1. Introduction

Surface plasmon resonance (SPR) is a well-known phenomenon that represents the resonant oscillation of conduction electrons at the interface between negative and positive permittivity material under the stimulation of an incident light [1,2]. This phenomenon occurs also on the surface of nano-sized metal objects where the resonant oscillation is spatially limited, which is therefore called localized surface plasmon resonance (LSPR) [3–6]. When many metallic nanoparticles are organized closely to each other, forming a so-called nanoparticles array (NPA) or plasmonic structure, the interaction between the resonance modes of the individual nanoparticles induces a propagating plasmon thanks to the plasmonic coupling of the LSPR modes [7,8]. These plasmonic effects are very interesting and useful for many applications in different domains, from fundamental physics to chemistry, biology and medical treatments [9–11].

Recently, the metallic nanoholes array (NHA), which is similar to metallic NPA, has received particular attention due to its extraordinary character of transmission [12–17]. There have been numerous studies for developing its potential applications, such as optical filter [18,19], biosensing [20–23], color printer [24–26], etc. Since the period of plasmonic structures (NHA or NPA) is very small, in the order of the excitation wavelength, the fabrication of those structures requires complicated and expensive methods. In general, we can distinguish two main methods to realize plasmonic nanostructures: indirect and direct fabrication methods. The most commonly used method is the indirect one, which is cheap but complicated, consisting in three steps. First, a polymeric template is fabricated by standard fabrication methods, such as electron-beam lithography [27], nanoimprint lithography [28] or soft UV nanoimprint lithography [20], nanosphere lithography [29], interference lithography [30], and direct laser writing (DLW) [31]. Then, the metallic thin film is deposited on the polymeric template by using thermal evaporation or sputtering method. Finally, the lift-off method is used to remove the polymeric template leaving the desired metallic structures on substrate. It is also possible to obtain plasmonic structure by direct fabrication method without the use of polymeric templates, but this requires an energetic source that enables defusing of a metallic thin film. The focused ion beam technique is the most commonly used [32] as direct fabrication method of plasmonic nanostructures. This fabrication method has the advantages of one-step and high resolution. But it has also some disadvantages, such as it needs a high vacuum system and it is expensive and easy to damage the substrate. This direct fabrication method is therefore not available to most research laboratories.

In this work, we report a new direct fabrication method for plasmonic nanostructures by using a one-photon absorption (OPA) based DLW assisted by a local thermal effect. We demonstrate that arbitrary gold nanohole arrays (Au NHAs) can be realized by this simple and low-cost technique, which can open the way for numerous applications. The paper is organized as the following. In section 2, we theoretically investigate the optically induced local thermal effect and experimentally demonstrate the realization of Au NHAs by a single-step DLW method using a continuous-wave green laser. In section 3, we realize the numerical calculation of the optical properties of these fabricated structures by using FDTD simulation method, and compare with those of ideal structures. The transmission spectra of fabricated structures will be also measured to confirm the simulation results. Finally, we give some conclusions of this work and show the main advantages of the structures realized by this direct fabrication, as well as their potential applications.

