Abstract

Metal nanoparticle arrays have proved useful for different applications due to their ability to enhance electromagnetic fields within a few tens of nanometers. This field enhancement results from the excitation of various plasmonic modes at certain resonance frequencies. In this article, we have studied an array of metallic nanocylinders placed on a thin metallic film. A simple analytical model is proposed to explain the existence of the different types of modes that can be excited in such a structure. Owing to the cylinder array, the structure can support localized surface plasmon (LSP) modes. The LSP mode couples to the propagating surface plasmon (PSP) mode of the thin film to give rise to the hybrid lattice plasmon (HLP) mode and anti-crossing phenomenon. Due to the periodicity of the array, the Bragg modes (BM) are also excited in the structure. We have calculated analytically the resonance frequencies of the BM, LSP and the corresponding HLP, and have verified the calculations by rigorous numerical methods. Experimental results obtained in the Kretschmann configuration also validate the proposed analytical model. The dependency of the resonance frequencies of these modes on the structural parameters such as cylinder diameter, height and the periodicity of the array is shown. Such a detailed study can offer insights on the physical phenomenon that governs the excitation of various plasmonic modes in the system. It is also useful to optimize the structure as per required for the different applications, where such types of structures are used.

© 2015 Optical Society of America

1. Introduction

Metallic structures at nanometric scale, smaller than the wavelength of light, have been studied in plasmonics for some time now due to their ability to enhance local electromagnetic field in their vicinity [1, 2]. Such enhancement of the local field has been attributed to the plasmon polaritons excited in such structures. In isolated metallic nanoparticles, the incident light can interact with the surface electrons of the conduction band of the metal, and the collective oscillations of these electrons can give rise to intense local electromagnetic fields at the metal-dielectric interface. This resulting localized surface plasmon (LSP) has been effectively used for numerous applications such as surface-enhanced Raman scattering (SERS), drug delivery, chemical sensing, cancer therapy, and new photonic devices [3–6]. The typical penetration depths of the confined field close to the metallic surface are of the order of a few tens of nanometers, and thus these nanoparticles can work as excellent transducers of local refractive index changes, which can be used for various applications of biomolecular detection. One such technique is the surface plasmon resonance (SPR) detection. However, unique nanoparticles have proved to be less efficient than thin films for this application due to their low spectral dispersion and weak scattering cross-sections.

Uniform metal-dielectric interfaces can sustain propagating surface plasmon polaritons (PSP), which have large spectral dispersion and are more conventionally used for SPR detections. Recent work has been aimed at coupling the excitation of these two plasmon polaritons by nanostructuration of the metal-dielectric interface [7–9]. Nanostructuration can induce coupling between various plasmonic modes excited in the structures [10–12]. Such couplings have been extensively studied, and various models have been developed to explain the existence of different modes in structures [13–15]. In most of the above cited articles, such coupling has been described as Fano-like resonances. However we will show in our work that the coupling between two plasmonic modes can be described by a harmonic oscillator model and not by Fano-resonances. The plasmonic modes which participate in the coupling are rather both “broad states” and Fano resonance occurs only for coupling of “broad” and “discrete” states.

In this article, we study an array of metallic nanoparticles placed on a thin metallic film. Such a structure is promising for sensor applications due to its ability to harmonically couple the LSP and PSP modes. Similar structures have been studied recently but with a sandwiched spacer layer between the nanostructures and the uniform film [16–18]. However, such a sandwiched dielectric layer, because it tends to concentrate the electromagnetic field into it severely limits the application of such structures for biodetection. In a recent publication [19], we have demonstrated that such all-metallic structure can give rise to the hybrid lattice plasmon (HLP) mode, which has a high field confinement characteristic of the LSP, but at the same time a high dispersion similar to the PSP. In order to optimize a structure for different applications, it is important to understand the basic mechanism behind the excitation of each plasmonic mode present in the structure. Such was not discussed in the above mentioned recent publication which was based on electric field properties of the modes rather than the mechanism of excitation of the modes. Modes similar to the ones presented here have been found in nanoparticle arrays on metallic thin film [20–23]. However, the complete mechanism of the mode excitation in the structure with analytical formulations, and its dependence on structural parameters was not discussed in the above-mentioned publications. We put forward a simple analytical model to predict the existence of different plasmonic modes and their excitation. In this model, we study the dependence of the structural parameters namely the periodicity, and the diameter of the cylinders on the coupling between the LSP and the PSP modes. These numerical calculations are furthermore validated by both rigorous numerical methods and experimental results obtained with a SPR imaging setup working in the Kretschmann configuration.

2. Numerical methods for rigorous calculations

The structure studied for this work consists of a gold nanocylinder array with a diameter D, a height h2, and a period Λ. The array is placed on a gold film of height (h1) of 30 nm. The refractive index of gold used for calculations are the values of Johnson and Christy [24]. The medium surrounding the cylinders is water (refractive index nw), keeping in mind the applications of these structures to biomolecular detection. The medium below the gold film is considered to be semi-infinite with the refractive index of BK7 glass (ng).

The numerical model used is a combination of two well-known methods namely the Fourier modal method (FMM) and the finite element methods (FEM) [19, 25, 26]. However, such rigorous numerical methods are time consuming and have high memory requirements. The time and memory requirements of such methods often become unreasonable even with the availability of commercial software and powerful computers [27]. We propose a simple analytical model, which can be used furthermore to better understand the physical excitation of the various modes, and calculate their resonance frequency dispersions with negligible requirements in terms of calculation time and memory. The analytical model was validated by rigorous numerical simulations and also by experimental results.

The structure geometry and a brief scheme of the rigorous calculation used are shown in Fig. 1. For the calculation, the light was considered to be TM polarized (electric field along x and z and magnetic field along y as per the coordinates in Fig. 1), because a component perpendicular to the metal-dielectric interface (z) is required to excite the PSP. For TE polarized light only the LSP can be excited, and thus all the other plasmonic modes based on the PSP, studied in this article were verified to be non-existent in the calculations and experiments.

 

Fig. 1 The studied structure geometry consists of an array of metallic cylinders of diameter D and height h2 placed on a thin metallic film of height h1. The refractive index on the side of the array was taken as nw while that on the other side was ng. A sketch of the numerical method is also shown, which uses a mesh around the nanostructured region to calculate the S matrix by FEM, and then uses FMM to calculate the far-field response of the system.

Download Full Size | PPT Slide | PDF

3. Analytical model for the plasmonic modes in the structure

3.1 The localized surface plasmon mode

The presence of the nanocylinders gives rise to a localized surface plasmon (LSP) mode. The resonance frequencies (ω = k0c where k0 is the free space wave-vector) for the LSP modes in the case of isolated nanoparticles can be found from the equation of the polarizability given by

α(ω)=const×nm2(ω)nd2nd2+L(nm2(ω)nd2)

where nm and nd are the refractive indices of metal and dielectric surrounding the cylinders, respectively.

We must mention here that the pole of the polarizability function is sufficient to calculate the resonance frequencies only for isolated nanoparticles. In this article, we will use Eq. (1) to calculate the resonance frequencies, and then demonstrate that this value can be used as a starting point to calculate the resonance frequencies of the other plasmonic modes that result from the coupling of LSP with the PSP. The parameter L is called the depolarization factor, and depends on the shape and size of the particles [28, 29]. L for cylinders can be written as L = 1-((h22)/(h22 + D2))1/2 where h2 is the height of the cylinder and D its diameter. This relation is similar to those obtained for dielectric structures [30, 31] however they also apply for metal cylinders presented in this work. It should be noted here that the depolarization factor used depends largely on the cylinder height, and thus the LSP mode that is excited, is oriented along the axis of the cylinder. To excite this mode, we need an electric field component along the cylinder axis (z-axis), and thus, this mode can be excited only for TM configuration. For TE configuration, only the LSP mode perpendicular to the cylinder axis can be excited and the relation for L will be different. However, we will not consider this mode in this article.

