1. Introduction

Surface plasmons (SPs) are collective oscillations of free electrons on a metal surface excited by incident light, and the plasmonics is a potential candidate of future technologies due to its high sensitivity and fast response in small dimensions. In particular, plasmonic color filters have been actively studied by many research groups in these days since a wavelength, intensity, and phase of light can be manipulated via plasmonic nanostructures instead of conventional dye-based filters [1–4]. Plasmonic color filters generally use nanoslit or nanohole arrays, which induce the extraordinary optical transmission phenomenon [5]. Their structural parameters, such as geometry and dimension, determine a specific resonance wavelength to express the corresponding color in transmission mode. Although they have significant advantages in terms of high resolution and miniaturization, there are mainly two inherent weaknesses to hinder the application of plasmonic color filters to displays. One is their static behaviors in expressing dynamic color images due to structural dependency of plasmonic resonances, and the other is their low transmission efficiency due to nano-sized holes or slits. We had proposed the plasmonic cavity-aperture as a solution of the former problem in our previous study [6]. It has the potential to function as a dynamic color pixel in imaging devices because the cavity-aperture enables a single pixel to control color and intensity simultaneously according to the polarization state of incident light.

However, the low transmittance problem is still an obstacle to overcome in the plasmonic color filters. We intend to find a clue in some previous researches of plasmonic nanoapertures. There have been suggested ways using unconventional nanoapertures, such as bow-tie [7–11], H [12,13], and C shapes [14–16]. Using these nanoapertures, the transmitted light forms a hot spot in near-fields and the intensity is a few hundred times higher than that of conventional circular nanoapertures. Therefore, we will investigate the shape and size of the nanoaperture in the center of the cavity-aperture to improve the transmission efficiency in this paper. In order to adopt an unconventional nanoaperture to the cavity-aperture, it must satisfy its necessary conditions in terms of incident polarization. It should have a novel geometry to efficiently transmit all incident lights with three polarization angles in the cavity-aperture, whereas most of unconventional nanoapertures have high transmission efficiency for incident light with a specific polarization angle [7–16].

In this study, we briefly mention the cavity-aperture and propose a triple-slit nanoaperture for high transmission of the cavity-aperture. The triple-slit aperture is investigated in both simulation and experiment for verification of its feasibility. In particular, the improvement of the transmission efficiency due to the proposed aperture will be supported by a comparison with a transmission behavior of a simple circular nanoapertures.

2. Concept of a triple-slit aperture

First, we explain the concept and the principle of the cavity-aperture in brief. It is composed of a metal cavity and a nanoaperture, as shown in Fig. 1(a). An optical cavity generally supports standing waves under matching conditions between a cavity length and incident wavelengths, and various standing waves with different wavelengths are able to coexist in one cavity. On the other hand, although light cannot pass through a small aperture with a few nanometer size, SPs can pass through a metal nanoaperture with high intensity due to the extraordinary transmission phenomena [5]. If we combine the two fundamental functions into a nanostructure, we can spatially distribute the nodes and antinodes of various standing waves according to their wavelength using the cavity, and we can extract only a light with a specific wavelength using the nanoaperture [6]. The schematic diagram in Fig. 1(b) indicates the physics in detail. For the same cavity-aperture, the green incident light has the maximum transmittance because the green standing wave forms one of antinodes on the nanoaperture in the upper image, whereas the transmittance of the red light becomes the minimum because the node of the red standing wave is located on the nanoaperture in the lower image. When three different cavity-apertures are overlapped with different rotational directions on a centered nanoaperture, they become a multiplexed cavity-aperture which can express three primary colors as well as their mixed colors according to a polarization direction of incident lights, as shown in Fig. 1(c). Three cavity lengths had been selected as 1.2 μm, 2.7 μm, and 3.1 μm for the maximum transmittance of red, green, and blue light sources, respectively, in our previous research [6].