2. Realization of Au NHAs by a single-step direct laser writing method

2.1 Experimental setup and fabrication mechanism

Figure 1(a) illustrates the sketch of the DLW system. A 532 nm continuous-wave (CW) laser was used as the light source for fabrication. The laser wavelength is located in the absorption band of the Au material, which allows converting the light energy to temperature, and which accordingly induces an evaporation effect. The laser power can be adjusted from 0 to 5 W, but the required laser power for all fabrications of this work was less than 400 milliwatts. A quarter-wave plate (QWP) was used to obtain a circular polarization of the incident light, which ensures a perfect circular focusing spot. The exposure time was controlled by an electronic shutter (S), with a minimum switching time of 2.5 $\mathrm{\mu}$s. The laser was focused into the Au sample by using an air-immersion objective lens (OL), which has a high numerical aperture (NA = 0.9). The focusing spot size was theoretically estimated to be 272 nm [33]. The sample was mounted on a three-dimensional piezoelectric translation stage (PZT) having a resolution of 0.1 nm. We note that the determination of the Au film position is very important, since the Au film thickness is only 50 nm. For that, a very weak but not negligible fluorescent signal from the surface of the Au sample is detected by a confocal system consisting of two lenses (L1, L2) and a pinhole (PH, diameter of 100 $\mathrm{\mu}$m). The beamsplitter (BS) was used to separate the green excitation beam and the fluorescent beam. The long-pass filter (F) having a cut-off wavelength at 580 nm was used to stop totally the residual green light and let only the fluorescent signal to the detector. Figure 1(b) represents a large view of the focusing area of the DLW method. The PZT was controlled by a computer and synchronised with others such as the shutter and the detector, allowing the realization of any one-, two-, and three-dimensional (1D, 2D, 3D) patterns with sub-wavelength size [34]. In this work, this DLW system was used to obtain desired 2D Au NHAs.

 

Fig. 1. (a) Schematic representation of the experimental setup used to realize metallic nanostructures. QWP: quarter-wave plate, S: electronic shutter, M: mirror, BS: beam splitter, L1/L2: lenses, OL: objective lens, PZT: piezoelectric translation stage, PH: pinhole, F: Long-pass filter. (b) Zoom in of the focusing area. (c) Illustration of the optically induced thermal effect. The green color represents the laser focusing beam while red color represents the simulation image of the corresponding induced temperature. (d) Plots of laser intensity and induced temperature distributions along one line indicated by $x$-axis in figure (c). (e) The simulation result of induced temperature as a function of the excitation laser intensity at the center of focusing spot for a 50 nm-thickness Au film. The evaporation of Au thin film happens at a minimum laser intensity corresponding to an induced temperature of about $600^{\circ }$C, called threshold.

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The mechanism of the direct fabrication method is illustrated in Fig. 1(c). This is called optically induced local thermal effect, which was previously demonstrated by our works [35,36] for very thin Au or Silver (Ag) samples. Actually, when a green laser is focused into a Au thin film, the Au material absorbs the light and converts it to temperature. This happens locally and temporally thanks to the confinement of the laser beam and the control of the light exposure. We have already investigated a laser heating model to modelling the thermal response of the Au thin film under a green focusing spot [35]. For that, we have applied the intensity distribution of a focused laser beam (high NA OL), which is rigorously calculated by using the vector Debye method [33], into the laser heating model [37]. By using the finite element method with a MATLAB PDE solver, the temperature distribution of absorbing material under a laser illumination was numerically solved to characterize the optically induced heat profile. In the focusing area of the CW green laser, the heat is accumulated and then the temperature increases and becomes stable after several milliseconds. Due to the thermal conductivity of the material, the temperature spot is broader than that of the light spot, as shown in Fig. 1(d). But depending on required temperature, the fabricated structure can be much smaller than the full width at half maximum (FWHM) of the hot spot [38]. Figure 1(e) shows the induced temperature at the laser focusing center as a function of different laser intensities. Experimentally, we found that with an excitation laser power of about 100 mW, corresponding to a theoretical value of the induced temperature of $600^{\circ }$C, a Au nanohole can be obtained in a Au film of 50 nm-thickness. This corresponds to a so-called threshold in Fig. 1(e). This threshold varies as a function of the Au film thickness, $i.e.$, it is lower for thinner Au film. For example, the threshold was about 60 mW for a Au film of 12 nm-thickness [35,36]. In literature, it was demonstrated that the melting temperature and the corresponding evaporation temperature of metallic thin films, such as Au and Ag [39,40] become much lower than those of bulk materials, which is higher than $1000^{\circ }$C. That is why with an induced temperature of about $600-700^{\circ }$C, Au thin film can be evaporated leaving an air hole. We note that this temperature is still lower than the melting temperature of glass substrate, which is in between $700-800^{\circ }$C [41]. Therefore the creation of Au NHs does not damage the glass substrate.

