) in the radiation simulation and its orientation is marked by the red arrow. (c) |E| distribution in an x-y cross section at z = 0.805 μm. (d) |E| distribution in a x-y cross section at z = 1.3 μm. (e) Enhancement factors for the induced Raman dipole, whose position is given in (b). The movies of |E| in the two processes can be found in Visualization 1 and Visualization 2.

Download Full Size | PDF

Generally, estimating EF_Loc is much more convenient than estimating EF_Rad, due to its dependence on dipole positions, dipole orientations, emission frequencies, etc. For simplicity, an approximation is carried out, the so-called |E|⁴-approximation, which is used extensively in publications and thus has been also used in our work. It is based on the condition that EF_Rad(ω)≈EF_Loc(ω) and ω_R≈ω_L, and this simplifies the global enhancement factor as EF ≈EF_Loc² = |E_Loc/ E_Inc|⁴, where E_Loc is the local plasmonic electric field and E_Inc is the incident electric field. In Fig. 3(e), EF_Loc and EF_Rad have similar spectral features, meaning that EF_Rad(ω)≈EF_Loc(ω). If ignoring the Raman shift, ω_R≈ω_L, the common |E|⁴-approximation is considered valid here. In the following parts, the |E|⁴-approximation will be used to calculate the global enhancement EF, and only the excitation process will be simulated.

4. Influence of the sensor geometry

The sensor is based on the coupling between the dielectric strip waveguide and the metallic slot waveguide. Thus, the influence of the geometrical modification on the sensor performance can be inferred via the modal analysis of the hybrid waveguide, particularly the effective refractive indexes (ERI) of the even/odd modes. Firstly, the ERI analysis of the hybrid waveguide is reported at λ = 720 nm, indicating the changing trends of the coupling efficiency, the propagation loss and the beating length when the hybrid waveguide is modified. Then, simulations are presented to demonstrate the influence of the geometrical parameters on the in-slot enhancement effect via the change of the modes.

4.1 Effective refractive index

Considering that the overlapping between the modes of the strip waveguide (labeled by 1) and the slot waveguide (labeled by 2) in the sensor is strong, the coupling process between them should be investigated using a strongly coupled-mode theory [25, 26]. According to this theory, the propagation constants $({\beta }_1,{\beta }_2)$and the conventional coupling coefficients $(K_{12},K_{21})$ of individual waveguides are all affected due to the mutual approach of the two waveguides. The corresponding modified parameters $({\gamma }_a,{\gamma }_b)$ and $(K_{ab},K_{ba})$ can be expressed as ${\gamma }_{a,b}={\beta }_{1,2}+(K_{11,22}-\overline{c}{K}_{21,12})/(1-{\overline{c}}^2)$and$K_{ab,ba}=(K_{12,21}-\overline{c}{K}_{22,11})/(1-{\overline{c}}^2)$where $K_{pq}=0.25\omega {\displaystyle \iint \left[ϵ\left(x,y\right)-{\epsilon }^{(q)}\left(x,y\right)\right][{\overrightarrow{E}}_t^{\left(p\right)}\cdot {\overrightarrow{E}}_t^{\left(q\right)}-({\epsilon }^{(p)}/\epsilon ){\overrightarrow{E}}_z^{(p)}\times {\overrightarrow{E}}_z^{(q)}]dxdy}$, $\overline{c}=(C_{12}+C_{21})/2$ and $C_{pq}=0.5{\displaystyle \iint [{\overrightarrow{E}}_t^{(q)}\times {\overrightarrow{H}}_t^{(p)}]\cdot \overrightarrow{z}dxdy}$ . The superscript p, q = 1, 2. ε(x, y) and ε^(q)(x, y) are the permittivity of the cross sections of the hybrid strip-slot waveguide and the isolated strip or slot guide. ${\overrightarrow{E}}^{(q)}$ and ${\overrightarrow{H}}^{(q)}$ are the mode field of the individual waveguide labeled by q. Here z is the propagation direction of waveguides. The subscript “z” means the z component of the mode field and “t” means the tangential component of the mode field, which is normal to the z axis. At the initial position z = 0, if the field in the strip b(z) = 1 and the field in the slot a(z) = 0, then the field in the hybrid waveguide can be expressed as:

