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Abstract
A kind of optical metasurface composed of arrayed nano-rhombus-shaped resonators is proposed. The metasurface as an arrayed optical antenna for highly efficient collecting incident lightwaves, can be utilized to perform light absorption and nano-focusing. The absorption peak can be modulated in a relatively broad spectral range only by adjusting the thickness of the functioned silver film coated. For the same thickness parameter, the key surface plasmons are effectively excited by incident lightwaves polarized along the short axis of the nano-rhombus can broaden the modulated spectral range compared to that along the long axis. Compared with a single nano-rhombus-aperture, a double nano-rhombus-shaped composite architecture (DNRCA) predicts a higher light absorption peak and a stronger near-field lightwave converging. The resonators present a dipole of resonant oscillation through compressing incident lightwaves into a resonant cavity with a very small gap, and then the net charges distribute over two opposite sidewalls of a single cavity. The coupling oscillation becomes stronger with the narrower air gap of the cavity. The achieved near-field light converging presents a typical focusing spot with a minimum size of ∼21 nm, which is one order of magnitude smaller than the incident wavelength of 633 nm, so as to greatly break the traditional diffraction limit.
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1. Introduction
Since the pioneering work on surface plasmon polaritons (SPPs) in thin metallic foils is already extended to localized surface plasmon (LSP) resonators, the optical confinement is no longer limited by the Abbe diffraction limit, so as to help to launch a field of plasmonics [1]. As early as 1997, the theory of achieving superfocusing at the tip of the wedge-like structure [2] has been researched, and then the nano-focusing of light energy in tapered plasmonic waveguides in 2004 [3], as well as the subsequent research on the trapping of plasmons based on nano-gratings [4,5], the capture and localization of lightwaves gradually became a research hotspot. As shown, the breakthrough in the sub-diffraction constraint enables relatively rapid development of several academic disciplines such as nanophotonics [6], metasurfaces and metamaterials [7], and enhanced molecular spectroscopy based on surface-enhanced Raman scattering [8] (SERS) or IR absorption [9] (SEIRA). A reasonable design of the functioned micro-nano-architectures over common metallic or semiconductive wafers can be performed by efficiently configuring and manipulating the localized lightfield energy state or surface wave momentum according to the excited regional surface plasmons (SPs) and their orientational transportation, which means a feasible strategy for efficiently controlling and adjusting the distribution and directional propagation and spatial resonant aggregation of surface lightfields stimulated in a specific wavelength band [10–12]. As demonstrated, the SPs converging towards a metal nano-tip enables a highly localized and enhanced lightfield in a nanoscale region far beyond the traditional diffractive limitation and thus achieves a near-field nano-focusing. Generally, the SPs nano-focusing relies not only on the interaction of the surface resonant waves excited according to the patterned micro-nano-architectures constructed, it also be defined as a transmission phenomenon [13–15]. The SPs outfrom a featured fashion of surface electron density waves, will propagate according to a specific polarization orientation of the incident lightwaves towards the apex of a nano-tip. With a smaller valid dimension of a single metallic nano-tip, the SPs can be more efficiently guided and then squeezed into a nanoscale space of the apex, and consequently presenting a strong near-field lightwave resonant enhancement owing to a much tighter lightfield confinement of nano-tips [16–19], which is generally determined by their sharpness.
In this paper, a kind of optical metasurface composed of an arrayed nano-rhombus-shaped resonant cavity is proposed. The developed metasurface as an arrayed optical antenna can be used to achieve an obvious modulation of spectral absorption in a relatively broad spectral range only by varying the surface nano-structure thickness. The featured SPs excited by the incident lightwaves polarized along the short axis of the nano-rhombus can achieve narrower band absorption than that along the long axis with the same thickness parameter. Compared with a single nano-rhombus-aperture, a double nano-rhombus-shaped composite architecture (DNRCA) predicts a higher spectral absorption peak and a stronger near-field lightwave convergence. It should be noted that the nano-structure as a resonator by compressing incident lightwaves into a patterned resonant cavity with a smaller gap size, and the net charges distributing over two opposite sidewalls of the cavity, already presents a dipole of resonant oscillation, and then the coupling oscillation becomes stronger with the narrower air gap of the cavity. So, the configurated metasurfaces exhibit a capability of achieving a relatively strong near-field lightwave convergence with a diverse appearance far beyond the traditional diffraction limit.