It has been shown elsewhere that the effect of the substrate can be analytically calculated using the pseudo-particle concept [32, 33], and the method of images [34]. In such a model, the refractive index of the medium surrounding the particles must be replaced with an effective refractive index (ne), which can be given as

ne2=nd2[1+ηT/1+γ1+ηT/1γ]

where γ = 1/(1-2L) and η = (nd2-nm2)/(nd2 + nm2) considering the substrate as the metallic film. The factor T depends on the shape, and the aspect ratio of the particles. For the cylinders, it can be evaluated to be T = −3ndχ/(π(1-2L)). The analytical calculation of α(k0) is shown in Fig. 2 (left) for a cylinder of height 30 nm, and diameter 50 nm as a function of k0. When the cylinder is supported by a metallic film, the resonance frequencies shift to lower energies and there is also a narrowing of the resonance linewidth.

 

Fig. 2 Left, the analytically calculated polarizability α(k0) for a nanocylinder of 30 nm height and 50 nm diameter in a homogenous medium nw (in red). The same for the cylinder placed on a semi-infinite gold medium (in blue). The calculated LSP frequency for the later configuration is k0 = 8.87 µm−1. Center, the HLP mode (green) dispersion, which results from the harmonic coupling of the LSP and PSP. Right, the calculated dispersion (k0-neff) for the PSP in a gold film with plasmons propagating in the medium nw. The resonance frequencies of the LSP (blue solid) and the PSP (blue dotted) are also shown. For this scheme, the period of the array was taken as 180 nm.

Download Full Size | PPT Slide | PDF

3.2 Harmonic coupling for the LSP and the PSP

The uniform gold layer can support the propagating surface plasmon (PSP) mode in the structure, the dispersion relation of which is given by the well-known equation

kpsp:d=k0nd2nm2nd2+nm2

The PSP mode propagates along the metal-dielectric interface, and has a propagation length of the order of few µm and penetration depths of around 150 nm. In Fig. 2 (right), the dispersion of the PSP is shown as a function of k0 and neff = kx/k0, where kx is the in plane wave-vector in the direction of the propagation of the PSP. We choose to use the notation neff inspired from its use in guided optics, mentioned in some plasmonic literature [35, 36], and as used in our recent publication [19]. In respect to plasmonic modes, kx serves as a direct representation of the dispersion. However, in terms of experimental configuration using neff directly shows the range of values that can be accessed, from 0 to that which corresponds to the refractive index of the incident medium. Also, for a dispersion map with respect to kx-k0 as it conventionally used, the PSP lies within a sharp cone between the light-line of the two dielectric media surrounding the metal film. In a representation neff-k0 this zone is broadened and thus easier to visualize.

We will now suppose that the modes in the complete structure can be explained by the combination of two resonant plasmonic modes namely the LSP and the PSP. For the range of values of neff, where both the modes can be excited, we will consider a harmonic coupling between them. Such harmonic coupling can be treated classically as shown by Novotny et al. [37] For two oscillators with resonance frequencies of ω1 = k1c and ω2 = k2c, the eigen-frequencies of the resulting characteristic equation in presence of coupling can be written as

ωHLP±2=12[ω12+ω22±(ω12ω22)2+4κ2]

where κ is a coupling parameter, and the only free parameter used in this model. The scheme of the coupling is displayed in Fig. 2. The coupling parameter κ has a dimension of 1/τ2 where τ has a unit of time (s). We have found that this value of τ does not depend on the periodicity of the structure, and depends weakly on the aspect ratio of the nanocylinders. The coupling parameter can be written as κ = (1/τ2) × (h2 + D)/Λ. This dependency, inversely proportional to period Λ, and directly proportional to h2 + D, will be justified from the results presented in subsequent sections of this article. Thus, the only parameter needed to fit for our results will be τ, and its value was found to be 0.37 ± 0.03 fs by fitting the rigorous numerical calculations with Eq. (4). We have used this same unique value for all the calculations.

Figure 3 shows the absorption map obtained by numerical calculations as a function of k0 and neff for Λ = 180 nm, and Λ = 300 nm for cylinder height of h2 = 30 nm, and D = 50 nm. The uniform gold film width (h1) was taken to be 30 nm. The resonance frequencies of the LSP and PSP are displayed (blue solid and blue dashed, respectively). The PSP splits around the LSP giving two branches of the coupled mode which we call the Hybrid Lattice Plasmon (HLP), the HLP+ with higher frequencies and the HLP- with lower frequencies. This phenomenon of anti-crossing and the existence of a bandgap are fundamental in cases of harmonic coupling between two oscillators, and the width of the bandgap is proportional to the coupling parameter κ [37, 38]. The analytical calculation of the resonance frequencies of the HLP given by Eq. (4), is also plotted for comparison. We observe that the dispersion of the HLP mode as calculated by Eq. (4) fits remarkably well to the numerically calculated absorption maxima of the structure.

 

Fig. 3 . (a) The normalized absorption (A) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm, and period Λ = 180 nm with the medium around the nanocylinders of refractive index nw. The lightline in the medium is defined as neff = nw. The proposed analytical calculation of the dispersion of different modes of the system are also shown: LSP (blue solid), PSP (blue dashed), HLP (green), and BMs (black solid and dashed). (b) Same as (a) for period Λ = 300 nm.

Download Full Size | PPT Slide | PDF

We must mention here that to excite the plasmonic modes, we must match the k0 and neff of the incident light to that of the modes. For neff < nw, the incident light can be coupled directly to the modes of the structure by illuminating it with a plane-wave from water at an incident angle θ, and the corresponding neff = nwsin(θ). To access the values of neff > nw, we need to use the Kretschmann configuration (with refractive index of the incident medium > nw) to excite the modes beyond the light-line in water.

3.3 The Bragg modes in a periodic structure

In Fig. 3, we also observe the existence of other bandgaps that can be attributed to the coupling of the HLP (and in turn the PSP) with the Bragg Modes (BM) of the structure. Such modes were reported in our earlier publication for a binary metallic grating, which shows that the existence of the BM is independent of the structure shape [39, 40]. In short, the presence of the array of nanocylinders affects the PSP, which is reflected, leading to an interference of the contra-propagating plasmons. Such interferences give rise to the Bragg-modes (BM), which results in a confinement of the electromagnetic fields around the nanostructures. The dispersion of these modes as shown elsewhere can be written as [41]

kBM=kpsp:d±mkB

where kB = 2π/Λ is the Bragg wave-vector, Λ is the periodicity of the structure and m is the order of the mode. For this type of structure, we can have two BMs resulting from the interference of the PSP propagating in the two different dielectric media on two sides of the metal film. The BM at higher frequencies (higher k0) results from the interference of the PSP propagating in the medium surrounding the cylinders (water, BMw, calculated using nd = nw in Eqs. (3) and Eq. 5) while that at lower k0 results from the PSP in the substrate (glass, BMg, calculated using nd = ng in Eqs. (3) and Eq. 5). They are shown in Fig. 3. Below the critical angle (neff < nw), only the BM can be excited, and the absorption of these modes is very weak as compared to the HLP mode. For values of neff, where the PSP and in turn the HLP are excited, we have a harmonic coupling between them, and the BM to form a bandgap. From Fig. 3(b), the absorption maxima are slightly shifted from the analytically calculated HLP- for values of k0 larger than the BM frequencies. This is due to splitting of the HLP by its coupling to the BM. A relation similar to Eq. (4) can be written to describe this coupling between the HLP and BM. We will not consider this for simplicity.

4. Dependence of the structural parameters on the coupling

4.1 Dependence of periodicity of the structure

The periodicity of the structure was varied within the range of 100 nm to 550 nm. In this range, the resonance frequencies of the LSP do not depend on the periodicity as the mode is strongly confined close to the cylinders with a penetration depth of a few tens of nanometers. Interaction between adjacent cylinders is negligible. The complete absorption maps as a function of k0 and neff for different periods of the structure were calculated [see, the Appendix Fig. 9].