The relationship between propagation constants β and effective refractive indexes (ERI) is β = k₀ERI = 2πERI / λ, where λ is the wavelength in vacuum. Considering that φL_Beating = π and L_Beating = λ / Real(ERI_even – ERI_Odd ), it is obtained that φ = 0.5k₀Real(ERI_even – ERI_Odd ) where ERI_even, ERI_Odd are respectively the indexes of the even mode and the odd mode of the hybrid waveguide. Figure 4 and Fig. 5 present the modal analysis of the hybrid waveguide at λ = 720 nm, which is the center point of the wavelength range concerned in the sensor. The modes of the isolated Au slot and isolated Si₃N₄ strip are reported with black curves in Fig. 4. For the beating length L_Beating = λ / Real(ERI_even – ERI_Odd ), it is obvious in Fig. 4 that no matter which parameter (S_m, S_D or Dis) increases, the difference of the even and odd indexes becomes smaller, and thus the beating length will become longer. Conversely, these parameters’ increase would make the value of φ lower. The imaginary part of the odd mode in the hybrid waveguide is much smaller (< 0.005) than that (> 0.04) of the even mode, thus 0.5k₀Imag(ERI_even) is the main contribution in propagation loss, ignoring the odd mode’s contribution and only the even mode is reported in Fig. 5. According to the imaginary part of the modal indexes, the propagation loss of the hybrid waveguide becomes smaller when S_m or Dis increases. However, the accompanying effect with a higher S_m is a weaker electromagnetic confinement in the slot, decreasing the enhancement effect. A higher Dis decreases the coupling efficiency η_slot and it also decreases the enhancement effect. Generally, it is seen that S_m and Dis mainly influence the even mode of the hybrid waveguide, while S_D mainly influences the odd mode in Fig. 4.

 

Fig. 4 Modal analysis of the hybrid waveguide with λ = 720 nm: (a) Real(ERI) of both isolated (black curves) and hybrid modes (colorful curves) are plotted as function of the slot size S_m for several spacings while S_D = 250 nm. (b) Real(ERI) of both isolated (black curves) and hybrid modes (colorful curves) are plotted as function of the strip size S_D for several spacings while S_m = 40 nm. The symbol real returns the real part of a complex number.

Download Full Size | PDF

 

Fig. 5 Modal analysis of the even mode of the hybrid waveguide at λ = 720 nm: (a) Imag(ERI) of the even mode are plotted as function of the slot size S_m for several spacings while S_D = 250 nm. (b) Imag(ERI) of the even are plotted as function of the strip size S_D for several spacings while S_m = 40 nm. The symbol Imag returns the imaginary part of a complex number.

Download Full Size | PDF

Based on the field distributions of the strip/slot guided modes and the mode indexes in Fig. 4 and Fig. 5, the efficiency η_slot of energy coupled into the slot at z = π/(2φ), which is the in-strip beating node, is plotted in Fig. 6. It is clearly seen that the increase of S_m will make the coupling stronger while the increase of S_D weakens the coupling. This results from that the fact S_m < S_D, therefore the increase of S_m will increase the interaction area between the slot mode field and the strip mode field while the increase of S_D will make the field in the interaction area weaker by reducing the energy density surrounding the strip. Although increasing S_m is beneficial to couple more energy into the slot part and to contain more analyte molecules, it makes the electromagnetic confinement weaker in the slot. There is a compromise between the two opposite effects to obtain the strongest enhancement in the slot. In Fig. 6, the maximum coupling efficiency is obtained at Dis = 10 nm. However, the parameter Dis does not influence the coupling dramatically because between the slot and the strip there is an obvious crosstalk which introduces a complementation between the slot and the strip. That means if energy transfers into the strip from the slot, part of this energy will extend into the slot by the evanescent field of the strip mode.

