When molecules approach a nanostructured metal surface that is illuminated by visible light, these molecules experience a very intricate electric field. On the one hand, the field results from light itself, which is incident on the nanostructures, scattered and diffracted from them or reflected from their interfaces. On the other hand, light's electromagnetic oscillations drive the electron density within the nanostructures and, in turn, these variations of electron density constitute the source of a very inhomogeneous surface electric field–the local field.1 Molecules placed in the local field experience electric forces along the field lines, which become very crowded in two sorts of regions on the nanostructures. First, in the sharp regions, such as corners or tips, where the field lines are pulled together by geometric constraints. And second, in the regions of highest electron density, where the electron charges constitute strong sources for the local field. These regions of crowded field lines, at the nanostructured metal surface, correspond to local field enhancements and are commonly referred to as “hotspots”. One of the reasons why such hotspots are very important, is because of what can happen to molecules within them.
Within hotspots, molecules can experience chemical transformations,2 photochemical reactions,3 catalytic reactions4, 5 and extreme enlargement of their optical properties.6, 7 A particularly spectacular example is surface enhanced Raman scattering,8 whereby the Raman signal can be increased up to fourteen orders of magnitude.9, 10 Unfortunately though, hotspots suffer from two limiting factors–they can become too hot and they are only spots.
Indeed, in an attempt to achieve ever greater enlargement of the optical response of molecules, the incident light intensity can be increased. Besides the desired increase of the local field intensity however, an undesired increase of nanostructure heating occurs. The heating is due to the local electric currents that are associated with the oscillations of the electron density, according to Joule's effect. It has thus been shown that, in the hotspots, laser-induced heating can melt the nanostructures and even give rise to hydrodynamic processes.11, 12 Therefore, there is an upper limit to how much the local field can be enhanced within a hotspot without inducing irreversible damage to the surface of the sample. In order to further benefit from enlarged optical response of molecules, a better choice might be to nanoengineer larger spots.
Recently, there has been considerable efforts towards engineering local field enhancements. Hotspots can thus be obtained at randomly roughened surfaces,13, 14 through plasmon excitations,15 due to nanostructuring,16 or by making use of antenna designs.17 In all of these cases, local field enhancement occurs only within a small region of the sample surface. From a practical point of view, it would be very interesting to expand the local field enhancements to the whole sample surface, thereby increasing the opportunity for interaction with molecules. Because it originates from the inhomogeneity of electron density in the nanostructures, such an expanded field can still be called “local” in nature, however it would no longer be localized in small spots. To avoid any confusion, from now on, we shall designate this field as the “near-field”. As we shall prove in this work, an effective approach to obtain near-field enhancements over the entire sample surface is to drive the electron surface currents along ring-shaped nanostructures.
Here we demonstrate that circularly polarized light imparts a sense of rotation on the electron density in ring-shaped gold nanostructures. As a consequence, the near-field enhancement becomes homogeneous on the surface of the nanostructures, thereby increasing the opportunity for interaction with molecules, see Figures 1a and 1b. Interestingly, for linearly polarized light oriented along the Y and X directions, a pattern of pronounced hotspots indicates strong coupling between the nanostructures along these directions. Upon rotating the direction of linearly polarized light, the pattern of hotspots does not always follow the direction of polarization but instead appears “pinned” by the strong coupling along the Y and X directions. Consequently, while for circularly polarized light the near-field is homogeneous, for randomly distributed linearly polarized light the near-field is inhomogeneous. This difference reflects the difference in electron density behavior, depending on the nature of light polarization. The work presented here is intended as a proof of principle; by varying the dimensions and the shape of the metallic rings, further device optimization can be obtained. As a guideline for such device optimization, we propose a quantitative figure or merit for homogeneity of surface near-fields. This type of nanostructured samples can find a broad range of applications in chemical processes where the interaction between molecules and local field enhancements play an important role. In order to maximize the useful sample surface, we avoided using circular rings, which do not pack very efficiently, and instead preferred square-rings.