Figure 4 summarizes the resonance frequencies of all the different modes (absorption maxima calculated by rigorous numerical methods) as a function of the structure period within the range of k0 = 5.2 µm−1 to 10.5 µm−1 for neff = 1.42. We can observe that the resonance frequencies of HLP+ and HLP- approach the frequency of the LSP for increasing period. We see in Eq. (4) that as the coupling parameter decreases, the frequencies of HLP approach the frequencies ω1 and ω2 which are of the PSP and the LSP respectively. Using κ = (1/τ2) × (h2 + D)/Λ, the calculated resonance frequencies of the HLP mode fits perfectly with absorption maxima of the structures obtained numerically and thus justifies that κ is proportional to 1/Λ The large dispersion of the HLP mode, similar in that respect to a classical propagating plasmon and the fact that the resonance frequency of the HLP can be tuned by changing the periodicity of the structure, can prove useful for various surface plasmon based applications.

 

Fig. 4 The resonance frequencies (k0) of all the modes in the structure (D = 50 nm, h2 = 30 nm) manifest as absorption maxima in the dispersion map calculated by rigorous numerical method (red dots) as a function of array period for neff = 1.42. We have superposed the analytically calculated frequencies of the modes as a function of period: LSP (blue), HLP (green), BMs calculated for kB = 2π/(Λ) (black solid and dashed) and BMs for kB = 2π/(Λ + D) (red dashed and solid).

Download Full Size | PPT Slide | PDF

Figure 4 also shows the numerical and analytical resonance frequencies of the different BM, with orders m in Eq. (5), which can be generated in these structures. For higher periods, the BM resulting from the periodicity of Λ + D can also be excited, satisfying Eq. (5) with kB = 2π/(Λ + D) and m = 2.

At the frequencies where the BM is excited, we have the appearance of bandgaps and absorption maxima around those bandgaps. The excellent agreement between the analytical model and the rigorous numerical calculations, over a wide range of periods, further validates the proposed analytical model which can be effectively used to calculate the resonance frequencies of the plasmonic modes present in the structure.

4.2 Effect of height and diameter of the cylinders

There is no effect of the gold film height (h1) on the resonance frequencies of the modes, and this was shown in our recent publication [19], and also by Chang et al [20] in a similar structure. Indeed, h1 affects only the PSP, and thus it can affect the contrast of absorption but not the resonance frequencies. It can be seen from Eq. (3) that the wave-vector of the PSP is independent of h1 and thus the dispersion and in turn the resonance frequencies are independent of the film height.

For the cylinders, the height (h2) and diameter (D) were varied within the range of 30 nm to 90 nm for Λ = 350 nm [see the Appendix, Fig. 10]. As can be seen from Eq. (1), the LSP resonance frequencies decrease (resonance wavelengths increase) with increasing height, and increase slightly with increasing diameter. It is interesting to note that this trend is opposite to what has been reported for arrays of cylinders on a glass substrate [42–44]. Indeed, in this configuration, the electric field along z-axis plays a major role in the excitation of the LSP, and thus the LSP is oriented along the cylinder axis. In the above cited works, the LSP mode perpendicular to the cylinder axis (x-y plane) was studied, and thus their dependences on D and h2 are opposite compared to that we report here. It must be noted that the Rayleigh approximation used to calculate the polarizability (α) for the cylinders breaks down for cylinders with diameters comparable to the wavelength of light. Thus we notice some deviations for analytical calculations from the numerical calculations for large diameters (D = 90nm, Fig. 10).

The resonance frequencies of the LSP as calculated by the analytical model, are shown in Fig. 5 (blue line) for different h2 and D for neff = 1.45. The resonance frequencies of HLP+ and HLP- (absorption maxima) calculated by the rigorous numerical method are also displayed in Fig. 5 (red dots) along with the analytically calculated HLP dispersion (green line). The HLP modes are pushed further away from the LSP for larger heights of the cylinder. This trend is opposite to what we have for increasing periods. This result indicates that the coupling parameter (κ) is proportional to h2. Now comparing Fig. 5(a) with Fig. 5(b) we see that the resonance frequencies of the HLP modes also pushed away from that of the LSP for larger diameters and thus κ is also proportional to D. Using κ = (1/τ2) × (h2 + D)/Λ we have an excellent fit with the absorption minima calculated numerically and the analytical model.

 

Fig. 5 (a) The resonance frequencies (k0) of HLP modes in the structure (Λ = 350 nm, D = 50 nm) manifest as absorption maxima in the dispersion map calculated by rigorous numerical method (red dots) as a function of cylinder height (h2) for neff = 1.45. We have superposed the analytically calculated frequencies of the modes as a function of h2: LSP (blue), HLP (green). (b) For D = 90 nm with the same period as previously.

Download Full Size | PPT Slide | PDF

Like the period, the height of the nanocylinders also has a major effect on the resonance frequencies of the HLP which can be tuned over a range of k0 = 6 µm−1 - 9 µm−1.

4.3 Reflection and transmission characteristics of the modes

The far field reflection and transmission properties of the structure, as a function of the incident wavelength and angle, needs to be studied as it corresponds to what is generally measured experimentally in an SPR setup. This is the subject of this section.

The reflection and transmission maps of the structure with period of 340 nm, h2 = 30 nm and D = 50 nm are displayed in Fig. 6. For this calculation, the Kretschmann configuration was considered to have access to all the values of neff from 0 to the light-line in glass (ng). Below the light-line in water neff = nw only the BM can be excited. We also observe transmission minima at the resonance frequency of the LSP. For neff > nw, we have total internal reflection, and we expect complete reflection and zero transmission. The excitation of the HLP mode can be seen from the drastic drop in reflection. However, an interesting feature of the HLP is that it can also radiate up to 25% of the energy into transmission. This transmission was found strictly for HLP- and for the resonance frequencies greater than the resonance frequencies of the BMw. Such transmission was reported numerous times for various structured arrays of nanoholes [45–47]. We observe this transmission only for the HLP- mode and for frequencies above the frequencies of BMw. Though no clear explanation for this phenomenon was found we believe that the transmission may be a result of the coupling of the HLP with the BMw, which itself is caused by the PSP propagating on the side of the cylinders.

 

Fig. 6 The normalized reflectivity (R) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm and period Λ = 340 nm with the medium around the nanocylinders of refractive index nw in the Kretschmann configuration. The lightline in the medium is defined as neff = nw. The analytical calculation of the dispersion of different modes of the system are also shown: LSP (blue solid), PSP (blue dashed), HLP (green) and BMs (black and red solid and dashed same as Fig. 4). (b) The transmission (T) for the same parameters.

Download Full Size | PPT Slide | PDF

5. Experimental results

The nanostructure studied was fabricated using e-beam lithography on a BK7 glass substrate and characterized with SEM measurements. On the same chip, we were able to obtain different gold nano cylinders arrays with a diameter of 50 nm and different periods ranging from 150 nm to 400 nm. This allows us to simultaneously observe all nanostructurated areas using an SPRI setup working in Kretschmann configuration. In this configuration, we have access to the values of neff beyond the critical angle of glass-water interface (neff > nw), and thus excite the PSP and all the other modes presented in this article.

The complete dispersion maps as a function of wavelength (λ) and incident angle (θ), were extracted for each zone with different periods of structures [see the Appendix, Fig. 11]. As an example, the complete reflectivity dispersion map as a function of k0 = 2π/λ and neff = ngsinθ (the refractive index of BK7 glass taken as ng = 1.513) for Λ = 300 nm is shown in Fig. 7(d). The experimental results are very close to the dispersion maps calculated numerically in Fig. 3(b) for the same structural dimensions. The contrast of the experimental reflectivity is a bit lower than that shown in Fig. 6(a) or that of the absorption map of Fig. 3(b), and this is mainly a result of absorption of the adhesion layer (2 nm of titanium).

 

Fig. 7 (a) Scheme of the SPR imaging system used to characterize the fabricated nanostructure in the Kretschmann configuration. (b) An image of the structured chip with 3 × 6 zones as obtained by the SPR imaging system. Each zone has a size of 500 × 500 µm2 and has the same structural parameters (diameter and periodicity of cylinders) along the rows. The period is changed from 150 nm to 400 nm along the columns as shown in the figure. (c) SEM images of cylinder with a diameter of 50 nm and periods of 150 nm, 250 nm and 400 nm. (d) The experimental reflectivity (R) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm and period Λ = 300 nm. The experimental reflectivity map should be compared to the numerical absorption map of Fig. 3(b), which has the same structural dimensions. The analytical calculation of the dispersion of different modes of the system is also shown.