 

Fig. 1 Schematic diagram of cavity-aperture. (a) Two basic functional structures, an optical cavity and a plasmonic nanoaperture, combine into a cavity-aperture. (b) Principle of the cavity-aperture. Incident light passes through the cavity-aperture with maximum and minimum intensities when a nanoaperture is located at anti-nodes and nodes of standing waves, respectively. Multiplexed cavity-apertures with (c) a circular aperture and (d) a triple-slit aperture.

Download Full Size | PDF

However, the transmittance was approximately 1%, which is not enough for practical devices. The cavity-aperture cannot transmit a large amount of light in comparison with conventional color filters because it has a very small aperture of nanometer dimensions. The low transmission problem must be solved for the cavity-aperture to be practically utilized in display pixel systems although it has the significant advantage to continuously filter a series of colors: the transmittance of commercial display pixels is generally about 5–10%. Since the transmittance will be naturally enhanced by enlarging the aperture size, the maximization of the transmission efficiency per unit area of the nanoaperture should be preferentially studied. the aperture size should be smaller than the anti-node of standing waves in the cavity-aperture because large aperture reduces its wavelength-selectivity. Considering all of them, we intend to improve the transmission efficiency per area of the nanoaperture by modifying it. In general, irregularly or specifically shaped nanoapertures, such as C- and bowtie-types, have been reported to have high transmission efficiency in comparison with simple circular and rectangular types, since SP resonances provoke the strong charge accumulations at their sharp edges depending on the shape of the nanoapertures [16–18].

Here we propose a triple-slit shape instead of a circular shape as the nanoaperture in the cavity-aperture to improve its transmission efficiency, as shown in Fig. 1(d). It has two advantages. One is that the triple-slit aperture can induce a strong confinement and transmission of electric fields due to SP resonances at different geometrical parts of the aperture, which are a pair of sharp wedges and a perpendicular nanoslit with respect to each angular direction of three cavities. The other is that it can enhance transmission efficiency at all three cavities, which are set to different angular directions of incident polarization, because the triple-slit shape has a six-fold rotational symmetry. Although the triple-slit aperture is not perfectly polarization-independent on a flat metal layer, it can be less sensitive to the incident polarization because the three cavities guide incident light into three angular directions before the triple-slit aperture. In the case of the previous unconventional nanoapertures including C- and bowtie-apertures, their transmission efficiencies are highly polarization-dependent because they have a line symmetry. In order to investigate the optical properties of the triple-slit apertures, we calculated their electric fields with the three-dimensional COMSOL simulation tool under an illumination condition of a horizontally polarized light with 671 nm wavelength. Although all primary colors of red, green, and blue must be considered for one cavity-aperture, we representatively study the efficient transmission of the triple-slit aperture for the red color in this paper because the similar method and process can be applied to those for the other colors.

3. Simulation of a triple-slit aperture

For a reasonable comparison among various nanoapertures, we calculated the electric field profile at the output plane of a nanoaperture and integrated the field intensity over the aperture area, as shown in Fig. 2. The field intensity can be a parameter to indicate the transmission efficiency of the nanoaperture [7–16]. In Fig. 2(a), the curves of A–E are the normalized field intensities of the triple-slit apertures having slit widths of 10 nm, 15 nm, 20 nm, 25 nm, and 30 nm, respectively, when a slit length increases from 120 nm to 220 nm. Since the maximum value of the field intensity curve indicates the efficient transmission of the triple-slit aperture, we can acquire 10 nm - 150 nm, 15 nm - 167 nm, 20 nm - 180 nm, 25 - 188 nm, and 30 nm - 192 nm as the efficient ratio of the slit width and length on the curves of A–E.

 

Fig. 2 (a) Normalized electric field intensities of the triple-slit apertures having various ratios of slit widths and lengths in simulation. The curves A-E are the intensities of the triple-slit apertures having constant widths of 10 nm (A), 15 nm (B), 20 nm (C), 25 nm (D), and 30 nm (E), respectively. (b) The simulation graph of the field intensity vs. size of the triple-slit and the circular apertures. Electric field profiles of (c) the circular aperture at the point F, (d) the triple-slit aperture at the point D, and (e) the cavity-aperture for a horizontally polarized light.