The square-ring shaped nanostructures are made of gold (30 nm thick) grown on top of SiO2 (100 nm)/Si(001) substrate, and are produced by electron beam lithography. More details on the deposition and on the rest of the sample preparation can be found in Ref. 18. The outer side of each square measures 1000 nm, the width of the metallic stripes is 200 nm, and all the nanostructures are 200 nm apart from each other, as shown in Figure 1c. The total area of the sample is 2.5 by 2.5 mm. When these structures are illuminated at the wavelength of 800 nm, a plasmon resonance is excited. The presence of the resonance was evidenced by numerically simulating the reflection and transmission spectra of the nanostructures, see Figure 2a. Moreover, for the purpose of completeness, the same nanostructures were deposited on a transparent substrate (glass), so that reflection and transmission spectra could also be experimentally verified, see Figure 2b. It should be noted that the small difference between the experimentally and computationally determined spectra is due to the fact that we did not include the substrate in the numerical simulations. As Figure 2 illustrates, this difference increases with the wavelength due to the frequency dispersion of both the index of refraction and of the absorption coefficient of the substrate. Despite the small difference in peak positions, the numerical simulation are in excellent agreement with the experimental measurements. At resonance, reflection from different interfaces, scattering, diffraction and various near-field enhancements can be observed. All of these phenomena are rigorously taken into account in numerical solvers of Maxwell equations, which are therefore suitable for mapping with high resolution the electromagnetic fields.
In order to accurately map the near-field enhancements at the surface of the gold nanostructures, we perform two independent numerical simulations. The first one, performed with RSoft's DiffractMOD,19 evaluates the electric fields in air, 1 nm above the gold surface. The second one, performed with MAGMAS,20, 21 evaluates the electric currents inside the gold layer, 1 nm below the surface. Both simulations assume monochromatic wave excitation under normal incidence (the wavelength of the incoming light is 800 nm) and periodic boundary conditions, which significantly reduces the simulation time. Figures 3a and 3b show the electric field intensity for vertically and horizontally polarized light, respectively. In both cases, intense hotspots can be observed, corresponding to near-field enhancements on the opposing sides of the square-rings that are perpendicular to the direction of polarization. Because, in the case of circularly polarized light, both vertical and horizontal field components are present in equal amplitudes (yet out-of-phase by π/2), one might initially expect circularly polarized light to simply produce a superposition of the field profiles in Figure 3a and 3b, i.e. four hotspots, one on each side of the square-rings. Figures 3c and 3d show, however, that this is not the case. Our result indicates that the phase between the vertical and horizontal field components of circularly polarized light plays a crucial role in the generation of the near-field.
Indeed, for circularly polarized light, Figure 3c and 3d demonstrate that instead of exhibiting hotspots, the electric field intensities are spatially much more homogeneously distributed than in Figures 3a and 3b. A more careful examination of Figure 3c reveals that the near-field enhancement pattern has a sense of rotation that is mirrored in Figure 3d, even though the nanostructures are clearly not chiral. Consequently, it is the chirality of light that is imparted onto the near-fields of the nanostructures. In order to better understand this physical mechanism, we can examine the distribution of the electric currents, which are induced by light at the surface of the nanostructures.
Upon examining the distribution of electric currents at 1 nm below the surface of the nanostructures, the similarities with the electric near-fields become obvious. First, for linearly polarized light, there are hotspots on the square-ring sides that are perpendicular to the direction of polarization, see Figures 3e and 3f. And second, for circularly polarized light, there is a sense of rotation in the pattern, which can be related to the direction of circularly polarized light. Henceforth, Figure 3 clearly illustrates the agreement between two complementary theoretical approaches. This is a strong indication for the validity of the results, however for the sake of scientific rigor, an experimental confirmation is necessary. The experimental study is performed with second harmonic generation (SHG) microscopy, a technique whose usefulness for visualizing field enhancements in nanostructures has been demonstrated in several works already.22–27 We use ultrafast pulsed lasers (∼100 fs, 82 MHz), which are capable of delivering very high electric field intensities to the electron population in the nanostructures. When the intense electric field of light becomes comparable with the electric near-fields, the oscillations of the electron density are driven in the nonlinear (anharmonic) regime. This nonlinear regime can be described by a mathematical expansion in series, corresponding to higher order frequency terms. The second harmonic generation technique consists in measuring the term in the nonlinear expansion series that is associated with the double frequency of the illumination. An intuitively very appealing explanation for this technique is to consider that, in response to the electric field of light, most electrons within the nanostructures are driven in the linear regime. However, in the hotspots, due to near-field enhancements, the electrons are driven in the nonlinear regime. As a consequence, second harmonic signal is generated precisely from the regions of near-field enhancements. In essence, the technique offers built-in light sources for the near-field enhancement signal, at a frequency that is easily separable from any noise at the illumination frequency, such as scattering, diffraction or reflection. Therefore, SHG microscopy can accurately map near-field enhancements in nanostructures, see Figure 4.