Download Full Size | PPT Slide | PDF

The results are summarized in Fig. 8(a) where we have shown the normalized reflectivity (TM reflectivity divided by TE reflectivity) spectra for each period (Λ) at an incidence angle (θ) of 71.14°, and corresponding to a value of neff = 1.43. The different minima of reflectivity observed experimentally are related to the various modes excited in the structure. The resonance frequencies (reflectivity minima) of the different modes are shown as a function of period in Fig. 8(b). This is similar to the results discussed in section 4.1. As in Fig. 4, we have also plotted the analytically calculated dispersions as a function of period for the HLP and the BMs. For the analytical calculation of the HLP, the coupling parameter was kept at the value of κ = (1/τ2) × (h2 + D)/Λ with τ = 0.37 fs as used before. The experimental resonance frequencies are in close agreement with the analytically calculated dispersions for all the modes.

 

Fig. 8 (a) Normalized reflectivity spectra at θ = 71.14° for different period (Λ) of the structure. Arrows show the reflectivity minima, which correspond to the various modes excited in the structure. (b) The resonance frequencies (k0) of all the modes (minima of reflectivity) are shown as red squares as a function of array period. The error bars correspond to the minimum step of incident wavelength (10 nm) used for the experiment. We have superposed the analytically calculated frequencies of the modes as a function of period: LSP (blue), HLP (green), BMs calculated for kB = 2π/(Λ) (black solid and dashed) and BMs for kB = 2π/(Λ + D) (red dashed and solid).

Download Full Size | PPT Slide | PDF

6. Conclusion

We have studied in detail an array of gold nanocylinders with an underlying thin gold film in TM configuration. We have analytically calculated the LSP resonance frequencies for nanocylinders on a metallic substrate with the electric field parallel to the cylinder axis. We demonstrated that the resonance frequencies of the LSP mode, in this configuration, decrease rapidly with increasing height (h2), while increasing slightly with increasing diameter (D), which is opposite to the expected trends in arrays on a glass substrate. For values of neff = k0/kx > nw, we can have a coupling between the LSP mode of the cylinders, and the PSP mode of the gold film. This HLP mode dispersion was calculated using a model based on harmonic coupling of two oscillators. The coupling parameter dependency on the structure dimensions is given by κ = (1/τ2) × (h2 + D)/Λ with τ = 0.37 fs. This was obtained by fitting the proposed analytical model to rigorous numerical calculations. The existence of Bragg modes (BM) is also shown, which appears in the dispersion map as weak extinctions below the critical angle, and as bandgaps above the critical angle. Reflection and transmission characteristics of the modes in the Kretschmann configuration are also shown. Finally, this analytical model was experimentally confirmed by SPR measurements on nanostructurated samples fabricated by e-beam lithography.

The proposed analytical model can accurately calculate the resonance frequencies of the various modes of the system. The model also offers a complete physical understanding of the modes present in such a structure. The HLP mode is highly tunable with structural parameters such as diameter D and height h2 while the BM depends solely on the periodicity Λ of the array. Similar structures are widely used for SERS and SPR biosensors, and the HLP mode can help to increase the sensitivity of such detection systems. Other modes, such as the BM, can prove to be useful to confine the electromagnetic field at nanometric scales around metallic nanoparticles. Thus, the proposed analytical model can help to optimize such structures for various applications.

Appendix

Numerical Simulations. The electric and the magnetic fields can be calculated for periodic structures using the matrix formulation of FMM. A two-dimensional array can be sliced along the plane parallel to the array, and the electric and magnetic fields along each slice can be related to the adjoined slice by the S-matrix [48]. However, FMM formulation is not suitable for complex structure geometry particularly involving metallic media, and leads to a convergence problem. FEM can overcome this problem by using a fine mesh to represent the structure geometry, but consumes enormous amount of memory and computational times. The in-house code developed in Matlab for this work, calculates the S-matrix (or related matrices that relates the electromagnetic fields at different slices along z-axis as shown in Fig. 1) using FEM for the nanostructured section of the geometry. Then, using the matrix formulation of FMM, we can relate the fields calculated around the nano-structures, to the far-field transmission (T) and reflection (R) of the complete array as a function of incident frequency (ω) and in-plane wave-vector (kx).

Nanostructure fabrication. The gold nanocylinder array was fabricated by electron beam lithography to assure homogeneity, and have stable control of the size and shape of nanostructures over a large area (500 × 500 µm2). After a cleaning step of BK7 using a Piranha solution, the gold film (height h1) was deposited by electron beam evaporation (EBE) on a thin layer of titanium (2 nm), which is used as adhesion layer. For the e-beam lithography step, a layer of polymethylmethacrylate A2 (PMMA A2) is exposed at a current of 1.8 to 2.2 nA with different dose. A solution of methylisobutylketone and isopropanol is used to develop the PMMA and gold nanocylinders (height h2) were deposited by another step of EBE. The sample was totally cleaned by acetone in order to remove the resist, and in O2 plasma to remove other residues. The film heights were measured by ellipsometry-spectroscopy and X-ray measurements with a relative uncertainty under 10%. The measured gold film height h1 = 31 nm, and that of gold nanocylinders h2 = 32 nm.

In the Fig. 7(c), we have presented the SEM images for several areas of nanocylinders with periodicities of 150 nm, 250 nm, and 400 nm. A mean diameter of around 53 ± 3 nm was found for the small periodicity (150 nm) by statistical analyses of SEM image treated with the Otsu’s method in order to extract the diameter of each nanostructure. For larger periods, due to the limited proximity charge effect during the e-beam lithography process, the mean diameter is around 51 ± 3 nm and closer than the simulated dimension of 50 nm.

Experimental setup. The SPR imaging system is based on a spectral scanning modality and the details have been previously reported [49, 50] and is shown in Fig. 7(a). The incident wavelength (λ) from a halogen lamp, was varied within a range of 550 nm to 1000 nm with steps of 10 nm using a motorized monochromator (iHR 320, HORIBA Scientific). A motorized polarizer was used to switch between TM and TE polarization. The angle of incidence (θ) was varied within the range of 63-78° with steps of 0.5°, which corresponds to the range of neff = ngsinθ = 1.35-1.48. The structure was placed in a micro-flow cell containing water with dimensions of 1 cm in diameter and 90 µm in depth, and the temperature in the flow-cell was controlled with a precision of 0.01°C. The light after reflection from the structure was imaged using a CCD camera (Pixelfly QE, 1280×1024 pixels with a full well capacity of 18000 e-). The normalized reflectivity was calculated by dividing the TM images by TE images.

Complete absorption and reflectivity dispersion maps

 

Fig. 9 The normalized absorption (A) dispersion maps calculated by numerical methods with varying period (Λ) as a function of k0 and neff for h2 = 30nm, D = 50nm. The analytically calculated dispersion of the various modes is also shown which fits accurately to the rigorously calculated numerical results.

Download Full Size | PPT Slide | PDF

 

Fig. 10 The normalized reflectivity (R) dispersion maps calculated by numerical methods with varying h2 and D function of k0 and neff for Λ = 350nm. The analytically calculated dispersion of the various modes is also shown and the color legend is same as Fig. 9.

Download Full Size | PPT Slide | PDF

 

Fig. 11 The normalized reflectivity (R) dispersion maps obtained experimentally with varying period (Λ) as a function of k0 and neff for h2 = 30nm, D = 50nm. The analytically calculated dispersion of the various modes is also shown and the color legend is same as Fig. 9.

Download Full Size | PPT Slide | PDF

Acknowledgments

This work is supported by the IDI 2012 project funded by the IDEX Paris-Saclay (ANR-11-IDEX-003-02), ANR P2N (ANR-12-NANO-0016), CNANO IDF as well as LUMAT for partial funding of the project. IOGS/CNRS is also part of the European Network of Excellence in BioPhotonics: Photonics for Life (P4L).