In this work, the Au film sample was prepared directly on a glass substrate (1 mm-thickness) by the sputtering method, which has been done in a vacuum chamber with a high voltage (Emitech K650 magnetron sputter). The thickness of the Au film is measured to be 55 $\pm$ 1 nm by using a profilometer (Dektak). Compared with the Au film prepared by the thermal or laser evaporation method, the Au film prepared by sputtering method does not have a high quality, but it is thick and smooth enough to be used as plasmonic surfaces.

2.2 Experimental results

By applying the OPA-based DLW method, desired 2D Au NHAs having different configurations, $e.g.$, square and hexagonal patterns, have been fabricated. The laser power was adjusted from 130 mW to 360 mW to change the holes diameters from 0.3 to 1 $\mathrm{\mu}$m, respectively. The periods of the structures were also changed from 300 nm to a few $\mathrm{\mu}$m. It was demonstrated that 2D Au NHAs structures with a period as small as 500 nm have been successfully elaborated. That minimum period is imposed by the diffraction limit of the optical system but also due to the thermal effect and the quality of the metallic thin film. Figure 2(a) shows, as an example, a scanning electron microscope (SEM) image of a square structure of Au NHAs (period =1 $\mathrm{\mu}$m), fabricated by a laser power of 160 mW. Each Au NHA is fabricated in an area of 100 $\mathrm{\mu}$m $\times$ 100 $\mathrm{\mu}$m, according the movement range of the PZT, in order to facilitate the transmission measurement. We can see that the Au NHA is perfectly uniform for the whole area, ensuring a good property of the plasmonic structure. The OPA-based DLW method is thus an excellent method allowing simplification of the plasmonic nanostructure fabrication in a single step. It is worth to mention that, since the creation of the air-hole is based on the thermal effect, the local induced temperature also has the effect on the Au film near focusing center. Indeed, as seen in Figs. 1(c) and 1(d), the thermal spot is much larger than the light focusing spot. The high temperature at the outer part of the thermal spot, even not high enough to induce the evaporation effect of the Au film, is close to its melting temperature [39,40], resulting in the movement of Au material. This thus deforms the Au film and produces a large number of tiny holes (few dozens nanometers) which randomly appear between the main air-holes created by the laser spot, as shown in Fig. 2(b) for the square structure and in Fig. 2(c) for the hexagonal structure. This surface deformation was also observed when the Au thin sample is put on a hot plate at $400-500^{\circ }$C. Figure 2(d) shows a statistic number of the random tiny nanoholes and desired air-holes and their corresponding sizes, which are calculated from the SEM image shown in Fig. 2(a). There are a large amount of small nanoholes whose size is smaller than 50 nm, together with intentionally fabricated nanoholes, which have a size of around 340 nm (Fig. 2(e)). Here again, the variation of the size and the shape of the large air-holes can be also explained by the deformation of the Au thin film during the evaporation effect. Nevertheless, as it will be demonstrated in the next section, the appearance of the small and randomly distributed nanoholes and the non-uniformity of large air-holes do not affect the plasmonic properties of the fabricated Au NHAs. We note that the influence of the thermal effect on the formation of nanoparticles was demonstrated depending on various experimental parameters [42–45], such as substrate (glass, silicon wafer, polymer, etc.), as well as the gas nature (Argon, Nitrogen, air, etc.) surrounding the metal. We believe that these experimental parameters could also influence on the formation of nano-hold arrays, which will be a subject of next study.

 

Fig. 2. (a) SEM image of a two-dimensional square Au NHAs. The structure size is $100\times 100~\mathrm{\mu}$m$^2$ and the periodicity is $1~\mathrm{\mu}$m. SEM images of enlarged images of square (b) and hexagonal (c) patterns of Au NHAs. (d) The nanoholes size distribution of fabricated square pattern shown in figure (a). (e) Zoom on the size distribution at large nanoholes.

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3. Theoretical calculation and experimental characterization of Au NHAs

Since the fabricated Au NHAs are not exactly the same as those fabricated by the standard multiple-step method, we have therefore theoretically investigated the optical properties of the fabricated structures and compared them with those of ideal ones.

