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Abstract
In this study, we investigated plasmonic field localization with trapezoidal nanopatterns under normal incident light excitation to find optimum structures for sensing and imaging. A finite element method was used to calculate the fundamental characteristics of the localized surface plasmon with varied trapezoidal nanopatterns. First, we describe how to localize the plasmonic fields on the trapezoidal patterns and then report our results from the investigation of the optimum properties of the nanopatterns for maximized field intensity. Initially, we expected that maximized field localization would lead to enhancement of the sensing sensitivity or imaging resolution in plasmon-based sensing and imaging systems. However, more interestingly, we found a field cancellation effect under specific modality conditions through the simulation. Thus, we thoroughly investigated the principle of the effect and extracted the modality conditions that induced field cancellation. In addition, specific modality conditions of nanopatterns that could be fabricated with conventional lithographic methods were numerically determined. Then, the field cancellation effect was experimentally verified using scanning nearfield optical microscopy. The results indicate that trapezoidal nanopatterns bring about enhanced field localization at the shaper edge of nanopatterns than do conventional rectangular nanopatterns and that plasmonic field cancellation can be observed under specific modality conditions of nanopatterns, even for conventional rectangular nanopatterns. Thus, it is suggested that careful fabrication and maintenance are needed to obtain strong plasmonic localization. Finally, the feasibility of providing a novel sensing platform using the field cancellation effect is suggested.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Localized surface plasmon resonance (LSPR) using noble metal nanostructures, which is associated with a collectively oscillating wave of free electrons, has received attention in recent years because of its astonishing optical properties including sharp spectral absorption [1,2], polarity of refracted light, and highly localized electromagnetic field [3,4]. The plasmonic interaction in the nanostructures yields highly localized hot spots and have thus offered remarkable opportunities to enhance optical signals beyond what is possible with incident light. The enhancement of optical signals can be explained as a spectral peak shift, increased optical intensity including Raman scattering [5,6], and extraordinary optical transmission [7,8]. Local electric-field focusing has immediate potential for plasmonic sensing [9,10,11,12] and imaging [13,14]. Till date, plasmon-mediated sensing and imaging have been widely adopted in many different research fields, including label-free detection of biomolecular interaction [15,16], as well as the imaging of locomotory behaviors of biomaterials on a nanometer scale [13,17].
The optical features of the hot spots typically depend on novel nanostructure geometry: the shape and size of the nanostructures, and the distance between them. First, the electric field intensity in the vicinity of a nanostructure with sharp corners or edges is dramatically enhanced when a surface plasmon is confined to a nanostructure of which the size is comparable to the wavelength of incident light. This is called the nanoantenna effect [18]. Second, hot spots can also be controlled by tuning the distance between plasmonic nanostructures. The individual localized surface plasmons in proximal nanostructures can be hybridized to generate a new set of surface-plasmon polaritons (SPPs) over the entire structure [19]. This is generally termed a nanogap plasmonic effect. Because significant progress in nanotechnology has enabled the fabrication of various noble metal nanostructures (such as nanoparticles [20], nanorods [21], nanowires [22], and nanoholes [23]), the strength and nature of the optical interaction between plasmonic metal nanostructures have been extensively studied. Of particular interest are nanopatterns with trapezoidal cross-sectional shapes, which provide sharp corners and gaps between the nanostructures. Thus, for such nanostructures, we expect a highly localized hot spot due to synergism between the nanoantenna and nanogap effects [24,25,26]. Despite the unique merit of trapezoidal-shaped nanopatterns, there is not yet a systematic computational model able to provide understanding of the localized plasmonic polaritons in those nanostructures and issues concerning the optimization of plasmon-based imaging performance remain to be studied.
In this study, the characteristics of localized surface plasmonic field distributions on the trapezoid nanostructures were analyzed using a finite element method (FEM). First, we determined the calculations needed to analyze quantitatively the conformations of new localized SPPs to be formed, by changing the geometries of the nanopatterns. We also investigated an unambiguous correlation between the improvement of electric field strength and induced electric field by the geometry of nanostructures under upward normal incident light. Through the simulation, we found that conventional nanopatterns which is practically accessible pattern also exhibit field cancellation phenomena under specific configurations. It drives that a practical way to achieve field cancellation with even conventional types of nanopatterns can be suggested with a certain nanopattern geometry that induce this interesting phenomenon. For confirmation, we subsequently examined this form of field cancellation in relation to a conventional rectangular cross-section nanopattern in a specific configuration using surface nearfield optical microscopy (SNOM). We then compared these results with the calculation results.