Figure 4a, presents a SHG micrograph from the top left corner of the nanostructure array, for incident light linearly polarized along the vertical direction, as indicated by the white arrow. An array of hotspots can be observed. Most of them occur in pairs, which are oriented along the direction of polarization. Upon superimposing the layout of the nanostructures on the SHG micrograph, it becomes clear that the location of these hotspots corresponds to the sides of the square-ring nanostructures, which are perpendicular to the polarization. The same trend can be observed for horizontally polarized light, as can be seen in Figure 4b. It should also be noted that the paired hotspots are significantly brighter than the singles ones, which are situated at the edge of the array. This difference in intensity indicates that near-field coupling (most likely of antenna type) takes place between the nanostructures, reinforcing the near-field enhancements. These experimental observations of hotspots are in perfect agreement with the theoretical simulations for linearly polarized light. What about circularly polarized light?
Figure 4c shows a SHG micrograph from the same regions of the sample, at the same illumination intensity, but, this time, upon illumination with circularly polarized light. Contrary to the case of linearly polarized illumination, here, no hotspots can be observed. Instead, the SHG signal is rather homogeneous throughout the entire array, the observable small variations being attributable to fabrication defects of the array. Within this array, all individual square-rings are clearly distinguishable. Note that in Figure 4a and 4b, the sides of the squares on which there is no field enhancement are not distinguishable at all. Because all images in Figure 4 were obtained for the same laser power (0.4 mW), we can conclude that the reason why the entire squares are distinguishable in Figures 4c and 4d is because of a homogeneous field enhancement throughout the nanostructures. Moreover, in both Figures 4c and 4d, the SHG signal is weaker from the edges of the array. It follows that, upon illumination with circularly polarized light, coupling is also taking place between the nanostructures. Because these nanostructures are 200 nm apart, this cannot be a direct coupling and is more likely of antenna type. Actually, the value of 200 nm is comparable to the resolution limit of the SHG microscope. Perhaps then the “homogeneous” SHG signal is simply a superposition of the four hotspots for vertical plus horizontal linearly polarized light, which appears homogeneous due to optical resolution limitations? The best way to answer this important question is to compare the results for circularly polarized light with those for randomly oriented linearly polarized light, with special attention devoted to polarization along +45° and –45°.
Figures 4e and 3d display SHG micrographs for linearly polarized light along +45° and –45°, respectively. As in the case of circularly polarized light, the nanostructures are clearly distinguishable but there is an important difference. Indeed, as it is emphasized by the white lines drawn diagonally across the nanostructured array, in the case of linearly polarized light at 45°, the SHG signal is no longer homogeneous. Figures 4a, 4b, 4e, and 4f, could create the impression that the pattern of hotspots in these nanostructures always follows the direction of linearly polarized light; in fact, this is far from being the case. For all intermediate polarization directions the pattern of hotspots appears “pinned” by the strong coupling along the Y and X directions, see the complementary information. Consequently, circularly polarized light is necessary in order to achieve homogeneous field enhancements. This strong experimental evidence, in combination with both sets of rigorous numerical simulations, indicate that circularly polarized light is capable of driving the electron density along ring-shaped nanostructures. Before we call this statement a proof however, there are two questions that remain to be clarified, regarding the origin of the SHG signal.
First, we have assumed that the SHG signal in Figure 4 is due to electric field enhancements, but what about the magnetic field? This is an important question because, previously, we have found that SHG originated from hotspots that corresponded to both electric and magnetic field enhancements.14 Numerical simulations of the magnetic fields at the surface of the square-rings are shown in Figure 5. More specifically, Figures 5a and 5b demonstrate that, for linearly polarized light, the magnetic field hotspots are situated on the sides of the square-rings that are parallel to the direction of polarization. In other words, in these particular nanostructures, electric and magnetic field enhancements are clearly distinguishable. A comparison of these fields with Figure 4a and 4b, shows unambiguously that the SHG originates from the electric and not the magnetic field enhancements. The same conclusion is reached by examining the location of the magnetic field enhancements observed in the case of circularly polarized light, see Figures 5c and 5d. Instead of a rather homogeneous field enhancements, as it is the case for electric field, these figures reveal pronounced hotspots. Such hotpots are not present in the SHG signal for circularly polarized light.
