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Abstract
Gap plasmon-based optical metasurfaces have been extensively used for demonstration of flat optical elements with various functionalities efficiently operating at near-infrared and telecom wavelengths. Extending their operation to the visible is however impeded by the progressively increased plasmon absorption for shorter wavelengths. We investigate the possibility to improve the performance of gap plasmon-based metasurfaces in the visible by employing monocrystalline gold flakes as substrates instead of evaporated polycrystalline gold films, while using the electron-beam lithography patterning of the evaporated thin gold films for fabrication of top gold nanobricks, which define gap-plasmon resonator elements of the metasurfaces. We demonstrate that the efficiency can be improved by modest but noticeable amount of $\approx 5\%$ if all other configuration parameters are preserved.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Development of the optical metasurfaces [1–3] in the recent years allowed to overcome the limitations of the conventional optical components [4–7]. The main advantages of the metasurfaces as compared to their traditional counterparts are compactness (sub-wavelength thickness) [8–10], multi-functionality [11–15], active and reversible control of the dynamic response [16–23]. This advantage revealed many features and functionalities that were not attainable with conventional optical components [24–27]. One of the classes of the metasurfaces – gap surface plasmon (GSP) [28–31] based – represented by metal-insulator-metal (MIM) configuration and typical operation in reflection mode, in theory, were reported to exhibit relatively high efficiency (up to 90% in the near infrared and 80% in the visible spectral range) [32].
However, in practice efficiency of the metasurface performance is significantly reduced by fabrication imperfections: in addition to deviations from the nanostructure design dimensions (typical tolerances are $\pm 5$ nm), it also suffers from roughness and polycrystallinity of the evaporated metal films, that are commonly employed. These intrinsic properties of the evaporated metal films lead to increased surface scattering and greater Ohmic losses that inevitably decrease the quality of fabricated devices and thus their efficiency. In fact, absorption and scattering losses in typical nanostructures fabricated using the evaporated gold films are so high, that in order to obtain realistic values for the efficiency in numerical simulations, the imaginary part of gold’s refractive index has to be pragmatically increased by a factor of 4 [28].
We distinguish two main factors that limit performance of the metasurfaces: deviation from the design dimensions of the constitutive elements caused by lithographic patterning imperfections and intrinsic defects in the polycrystalline metal films that are typically used in the fabrication. Polycrystalline and amorphous noble metals are commonly used for plasmonic metasurface fabrication due to wide availability, relative cheapness and technological simplicity. Thin metal films are typically deposited by thermal evaporation, electron beam physical vapor deposition or sputtering [33]. While improving the nanofabrication accuracy might require heavy investments in more sophisticated equipment, elimination of material imperfections can be achieved by modifying (at a reasonable cost) the fabrication recipes.
An alternative material platform, which has been receiving increasing attention in the plasmonic community over recent years, is represented by chemically synthesized monocrystalline flakes, also referred to as platelets [34–36]. Due to their atomic flatness and well-defined crystal structure, such plasmonic films and nanoparticles exhibit larger plasmon propagation lengths and sharper resonances due to lower Ohmic losses and reduced surface scattering [37,38]. These superior plasmonic properties have been utilized in the fabrication of plasmonic nano-circuits [39,40], nano-antennae [37,41,42], and other structures [43–45]. It is therefore relatively easy to eliminate material imperfections (at least) in the substrate by using monocrystalline flakes, a seemingly straightforward approach that promises the GSP-based metasurface efficiency improvement by modest, but noticeable $\approx 5\%$, as suggested by the numerical simulations discussed below.
In this work, using numerical simulations and experimental investigations, we study the possibility to improve the performance of beam-steering GSP metasurfaces in the visible by employing monocrystalline gold flakes as substrates (Fig. 1), while using the widely available and well-established electron-beam lithography (EBL) patterning of the evaporated thin gold films for fabrication of top gold nanobricks defining GSP elements of the metasurfaces.