Download Full Size | PDF

Figure 2(b) shows the change of the field intensities transmitted through the triple-slit and circular apertures depending on the aperture size. The graphs are plotted with interpolation based on the twenty simulation data including the points A–F. In order to compare the intensities for two types of apertures having same area, we introduce an effective diameter as the aperture size on the x-axis in both cases of the triple-slit and the circular apertures: it is the same value with the diameter of the circular aperture and the size of the triple-slit aperture is converted to the effective diameter. The field intensity of the triple-slit aperture increases more rapidly than that of the circular aperture when the aperture size increases, as shown in Fig. 2(b). The strong electric fields at the output plane of the triple-slit aperture imply that the incident light passes through the proposed aperture with higher transmission efficiency than the circular aperture. The maximum values of the curves of A–E in Fig. 2(a) can be marked with the points of A–E on the intensity curve of the triple-slit aperture because the field intensity of the triple-slit aperture is calculated in the optimized ratios of slit widths and lengths. The slope of the intensity curve of the triple-slit aperture decreases with increasing aperture size. Due to the slow increase of the transmission efficiency in a range of large sizes, we select the width and the length of the point D as the triple-slit aperture size and compare it with a circular aperture of the point F. The electric field intensity of the triple-slit aperture is approximately four times higher than that of the circular aperture in spite of the same transmission area.

Their electric fields are also differently distributed in the apertures, as shown in Figs. 2(c) and 2(d). The fields of the triple-slit aperture are strongly confined at the centered slit of a few ten nanometers, whereas those of the circular aperture are separately distributed at the left and right sides of about a hundred nanometers. Although the field intensity of the circular aperture continuously increases in a range of larger sizes than the aperture size of the point F, the intensity of a circular aperture having a diameter of 200 nm, which is the maximum diameter in the cavity, is lower than that at the point D. It is quite ineffective in terms of transmittance per unit area of an aperture. In Fig. 2(e), the field profile at the interface plane of the cavity and the nanoaperture shows that the cavity-aperture properly forms the standing wave along the incident polarization and the anti-node is exactly located at the triple-slit aperture. Each nanoslit of the triple-slit aperture should be perpendicularly aligned with the direction of each cavity at the center of the cavity-aperture for maximum transmission efficiency. It is because the cavity guides a standing wave with parallel polarization, and the light can be maximally transmitted when each nanoslit is perpendicular to its polarization.

In order to analyze the SP modes contributing to the high transmission efficiency of the triple-slit aperture, we decomposed the triple-slit aperture into two component apertures of X-shape and l-shape. Decomposition of a complex nanostructure has been utilized in studying plasmon resonances with plasmonic hybridization because it can provide a simple and clear insight for understanding plasmonic properties [19–21]. Depending on the combination between the available plasmonic modes of the X- and l-apertures, the coupled modes of the triple-slit aperture at the center of the cavity-aperture can be expressed with their symmetric and anti-symmetric bonding states, as shown in Fig. 3(a). If we compare two coupled modes with the electric field profile of the triple-slit aperture calculated at the incident light of 671 nm in Fig. 3(b), we can confirm that the dominant coupled mode of the triple-slit aperture significantly resembles the symmetric bonding state.

 

Fig. 3 (a) Schematic energy diagram of the triple-slit aperture in symmetric and anti-symmetric bonding states, which are coupled between the plasmonic modes of X- and l-apertures under horizontal polarization. (b) E_z-field profile of the triple-slit aperture at the center of the cavity-aperture under incident light of 671 nm.