 

Fig. 6 Coupling efficiency η_slot of energy from the strip to the slot at λ = 720 nm and z = π/(2φ): (a) as function of the slot size S_m for several spacings while S_D = 250 nm. (b) as function of the strip size S_D for several spacings while S_m = 40 nm.

Download Full Size | PDF

4.2 Enhancement factor

In the detection of SERS signals, the incident light needs to be monochromatic, and the length of the hybrid part (a beating length, L) in Fig. 1 should be fixed for only one wavelength, such as 720 nm in Fig. 3. Although a simulation of the electromagnetic field in Fig. 1 covers a certain wavelength range, the electromagnetic field of most wavelengths are not coupled back totally into the Si₃N₄ strip at the slot end and the remnant field is reflected back and forth in the slot. To demonstrate clearly the electromagnetic beating distributions for different wavelengths in a wide band, the structure described in Fig. 7 is used. For different wavelengths, the beating length in Fig. 7 can be obtained via the node position of the in-slot field beating distribution in the calculation results.

 

Fig. 7 Layout of the simulated structure: (a) Cross profile and (b) Side view.

Download Full Size | PDF

Figure 8 shows the influence of the geometry on the beating length based on simulations of the structure in Fig. 7. As shown in the section 4.1, the increase of the parameters S_m, S_D or Dis leads to a longer beating length. The fluctuation of the curves in Fig. 8 is due to the fact that the electromagnetic field distribution of the slot is disturbed by the evanescent field of the photonic mode in the strip at the node position. This is confirmed by the fact that further away from the strip, the fluctuation is weaker (Fig. 11 in Appendix).

 

Fig. 8 Beating length as function of (a) the slot size S_m, (b) the strip size S_D and (c) the interval distance Dis.

Download Full Size | PDF

Figure 9 shows the influence of the geometry on the enhancement factor in the 1st beating volume: - S_m/2 ≤ x ≤ S_m/2, 0 ≤ y ≤ S_m, 0.5 μm ≤ z ≤ 0.5 μm + one beating length. In these graphs, it is noting that the EF value for a different wavelength is calculated within a different volume because the beating length changes with the wavelength. The upper three graphs present the maximum EFs in this volume, and the lower three graphs show the average EFs over the whole volume of the slot. The maximum of the enhancement factor always appears near the slot corners, due to the sharp features. Because the SiO₂ substrate has a larger refractive index than water, the bottom corners have stronger enhancement than the upper corners. The fluctuation of the EF curves is caused by the evanescent field of the strip mode and the average frequency term 0.5(k₁ + k₂) = 0.5k₀(ERI_even + ERI_odd) in the beating formula amplitude A = 2cos[0.5(k₁ - k₂)Z]cos[0.5(k₁ + k₂)Z]. The effect of the term 0.5k₀(ERI_even + ERI_odd) is observed clearly in the strip as shown in Fig. 12 in Appendix. It is mentioned above that when the slot size S_m increases, there are two opposite effects: more energy coupled into the slot but less confined electromagnetic field. In Fig. 9(a), the former effect dominates for wavelengths < 750 nm, and the latter effect dominates for wavelengths > 750 nm. When the strip size S_D increases, the EF maximum decreases for wavelengths <700 nm. For longer wavelengths (>700 nm), the highest value is achieved with S_D = 240 nm. The curves with S_D = 160 nm in Figs. 9(b) and 9(e) don’t behave like the cases with other S_D values. This is because 160 nm is the diffraction limit of 640 nm in the Si₃N₄ strip and the strip with S_D = 160 nm cannot confine effectively the field with a wavelength longer than 640 nm. When the distance Dis between the slot and the strip becomes smaller, the enhancement will increase. The enhancement averaged over the whole first beating volume is always very small as shown in Figs. 9(d), 9(e) and 9(f). This is because the electric field is confined at the metallic surfaces i.e. the slot sidewalls. It is obvious that a smaller slot demonstrates a larger average EF because of a better confinement of electromagnetic fields. Based on the previous analysis of modal indexes, a lower S_D or a lower Dis strengthens the coupling between the slot and the strip, so the average EF increases. However, if Dis equals 0 nm, the average EF will decrease.