2. Results and discussion
In order to directly evaluate the influence of the material quality of the substrate on the performance of the GSP metasurfaces, we have chosen one of the the simplest designs – the so-called beam steering metasurface that functionally mimics blazed grating, in which a greater part of the incident power is deflected into the non-zero diffraction order. Implementation of such functionality is well studied [28,46] and it is obtained by imposing a linear reflection phase gradient:
where $\theta _r$ is the beam-steering (first diffraction order) angle, $\lambda _0$ is the free space wavelength, $\Lambda _{s}$ is the period of the metasurface supercell or grating periodicity as will be explained further. We have chosen the design wavelength $\lambda _0=633$ nm, as we expected to observe more pronounced difference between monocrystalline and polycrystalline substrate in the visible range. Besides, this wavelength is the operational wavelength of the widely used helium-neon (He-Ne) laser. As another design constraint, we have chosen $\theta _r\approx 20^\circ$ due to practical reasons, as it gives well-measurable separation of the diffraction orders and lies in the range of acceptance cone of an objective to be used for optical characterization (which has a numerical aperture of $\textrm {NA}=0.5$, see Methods sections for the details).The constitutive elements, or unit cells, of the metasurface are comprised of a widely used configuration – gap plasmon resonator, consisting of a top nanobrick and a thick substrate made of gold, which are separated by a thin silicon dioxide layer, as schematically illustrated in Fig. 2(a). The two degrees of freedom in this system are the lateral dimensions of the nanobrick $L_x$ and $L_y$, which allow to engineer the local reflection phase and amplitude response, whereas other dimensions – thicknesses of the layers $t=50$ nm and $t_s=50$ nm, as well as unit cell period $\Lambda =180$ nm are kept constant. Reflection amplitude and phase response of the described system is simulated using a commercially available finite-element method (FEM) frequency-domain solver (see Methods section for the details). Based on these simulations we design the supercell of the metasurface, that is represented by a sequence of unit cells, which satisfies the imposed phase gradient (Eq. (1)) in a number of abrupt steps. Given that the unit cell period is $\Lambda =180$ nm, we have chosen the number of the elements in the supercell $n_\textrm {el}$ to be 10, which results in the value of 1st order diffraction angle $\theta _r\approx 20.5$, as
Fig. 2. Design and fabrication of the beam steering gradient GSP metasurface: (a) metasurface unit cell; (b) reflection phase and amplitude of the elements of the supercell; (c) dimensions of the supercell elements; (d) Scanning-electron microscope (SEM) image of the fabricated metasurface supercell.
The dimension $L_x$ and $L_y$ of the elements in the supercell are chosen to have the highest possible reflection amplitude and the smallest deviation from the imposed relative reflection phase, as shown in Fig. 2(b)–(c).
Furthermore, we numerically explore the potential to improve the efficiency of the performance of the metasurface. For that, we carry out full-field simulations of the metasurface supercell to calculate the power distribution diffraction over the diffraction orders. In the simulations we represent the optical response of the monocrystalline gold described by the electric permittivity $\varepsilon =\varepsilon '+i\varepsilon ''$, obtained from the experimental data from Johnson and Christy [47]. In turn, evaporated gold is described by the same permittivity functions, only with the imaginary part $\varepsilon ''$ increased by a factor of 4, which mimics additional losses of the polycrystalline material [28]. We compare two cases: a system where both substrate and top nanobricks are described by a lossy permittivity function, and a system where only the top nanobricks are described by the dielectric function with increased imaginary part, whereas the substrate is considered to have less losses. As can be seen from Fig. 3, under the above-mentioned assumptions, the efficiency could improve by modest, but noticeable $\approx 5\%$.
Fig. 3. Efficiency characterization of the metasurface: comparison of numerical simulations (dashed lines) and experiment (solid lines).
For experimental demonstration, we fabricate the designed metasurfaces on two types of gold substrates: evaporated polycrystalline films and chemically synthesized monocrystalline flakes. Descriptions of the preparation of the both substrates can be found in the Methods section. As can be seen from Fig. 3, in practice the effect is not as pronounced as numerical simulations predicted, presumably due to a number of experimental limitations and issues, which will be discussed further.
First of all, significant decrease in the performance efficiency of prototypes as compared to the numerical simulations is ascribed to the fabrication imperfections and uncertainties in the material properties. Tolerances of the EBL fabrication are $\pm 5$ nm that undoubtedly lowers the overall performance of the metasurfaces. As for comparison between monocrystalline and polycrystalline substrates, deviations from the imposed nanobrick dimensions are further increased due to uneven resist deposition on the surface of the flakes caused by a step height at the edges of the flakes, which makes the exact reproducibility of the metasurface very challenging. In order to address this issue, we have fabricated several metasurface patterns with different exposure doses (in a range of $\pm 30\%$ from the dose found to be optimal for the polycrystalline gold substrate).