2. Materials and methods
2.1. Numerical method
The FEM calculations were carried out using a mathematical tool with the numerical analysis and programming environment needed to solve the time-domain wave equation:
Fig. 1. (a) Schematic image of a trapezoidal nanopattern: The parameters of the nanostructure are defined as ℓt, ℓb, h, and d. Inset shows k-vector and polarization of incidence light source. (b) Plasmonic field distribution on the trapezoidal structure with diverse ℓt when ℓb is fixed as 100 nm. The colors represent the |E| field intensity, as shown in the color bar.
2.2. Fabrication
After cleaning the glass substrate with acetone, alcohol, and DI water, a 40 nm-thick gold film was deposited using an evaporator, onto BK7 substrate with a 5 nm-thick Cr adhesion layer. To fabricate the nanowire pattern on the substrates, electron-beam (e-beam) lithography was employed. For this, an approximately 220 nm-thick positive e-beam resist of poly (methylmetacrylate) (PMMA; AR-P 679.045, Allresist GmbH, Strasberg, Germany) was deposited on the substrates using a spin coater. With an e-beam lithographic system (Draw beam, TESCAN, Brno, Czech Republic), the nanostructures were patterned to have a width of 170, 240, 270, 280, and 290 nm with 2 µm-period. The resist was developed using 3:1 isopropyl alcohol (IPA) and methyl isobutyl ketone solution for 3 min, and then immersed in IPA solution for 2 min. After deposition of a 100 nm-thick gold layer onto the developed substrates, the remaining e-beam resist was removed by a lift-off process after using acetone for 10 min. Finally, rectangular cross-section gold nanowire patterns (ℓt = ℓb=170, 240, 270, 280 and 290 nm) were fabricated on the substrate and the fabricated patterns were confirmed using scanning electron microscopy (SEM, VEGA3, TESCAN, Brno, Czech Republic) which can sufficiently replace the trapezoidal structures by performing similar localization or cancellation of the electric fields.
3. Results
To apply a nanostructure as a sensitivity enhanced LSPR sensor, it is essential to design an optimal structure able to confine effectively an electromagnetic field on the structure. For this reason, we performed a simulation to estimate the field localization and normalized |E| intensity relative to experimental nanopatterns to find the optimal features of the trapezoidal structure to localize electromagnetic field strongly. As a representative model, we fixed ℓb of the trapezoidal structures to 100 nm, and the confinement of electromagnetic field was calculated when ℓt of the trapezoidal structure was varied from 100 to 300 nm. Some of the more noteworthy results are presented in Fig. 1(b). The values of the field intensity at each x-y coordinate are indicated in different colors, as shown in the color bar. Interestingly, we observed that the field localization was extremely different depending on the ratio of ℓt to ℓb. As shown in the image, extremely high intensities in the localized field were observed at ℓt = 150, 180, and 200 nm when ℓb = 100 nm. On the other hand, extremely attenuated fields were observed for a trapezoidal structure with ℓt = 168 nm and ℓb = 100 nm. To investigate the trends of field extinction and localization of the trapezoidal structures, the field distributions for the four configurations of trapezoidal structures were analyzed and the spectra are presented in Fig. 2(a). The ℓt was varied in 1 nm steps to have a ℓt to ℓb ratio of 1–3, when ℓb = 50 nm (black dots), 100 nm (red dots), 150 nm (green dots), and 200 nm (blue dots). As indicated by the red dotted line (ℓb = 100 nm), the intensity of the confined field gradually increased when ℓt of the structure was increased to 150 nm, and the maximum electrical intensity reached ∼11 kV/m. After that, the electrical intensity suddenly decreased until the ratio of ℓt to ℓb was 1.68. The intensity of the confinement was almost completely cancelled (nearly 0 kV/m), when the ℓt of the structure was approximately 168 nm. Remarkably, the localization of the fields on the wire structure recovered dramatically to around 70% of the highest previous field intensity states, when the ℓt was about 180 nm, while retaining ℓb = 100 nm. The maximum field intensity on the ℓt = 180 nm structure was 2.93 times higher than that of a ℓt = 100 nm structure. When setting ℓt to >180 nm, the intensity of the localized electromagnetic field was observed to decrease gradually. The localized electrical intensity of the structures with ℓb = 50, 150, and 200 nm had extinction points at the ℓt to ℓb ratios of 2.98, 1.26, and 1.085, respectively.