References and links

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef]   [PubMed]  

2. J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007). [CrossRef]  

3. T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014). [CrossRef]   [PubMed]  

4. P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008). [CrossRef]   [PubMed]  

5. G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006). [CrossRef]  

6. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010). [CrossRef]   [PubMed]  

7. S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015). [CrossRef]  

8. A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013). [CrossRef]   [PubMed]  

9. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010). [CrossRef]   [PubMed]  

10. N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75(23), 235426 (2007). [CrossRef]  

11. Y. Chu and K. B. Crozier, “Experimental study of the interaction between localized and propagating surface plasmons,” Opt. Lett. 34(3), 244–246 (2009). [CrossRef]   [PubMed]  

12. C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013). [CrossRef]  

13. T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010). [CrossRef]   [PubMed]  

14. J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013). [CrossRef]   [PubMed]  

15. Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012). [CrossRef]   [PubMed]  

16. F. Zhou, Y. Liu, and W. Cai, “Huge local electric field enhancement in hybrid plasmonic arrays,” Opt. Lett. 39(5), 1302–1305 (2014). [CrossRef]   [PubMed]  

17. K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013). [CrossRef]  

18. D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund Jr, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012). [CrossRef]   [PubMed]  

19. M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015). [CrossRef]  

20. Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015). [CrossRef]  

21. V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015). [CrossRef]  

22. A. Hohenau and J. R. Krenn, “Plasmonic modes of gold nano-particle arrays on thin gold films,” Phys. Status Solidi 4(10), 256–258 (2010). [CrossRef]  

23. S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015). [CrossRef]  

24. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]  

25. J. P. Hugonin, M. Besbes, and P. Lalanne, “Hybridization of electromagnetic numerical methods through the G-matrix algorithm,” Opt. Lett. 33(14), 1590–1592 (2008). [CrossRef]   [PubMed]  

26. M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

27. D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014). [CrossRef]   [PubMed]  

28. C. Noguez, “Surface plasmons on metal nanoparticles: The influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007). [CrossRef]  

29. R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015). [CrossRef]  

30. A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).

31. A. Mejdoubi and C. Brosseau, “Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031405 (2006). [PubMed]  

32. K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010). [CrossRef]   [PubMed]  

33. T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009). [CrossRef]  

34. V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008). [CrossRef]   [PubMed]  

35. H. Raether, “Surface-plasmons on smooth and rough surfaces and on gratings,” Springer Tr. Mod. Phys. 111, 1–133 (1988).

36. M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009). [CrossRef]   [PubMed]  

37. L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010). [CrossRef]  

38. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996). [CrossRef]   [PubMed]  

39. M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014). [CrossRef]  

40. M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014). [CrossRef]  

41. H. Gao, J. M. McMahon, M. H. Lee, J. Henzie, S. K. Gray, G. C. Schatz, and T. W. Odom, “Rayleigh anomaly-surface plasmon polariton resonances in palladium and gold subwavelength hole arrays,” Opt. Express 17(4), 2334–2340 (2009). [CrossRef]   [PubMed]  

42. D. Barchiesi, S. Kessentini, N. Guillot, M. L. de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21(2), 2245–2262 (2013). [CrossRef]   [PubMed]  

43. J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005). [CrossRef]  

44. X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012). [CrossRef]  

45. F. Marquier, J. Greffet, S. Collin, F. Pardo, and J. Pelouard, “Resonant transmission through a metallic film due to coupled modes,” Opt. Express 13(1), 70–76 (2005). [CrossRef]   [PubMed]  

46. A. T. M. A. Rahman, P. Majewski, and K. Vasilev, “Extraordinary optical transmission: coupling of the Wood-Rayleigh anomaly and the Fabry-Perot resonance,” Opt. Lett. 37(10), 1742–1744 (2012). [CrossRef]   [PubMed]  

47. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998). [CrossRef]  

48. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995). [CrossRef]  

49. M. Nakkach, A. Duval, B. Ea-Kim, J. Moreau, and M. Canva, “Angulo-spectral surface plasmon resonance imaging of nanofabricated grating surfaces,” Opt. Lett. 35(13), 2209–2211 (2010). [CrossRef]   [PubMed]  

50. A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014). [CrossRef]   [PubMed]  

References

  • View by:
  • |
  • |
  • |

  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
    [Crossref] [PubMed]
  2. J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
    [Crossref]
  3. T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
    [Crossref] [PubMed]
  4. P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
    [Crossref] [PubMed]
  5. G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006).
    [Crossref]
  6. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
    [Crossref] [PubMed]
  7. S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
    [Crossref]
  8. A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
    [Crossref] [PubMed]
  9. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
    [Crossref] [PubMed]
  10. N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75(23), 235426 (2007).
    [Crossref]
  11. Y. Chu and K. B. Crozier, “Experimental study of the interaction between localized and propagating surface plasmons,” Opt. Lett. 34(3), 244–246 (2009).
    [Crossref] [PubMed]
  12. C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
    [Crossref]
  13. T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
    [Crossref] [PubMed]
  14. J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
    [Crossref] [PubMed]
  15. Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012).
    [Crossref] [PubMed]
  16. F. Zhou, Y. Liu, and W. Cai, “Huge local electric field enhancement in hybrid plasmonic arrays,” Opt. Lett. 39(5), 1302–1305 (2014).
    [Crossref] [PubMed]
  17. K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
    [Crossref]
  18. D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
    [Crossref] [PubMed]
  19. M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
    [Crossref]
  20. Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015).
    [Crossref]
  21. V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015).
    [Crossref]
  22. A. Hohenau and J. R. Krenn, “Plasmonic modes of gold nano-particle arrays on thin gold films,” Phys. Status Solidi 4(10), 256–258 (2010).
    [Crossref]
  23. S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
    [Crossref]
  24. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [Crossref]
  25. J. P. Hugonin, M. Besbes, and P. Lalanne, “Hybridization of electromagnetic numerical methods through the G-matrix algorithm,” Opt. Lett. 33(14), 1590–1592 (2008).
    [Crossref] [PubMed]
  26. M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).
  27. D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
    [Crossref] [PubMed]
  28. C. Noguez, “Surface plasmons on metal nanoparticles: The influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007).
    [Crossref]
  29. R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015).
    [Crossref]
  30. A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).
  31. A. Mejdoubi and C. Brosseau, “Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031405 (2006).
    [PubMed]
  32. K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
    [Crossref] [PubMed]
  33. T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009).
    [Crossref]
  34. V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
    [Crossref] [PubMed]
  35. H. Raether, “Surface-plasmons on smooth and rough surfaces and on gratings,” Springer Tr. Mod. Phys. 111, 1–133 (1988).
  36. M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
    [Crossref] [PubMed]
  37. L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010).
    [Crossref]
  38. W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
    [Crossref] [PubMed]
  39. M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
    [Crossref]
  40. M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
    [Crossref]
  41. H. Gao, J. M. McMahon, M. H. Lee, J. Henzie, S. K. Gray, G. C. Schatz, and T. W. Odom, “Rayleigh anomaly-surface plasmon polariton resonances in palladium and gold subwavelength hole arrays,” Opt. Express 17(4), 2334–2340 (2009).
    [Crossref] [PubMed]
  42. D. Barchiesi, S. Kessentini, N. Guillot, M. L. de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21(2), 2245–2262 (2013).
    [Crossref] [PubMed]
  43. J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
    [Crossref]
  44. X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
    [Crossref]
  45. F. Marquier, J. Greffet, S. Collin, F. Pardo, and J. Pelouard, “Resonant transmission through a metallic film due to coupled modes,” Opt. Express 13(1), 70–76 (2005).
    [Crossref] [PubMed]
  46. A. T. M. A. Rahman, P. Majewski, and K. Vasilev, “Extraordinary optical transmission: coupling of the Wood-Rayleigh anomaly and the Fabry-Perot resonance,” Opt. Lett. 37(10), 1742–1744 (2012).
    [Crossref] [PubMed]
  47. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
    [Crossref]
  48. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
    [Crossref]
  49. M. Nakkach, A. Duval, B. Ea-Kim, J. Moreau, and M. Canva, “Angulo-spectral surface plasmon resonance imaging of nanofabricated grating surfaces,” Opt. Lett. 35(13), 2209–2211 (2010).
    [Crossref] [PubMed]
  50. A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
    [Crossref] [PubMed]