Another source of the deviation from numerical predictions is caused by the fact that we had to deposit 2 nm of titanium on both, evaporated and monocrystalline gold surfaces for the adhesion purposes, before and after depositing SiO$_2$ spacer layer. Without this preparatory step, during the sputtering process SiO$_2$ does not stick uniformly to the gold surface, but rather forms droplets and bubbles that are easy to remove from the surface. Furthermore, we believe that this auxiliary titanium layer contaminates the monocrystalline gold substrate to the extent, that its presence counterbalances the 5% improvement in the efficiency anticipated from the simulations. Also, unsystematic errors in the resist thickness contributes to the reduced observed difference between mono- and polycrystalline substrates by introducing unavoidable deviations from the design supercell dimensions.
In general, beam-steering GSP metasurfaces are expected to exhibit broadband operation [28]. However, it is somewhat surprising that both experimental and simulated wavelength dependences of the metasurface efficiency exhibit a clear tendency of increasing for longer (than the design) wavelength. We attribute this tendency to the fact that Ohmic losses in gold decrease rapidly when tuning the wavelength away from the interband absorption range towards longer wavelengths. As a result, the metasurfaces operate even more efficiently at wavelengths longer than the design wavelength of 633 nm, reaching efficiencies of $\approx 60\%$ in theory and $\approx 45\%$ in experiment at 700 nm (Fig. 3). Concerning the fact that the efficiency of the metasurface on the polycrystalline substrate surpasses that on the monocrystalline one by few percent at longer wavelengths, we ascribe it to the aforementioned fabrication limitations that become progressively more important for weaker absorption contributions.
Though experimental comparison did not show prominent difference between metasurfaces with mono- and polycrystalline substrates, we have conducted another experiment to clearly demonstrate the superior plasmonic properties of the monocrystalline gold flakes in the absence of fabrication imperfections described above. Specifically, we have measured the propagation length of surface plasmon polaritons (SPP) at the gold-air interface, using the so-called direct scattered intensity (DSI) measurement, that is known to be straightforward and robust method [48,49]. Here, using EBL, we have fabricated a series of ridge gratings at different separations (see inset of Fig. 4 and Methods section for further details). Each grating consists of 3 ridges with thickness 50 nm, width 200 nm and length 20 $\mu$m and period 605 nm that approximately corresponds to the SPP wavelength at the vacuum wavelength of $\lambda _0=633$ nm. As can be seen from Fig. 4, SPP propagation length measurements suggest that propagation losses at the wavelength of interest are significantly (by $\approx 1.6\,\mu$m, $\approx 11.1\,\mu$m for monocrystalline gold versus $\approx 9.5\,\mu$m for polycrystalline gold) smaller at the surface of monocrystalline gold.
Fig. 4. SPP propagation length measurement at $\lambda _0=633$ nm: measured data points and exponential fit. Inset: DF optical image of the gratings fabricated on the gold flake for $L_\textrm {SPP}$ measurement.
3. Methods
In this section details on experiments and simulations are provided.
3.1 Numerical simulations
Simulations were performed in frequency domain using the wave optics module of the commercially available FEM solver Comsol Multiphysics 5.3. The model implements an excitation by a plain wave at a normal incidence launched from the excitation port, exploiting also appropriate periodic boundary conditions at the borders of the unit cell (or super cell) and receiving port for reflection coefficient (or power distribution over the diffraction orders for the super cell simulation). Tetrahedral meshing (with maximum element sizes of 5 nm in metal, 10 nm in dielectric spacer and 40 nm in air) and third-order polynomial basis functions are used in the simulations to ensure numerically well-converged results. For the permittivity function of gold we have used interpolated experimental data by Johnson and Christy [47], with the imaginary part increased four times in some simulations to mimic the losses caused by fabrication imperfections [28]. The refractive index of dielectric spacer is kept constant ($n=1.45$). By performing a mesh refinement study we have estimated the relative error in the simulated spectra to be less than one percent.
