1. Introduction

Ultrathin surfaces that interact strongly with electromagnetic radiation on length scales far below their free space wavelength are commonly referred to as metasurfaces. These surfaces stand in stark contrast to traditional bulky optical components that require interaction scales comparable to the wavelength of light [1]. While these ultrathin metasurfaces could enable flat optical components [2] with high field concentration on their surface, there is an inherent difficulty associated with their fabrication. Optical metasurfaces have traditionally relied upon electron beam lithography to produce the required feature size and spatial gradients [3]. An alternative approach, based on directed self-assembly, has been used to fabricate plasmonic metasurfaces consisting of a monolayer of hexagonally close packed (HCP) ligand capped gold nanospheres [4]. The directed self-assembly approach provides a platform capable of creating centimeter-scale metasurfaces with tunable subnanometer gaps [5]. This approach, however, does not allow for spatial patterning and is typically designed for a single resonant wavelength. Recently, laser light has been utilized to tune the morphology and hence optical response of nanophotonic structures [6–9]. Berzins et al. demonstrated the capability to post-process metasurfaces using light to thermally tailor the optical properties of high-index dielectric metasurfaces [10]. Here, intensity-mediated continuous wave laser lithography is used to spectrally and spatially control the resonance of a hexagonally packed plasmonic gold nanosphere metasurface. This irreversible tuning, or reconfiguration, of the metasurface enables the demonstration of a spectrally selective Fresnel zone plate. Controlling the properties of light through these metasurfaces using laser lithography may enable a novel approach to realize scalable flat optics [11–13].

2. Results and discussion

2.1 Self-assembly of plasmonic gold nanosphere metasurfaces

The gold metasurfaces are formed by directed self-assembly [4,5]. Commercially produced gold nanospheres (Ted Pella, Inc.) are first stabilized in an aqueous sodium citrate solution. A second solution consisting of tetrahydrofuran $(1~mL)$, monothiol $(1 ~\mu L)$, and dithiol alkane ligands $(1~\mu L)$ is also prepared. The aqueous nanosphere solution and the tetrahydrofuran solutions are combined, leading to a selective binding of the ligand with the gold nanospheres, causing them to phase separate from the solution and migrate to the liquid/air interface. Thoroughly cleaned glass substrates (Eagle XG) are pre-wetted and placed on end so that they are partially submerged in the mixed solution. Surface tension facilitates the self-assembly of the gold nanospheres into a HCP monolayer along the length of the glass slide. The spacing between the gold nanospheres can be adjusted by selecting ligands of various lengths. A mixture of 1-hexanethiol and 1,6-hexanedithiol ligands, corresponding to a gap of approximately $1~nm$, were used to cap the nanospheres and will be referred to as the $C6$ metasurface throughout this work [5].

2.2 Laser lithography

A confocal Raman microscope (WiTEC AlphaRAS) was used to carry out laser lithography and characterization. A $403~nm$ continuous wave diode laser (Thorlabs LP405-10) was used to pattern the metasurfaces, since the interband absorption in gold is large at $403~nm$ [14]. The laser was fiber coupled to the microscope while the metasurfaces were irradiated using a $100\times$ $0.9$ NA objective (Ziess Epiplan-Neofluar DIC). The sample position was controlled by a piezoelectric flexure stage (Physik Instrumente P-517K093) with a velocity of $10~\mu m/s$. The spectral shift of the patterned films was measured in situ with an integrated imaging spectrometer.

The HCP gold nanosphere metasurfaces were measured to be $16.5~nm$ thick using atomic force microscopy (AFM), consistent with a $15~nm$ gold sphere capped with a $1~nm$ ligand. Parametric processing tests consisting of intensity $(1.5-3.0~MW/cm^2)$, hatch spacing $(100-500~nm)$, and feed rates $(5, 10, 30~\mu m/s)$ were performed. Optical microscopy and reflectance spectroscopy were used for parameter optimization in an effort to determine the largest spectral shift without degrading the plasmon resonance. The optimal parameters were found to be: feed rate = $10~\mu m/s$, hatch spacing = $150~nm$ (50% overlap), and intensity = $2.2~MW/cm^2$.