2015 (6)

S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
[Crossref]

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015).
[Crossref]

V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015).
[Crossref]

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015).
[Crossref]

2014 (7)

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

F. Zhou, Y. Liu, and W. Cai, “Huge local electric field enhancement in hybrid plasmonic arrays,” Opt. Lett. 39(5), 1302–1305 (2014).
[Crossref] [PubMed]

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

2013 (5)

D. Barchiesi, S. Kessentini, N. Guillot, M. L. de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21(2), 2245–2262 (2013).
[Crossref] [PubMed]

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
[Crossref]

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

2012 (4)

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012).
[Crossref] [PubMed]

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
[Crossref]

A. T. M. A. Rahman, P. Majewski, and K. Vasilev, “Extraordinary optical transmission: coupling of the Wood-Rayleigh anomaly and the Fabry-Perot resonance,” Opt. Lett. 37(10), 1742–1744 (2012).
[Crossref] [PubMed]

2010 (7)

M. Nakkach, A. Duval, B. Ea-Kim, J. Moreau, and M. Canva, “Angulo-spectral surface plasmon resonance imaging of nanofabricated grating surfaces,” Opt. Lett. 35(13), 2209–2211 (2010).
[Crossref] [PubMed]

L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010).
[Crossref]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

A. Hohenau and J. R. Krenn, “Plasmonic modes of gold nano-particle arrays on thin gold films,” Phys. Status Solidi 4(10), 256–258 (2010).
[Crossref]

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

2009 (4)

2008 (3)

P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
[Crossref] [PubMed]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

J. P. Hugonin, M. Besbes, and P. Lalanne, “Hybridization of electromagnetic numerical methods through the G-matrix algorithm,” Opt. Lett. 33(14), 1590–1592 (2008).
[Crossref] [PubMed]

2007 (3)

C. Noguez, “Surface plasmons on metal nanoparticles: The influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007).
[Crossref]

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75(23), 235426 (2007).
[Crossref]

2006 (2)

G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006).
[Crossref]

A. Mejdoubi and C. Brosseau, “Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031405 (2006).
[PubMed]

2005 (2)

F. Marquier, J. Greffet, S. Collin, F. Pardo, and J. Pelouard, “Resonant transmission through a metallic film due to coupled modes,” Opt. Express 13(1), 70–76 (2005).
[Crossref] [PubMed]

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

2002 (1)

A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

1996 (1)

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

1995 (1)

1988 (1)

H. Raether, “Surface-plasmons on smooth and rough surfaces and on gratings,” Springer Tr. Mod. Phys. 111, 1–133 (1988).

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Adam, P. M.

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Adibi, A.

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

Appavoo, K.

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Atabaki, A. H.

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Barbillon, G.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Barchiesi, D.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

Bartenlian, B.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Besbes, M.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

J. P. Hugonin, M. Besbes, and P. Lalanne, “Hybridization of electromagnetic numerical methods through the G-matrix algorithm,” Opt. Lett. 33(14), 1590–1592 (2008).
[Crossref] [PubMed]

Bijeon, J. L.

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Borghs, G.

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

Brosseau, C.

A. Mejdoubi and C. Brosseau, “Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031405 (2006).
[PubMed]

Bryche, J.-F.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Cai, W.

Cambril, E.

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
[Crossref]

Canva, M.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

M. Nakkach, A. Duval, B. Ea-Kim, J. Moreau, and M. Canva, “Angulo-spectral surface plasmon resonance imaging of nanofabricated grating surfaces,” Opt. Lett. 35(13), 2209–2211 (2010).
[Crossref] [PubMed]

Chamtouri, M.

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

Chang, Y.

Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015).
[Crossref]

Chen, S.

S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
[Crossref]

Chilkoti, A.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Chong, C. T.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Chu, Y.

Ciracì, C.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Colliex, C.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Collin, S.

Coutrot, A.-L.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Crozier, K. B.

Dal Negro, L.

C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
[Crossref]

Davis, T. J.

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009).
[Crossref]

de Abajo, F. J. G.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

de la Chapelle, M. L.

D. Barchiesi, S. Kessentini, N. Guillot, M. L. de la Chapelle, and T. Grosges, “Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties,” Opt. Express 21(2), 2245–2262 (2013).
[Crossref] [PubMed]

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Dhawan, A.

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

Duval, A.

Ea-Kim, B.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Eftekhar, A. A.

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

Ermini, M. L.

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

Etchegoin, P. G.

P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
[Crossref] [PubMed]

Fernández-Domínguez, A. I.

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Forestiere, C.

C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
[Crossref]

Francescato, Y.

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012).
[Crossref] [PubMed]

Funston, A. M.

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Gallinet, B.

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

Gao, H.

García de Abajo, F. J.

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Gaylord, T. K.

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Ghalila, H.

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

Giannini, R.

R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015).
[Crossref]

Giannini, V.

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012).
[Crossref] [PubMed]

Giessen, H.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Gogol, P.

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
[Crossref]

Gomez, D. E.

T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009).
[Crossref]

Gómez, D. E.

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

Grand, J.

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Grann, E. B.

Gray, S. K.

Greffet, J.

Grosges, T.

Guillot, N.

Hafner, C. V.

R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015).
[Crossref]

Haglund, R. F.

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Halas, N. J.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Henrard, L.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Henzie, J.

Hill, R. T.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Hohenau, A.

A. Hohenau and J. R. Krenn, “Plasmonic modes of gold nano-particle arrays on thin gold films,” Phys. Status Solidi 4(10), 256–258 (2010).
[Crossref]

Homola, J.

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009).
[Crossref] [PubMed]

Hu, J. W.

S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
[Crossref]

Hugonin, J. P.

Jablonku, J.

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

Jiang, Y.

Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015).
[Crossref]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kessentini, S.

Kitson, S. C.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

Kociak, M.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Krenn, J. R.

A. Hohenau and J. R. Krenn, “Plasmonic modes of gold nano-particle arrays on thin gold films,” Phys. Status Solidi 4(10), 256–258 (2010).
[Crossref]

Lagae, L.

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

Lalanne, P.

Lassiter, J. B.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Le Ru, E. C.

P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
[Crossref] [PubMed]

Lee, M. H.

Lei, D. Y.

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Liu, Y.

Liz-Marzan, L. M.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Liz-Marzán, L. M.

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Lodewijks, K.

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

Löffler, J. F.

R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015).
[Crossref]

Lovera, A.

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

Luk’yanchuk, B.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Maier, S. A.

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012).
[Crossref] [PubMed]

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Maillart, E.

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

Majewski, P.

Marquier, F.

Martin, O. J. F.

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

McGuire, F.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

McMahon, J. M.

Mejdoubi, A.

A. Mejdoubi and C. Brosseau, “Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031405 (2006).
[PubMed]

Meng, L. Y.

S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
[Crossref]

Miano, G.

C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
[Crossref]

Mock, J. J.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Moharam, M. G.

Moreau, J.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

M. Nakkach, A. Duval, B. Ea-Kim, J. Moreau, and M. Canva, “Angulo-spectral surface plasmon resonance imaging of nanofabricated grating surfaces,” Opt. Lett. 35(13), 2209–2211 (2010).
[Crossref] [PubMed]

Mulvaney, P.

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Myroshnychenko, V.

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Nakkach, M.

Nelayah, J.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Noguez, C.

C. Noguez, “Surface plasmons on metal nanoparticles: The influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007).
[Crossref]

Nordlander, P.

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Novo, C.

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Novotny, L.

L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010).
[Crossref]

Obelleiro, F.