Second, in Figures 4a and 4b, the nanostructures themselves are not visible and, in order to determine the origin of the SHG hotspots, we have superimposed the layout of the nanostructured array on top of the micrographs. How unique is this superposition? In order to precisely locate the SHG hotspots, we increased the laser power to approximately 1 mW, i.e. above the damage threshold of these nanostructures. The results for vertical and horizontal linearly polarized light can be seen in Figures 5e and 5f, respectively. These figures present scanning electron microscopy images of the nanostructures, obtained after illumination. In each case, plasmon-assisted sub-wavelength laser-ablation can be observed on some of the square rings. The ablated regions correspond to the same regions, which are indicated by superposition of the layout in Figure 4a and 4b. Consequently, there can be no doubt as to how reliable these data are. Yet, sometimes, “truth is in the eye of the beholder”.
Upon looking at Figure 4, it is quite obvious that the SHG signal for circularly polarized light is more uniformly distributed over the surface of the nanostructures, than the SHG signal for linearly polarized light. Why is this so obvious? To be more specific, In Figure 4, the SHG signal consists of non-zero pixels. What we mean by “uniformly distributed signal” is that these pixels are equally spaced, that there are no large gaps in between them and that there are no large variations of pixel intensity. The human eye can verify these conditions with great efficiency, however, for the purpose of better distributing the near-field on a nanostructured surface, it would be useful to be able to quantify the information.
Calculating a figure of merit for the uniformity in the near-field distribution can be done in the following manner. We begin by converting the color-scale of the SHG micrographs to grayscale, where pixel intensity is normalized to 1–white color. The black color corresponds to pixel intensity 0 and it is set at the experimental noise level. Next, for every pixel (xi, yj), we calculate the minimum distance to a non-zero pixel:
While in regions with uniform field distribution Δdi is always small, in regions with large gaps within the field Δdi is large. The average minimum distance, out of a total of N pixels, is then given by:
Extensive regions of uniformly distributed near-field drive this average towards a small value. Consequently, in regions with large gaps, Δdi deviates significantly from the average. A measure of this deviation can therefore serve as a measure of the uniformity in the near-field distribution:
where we can see that the smaller D, the more uniformly distributed the near-field is; for a perfectly uniform distribution, and D = 0.
Upon applying this measure to the SHG micrographs, we find that, for linearly polarized light (Figure 4b), D = 1.36. However, for circularly polarized light (Figure 4c), D = 0.68, which proves that the SHG signal is more homogeneous in the case of circularly polarized. Moreover, the variation in the pixel intensity can be evaluated upon measuring the second Pearson's skewness coefficient , where m is the mean, μ is the median and σ is the standard deviation. This measure on skewness evaluates the symmetry in the distribution of pixel intensities. For linearly polarized light, we find that γ = 1.12, which is a clear sign of a skewed distribution, due to the presence of hotspots. However, for circularly polarized light, we find that γ = 0.47, indicating that the distribution is more symmetric. It should be noted that the measure of homogeneity in Equation 3 is best suited for analyzing experimental results, since it relies on the noise level of the instrument in order to set the zero pixel intensity. The second Person's skewness coefficient though can be readily applied to simulation results as well. Thus, for the case of linearly polarized light in Figure 3b, γ = 0.94, while for the case of circularly polarized light in Figure 3c, γ = 0.46. These γ values are remarkably close to those obtained from the experimental results.
In conclusion, we have demonstrated that near-field enhancements can be extended over an entire nanopatterned gold surface, thereby increasing the interaction cross-section with molecules for chemical and sensing applications. The extension of the near-field is achieved by driving the electron density along loop-shaped nanostructures with circularly polarized light. The concept is validated by two sets of complementary, rigorous, numerical simulations and a clear experimental confirmation. The proof of principle presented here makes use of square-rings, which pack more efficiently than circular rings. For the purpose of obtaining more homogeneous field enhancements on a larger surface area, hexagonal rings and smaller dimensions could perhaps be investigated.