3.1 Numerical calculation by FDTD method

To study the optical properties of Au NHAs structures, we first performed numerical simulations using a commercial three-dimensional finite-difference time-domain (FDTD) solver (Lumerical software). A single unit cell was simulated using periodic boundary conditions in the in-plane dimensions and perfectly matched layers in the out-of-plane dimension. Dispersive materials were obtained from the optical material database of [46] for Au and [47] for $\textrm{SiO}_{2}$ (Glass). The thickness of the Au layer is kept constant at 50 nm for all calculations. We note that we have done convergence testing for grid sizes. Moreover, we have added to the simulation space an “override mesh region” around the air holes with a mesh size of 5 nm for the $x-$axis and $y-$axis, and of 1 nm for the $z$-axis (see Fig. 8 in appendix). This ensures the correctness of the simulation results.

Figure 3(a) shows the simulated transmission spectrum of an ideal Au NHAs structure having a period P = $1~\mathrm{\mu}$m and a hole diameter D = 400 nm for two polarizations of the incident light: circular (blue solid curve) and linear (red dashed curve). It can be seen that the transmission spectrum is independent of the polarization properties of the incident light. Thus, in further simulations, we will only use the circularly polarized incident light. In the $0.9-1.6~\mathrm{\mu}$m wavelength range, which corresponds to the wavelengths range we can experimentally measure by our spectrometer, the simulated transmission spectrum shows three dips at 1.02 $\mathrm{\mu}$m, 1.09 $\mathrm{\mu}$m, and $1.52~\mathrm{\mu}$m and one peak at $1.58~\mathrm{\mu}$m (Fig. 3(a)). Their nature is indicated by the electric field intensity distributions, as shown in Figs. 3(b)-(e), respectively. The dip at 1.02 $\mathrm{\mu}$m corresponds to SPR at the Au/air interface, the two dips at 1.09 $\mathrm{\mu}$m and 1.52 $\mathrm{\mu}$m correspond to SPR at the Au/glass interface. At the transmission peak $\lambda _4$, the field is strongly concentrated at the edge of the hole and distributed on both sides of the Au layer, thanks to the coupling field between two interfaces. That allows the light transmitting with a large amount at a specific wavelength. This was well-known as an extraordinary transmission effect [12].

 

Fig. 3. (a) Simulated transmission spectra of an ideal Au NHAs having a period of 1 $\mathrm{\mu}$m and a holes diameter of 0.4 $\mathrm{\mu}$m, using an incident light with linear (red dash line) or circular (blue line) polarization. (b-e) Simulated electric field intensity distributions in the ($x-z$)-plane passing through the center of the hole at different wavelengths corresponding to the dips ($\lambda _1,\lambda _2, \lambda _3$) and peak ($\lambda _4$) in the transmission spectrum.

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In practice, the structures fabricated by the DLW method have holes which are not circular but rather random in shape (Figs. 2(b)-(c)). Although there have been a few numerical simulation studies related to the imperfections of the Au NHA structure by taking into account the sidewall curvature of the air holes [48] or the roughness of the Au film surface [9], so far there has been no research investigating the influence of the random shape of the air holes. To study the effect of the heterogeneous shape of holes on the optical properties of the NHAs structure, we have numerically created Au NHAs having holes with random shapes using Matlab (Fig. 4(b)). These holes are characterized by a parameter called “variation” (denoted by V), which is defined as the maximum deviation of the real hole border with respect to a circular one (Fig. 4(d)). In this way, we can examine independently the role of the hole diameter and the hole edge roughness. In addition, as mentioned above, there also exist many tiny holes with diameters below 50 nm on the fabricated structures (Figs. 2(b)-(d)). Therefore, we have also generated small holes with diameters in the range of $30-50$ nm and randomly distributed them on the Au layer (Fig. 4(c)). All of these structures are then imported to the FDTD solver for simulations.