 

Fig. 9 Maximum and Average of EF in the 1st beating area: - S_m/2 ≤ x ≤ S_m/2, 0 ≤ y ≤ S_m, 0.5 μm ≤ z ≤ 0.5 μm + one beating length. They are reported as function of (a, d) the slot size S_m, (b, e) the strip size S_D and (c, f) the interval distance Dis.

Download Full Size | PDF

To demonstrate the detection capability of the sensor, the intensity of SERS signals scattered by rhodamine 6G (RH6G) and benzotriazole dye 2 (BTZ) are calculated as function of the concentration of molecule probes, which is reported in Fig. 10. The 1510 cm⁻¹ mode of RH6G and the 1412 cm⁻¹ of BTZ are chosen in this graph. The intensity of incident is 10 mW and the wavelength is 720 nm. The sensor parameters are set as S_m = 30 nm, S_D = 200 nm and Dis = 10nm. The molecules are supposed to uniformly and randomly distribute in the slot. The minimum detectable power of a CCD linear array, SONY2048, is chosen as the threshold value of detectability. It is seen that the signal of RH6G is detectable when the concentration is above 1.3 mole/L while the minimum detectable concentration of BTZ is 13.3 mole/L. In reality these molecules could be physisorbed or chemisorbed onto gold and not uniformly distribute, so the minimum concentration that the sensor can detect should be lower than 1.3 mole/L or 13.3 mole/L. A narrow metallic slot has a strong electromagnetic confinement and the high enhancement factor. However, this may reduce the coupling efficiency as shown in Fig. 6 and stop adequate analyte molecules entering into the slot. Thus, there is a compromise between the electromagnetic confinement and the number of molecules. This makes the enhancement factor relatively low in this paper. Another approach to improve the enhancement of the sensor is to implant some metallic nanoparticles inside. They can introduce the gap effect (hotspot areas) into the slot and enhance Raman scatterings dramatically.

 

Fig. 10 Intensity of SERS signals given out by the sensor when rhodamine 6G (RH6G) or benzotriazole dye 2 (BTZ) solution is dripped into the slot. In this graph, $\Delta \stackrel{}{\overline{v_R}}$is Raman shift of these probes and the dotted line is the minimum detectable power of a CCD (SONY2048) of Sony, Inc.. The sensor parameters are chosen as S_m = 30 nm, S_D = 200 nm and Dis = 10nm. The intensity of incident is 10mW and the wavelength is 720 nm.

Download Full Size | PDF

4. Conclusions

In this paper, it was shown theoretically that a SERS nanosensor based on slot-strip hybrid waveguides could enhance Raman signals in a micro frame. The simulations demonstrate that the hybrid waveguide can transform effectively energy between photonic mode and plasmonic mode, solving the main challenge of extracting scattering signals in the nanosensor. The SERS processes, excitation of intense local plasmonic field in slots and radiation of induced Raman dipoles, are simulated to demonstrate the working procedure of the sensor. Based on the modal analysis, the influence of the geometrical parameters on the coupling in hybrid waveguide is investigated to show the strategy to optimize the electromagnetic field intensity in the metallic slot and the enhancements there. These results show that a SERS nanosensor with 10² - 10³ EF could be realized on a compatible chip with the well-established CMOS technology.

Appendix

 

Fig. 11 Fluctuation of electromagnetic beating lengths obtained on different lines in the z direction while S_m = 70 nm, S_D = 200 nm and Dis = 20 nm.