Fig. 2. (a) Calculated plasmonic intensity on the trapezoidal structures. The trends of intensity are based on calculations according to length ratio (ℓt / ℓb). With some ℓb conditions (50, 100, 150, and 200 nm), the plasmonic intensities are drastically reduced at some points. (b) Reflectance also fluctuates at the same point of the reduction conditions shown in (b). The inflection points of the graphs matched well the field-cancellation conditions of the graph in (a).
As shown in Fig. 2, plasmonic field intensities can be sensitively adjusted by changing the properties of the nanopatterns. Figure 2(a) shows that the maximum field intensity of |E| changes with changes in the nanopattern shape. Nanopatterns with bottom lengths of 50, 100, 150, and 200 nm, showed maximum field localization when their top lengths were around 130, 150, 170, and 190 nm, respectively. As the bottom length increases, the top length should be decreased to obtain the strongest field intensity. This means that trapezoidal nanopatterns with bottom lengths <180 nm are required for optimal field localization. In contrast, for bottom lengths >180 nm, pyramidal nanopattern designs are better for achieving optimal field localization. In addition, we confirm that the maximum field intensity increased to ∼ 11 kV/m2 for a nanopattern with ℓb = 100 nm and ℓt = 150 nm, or with ℓb = 50 nm and ℓt = 130 nm. The results indicate that trapezoidal nanopatterns may simply be better than pyramidic nanopatterns for creating strong field intensity without any other requirements.
Here, as shown in Fig. 2(a), we made the interesting observation that the field intensity was suddenly damped after reaching the maximum field intensity as the top length increased, in all cases. The unexpected damping phenomenon resulted in abrupt decline of the field intensity on the nanopatterns to nearly zero. To explain the phenomenon, we calculated the reflectance of incident light for nanopatterns with two different ratios (Fig. 2(b)). The relation between extinction point and absorption properties was investigated using the reflectance spectra from the nanopatterns. We predicted that the electrical properties of specific configurations of the nanopatterns would affect their optical properties, especially under the field damping conditions. As expected, the highest reflection points in the spectra coincided with the damping points in Fig. 2(a). Consequently, we have confirmed that the electrical properties in a particular nanopattern can be detected using spectral changes related to correlation of electrical conditions with the incident light. Therefore, we needed to investigate the electric field flow using Poynting vectors to observe the changes in electrical characteristics that occur around and inside the structures; the plots are presented in Fig. 3.
Fig. 3. Poynting vectors of electrical fields on a trapezoidal structure with fixed 100 nm ℓb and varied ℓt ; (a) 150 nm, (b) 168 nm, and (c) 180 nm. Electrical fields are drastically reduced in (b). As ℓt increases after condition (b), a strong electric field is re-generated, but in the opposite direction. (d) Schematic circuit model of the trapezoidal structure.
Poynting vectors of electric field flow are represented by arrows near trapezoidal nanopatterns with fixed 100 nm ℓb and varied ℓt (150, 168, and 180 nm) in Figs. 3(a)–(c). Each arrow indicates the direction of the electric field and magnitude proportional to the intensity. As shown in Fig. 3(a), the ℓt = 150 nm structure is affected by strong electrical fields in the same direction as the electrical component of the incident light. At that time, the electric field flows through the film and structure like a conducting wire that has a partially thick area. In addition, it changes direction according to the incident light wave. As ℓt increases, the size of the relevant arrow becomes very small, meaning that the field intensity has dropped sharply. The structure with ℓt = 168 nm (showing decline to almost zero of the field intensity) is presented in Fig. 3(b). When ℓt was 180 nm, the arrow became larger again, and the recovered field intensity is presented in Fig. 3(c). As shown in Fig. 2(a), the 180 nm (ℓt) structure has a strong electric field flow as on the 150 nm (ℓt) structure. However, it is noteworthy that the predominant direction of flow is different in the two structures. We can confirm that the direction changed at a structure size of 163 nm (ℓt), which shows nearly zero field intensity. Therefore, it is understood that such a change in the electric field will cancel the existing flow, subject to a phenomenon that affects the optical characteristics as well. Consequently, we call the phenomenon as “field cancellation” by which electric field flows are damped under specific conditions.