2. Polarization properties
At first, an arrayed nano-rhombic metasurface is designed using a common silicon wafer with a silver film predeposited over its top surface, as shown in Fig. 1. A typical 3D model of a nano-rhombus array as an arrayed optical antenna is demonstrated in Fig. 1(a). A basic DNRCA consists of a nano-rhombus-aperture with an inner nano-rhombus-block. A brown arrow indicates a selected initial polarization orientation of incident lightwaves, which is also the polarization electric field vector E, where θ is the incident angle and φ the polarization angle between the projection component Exoy in the x-y plane and the negative direction of the y-axis. Other main nano-structural parameters including the arrangement period T and the thickness H of the silver film precoated are also presented in the figure. A top view of the surface morphology of a single DNRCA is further exhibited in Fig. 1(b), including several key dimensional parameters of the long and short axes L1 and S1 of a single nano-rhombus-aperture and also the long and short axes L2 and S2 of the inner nano-rhombus-block. The common finite difference time domain method (Lumerical Solutions FDTD) is used to simulate the light absorption behaviors of the DNRCA array as a kind of optical antenna according to a set of the main nano-structural parameters of T = 1 µm, L1 = 800 nm, S1 = 400 nm, L2 = 300 nm, S2 = 150 nm, and θ=0°. Two different polarization states corresponding to the x- and y-polarizations of the incident lightwaves are considered in the simulations, which are the polarization directions along the x-axis (φ=90°) and the y-axis (φ=0°), respectively. A single DNRCA using common periodic boundary conditions at both the x- and y-axes to avoid edge effect, and the perfectly matched layer (PML) boundary condition at the z-axis are also selected. The simulation period is firstly set as 1 µm and the incident lightwaves in a wavelength range from 0.4 to 2 µm incident normally from the top.
Fig. 1. Featured nano-architecture and several typical light absorption simulations of the metasurface constructed. (a) A 3D model of an arrayed DNRCA with a silicon substrate and a surface thin silver film. A brown arrow presents the incident lightwave with an initial polarization orientation, where θ is the incident angle and φ the polarization angle. (b) The morphology of a single DNRCA with main nano-structural parameters of L1, L2, S1, S2. (c) and (d) Spectral absorption maps obtained by performing a thickness sweeping about the functioned silver film corresponding to incident lightwaves with x-polarization (θ=0°, φ=90°) and y-polarization (θ=0°, φ=0°), respectively, and the light absorption curves corresponding to the mentioned silver film thickness are also inserted on the right.
A parametric sweep of the silver film thickness yields the different absorption spectrograms, as shown in Figs. 1(c) and (d), where (c) is along the x-polarization and (d) the y-polarization. The color variance from blue to red in the graphs represents a gradually increasing trend in the lightwave absorption rate. Several typical thicknesses such as 0.05 µm, 0.125 µm, 0.22 µm, 0.28 µm, 0.6 µm, and 0.8 µm, are selected for presenting the light absorption character, where the corresponding absorption curves are attached to the right. As shown, a full width at half maximum (FWHMs) of the absorption peaks based on the x-polarization is narrower than that in the y-polarization. As increasing the thickness of the functioned silver film, the absorption peaks in both polarization states show a rising trend with increasing wavelength (red-shift). Among them, to the x-polarization orientation, the maximum light absorptivity of 0.047, 0.139, 0.569, 0.648, 0.905, and 0.778, comes about at corresponding peak wavelengths of 1.019 µm, 1.019 µm, 1.019 µm, 1.027 µm, 1.091 µm, and 1.156 µm, respectively. To the y-polarization orientation, the peak absorptivity of 0.064, 0.417, 0.801, 0.595, 0.616, and 0.586, appears at the wavelength of 1.019 µm, 1.043 µm, 1.091 µm, 1.140 µm, 1.381 µm, and 1.429 µm, respectively. It can be seen that the peak red-shift spans ∼410 nm in the y-polarization and ∼137 nm in the x-polarization, which means that a peak modulation by only adjusting the silver film thickness can be achieved in a relatively wide spectral range. As shown, the absorption peak corresponding to the y-polarization orientation is extremely sensitive to the thickness selected, so as to allow for a broad-spectrum modulation. In contrast, the modulation range corresponding to the x-polarization orientation is much narrower also through varying the top silver film thickness. It is worth pointing out that the absorption peak is gradually increased with the increase of the thickness below 0.6 µm, but decreased when it increases to 0.8 µm, and then two absorption peaks appear. For the nanoscale thickness, the strong coupling of the SPs excited at both air-Ag and Si-Ag interfaces leads to a strong resonance peak. When the thickness reaches the micron scale, the SPs on the upper and lower surfaces of the silver film cannot be coupled, so as to result in two absorption peaks.
3. Comparison of single nano-rhombus-aperture and DNRCA
A single nano-rhombus-aperture without the inner rhombus-shaped square is designed for comparison with the DNRCA, and their light absorption spectrums are simulated. In order to verify the simulation results, the samples with the two nano-structures mentioned are fabricated, and the absorption spectrums are measured. The nano-structural parameters are as follows: T = 1 µm, L1 = 800 nm, S1 = 400 nm, L2 = 300 nm, S2 = 150 nm, and θ=φ=0°. The main technological processes are as follows. Firstly, an electron beam evaporation technology (Ebeam-500S, ALPHA-PLUSCO. Ltd, Korea) is utilized to deposit a 125 nm thick silver film over a 500 µm thick silicon substrate. Next, a focused ion beam etching (FIB, Helios NanoLab G3 CX) is used to transfer the layout pattern to the silver film.