 

Fig. 4. NHAs structures are created using Matlab for the case of (a) circular holes, (b) holes of random shape (variation = 50 nm), and (c) holes of random shape (variation = 50 nm) with many surrounding small holes. The black color represents the air-holes. (d) The interpretation of “variation”: dot circular ring represents the circular hole and the blue curve represents the arbitrary hole shape. The maximum size difference between the two curves is called “variation” (V).

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The goal is to study the transmission spectra of the Au NHAs as a function of various parameters including the variation V, the structure period P, and the hole diameter D by changing each parameter while keeping others unchanged. Figure 5(a) shows the simulated transmission spectrum of Au NHAs with P = $1000$ nm, D = 400 nm, and with different V values. The results indicate that when V increases, the transmission spectrum does not change much. Only the transmission peak was slightly red-shifted and became broader. In comparison with the ideal NHAs structure (V = 0 nm), the peak transmittance is reduced by about 20$\%$ and 30$\%$ for the case of V = 50 nm and V = 100 nm, respectively. In addition, the small holes have no effect on the observed transmission spectra from 900 nm to 2000 nm, as shown in Fig. 5(b). Actually, these small nanoholes possess a LSPR. With their sizes in the range of 50 nm, no matter how are their forms, the LSPR peak/deep appears in a range of 530 nm. However, with a low density of these small nanoholes as in our case, their LSPR peak/deep is too weak, and cannot be distinguished from the SPR transmission peak of the 50 nm–thin film (see Fig. 9 in appendix). Therefore, the Au NHAs fabricated by our method can be considered as suitable as the ideal ones having circular holes.

 

Fig. 5. Simulated transmission spectra of Au NHAs structures as a function of different parameters (period, P; variation, V; hole diameter, D). (a) V varies, while P = 1000 nm and D = 400 nm. (b) Comparison of transmission with and without the presence of small holes in the case of V = 50 nm, P = 1000 nm and D = 400 nm. (c) P varies, V = 0 nm and D = 400 nm; (d) P varies, V = 50 nm and D = 400 nm. (e) D varies, V = 0 nm and P = 800 nm. (f) D varies, V =50 nm and P = 800 nm.

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We then continue to examine the effect of P and D. These two parameters affect directly the structure filling factor, which is defined by the hole area divided by the NHA unit cell. The results are shown in Figs. 5(c-f). Figures 5(c) and 5(d) show a comparison for two cases, V = 0 nm and 50 nm, respectively. In each situation, the holes diameters are fixed at D = $400$ nm, and the structure periods are varied. As we can see, when keeping D unchanged while reducing P, the transmission spectrum is blue-shifted and the transmission peak is broader and higher (Figs. 5(c)-(d)). Similarly, when P is keeping constant and D is varied, the transmission peak is red-shifted and broader. Figures 5(e) and 5(f) show the dependence on the holes diameters for again two situations: V = 0 nm and 50 nm, respectively. In this case, the period is fixed at P = 800 nm while the holes diameters are varied from 300 nm to 500 nm. We can see that the transmission peak position is shifted and the FWHM became broader, while all the dips positions are almost unchanged. Our previous studies on perfect circular structure have also shown similar result [49]. We note that, if the D/P ratio remains unchanged and the period P is reduced, the transmission spectrum is blue-shifted but the larger of the transmission peak remains almost the same. Actually, the positions of the transmission dips depend only on the period and the refractive index of the dielectric medium surrounding the Au NHAs structure. Besides, Figs. 5(d) and 5(f) representing the results obtained with V = 50 nm also reveal that the transmission peak becomes rougher as the ratio V/P or V/D increases. In general, simulated transmission spectrum of Au NHAs structure depends on many other parameters such as the type of dispersive materials used, the spectrum of the incident light source, and so on, but the results regarding the effects of P and D mentioned above are similar to other studies [9,48–50]. With these results, we confirm that the optical properties of the fabricated structures are very close to the ideal circular holes plasmonic structures. This again confirms that the OPA-based DLW method is an excellent method to produce desired plasmonic structures in a single step.