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

Odom, T. W.

Olivéro, A.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Palpant, B.

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
[Crossref]

Papanikolaou, N.

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75(23), 235426 (2007).
[Crossref]

Pardo, F.

Pastoriza-Santos, I.

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Pelouard, J.

Pendry, J. B.

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Piliarik, M.

Polman, A.

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Pommet, D. A.

Preist, T. W.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

Raether, H.

H. Raether, “Surface-plasmons on smooth and rough surfaces and on gratings,” Springer Tr. Mod. Phys. 111, 1–133 (1988).

Rahman, A. T. M. A.

Ramirez, A.

A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).

Rodríguez-Fernández, J.

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

Royer, P.

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Ryken, J.

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

Sambles, J. R.

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

Sarkar, M.

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

M. Chamtouri, M. Sarkar, J. Moreau, M. Besbes, H. Ghalila, and M. Canva, “Field enhancement and target localization impact on the biosensitivity of nanostructured plasmonic sensors,” J. Opt. Soc. Am. B 31(5), 1223–1231 (2014).
[Crossref]

Schatz, G. C.

Sereda, A.

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

Shams Mousavi, S. H.

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

Smith, D. R.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Solís, D. M.

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

Sonnefraud, Y.

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Špacková, B.

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

Špringer, T.

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

Stephan, O.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Taboada, J. M.

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

Taverna, D.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Tence, M.

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Van Dorpe, P.

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

Van Duyne, R. P.

G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006).
[Crossref]

Van Roy, W.

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

Vasilev, K.

Vernon, K. C.

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009).
[Crossref]

Vial, A.

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Vo-Dinh, T.

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

Wang, X. L.

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
[Crossref]

Wiley, B. J.

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Yang, Z. L.

S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
[Crossref]

Yannopapas, V.

V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015).
[Crossref]

Young, M. A.

G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006).
[Crossref]

Zehe, A.

A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).

Zheludev, N. I.

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

Zhou, F.

ACS Nano (4)

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of fano resonances in coupled plasmonic systems,” ACS Nano 7(5), 4527–4536 (2013).
[Crossref] [PubMed]

D. Y. Lei, A. I. Fernández-Domínguez, Y. Sonnefraud, K. Appavoo, R. F. Haglund, J. B. Pendry, and S. A. Maier, “Revealing plasmonic gap modes in particle-on-film systems using dark-field spectroscopy,” ACS Nano 6(2), 1380–1386 (2012).
[Crossref] [PubMed]

Y. Francescato, V. Giannini, and S. A. Maier, “Plasmonic systems unveiled by fano resonances,” ACS Nano 6(2), 1830–1838 (2012).
[Crossref] [PubMed]

D. M. Solís, J. M. Taboada, F. Obelleiro, L. M. Liz-Marzán, and F. J. García de Abajo, “Toward ultimate nanoplasmonics modeling,” ACS Nano 8(8), 7559–7570 (2014).
[Crossref] [PubMed]

ACS Photonics (2)

S. H. Shams Mousavi, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “Band-edge bilayer plasmonic nanostructure for surface enhanced Raman spectroscopy,” ACS Photonics 10, 500487 (2015).
[Crossref]

M. Sarkar, M. Besbes, J. Moreau, J.-F. Bryche, A. Olivéro, G. Barbillon, A.-L. Coutrot, B. Bartenlian, and M. Canva, “Hybrid plasmonic mode by resonant coupling of localized plasmons to propagating plasmons in a kretschmann configuration,” ACS Photonics 2(2), 237–245 (2015).
[Crossref]

Am. J. Phys. (1)

L. Novotny, “Strong coupling, energy splitting, and level crossings: A classical perspective,” Am. J. Phys. 78(11), 1199–1202 (2010).
[Crossref]

Anal. Chem. (1)

T. Špringer, M. L. Ermini, B. Špačková, J. Jabloňků, and J. Homola, “Enhancing sensitivity of surface plasmon resonance biosensors by functionalized gold nanoparticles: Size matters,” Anal. Chem. 86(20), 10350–10356 (2014).
[Crossref] [PubMed]

Biosens. Bioelectron. (1)

A. Sereda, J. Moreau, M. Canva, and E. Maillart, “High performance multi-spectral interrogation for surface plasmon resonance imaging sensors,” Biosens. Bioelectron. 54, 175–180 (2014).
[Crossref] [PubMed]

Chem. Soc. Rev. (1)

V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008).
[Crossref] [PubMed]

J. Nanopart. Res. (1)

Y. Chang and Y. Jiang, “Multiple surface plasmon polaritons modes on thin silver film controlled by a two-dimensional lattice of silver nanodimers,” J. Nanopart. Res. 17(1), 1–8 (2015).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. C (3)

X. L. Wang, P. Gogol, E. Cambril, and B. Palpant, “Near- and far-field effects on the plasmon coupling in gold nanoparticle arrays,” J. Phys. Chem. C 116(46), 24741–24747 (2012).
[Crossref]

C. Noguez, “Surface plasmons on metal nanoparticles: The influence of shape and physical environment,” J. Phys. Chem. C 111(10), 3806–3819 (2007).
[Crossref]

R. Giannini, C. V. Hafner, and J. F. Löffler, “Scaling behavior of individual nanoparticle plasmon resonances,” J. Phys. Chem. C 119(11), 6138–6147 (2015).
[Crossref]

Nano Lett. (3)

K. C. Vernon, A. M. Funston, C. Novo, D. E. Gómez, P. Mulvaney, and T. J. Davis, “Influence of particle-substrate interaction on localized plasmon resonances,” Nano Lett. 10(6), 2080–2086 (2010).
[Crossref] [PubMed]

T. J. Davis, D. E. Gómez, and K. C. Vernon, “Simple model for the hybridization of surface plasmon resonances in metallic nanoparticles,” Nano Lett. 10(7), 2618–2625 (2010).
[Crossref] [PubMed]

J. B. Lassiter, F. McGuire, J. J. Mock, C. Ciracì, R. T. Hill, B. J. Wiley, A. Chilkoti, and D. R. Smith, “Plasmonic waveguide modes of film-coupled metallic nanocubes,” Nano Lett. 13(12), 5866–5872 (2013).
[Crossref] [PubMed]

Nat. Mater. (2)

B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mater. 9(9), 707–715 (2010).
[Crossref] [PubMed]

H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[Crossref] [PubMed]

Nat. Phys. (1)

J. Nelayah, M. Kociak, O. Stephan, F. J. G. de Abajo, M. Tence, L. Henrard, D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzan, and C. Colliex, “Mapping surface plasmons on a single metallic nanoparticle,” Nat. Phys. 3(5), 348–353 (2007).
[Crossref]

Nature (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Photonics (1)

V. Yannopapas, “Periodic arrays of film-coupled cubic nanoantennas as tunable plasmonic metasurfaces,” Photonics 2(1), 270–278 (2015).
[Crossref]

Phys. Chem. Chem. Phys. (1)

P. G. Etchegoin and E. C. Le Ru, “A perspective on single molecule SERS: current status and future challenges,” Phys. Chem. Chem. Phys. 10(40), 6079–6089 (2008).
[Crossref] [PubMed]

Phys. Rev. B (5)

N. Papanikolaou, “Optical properties of metallic nanoparticle arrays on a thin metallic film,” Phys. Rev. B 75(23), 235426 (2007).
[Crossref]

C. Forestiere, L. Dal Negro, and G. Miano, “Theory of coupled plasmon modes and Fano-like resonances in subwavelength metal structures,” Phys. Rev. B 88(15), 155411 (2013).
[Crossref]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009).
[Crossref]

J. Grand, M. L. de la Chapelle, J. L. Bijeon, P. M. Adam, A. Vial, and P. Royer, “Role of localized surface plasmons in surface-enhanced Raman scattering of shape-controlled metallic particles in regular arrays,” Phys. Rev. B 72(3), 033407 (2005).
[Crossref]

Phys. Rev. B Condens. Matter (1)

