A. Qualitative Analysis
In the following influences of the variation of the grating constant along the x and the y directions on the sensitivity will be presented qualitatively. For this goal, we calculate the plasmon resonance shift ∆λ for a nanocylinder with a diameter d = 150nm, and a height h = 60nm as well as for a nanocylinder with diameter d = 100nm and the same height. In figure 2 we represent in color the shift ∆λ for different px and py. It shows that the variation of the distance py has greater impact on the sensitivity (S is proportional to ∆λ) as compared to px. The highest sensitivity is observed for an asymmetric array with approximatively (py = 2 px ). We explain our result qualitatively by the 2D periodicity of the nanoparticle array. In fact, the geometrical arrangement may reduce for certain distance py the radiative losses as the energy scattered could be captured into plasmon, leading to a higher sensitivity to the refractive index change . In the following, we will focus on the effect of the distance py on the sensitivity S as well as the effect of reducing the symmetry in each cell in the array.
B. Quantitative Analysis
In this section we investigate the effect of the variation of py (perpendicular to the incident light polarization) on the sensitivity for an array of nanocylinders with diameter d = 150nm.
Results are plotted in figure 3a, where we observe a non-monotonic variation with a little variation of the sensitivity for py < 350nm, then a strong increase for py >= 375nm. We attribute the enhancement of S to constructive interference between nanoparticles, especially the diffracted wave that ensure the coupling between proximal nano particle in the far field region. Note that S increases especially when the interparticle spacing multiplied roughly by the local refractive index (effective index of substrate, NP and polymer) approaches the wavelength of the isolated nanoparticle plasmon resonance (we reach 3 folds enhancement).
Similar results are observed for smaller nanoparticle (figure 3b).
Our numerical results show that the variation of the grating constant in the direction perpendicular to the polarization of the incident wave has significant influences on sensitivity. Unlike the isolated particle , the increase of the sensitivity here is not correlated to the red shift of the plasmon resonance wavelength (inset of figure 3). The asymmetric array with py > 2 px will exhibit the highest plasmon resonance shift. Our calculations are made for py > 200nm, for distance below 200nm we expect near field coupling to dominate, however such array will be more challenging for fabrication and are out of our interest.
Another interesting aspect of the asymmetric array is that the density of the metal in the nanoarray is greater than the symmetric array leading to a stronger signal detected in the sensor.
In the following, we further reduce the symmetry of the system, by investigating asymmetric nanoparticle in the asymmetric array. For this goal we investigate the plasmon resonance shift for three types of nanorods as well as for a nanotriangle. The major axis (parallel to the x direction) for each nanorods is fixed to 150nm. The aspect ratio will be varied from 1 to 3. In order to make a comparison between those nanorods, we normalize the shift ∆λ with the surface area of each nanorods. Results are depicted in Fig. 4a where we observe that the sensitive could be enhanced by 3 times if we increase the aspect ratio of the nanorod. In Fig. 4b, we further con- firm our result by comparing the sensitivity of an array of nanotriangle and an array of nanocylinder. We choose the dimension of the nanotriangle such us it has approximatively the same surface area of the nanocylinder, i.e. same contact surface with the target molecule. We observe that with a nanotriangle we could reach the highest plasmon resonance shift. We attribute the increase of sensitivity, to the larger confinement of the electron cloud due to the geometry of the nanoparticle.
In conclusion we suggest that adding to the asymmetry of the array the asymmetry of each nanoparticle improve significantly the sensitivity of the nano system. The decrease of the symmetry in the nanograting could lead to higher near field confinement in each nanoparticle as well as efficient far field coupling between neighboring nanoparticles. The combination of these two factors leads then to the increase of the sensitivity (up to 6 times when comparing to a symmetric array).