Download Full Size | PDF

Considering electric field profiles of the two component apertures in Figs. 4(a)–4(c), the X-aperture has the electric fields at the two acute wedges as well as at the four oblique half-length slits for incident polarization in Fig. 4(b), while the l-aperture has field profiles of typical SP excitation at a nanoslit perpendicular to incident polarization in Fig. 4(c). As the X- and l-shapes are combined into the triple-slit aperture, the fields distributed widely around the two obtuse wedges of the X-aperture are highly confined at new four acute wedges of the triple-silt aperture, and the fields at the center of the l-slit are redistributed to the six acute wedges of the triple-slit aperture in Figs. 4(a)–4(c). We provide two field profile images of the folded slit aperture (<-aperture) and the oblique slit aperture (⁄-aperture) to investigate the effect of the acute wedges on the field enhancement in Figs. 4(d) and 4(e). The maximum intensity at the wedge of the <-aperture is about five times higher than that of the ⁄-aperture. We infer that the strong confinement and enhancement is induced by the wedge effect because the only difference of the two apertures is the one acute wedge of the <-aperture: they have same area and oblique angle since the <-aperture is a folded form of the ⁄-aperture. For quantitative comparison, the field intensities of various nanoapertures in Figs. 4(a)–4(f) are shown in Fig. 4(g). The intensity increases in order of the triple-slit, X-, l-, <-, ⁄-, and circular apertures. The field intensity of the ⁄-aperture is lower than that of the l-aperture because only the components perpendicular to the oblique slit of polarized light contribute to SP excitation of the oblique slit. The intensity of the <-aperture is a level between those of the l- and the ⁄-aperture, the X-aperture has two times higher intensity than the <-aperture. Although the X-, l-, <-, ⁄-apertures have smaller areas than the circular aperture, the formers confine and transmit light with higher intensities than the latter. Therefore, it is desirable to adopt a narrow slit as a basic structure instead of a circular aperture and to change it into a triple-slit shape with six-fold rotational symmetry for efficient SP excitation by incident light with three polarization directions.

 

Fig. 4 Electric field profiles of (a) triple-slit, (b) X-, (c) l-, (d) <-, (e) ⁄-, (f) circular apertures. (g) Comparison of their electric field intensities. The field profile images of (a)-(f) indicate the corresponding intensity curves with arrows. The X- and l-apertures are decomposed from the triple-slit aperture and the triple-slit and the circular apertures have same area.

Download Full Size | PDF

4. Experiment of a triple-slit aperture

In order to realize the simulation results in experiments, we made the triple-slit and the circular apertures in the cavity-apertures on a silver thin layer as follows. A thin silver layer of 150 nm thickness was deposited on a clean glass substrate using an e-beam evaporator (KVE-3004, Korea Vacuum Tech.). Three cavities with a depth of 150 nm, a width of 200 nm, and a length of 1.2 μm, 2.7 μm, and 3.1 μm were milled with a focused ion beam (FIB; Quanta 200 3D, FEI) of 30 kV and 0.1 nA. A thin silver layer of 150 nm thickness was deposited on the cavity sample again, and then triple-slit or circular apertures were milled at the cavities with the FIB of 20 kV and 4 pA. The fabricated samples were measured by a field emission SEM (JSM 6700F, JEOL), as shown in Figs. 5(a) and 5(b). We arranged the various nanoapertures by shape and size in the same region in order to measure them at the same time under the same illumination of incident light for an accurate comparison. The upper and the lower cavity-apertures in Fig. 5(c) have the different nanoapertures of the triple-slit and the circular shape, respectively. The slit lengths of the triple-slit aperture are 40 nm, 80 nm, 130 nm, 180 nm, and 200 nm from left to right in keeping the slit width of 20 nm, while the diameters of the circular apertures are 36 nm, 60 nm, 80 nm, 97 nm, and 102 nm, which correspond with the areas of the triple-slit apertures. The optical microscopic transmission images of the samples illuminated by red laser of 671 nm are provided in Fig. 5(d). The transmission intensity increases as the size increases from the left to the right aperture. In comparison of the upper and lower apertures, the intensities of the triple-slit apertures are mostly stronger than those of the circular apertures. Although the triple-slit apertures show a little anisotropic shapes in the upper transmitted spots, they are expected not to be distinguished by human eyes having resolution of a few tens micrometers in displays as potential applications.

 

Fig. 5 Magnified SEM images of (a) the triple-slit aperture and (b) the circular aperture of cavity-apertures. (c) SEM and (d) optical microscope images of the triple-slit and the circular apertures in the cavity-aperture array for their comparison. There are triple-slit and the circular apertures of five different sizes in the upper and the lower cavity-apertures, respectively. Their areas are same in the same column and increases from left to right. Slit lengths and diameters are noted near the triple-slit and the circular apertures, respectively.