Download Full Size | PDF

 

Fig. 12 Distributions of electric field |E| on one z-y cross section in the strip with (a) S_m = 30 nm, x = 15 nm and (b) S_m = 70 nm, x = 35 nm while S_D = 200 nm, Dis = 20 nm. The high frequency of field variation in the z direction is caused by the (k₁ + k₂)/2 term in beating where k_1, k₂ are the wave vectors of the even mode and the odd mode.

Download Full Size | PDF

Acknowledgment

The authors are grateful for the support provided by the ROMEO computing center of the University Reims Champagne-Ardenne (https://romeo.univ-reims.fr/). Feng TANG thanks the Chinese Scholarship Council for funding his PhD scholarship in France. This work was performed in the context of the COST Action MP1302 Nanospectroscopy.

References and links

1. G. McNay, D. Eustace, W. E. Smith, K. Faulds, and D. Graham, “Surface-enhanced Raman scattering (SERS) and surface-enhanced resonance Raman scattering (SERRS): a review of applications,” Appl. Spectrosc. 65(8), 825–837 (2011). [CrossRef]   [PubMed]  

2. B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne, “SERS: materials, applications, and the future,” Mater. Today 15(1-2), 16–25 (2012). [CrossRef]  

3. K. C. Bantz, A. F. Meyer, N. J. Wittenberg, H. Im, O. Kurtuluş, S. H. Lee, N. C. Lindquist, S.-H. Oh, and C. L. Haynes, “Recent progress in SERS biosensing,” Phys. Chem. Chem. Phys. 13(24), 11551–11567 (2011). [CrossRef]   [PubMed]  

4. S. Shanmukh, L. Jones, Y.-P. Zhao, J. D. Driskell, R. A. Tripp, and R. A. Dluhy, “Identification and classification of respiratory syncytial virus (RSV) strains by surface-enhanced Raman spectroscopy and multivariate statistical techniques,” Anal. Bioanal. Chem. 390(6), 1551–1555 (2008). [CrossRef]   [PubMed]  

5. S. Efrima and L. Zeiri, “Understanding SERS of bacteria,” J. Raman Spectrosc. 40(3), 277–288 (2009). [CrossRef]  

6. T. Murphy, S. Lucht, H. Schmidt, and H. D. Kronfeldt, “Surface ‐ enhanced Raman scattering (SERS) system for continuous measurements of chemicals in sea‐water,” J. Raman Spectrosc. 31(10), 943–948 (2000). [CrossRef]  

7. K. R. Strehle, D. Cialla, P. Rösch, T. Henkel, M. Köhler, and J. Popp, “A reproducible surface-enhanced raman spectroscopy approach. Online SERS measurements in a segmented microfluidic system,” Anal. Chem. 79(4), 1542–1547 (2007). [CrossRef]   [PubMed]  

8. K. R. Ackermann, T. Henkel, and J. Popp, “Quantitative Online Detection of Low-Concentrated Drugs via a SERS Microfluidic System,” ChemPhysChem 8(18), 2665–2670 (2007). [CrossRef]   [PubMed]  

9. K. Kodate and Y. Komai, “Compact spectroscopic sensor using an arrayed waveguide grating,” J. Opt. A, Pure Appl. Opt. 10(4), 044011 (2008). [CrossRef]  

10. M. Hochberg, T. Baehr-Jones, C. Walker, and A. Scherer, “Integrated plasmon and dielectric waveguides,” Opt. Express 12(22), 5481–5486 (2004). [CrossRef]   [PubMed]  

11. N. Ismail, A. C. Baclig, P. J. Caspers, F. Sun, K. Wörhoff, R. M. de Ridder, M. Pollnau, and A. Driessen, “Design of low-loss arrayed waveguide gratings for applications in integrated Raman spectroscopy,” in Conference on Lasers and Electro-Optics, (Optical Society of America, 2010), paper CFA7. [CrossRef]  