3.2 Sample fabrication
For the monocrystalline gold flake preparation was used the modified Brust–Schiffrin [50] method for colloidal gold synthesis in a two-phase liquid-liquid system via thermolysis [51], as described in details in the preceding paper [52]. In short, the samples were prepared as following: an aqueous solution of the chloroauric acid in concentration 0.5 M is mixed with a solution of tetraoctylammonium bromide (TOABr) in toluene. After vigorous stirring, the mixture is left in rest allowing aqueous and organic phases to separate. Further, few microlitres of the organic phase are drop-casted onto a substrate (pre-cleaned silicon substrate) which is then kept on the hot-plate at 160$^\circ$C for 30 minutes. After that the sample is cleaned sequentially in hot toluene, acetone and IPA, that promotes removal of organic solvent. After that the sample is dried under the nitrogen flow, leaving a variety of gold flakes on the surface of the substrate.
For the polycrystalline gold substrate we deposited a 150 nm-thick layer of Au, using standard thermal evaporation method (Cryofox TORNADO 405 evaporation system by Polyteknik) .
Further, a 2 nm-thin titanium layer (for adhesion purpose) was evaporated and 50 nm of SiO$_2$ was radio-frequency sputtered on both substrates.
Further, a 100 nm layer of PMMA 950 A2 e-resist (MicroChem), was spin-coated and metasurface pattern was written using standard EBL (JEOL-640LV SEM with an ELPHY Quantum lithography attachment). The top part of the gap plasmon resonators were formed by thermal evaporation of 2 nm of Ti and 50 nm of Au followed by a lift-off process (etching away stencil material).
3.3 Metasurface optical characterization
Characterization of the metasurfaces performance was performed using Fourier imaging spectroscopy, which allows to clearly observe diffraction orders and evaluate power distribution among them. Optical measurements were performed using the Zeiss Observer microscope (Epiplan-Neofluar HD objective 20$\times$, $\textrm {NA}=0.5$) and Andor Kymera 193i spectrograph equipped with Andor Newton CCD camera. Additional lens (achromatic doublet with focal 20 cm) was used to transform real image at the output port of the port of the microscope to Fourier image and project it onto the camera screen. A standard tungsten-halogen lamp was used as an illumination unit in this setup with narrowly closed aperture diaphragm to imitate normal plane wave-like illumination. Obtained spectra were normalized using reference reflection spectra of silver mirror. Measurements were repeated for several samples ($N=3$) and presented results are averages.
3.4 SPP propagation length measurement
The same equipment was used for SPP propagation length measurement, with an additional lens to produce real image on the camera screen. As a light source was used super-continuum white light laser (Super K Extreme by NKT Photonics) in conjunction with acousto-optic filter (Super K select) tuned at 633 nm wavelength. The excitation spot was aligned with excitation grating to provide maximum out-coupling signal, which was subsequently recorded, and this procedure was repeated for 8 different separations of the in- and out-coupling gratings. For the determination of propagation distance measurements were fitted with an exponential function.
4. Conclusions
Despite the recent advancement in the nanofabrication methods, the ease of EBL technique is still attractive due to wide availability and low cost. Focused ion beam (FIB) milling technology, that is more expensive, offers better fabrication tolerances, but has other drawbacks, such as surface contamination due to the contamination with working material (e.g. gallium) and re-deposition of the removed material. This fact makes attractive investigation of alternative possibilities for fabrication of plasmonic metasurfaces with improved efficiency.
In this work we show that it is possible to get rid of material imperfections, haunting the performance of plasmonic metasurfaces in the visible, at least in the substrate. Thus, the beam-steering GSP metasurface efficiency can be improved by modest, but noticeable amount of $\approx 5\%$ if all other configuration parameters are preserved. In the practice, however, the effect might not be that pronounced due to other experimental limitations, such as the necessity to deposit few nanometers of titanium as an adhesion layer for SiO$_2$ spacer layer, unequal deposition of the resist material on the flake surface, and intrinsic tolerances of the EBL fabrication method. The results obtained should serve as guidelines in ever continuing developments towards improving the performance and increasing the efficiency of plasmonic metasurface-based flat optical components.
Funding
H2020 Marie Skłodowska-Curie Actions (713694); H2020 European Research Council (341054); Villum Fonden (16498); V. Kann Rasmussen Foundation (Award in Technical and Natural Sciences 2019); Syddansk Universitet (SDU 2020).
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