W. L. Barnes, T. W. Preist, S. C. Kitson, and J. R. Sambles, “Physical origin of photonic energy gaps in the propagation of surface plasmons on gratings,” Phys. Rev. B Condens. Matter 54(9), 6227–6244 (1996).
[Crossref] [PubMed]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

A. Mejdoubi and C. Brosseau, “Finite-element simulation of the depolarization factor of arbitrarily shaped inclusions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74(3 Pt 1), 031405 (2006).
[PubMed]

Phys. Status Solidi (1)

A. Hohenau and J. R. Krenn, “Plasmonic modes of gold nano-particle arrays on thin gold films,” Phys. Status Solidi 4(10), 256–258 (2010).
[Crossref]

Plasmonics (3)

S. Chen, L. Y. Meng, J. W. Hu, and Z. L. Yang, “Fano interference between higher localized and propagating surface plasmon modes in nanovoid arrays,” Plasmonics 10(1), 71–76 (2015).
[Crossref]

K. Lodewijks, J. Ryken, W. Van Roy, G. Borghs, L. Lagae, and P. Van Dorpe, “Tuning the Fano resonance between localized and propagating surface plasmon resonances for refractive index sensing applications,” Plasmonics 8(3), 1379–1385 (2013).
[Crossref]

M. Chamtouri, A. Dhawan, M. Besbes, J. Moreau, H. Ghalila, T. Vo-Dinh, and M. Canva, “Enhanced SPR Sensitivity with nano-micro-ribbon grating-an exhaustive simulation mapping,” Plasmonics 9(1), 79–92 (2014).
[Crossref]

Rev. Mex. Fis. (1)

A. Zehe and A. Ramirez, “The depolarization field in polarizable objects of general shape,” Rev. Mex. Fis. 48, 427–431 (2002).

Sensor Actuat. Biol. Chem. (1)

M. Sarkar, M. Chamtouri, J. Moreau, M. Besbes, and M. Canva, “Introducing 2D confined propagating plasmons for surface plasmon resonance sensing using arrays of metallic ribbons,” Sensor Actuat. Biol. Chem. 191, 115–121 (2014).

Springer Tr. Mod. Phys. (1)

H. Raether, “Surface-plasmons on smooth and rough surfaces and on gratings,” Springer Tr. Mod. Phys. 111, 1–133 (1988).

Top. Appl. Phys. (1)

G. C. Schatz, M. A. Young, and R. P. Van Duyne, “Electromagnetic mechanism of SERS,” Top. Appl. Phys. 103, 19–45 (2006).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1 The studied structure geometry consists of an array of metallic cylinders of diameter D and height h2 placed on a thin metallic film of height h1. The refractive index on the side of the array was taken as nw while that on the other side was ng. A sketch of the numerical method is also shown, which uses a mesh around the nanostructured region to calculate the S matrix by FEM, and then uses FMM to calculate the far-field response of the system.
Fig. 2
Fig. 2 Left, the analytically calculated polarizability α(k0) for a nanocylinder of 30 nm height and 50 nm diameter in a homogenous medium nw (in red). The same for the cylinder placed on a semi-infinite gold medium (in blue). The calculated LSP frequency for the later configuration is k0 = 8.87 µm−1. Center, the HLP mode (green) dispersion, which results from the harmonic coupling of the LSP and PSP. Right, the calculated dispersion (k0-neff) for the PSP in a gold film with plasmons propagating in the medium nw. The resonance frequencies of the LSP (blue solid) and the PSP (blue dotted) are also shown. For this scheme, the period of the array was taken as 180 nm.
Fig. 3
Fig. 3 . (a) The normalized absorption (A) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm, and period Λ = 180 nm with the medium around the nanocylinders of refractive index nw. The lightline in the medium is defined as neff = nw. The proposed analytical calculation of the dispersion of different modes of the system are also shown: LSP (blue solid), PSP (blue dashed), HLP (green), and BMs (black solid and dashed). (b) Same as (a) for period Λ = 300 nm.
Fig. 4
Fig. 4 The resonance frequencies (k0) of all the modes in the structure (D = 50 nm, h2 = 30 nm) manifest as absorption maxima in the dispersion map calculated by rigorous numerical method (red dots) as a function of array period for neff = 1.42. We have superposed the analytically calculated frequencies of the modes as a function of period: LSP (blue), HLP (green), BMs calculated for kB = 2π/(Λ) (black solid and dashed) and BMs for kB = 2π/(Λ + D) (red dashed and solid).
Fig. 5
Fig. 5 (a) The resonance frequencies (k0) of HLP modes in the structure (Λ = 350 nm, D = 50 nm) manifest as absorption maxima in the dispersion map calculated by rigorous numerical method (red dots) as a function of cylinder height (h2) for neff = 1.45. We have superposed the analytically calculated frequencies of the modes as a function of h2: LSP (blue), HLP (green). (b) For D = 90 nm with the same period as previously.
Fig. 6
Fig. 6 The normalized reflectivity (R) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm and period Λ = 340 nm with the medium around the nanocylinders of refractive index nw in the Kretschmann configuration. The lightline in the medium is defined as neff = nw. The analytical calculation of the dispersion of different modes of the system are also shown: LSP (blue solid), PSP (blue dashed), HLP (green) and BMs (black and red solid and dashed same as Fig. 4). (b) The transmission (T) for the same parameters.
Fig. 7
Fig. 7 (a) Scheme of the SPR imaging system used to characterize the fabricated nanostructure in the Kretschmann configuration. (b) An image of the structured chip with 3 × 6 zones as obtained by the SPR imaging system. Each zone has a size of 500 × 500 µm2 and has the same structural parameters (diameter and periodicity of cylinders) along the rows. The period is changed from 150 nm to 400 nm along the columns as shown in the figure. (c) SEM images of cylinder with a diameter of 50 nm and periods of 150 nm, 250 nm and 400 nm. (d) The experimental reflectivity (R) dispersion map as a function of k0 and neff for h2 = 30 nm, D = 50 nm and period Λ = 300 nm. The experimental reflectivity map should be compared to the numerical absorption map of Fig. 3(b), which has the same structural dimensions. The analytical calculation of the dispersion of different modes of the system is also shown.
Fig. 8
Fig. 8 (a) Normalized reflectivity spectra at θ = 71.14° for different period (Λ) of the structure. Arrows show the reflectivity minima, which correspond to the various modes excited in the structure. (b) The resonance frequencies (k0) of all the modes (minima of reflectivity) are shown as red squares as a function of array period. The error bars correspond to the minimum step of incident wavelength (10 nm) used for the experiment. We have superposed the analytically calculated frequencies of the modes as a function of period: LSP (blue), HLP (green), BMs calculated for kB = 2π/(Λ) (black solid and dashed) and BMs for kB = 2π/(Λ + D) (red dashed and solid).
Fig. 9
Fig. 9 The normalized absorption (A) dispersion maps calculated by numerical methods with varying period (Λ) as a function of k0 and neff for h2 = 30nm, D = 50nm. The analytically calculated dispersion of the various modes is also shown which fits accurately to the rigorously calculated numerical results.
Fig. 10
Fig. 10 The normalized reflectivity (R) dispersion maps calculated by numerical methods with varying h2 and D function of k0 and neff for Λ = 350nm. The analytically calculated dispersion of the various modes is also shown and the color legend is same as Fig. 9.
Fig. 11
Fig. 11 The normalized reflectivity (R) dispersion maps obtained experimentally with varying period (Λ) as a function of k0 and neff for h2 = 30nm, D = 50nm. The analytically calculated dispersion of the various modes is also shown and the color legend is same as Fig. 9.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

α(ω)=const× n m 2 (ω) n d 2 n d 2 +L( n m 2 (ω) n d 2 )
n e 2 = n d 2 [ 1+ηT/1+γ 1+ηT/1γ ]
k psp:d = k 0 n d 2 n m 2 n d 2 + n m 2
ω HLP ± 2 = 1 2 [ ω 1 2 + ω 2 2 ± ( ω 1 2 ω 2 2 ) 2 +4 κ 2 ]
k BM = k psp:d ±m k B

Metrics