12. N. Ismail, L.-P. Choo-Smith, K. Wörhoff, A. Driessen, A. C. Baclig, P. J. Caspers, G. J. Puppels, R. M. de Ridder, and M. Pollnau, “Raman spectroscopy with an integrated arrayed-waveguide grating,” Opt. Lett. 36(23), 4629–4631 (2011). [CrossRef]   [PubMed]  

13. N. Ismail, F. Sun, G. Sengo, K. Wörhoff, A. Driessen, R. M. de Ridder, and M. Pollnau, “Improved arrayed-waveguide-grating layout avoiding systematic phase errors,” Opt. Express 19(9), 8781–8794 (2011). [CrossRef]   [PubMed]  

14. Y. Jun, R. Kekatpure, J. White, and M. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008). [CrossRef]  

15. G. Veronis and S. Fan, “Guided subwavelength plasmonic mode supported by a slot in a thin metal film,” Opt. Lett. 30(24), 3359–3361 (2005). [CrossRef]   [PubMed]  

16. C. Delacour, S. Blaize, P. Grosse, J. M. Fedeli, A. Bruyant, R. Salas-Montiel, G. Lerondel, and A. Chelnokov, “Efficient directional coupling between silicon and copper plasmonic nanoslot waveguides: toward metal-oxide-silicon nanophotonics,” Nano Lett. 10(8), 2922–2926 (2010). [CrossRef]   [PubMed]  

17. L. Chen, J. Shakya, and M. Lipson, “Subwavelength confinement in an integrated metal slot waveguide on silicon,” Opt. Lett. 31(14), 2133–2135 (2006). [CrossRef]   [PubMed]  

18. E. Le Ru and P. Etchegoin, Principles of Surface-Enhanced Raman Spectroscopy: and Related Plasmonic Effects (Elsevier, 2008).

19. S. Bisschop, A. Guille, D. Van Thourhout, Z. Hens, and E. Brainis, “Broadband enhancement of single photon emission and polarization dependent coupling in silicon nitride waveguides,” Opt. Express 23(11), 13713–13724 (2015). [CrossRef]   [PubMed]  

20. B. De Geyter, K. Komorowska, E. Brainis, P. Emplit, P. Geiregat, A. Hassinen, Z. Hens, and D. Van Thourhout, “From fabrication to mode mapping in silicon nitride microdisks with embedded colloidal quantum dots,” Appl. Phys. Lett. 101(16), 161101 (2012). [CrossRef]  

21. M. K. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE J. Sel. Top. Quant. 2(2), 236–250 (1996). [CrossRef]  

22. Z. Yang, Q. Li, F. Ruan, Z. Li, B. Ren, H. Xu, and Z. Tian, “FDTD for plasmonics: Applications in enhanced Raman spectroscopy,” Chin. Sci. Bull. 55(24), 2635–2642 (2010). [CrossRef]  

23. A.-S. Grimault, A. Vial, and M. L. De La Chapelle, “Modeling of regular gold nanostructures arrays for SERS applications using a 3D FDTD method,” Appl. Phys. B 84(1-2), 111–115 (2006). [CrossRef]  

24. H. C. Kim and X. Cheng, “SERS-active substrate based on gap surface plasmon polaritons,” Opt. Express 17(20), 17234–17241 (2009). [CrossRef]   [PubMed]  

25. S.-L. Chuang, “Application of the strongly coupled-mode theory to integrated optical devices,” IEEE J. Quantum Electron. 23(5), 499–509 (1987). [CrossRef]  

26. R. Salas-Montiel, A. Apuzzo, C. Delacour, Z. Sedaghat, A. Bruyant, P. Grosse, A. Chelnokov, G. Lerondel, and S. Blaize, “Quantitative analysis and near-field observation of strong coupling between plasmonic nanogap and silicon waveguides,” Appl. Phys. Lett. 100(23), 231109 (2012). [CrossRef]