The optical micrographs in Fig. 1 show broadband reflectivity of the optimized test patterns as a function of laser intensity. Qualitatively, there is a significant difference in the reflection between the unirradiated and modified metasurfaces. The shift in optical resonance peak is related to the total exposure of the sample to localized optical illumination. To quantify these shifts, spectroscopic reflection and transmission measurements were performed on the laser modified regions of the metasurfaces. Figure 2(a) shows the evolution of the reflectance spectrum with laser intensity. The spectrum both red-shifts and decreases in magnitude with increasing laser intensity. The transmission spectra in Fig. 2(b) also red-shift and exhibit increased transmission in the regions with higher optical exposure. The absorption in Fig. 2(c) is calculated from the measured reflection and transmission spectra. These spectra show that the plasmonic response progressively red-shifts with increasing intensity, but maintains a constant level of absorption. The unirradiated metasurface has an absorption resonance at $633~nm$ and a peak absorption of $0.36$, which shifts to $833~nm$ when irradiated at $3.0~MW/cm^2$. At this intensity, the reflection, transmission, and absorption peaks broaden due to the onset of nanosphere coalescence, changing the plasmonic resonance parameters. These results show that it is possible to tune the plasmonic absorption resonance up to $200~nm$ by exposing the metasurface to optical radiation.

 

Fig. 1. Optical micrographs of $10~\mu m$ $\times$ $10~\mu m$ laser patterned $C6$ metasurface in reflection (top) as a function of increasing laser intensity (left to right). Atomic force micrograph of each metasurface is also shown (bottom). Note: AFM scale bar is 1 $\mu$m.

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Fig. 2. Experimentally measured (a) reflection, (b) transmission, and (c) absorption spectra of the $C6$ metasurface under different laser processing conditions, ranging from $0$ to $3.0~MW/cm^2$.

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2.3 Thermal evolution

As a control experiment, to further understand the mechanism responsible for the large spectral shift, a $C6$ metasurface was globally heated in $10 ~^{\circ }C$ steps at five minute intervals by mounting a heater block on the glass substrate underneath the metasurface, to contrast the localized photothermal heating from the laser. Figure 3(a) shows that the $685~nm$ reflection peak shifts slightly as the temperature is increased from $130~^{\circ }C$ to $190~^{\circ }C$, where the reflection peak nearly flattens out over the entire visible and near-infrared spectrum at $190~^{\circ }C$. These results demonstrate that the sintering and subsequent coalescence of the nanospheres by global heating destroys the plasmonic response and does not account for the spectrum evolution in Fig. 2.

 

Fig. 3. (a) Temperature dependent reflection spectra of $C6$ metasurface due to global heating at various temperatures ranging from unirradiated up to $190~^{\circ }C$. (b) Calculated temperature rise upon irradiation at 1.5, 2.2, and $3.0~MW/cm^2$.

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Both the laser irradiated and thermally annealed metasurface reflection spectra approach the same wavelength limit in the case of highest laser exposure and temperature. However, the evolution of the spectral shift between the two methods is quite different. The melting point of gold decreases significantly from the bulk value of $1064~^{\circ }C$ as the particle size decreases, but for $15~nm$ gold nanoparticles the melting point is only suppressed to $~975~^{\circ }C$ [15]. However, sintering of the gold nanoparticles can occur at much lower temperatures due to the high surface area and small ($\sim 1~ nm$) interparticle gaps [16,17], which is in agreement with the observations in Fig. 3(a).

The metasurface is irradiated with a continuous wave laser but the combination of the small laser spot and stage velocity results in the metasurface experiencing an effective laser exposure time of $\sim 32~ms$. This exposure time is referred to as a pulse in order to emphasize the time dynamics (see Fig. 3(b)). The time dynamics of the heating and cooling process are hypothesized to be responsible for the observed differences. The rapid thermal cycling produced by optical excitation allows the metasurface to be heated to temperatures beyond their melting temperatures without observing sintering. Moreover, the largest local electric field concentration occurs in between the nanospheres, which leads to a significant increase in temperature. This causes ligand displacement, thereby decreasing the interparticle gap. This reduction in interparticle gap results in the red-shift of the plasmonic resonance [5]. The observed morphological changes of the metasurface are attributed to reshaping or sintering of the nanoparticles without complete coalescence [18,19].

Through the use of AFM, the morphology of the metasurfaces were analyzed. The phase contrast images are shown in Fig. 1 as a function of laser intensity and provide a detailed view of metasurface morphology. While it is possible to image individual gold nanospheres via AFM, the results presented here focus on length scales comparable to the wavelength of light used in this study. The $10~nm$ AFM tip allowed for the imaging of $100+$ nanospheres while measuring the average surface roughness.