Download Full Size | PDF

We plot a graph with the experimental data for quantitative analysis, as shown in Fig. 6(a). After measuring the microscope images of transmitted light through the cavity-aperture and bare light without the sample, we acquire the transmittance by calculating the intensity ration of the former and the latter. They are average transmittances of ten samples and the standard deviations are marked with error bars. The upper blue circular points and the lower red rectangular points indicate the transmittances of the triple-slit and the circular apertures, respectively. The x-axis is the effective diameter of the aperture and the corresponding lengths of the triple-slit apertures are noted near the blue circular points. The transmittance of the triple-slit aperture are enhanced from about 1.2% to about 4.6% as the slit length increases from 40 nm to 200 nm. It increases more rapidly than the transmittance of the circular aperture. In order to compare the experimental data with simulation data, we integrate the output power through the cavity-aperture over a parallel plane away from it by 1.5 μm, and then obtain the transmittance from the ratio of the output and the input powers. Assuming the nanoaperture at the center of the cavity-aperture radiates light like a single point dipole and the distance of 1.5 μm satisfies the far-field condition of Fraunhofer region in antenna theory, the integration of the outward power over solid angle may is proportional to the transmittance in far-fields. The behaviors of the experimental transmittances are similar to those of the simulation data, as shown in Figs. 6(a) and 6(b). The curves in the green dotted box on the simulation graph are corresponding to the experimental data. In spite of the qualitative similarity, there is a difference between them. The difference between the intensities of two experimental curves are smaller than those between two simulation curves. The maximum transmittance of the triple-slit aperture is lower in the experimental graph than in the simulation graph, whereas two curves of the circular aperture are significantly similar to each other except a shift along y-axis. In terms of simulation, it may be because a kind of errors due to non-ideal radiation pattern of the triple-slit aperture as shown in Fig. 5(d). In terms of experiment, the reason may be that the plasmonic effect of the triple-slit aperture does not fully contribute to the transmittance in experiment because of fabrication errors including blunt edges in FIB milling process: the triple-slit aperture has more sharp edges than in the circular aperture. In addition, the roughness of the silver layer may also influence the discrepancy because the rough metal surface can obstruct SP propagation in the experiment. Therefore, we think that the experimental results sufficiently support the improvement of transmittance by the triple-slit aperture in spite of the differences.

 

Fig. 6 Size-dependent transmission behaviors of the triple-slit and the circular apertures in (a) experiment and (b) simulation. The slit lengths of the triple-slit aperture are noted near the corresponding points. The region marked by the green dotted box on the simulation graph is corresponding to that of the experimental graph.

Download Full Size | PDF

5. Conclusion

In this study, we suggested the triple-slit aperture as the nanoaperture in the cavity-aperture, which has to transmit incident light with high efficiency. The transmittance of the proposed nanoaperture is theoretically about five times and experimentally about two times higher at an optimized ratio of the slit width and length than that of the circular aperture. In considering the transmittance of about 1% in the previous research [6], the transmittance of about 4.6% in the triple-slit aperture implies significant improvement in the transmission efficiency of the cavity-aperture. In particular, the triple-slit aperture can have high transmittances at all three angular directions of incident polarization. It is possible thanks to the strong confinement and transmission of electric fields by plasmonic resonances at the nanoslit and the wedge structures: the triple-slit aperture provides always one slit and two symmetric acute wedge nanostructures to each of three cavities. The rotational symmetric geometry of the triple-slit aperture can be expanded to research of polarization-insensitive nanoapertures with high transmission efficiency in considering that most of unconventional nanoapertures including C- and bowtie-apertures are significantly polarization-dependent. Since it is reported that polarization-insensitive plasmonic color filters can reduce crosstalk of colors and contribute to clear and bright images [22], various studies on a modification of the triple-slit aperture or a design of polarization-insensitive apertures will be meaningful in expanding plasmonic application area.