3.2 Experimental results and comparison to the simulations

Figure 6(a) illustrates the setup used for characterization of the transmission spectra of fabricated Au NHAs. A white light source (Quartz Tungsten-Halogen Lamp) was used as the incident light source. The light beam was first collimated by a system consisting of a diaphragm (1 mm-diameter) and two lenses (same focal length of 10 cm), then focused into the Au NHAs sample (100 $\mathrm{\mu}$m $\times$ 100 $\mathrm{\mu}$m) through an OL (Lens1, NA = 0.4). An optical microscope was used (not shown in Fig. 6(a)) to ensure that the focused light beam passed thought the Au NHAs structure. Careful adjustment was done to be sure that the light beam is almost collimated at the position of the Au NHA sample, $i.e.$ the incident angle of the light beam is close to 0 degree. By using a coupling lens (Lens2), the transmitted light is collected and sent to an infrared spectrometer (Ocean Optics Nirquest), which allows to detect the wavelengths in the range from 900 nm to 1650 nm.

 

Fig. 6. (a) Experimental setup used to characterize the transmission spectra of Au NHAs. Lens 1 is an objective lens ($\times ~20$, numerical aperture is 0.4). Lens 2 is a focusing lens of the spectrometer fiber. (b) Experimental results obtained with Au NHAs having different periods. The holes diameters are about 350 nm, as shown in Fig. 2(e). (c) Experimental results obtained with Au NHAs having different holes diameters, which are realized by different laser powers. The period of these structures is 800 nm.

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Figure 6(b) shows the experimental results of the transmission spectra of Au NHAs with different periods. These structures were assumed to have same holes diameters since they were fabricated by the same laser power of 160 mW. The transmittance of each structure having different period was normalized for comparaison. Actually, the intensity of the transmitted signal is related to the size of the air-holes and the period of the NHA. For the period in the range of 500-700 nm, the transmittance was experimentally measured to be about 10%, and for the period ranging from 800 nm to 1000 nm, $i.e.$ smaller D/P ratios, the transmittance decreased to about 7%. We can clearly see the dependence of the transmission peak on the Au NHAs period. Namely, the transmission peak red-shifts and its FWHM becomes narrower when the period of the Au NHA increases. These results are consistent with those predicted by the simulations shown in Fig. 5(d). However, we note that the position of the resonant wavelength corresponding to each period is slightly red-shifted and the FWHM of the peak is a bit larger than those of the simulation. This can be explained by different reasons. Firstly, the simulation is based on a limited number of air-holes, corresponding to a unit cell made by $3\times 3$ holes in our case, whereas the experimental results are obtained by a light beam which passes through an assemble of more than $10\times 10$ air-holes. Secondly, the white light beam is not perfectly parallel at the sample position as that used in simulation. Furthermore, we have also measured the transmission spectra as a function of the filling factor of the Au NHAs. Figure 6(c) shows the experimental result of the transmission spectra of different square Au NHAs possessing the same period of 800 nm but having different holes sizes. These structures were fabricated by changing only the laser power, resulting in different Au holes sizes. As previously mentioned, the transmission dip remains unchanged, since it is determined by the structure period, while the transmission peak varies with the holes size (or filling factor). This is again consistent with the simulation result shown in Fig. 5(f). These experimental transmission spectra results thus confirm the quality of the fabricated Au NHAs and again demonstrate the versatility of the direct fabrication of plasmonic structure via DLW. Moreover, even if there exists some defects in these fabricated structures, such as the non-uniformity of the air-holes or the existence of tiny and randomly distributed nanoholes, the Au NHAs still possess plasmonic properties as those obtained in perfect structures. In plasmonics, these defects even offer some advantages as compared to those of perfect plasmonic structures (see below).