For laser intensity up to $1.5~MW/cm^2$, little change is observed spectrally in Fig. 2 and in the AFM images in Fig. 1. As the laser intensity is increased to $2.2~MW/cm^2$, a significant $100~nm$ red-shift in the resonance peak occurs, while preserving a relatively high Q-factor, indicating the spheres are not aggregating or coalescing. For laser intensity from $2.2~MW/cm^2$ to $3.0~MW/cm^2$, the resonance peak continues to red-shift (Fig. 2); however, the magnitude of the resonance peak begins to decrease and broaden, inferring that the nanospheres have begun to touch and coalesce into larger $>50~nm$ structures (Fig. 1). It should be noted that AFM analysis of the globally heated sample shows particle coalescence similar to the laser irradiated samples seen at $3.0~MW/cm^2$, as seen in Fig. 1.

To understand the metasurface temperature evolution during laser irradiation, finite element simulations were performed. Time dependent electromagnetic and heat transfer simulations were carried out using COMSOL Multiphysics. The simulations assume the metasurfaces are irradiated at $403~nm$ with a 0.9 NA microscope objective with a $\sim 286 ~nm$ spot, traversing the sample at $10~\mu m/s$. The calculated temperature evolution is shown in Fig. 3(b). As the Gaussian beam translates over the metasurface, the expected Lorentzian temperature profile is observed with a FWHM of $\sim 32~ms$ with an intensity dependent peak temperature.

The temperature from the simulations exceeded $200\;^{\circ }C$ in Fig. 3(b) surpassing the maximum temperature of the steady state global measurement at $190\;^{\circ }C$. This difference in temperature and optical behavior can be attributed to the time dynamics (i.e. pulsed vs. steady state). Previous work showed that the time and temperature required for nanoparticle sintering and coalescence is intensity and time dependent [18].

2.4 Disorder effects

While it is well understood that the plasmonic peak wavelength red-shifts as the interparticle gap decreases as discused above [5], the effects of nanosphere packing and disorder on the plasmonic response are not well understood.

To investigate this relationship, calculations of various imperfect HCP metasurfaces with average gaps of $\sim 1~nm$ were performed using COMSOL Multiphysics, v5.5. In these calculations, the standard deviation of the radius of the particles, and the standard deviation of the $x-$ and $y-$ coordinates from a perfect HCP lattice were allowed to vary. If a given particle were to overlap an already placed particle, that particle was not added to the calculation domain. The calculations were performed in the frequency domain, solving for the scattered field. These models assumed an infinitely wide metasurface (periodic supercell) by specifying the boundaries parallel to the background electric field polarization as perfect magnetic conductors (PMC) and the perpendicular boundaries as perfect electric conductors (PEC). Upper and lower boundaries were surrounded by perfectly matched layers (PML) to absorb reflections. The metasurfaces were suspended in a uniform medium with an effective refractive index ($n=1.3$) to account for the air/glass interface and the hexanethiol ligands while decreasing the demands of the calculation. Absorbance, scattering, and extinction cross sections were calculated as in [20]. The peak wavelength shift as a function of metasurface order parameter is shown in Fig. 4.

 

Fig. 4. Peak wavelength shift as a function of metasurface order parameter. Imperfections include missing nanospheres, nanosphere radii with various standard deviations, and $x-$ and $y-$ particle locations with various standard deviations. The plasmon resonance is not greatly affected by these imperfections.

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The scikit-image toolkit [21] for Python was used to generate an order parameter to quantify the degree to which a generated metasurface conformed to the ideal HCP packing. In brief, a convex hull was created around each particle with each side of the convex hull being shared by two particles. The vertices surrounding each particle were then determined, and the scalar order parameter for each particle, $S_{\textrm {particle}}$, was calculated as the following average, $S_{\textrm {particle}} = \frac {\sum {\cos \left (6\angle _{i}\right )}}{6}$, where $\angle _{i}$ are all of the angles between clockwise adjacent vertices for a given particle. The scaling factor of 6 ensures that the cosine returns a value in the range of 0–1. In this case, $S = 1$ would correspond to a perfect HCP lattice. The overall order parameter, $S$, was found as the average of all $S_{\textrm {particle}}$.