The phenomenon of a rotating electric field near a metallic structure caused by normal incident light has been described as a closed-circuit model in nanoparticles [29], nanorods [30], and nanowires [31]. Therefore, a model was introduced to understand better the field-cancellation phenomenon. The phenomenon of looped electrical fields is a diamagnetic response based on a time-oscillating magnetic field, which induces an eddy-current at the metal structure and a displacement current in the dielectric material. The material between the two metal layers was modeled as a dielectric, denoted by Cg and Ca respectively, where Cg is capacitance model based on dielectric material gap generated between top metal edge and bottom metal and Ca is capacitance model generated by air between nanowires. The charge movement and drift current relative to the frequency of the incident light create inductance Ln in the metallic nanostructure and Lf in the thin metallic film. The circuit model was designed based on the previous articles [32,33]. As ℓt increases, Ln becomes larger and Cg becomes smaller. Consequently, the electrical field from Ln gradually becomes stronger and suppresses the electrical field from the film. At this moment, the looped electric field and the electric field caused by the film cancel each other, and the intensity decreases at a specific ℓt/ℓb ratio. When ℓb increases, the metal structure admits more magnetic fields and forms a stronger looped field, resulting in a smaller ratio as a decreasing condition; however, due to the large structure volume, the overall field strength is reduced.
The results presented in Figs. 1–3, provide valuable insight into the issue of plasmonic field cancellation and localization on trapezoidal nanopatterns. It also suggests optimized conditions of trapezoidal nanopatterns for creating strong field localization. However, techniques by which to fabricate a nanopattern with trapezoidal cross-section with high accuracy is still in the developmental stage. Therefore, this should be addressed by finding a nanopattern that could be both easily fabricated and employable to enhance field localization. Here, the conformational conditions of the most widely used conventional nanopattern shapes that might be used to achieve extreme field localization were investigated. Calculations were performed with ℓb = ℓt for the interval from 100 to 500 nm, and the maximum intensity for each condition is presented in Fig. 4(a). As we expected, the interesting damping phenomenon was also observed in a graph of a nanopattern with rectangular cross-section. According to the data, a highly localized field was obtained when ℓb = ℓt = 157.7 nm. Moreover, the most drastic decrease in the localized field intensity was obtained when ℓb = ℓt = 240 nm. When these conditions were exceeded, the rectangular cross-section nanopatterns had nearly no ability to localize a plasmonic field. The highest field intensity localized on the pattern with ℓt = ℓb = 157 nm, was 100 times higher than the lowest field intensity when the width of the nanopattern with rectangular cross-section was 240 nm. Moreover, the maximum localized field intensity drastically decreased to 60% when the length of the nanopattern with rectangular cross-section was changed from 175 to 200 nm. This result means that a slight difference in the width of fabricated nanopattern, such as might occur from inherent fabrication error, decreased the field localization performance. Figure 4(b) shows that the localization and cancellation of electric fields also occurred for rectangular nanopatterns of a variety of widths, as was observed on the trapezoidal nanopattern seen in Figs. 1–3. The 2D profile of the electric field strength on the rectangular nanopatterns with ℓb = ℓt = 100, 157, 240, and 300 nm are depicted. As a result, when a rectangular (cross-section) nanopattern had ℓb = ℓt = 157 nm and a height of 100 nm, it formed a highly localized field on the pattern when exposed to upward-directed incident light at 633 nm. As shown in Fig. 4, the field strength decreased drastically when a nanopattern with rectangular cross-section had a width of 157.5 nm or more.
Fig. 4. (a) The plot of maximum electric field intensity |E| on ℓt = ℓb rectangular nanopatterns when the width of rectangular nanopattern is the range from 100 nm to 500 nm. (b) 2D contour map images of the electric field strength on rectangular nanopatterns with ℓt = ℓb = 100, 157, 240, and 300 nm.