3.3 Simulation of the localised field enhancement

As mentioned above, the main drawback of the DLW-based fabrication method is the generation of air holes having uncontrollable shapes. This affects slightly the optical properties of the Au NHAs structures as described in previous sections. However, in another aspect, the hole edge roughness can be seen as an advantage. Specifically, Fig. 7(b) shows the electric field intensity distribution in the ($x$-$y$)-plane for the case V = 50 nm, where we can observe some hot spots indicating that the electric field is increased strongly as compared to the case of uniform circular holes (Fig. 7(c)). Figure 7(d) shows the comparison of the simulated electric field intensity distribution along the two yellow dashed lines in Figs. 7(b-c). In future, the results indicate that the field intensity could be enhanced by several times as compared to the ideal NHAs structure. This localised plasmonic effect can be exploited for applications in fluorescence enhancement or nonlinear optics.

 

Fig. 7. Comparison of the simulation results of electric field intensity distributions in different structures. (a), (b) Electric field intensity distribution in ($x$-$z$)- and ($x$-$y$)-planes of the Au NHA having 50 nm–variation. The field plotted in ($x$-$z$)-plane is obtained at a $y$-position as indicated by a dash line shown in (b), and the field plotted in ($x$-$y$)-plane is obtained at a $z$-position, located 10 nm above the Au/air interface, as indicated by a dash line shown in (a). (c) Similar electric field intensity distribution in ($x$-$y$)-plane of a perfect Au NHA (0 nm–variation). (d) Comparison of the electric field intensity distributions along the two yellow dashed lines in figures (b) and (c).

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4. Conclusion

In this work, we have demonstrated a simple and direct method which allows obtaining desired gold nanoholes arrays in a single step by using the direct laser writing method. Thanks to the optically induced thermal effect, via the use of a continuous-wave laser whose wavelength (532 nm) is located in the absorption band of the target material (gold in our work), the local temperature reaches a high value (for example $600^{\circ }$C), allowing evaporation of the metallic material thin film in a small area corresponding to the focusing laser spot. By moving the later one, any two-dimensional gold structure can be directly obtained without using a polymeric template and lift-off process. The period of fabricated patterns is demonstrated to be controlled from 500 nm to several micrometers. The shape of the fabricated nanoholes is not circular as those obtained by the standard fabrication method, $i.e.$ combination of polymeric template, evaporation of metallic thin film and lift-off process, and this is also explained by the thermal effect and the quality of the metallic thin film. Nevertheless, we have numerically and experimentally demonstrated that the optical properties of the fabricated structures are quite similar to those fabricated by the commonly used method. Only, due to the non-perfect circular holes, the transmission peak of the resonant Au NHAs is slightly red-shifted and broader. The simulation results agree well with experimental measurements. Besides, the hole edge roughness can be seen as an advantage. Indeed, the electric field intensity in fabricated structures is strongly increased as compared to the case of circular holes. This localised plasmonic effect can be useful for different applications requiring an amplification of the excitation light intensity, such as fluorescence enhancement, laser, and nonlinear optics. This work is therefore very useful to make desired two-dimensional plasmonic NHAs, not only in gold material but also in other desired noble ones such as Ag, which open a new way for different applications.

Appendix

 

Fig. 8. Test of mesh size convergence. Peak positions of the transmission spectra obtained with different mesh sizes: (a) Mesh sizes $d_x$ = $d_y$ = 5 nm and mesh size $d_z$ varies; (b) Mesh sizes $d_z$= 1 nm and mesh size $d_x$ (= $d_y$) varies.

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Fig. 9. Comparison of transmission spectra obtained with different configurations, with and without small nanoholes of 50 nm (average value). (a-d) Illustrations of different substrates: holes (with deformed shape) array (a); holes array containing small nanoholes of 50 nm (b); small nano-holes of 50 nm randomly distributed in a gold film (of 50 nm–thickness) (c); perfect gold film having a thickness of 50 nm (d). (e) Transmission spectra of all four configurations.

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Funding

Agence Nationale de la Recherche (ANR-17-CE09-0047); Ministry of Science and Technology, Taiwan (107-2923-M-194-001-MY3); FACE Foundation (MicroRNA Detection).

Disclosures

The authors declare no conflicts of interest.

Data availability

No data were generated or analyzed in the presented research.

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