We find in Fig. 4 that the plasmon resonance wavelength is relatively unaffected by defects in the metasurface or variations in the standard deviations of the interparticle gap distance. This indicates that the average interparticle gap distance of the nearest neighbors is the predominate factor that determines the global plasmonic response of the metasurface. It should be noted that as the order parameter decreases, so does the quality factor and achievable phase shift.

These results imply that at modest laser intensities, $<2.2~MW/cm^2$, the photothermal laser mechanism is decreasing the gap between the nanospheres, causing the plasmonic peak wavelength to red-shift. At larger intensities, the ligands are displaced, allowing the nanospheres to touch and coalesce in the beam area (Fig. 1), and for intensity $>3.0~MW/cm^2$ the nanospheres are ablated from the glass substrate. In contrast, when the metasurfaces are globally heated the plasmonic peak does not shift in wavelength, but rather decays and broadens in magnitude, most likely due to longer exposure to elevated temperatures.

2.5 Spectrally selective Fresnel zone plate

To highlight the practicality of our method, we fabricated a large scale, frequency selective flat optic using our laser processing technique. A Fresnel zone plate (FZP) was patterned onto a $C6$ metasurface that enables a spectrally selective focusing element that is optically thin $(\lambda _0/42)$. Based on the previous work of Doyle et al. [5], it was determined that the maximum achievable phase shift was $30^{\circ }$ and, therefore, it was not possible to achieve a 2$\pi$ phase shift from the laser processed metasurface. This is not unexpected because of the short optical path length $(\lambda _0/42)$ and modest quality factor (slowly varying phase) of the metasurface. Because of these factors, a spectrally selective binary Fresnel zone plate was designed such that focusing was achieved through the constructive interference of light passing through the laser processed and pristine metasurface zones, respectively. Accordingly, it is the optical path difference between the zones that is responsible for the focusing, not the phase shift of the metasurface itself. The $35~\mu m$ FZP with a focal length of $50~\mu m$ at $633~nm$ was designed to match the unirradiated metasurface absorption peak and the $632.8~nm$ laser line of the tunable helium neon laser used for characterization. An optical micrograph of the five element zone plate is shown in Fig. 5(a).

 

Fig. 5. (a) Binary zone plate consisting of unirradiated (light) and irradiated ($2.2~MW/cm^2$) regions (dark). Center region is $10~\mu m$ in diameter. (b) On-axis line intensity profile showing both calculated (dashed line) and experimental (solid line) data for plasmonic zone plate. (c) Off- and on-resonance measured zone plate data (left and center panels). Calculated on-resonance map (right panel).

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The metasurface based zone plate was characterized by illuminating at $544~nm$ and $633~nm$ (off- and on-resonance) and spatially mapping the intensity behind the zone plate. A fiber coupled tunable helium neon laser (Research Electro-Optics) was free space coupled and collimated, providing uniform plane wave illumination over the lateral extent of the zone plate ($1.1~mm$ beam diameter). The same $100\times$ $0.9$ NA objective used for the laser patterning was used as the collection optic for the imaging spectrometer. The intensity maps shown in the left and center panels of Fig. 5(c) were constructed pointwise via sampling of the $xz$-plane. The zone plate transmission efficiency was measured to be 32%. Here it is clear that the strong frequency selective response of the plasmonic metasurface selectively focuses the red light $(633~nm)$ but leaves the blue light $(544~nm)$ unchanged. To simulate the performance of the Fresnel zone plate, a field map was constructed using a conventional Green’s function approach [22] where the magnitude and phase from the patterned and non-patterned regions of the zone plate were programmed into the source ($xy$-) plane. The resulting field was evaluated above the plane (at a distance $y$ from the source plane) along the $x$-axis. In this calculation, bulk values from the spectral data were used to estimate the amplitude and phase of the Green’s function. The corresponding plot down the optical axis of the FZP shows good focusing of the FZP at the designed distance of $50~\mu m$ (Fig. 5(b)).

3. Conclusion

The irreversible spectral tuning of metasurfaces comprised of HCP gold nanospheres via laser lithography was demonstrated. The laser modification of the plasmonic resonance was observed to spectrally shift in the patterned regions by nearly $200~ nm$ at the highest laser intensities. We find the spectral shift is predominately governed by photothermal changes in the interparticle gap. A spectrally selective focusing zone plate was demonstrated, highlighting the robustness of this approach which could enable spectrally selective flat optics. This large-area, high throughput technique offers a route for the fabrication of flat optics that are both compact and lightweight.