To verify the field cancellation indicated in Fig. 4, we fabricated nanopatterns with rectangular cross-sections of various widths (170, 240, 270, 280, and 290 nm) and then measured the nearfield distributions on those nanopatterns using a nearfield scanning optical microscope (SNOM, WITec, Alpha 300RS). The measured nearfield distributions on those fabricated nanopatterns are shown under the respective SEM images. For the measurement, a 633 nm He-Ne laser source (the same wavelength used in the simulations) was used in transmission mode. A cantilever tip with a 60 nm aperture was used to scan fully the nanopattern surface in 1 nm steps using an XYZ stage. The SNOM data show dramatic reversal states of field localization with approximately 100 nm-wide increments. Strong localized plasmonic fields were observed with 170 nm-wide nanopatterns, while very low field intensity (close to zero) was measured for the 290 nm-wide nanopatterns. To compare the correspondence of the measured reversal mode of the electric field with that of the simulation data, the trends were compared and are shown in Fig. 5(b). The gray dash line represents the simulation results and the red hollow square symbols represent the measured maximum field intensity using SNOM with an upward directed 633 nm laser source. As presented, the measured SNOM data matches well the simulation data. Consequently, it should be noted that when the 633 nm laser was vertically incident from below, the intensity of the nearfield on the nanopatterns dissipated rapidly for widths of ∼175–225 nm due to the field cancellation phenomenon presented in Fig. 3. These results suggest two meaningful possibilities. First, when we design a nanostructure for electric field localization for any reason, the outcome field confinement obtained with the fabricated nanopattern may be very sensitively modulated, while retaining the sample quality. Second, the dramatic field reversal has the potential to provide a highly sensitive sensing platform. In this paper, all structures were simulated in air without any change in refractive index. In the case that we find optimal conditions that cause dramatic changes in intensity with change in the refractive index of the medium, such structures might be applied as highly sensitive plasmonic sensors.
Fig. 5. (a) Measured nearfield image of a 200 nm-wide nanopattern. (b) Comparison on nearfield intensity measured by SNOM data (red square dot) with that of simulation data (grey dashed line).
4. Conclusions
In this paper, we conducted a simulation to find the optimal ℓt to ℓb ratio of nanopatterns with trapezoidal cross-sections to obtain extremely localized electric fields at the edges of the nanopatterns. We observed that the trapezoidal nanopattern confines the electric field drastically when ℓb = 100 nm and ℓt = 150 nm, or when ℓb = 50 nm and ℓt = 130 nm. However, we also observed a contradictory phenomenon in which not only extreme confinement of the electric field, but also extreme cancellation of the electric field on trapezoidal nanopatterns occurred. According to the simulation results, the extreme localization and cancellation of the plasmonic fields on nanopatterns was affected by a specific ℓt to ℓb ratio of the trapezoidal nanopatterns. This means that the ℓt to ℓb ratio of the nanostructure is an important factor for determining the intensity of the plasmonic fields generated on the structures. This interesting phenomenon can be adjusted by changing the ℓt to ℓb ratio of metallic nanopatterns with a trapezoidal cross-section. In particular, an approximate 10 nm difference in ℓt when ℓb is 100 nm, resulted in extreme loss of localization and this could be a critical issue when applied to a practical tool. There are some researches that could be applied for or presenting feasibility for fabricating a trapezoidal nanowire pattern [34,35]. However, as the fabrication techniques are still in development for fabricating highly accurate trapezoidal nanopatterns, there might be a need for finding similar phenomena with accessible nanopatterns that can be produced presently. Thus, we conducted more simulations to observe the field cancellation and confinement effects at a specific length ratio (ℓt = ℓb) of nanopatterns with rectangular cross-sections. For practical confirmation, we fabricated rectangular nanopatterns of particular proportions and observed the effects on field confinement and cancellation effects using nearfield measurement with SNOM. According to the results, approximately 40% of unexpected field loss can occur due to differences of as little as 25 nm within a specific range of nanowire width. Thus, it is essential to fabricate nanostructures to exact design criteria to obtain effective results for strong field localization with newly designed nanopatterns.
Funding
National Research Foundation of Korea (2017M3D1A1039287, 2017R1C1B1009059, 2018R1A4A1025623).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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