The surface morphologies of the fabricated nano-structures are characterized by a traditional scanning electron microscope (SEM, Hitachi SU8220) as shown in Figs. 2(a) and (b), with the nano-structural array shown in (a-1) and (b-1) and the enlarged view of a single structural unit shown in (a-2) and (b-2). The simulated light absorption curve of the single nano-rhombus-aperture and the DNRCA are carefully compared, as shown in Fig. 2(c). Considering the situation of being consistent with the wavelength range of the actual measurement, the wavelength of the incident lightwaves is limited to a range of 0.4 to 1.8 µm. It is shown two typical cases of lightwave absorptivity corresponding to a single nano-rhombus-aperture indicated by blue and a DNRCA by red, respectively. As demonstrated, both curves follow a similar variance trend and present an obvious absorption at the wavelength of 1.05 µm, but the absorption peak of the DNRCA is much higher than that of the nano-rhombus-aperture, as shown by the peak amplitude of 0.42 to 0.17.
Fig. 2. Simulations and experiments about the single nano-rhombus-aperture and the DNRCA with the incident lightwaves of y-polarization (θ=0°, φ=0°). (a) Surface morphology of the fabricated DNRCA with the nano-structural array shown in (a-1) and the enlarged view of a single structural unit shown in (a-2). (b) Surface morphology of the fabricated single nano-rhombus-aperture with the array shown in (b-1) and the enlarged view of a single structural unit shown in (b-2). (c) and (d) Light absorption curves based on the simulations and experiments of the two nano-structures mentioned. The blue curve corresponds to a single nano-rhombus-aperture and the red to a DNRCA.
The dispersive spectrometer produced in HORIBA (model iHR550), has the following parameters: focal length of 550 mm, resolution of 0.06 nm, and grating size of 76 mm×76 mm. The spectral range of the spectrometer is 0.4 to 1.8 µm, which already covers the visible and partial near-infrared bands. The reflection (R) and transmission (T) components can be obtained by direct measurement, and the absorption part is converted according to A = 1-R-T. The obtained absorption curves by experiment are shown in Fig. 2(d). The red curve corresponds to the DNRCA, and the blue to the absorption spectrum of the single nano-rhombus-aperture. Similar to the simulations, there is also an absorption peak at 1.05 µm and absorptivity of 0.25 of the DNRCA, which is significantly higher than that of the single nano-rhombus-aperture. Although the actual measured absorptivity presents a slight loss compared to the simulations, but the overall trend is the same, so as to verify the correctness of the simulation results.
Generally, the absorption peak often predicts unique near-field properties, so the electric field distribution of the two nano-structures mentioned at 1.05 µm is simulated, and the simulation results are shown in Fig. 3. Figure 3(a) shows four cross-sections of the patterned silver film, namely, the upper and lower surfaces of Sup and Sblow, the cross-section Sxoz and Syoz shaped along the long and short axes of the nano- rhombus. The simulated electric field intensity |Eup| and |Eblow| and |Exoz| and |Eyoz| at the peak wavelength in the above four cross-sections are shown in Figs. 3(b). To a single nano-rhombus-aperture, the electric field on the upper surface of the silver film is almost converged over four sidewalls, as shown in Fig. 3(b-1). The colorbar indicates the magnitude of the electric field enhancement factor |E|/|E0|.
Fig. 3. The simulated electric field distribution about a single nano-rhombus-aperture and a basic DNRCA with the incident lightwaves of y-polarization (θ=0°, φ=0°). (a) Schematic diagrams of a nano-rhombus-aperture including the upper (Sup) and lower (Sblow) surfaces of the silver film, the cross-section Sxoz along the long axis and the Syoz along the short axis of the nano-rhombus. (b) Typical distribution of the electric fields |Eup| and |Eblow| and |Exoz| and |Eyoz| corresponding to a single nano-rhombus-aperture based on different profiles indicated by Sup, Sblow, Sxoz, and Syoz, shown in (b-1) to (b-4), respectively. (c) Schematic diagrams of the cross-sections Sup, Sblow, Sxoz, and Syoz of a DNRCA. (d) Typical electric field distribution in a DNRCA corresponding to different component profiles, where (d-1) to (d-4) corresponds to |Eup| and |Eblow| and |Exoz|and |Eyoz|, respectively.
The free-electrons distributed over the metal surface will oscillate mainly along with the electric field polarization orientation and further coupled with the surface waves excited, so as to form a surface plasmon (SP) mode propagating over the metal surface. As a longitudinal mode, the surface wave vector direction is basically in accordance with the relatively strong excitation electric field. Generally, the wave vector is jointly determined by both the dielectric and the metal over the interface, i.e.
It is known that at the metal-air interface, the net free-electron oscillations are directly affected by the incident electric field. The SPs excited on both sides of a symmetric nano-structure are in anti-phase according to the polarization orientation of the incident electric field [20]. So, the ksp on both sides of the long axis of a single nano-rhombus-aperture is in opposite direction marked by red arrows in Fig. 3(b-1). The ksp at the nano-structure boundary can be decomposed into two components in tangential and vertical directions, marked by black and pink arrows. The vertical component will propagate through the air and then trap in the nano-rhombus-shaped cavity, and the tangential component continues to propagate along the boundary. The SPs are diverged at corner-3 and -4 and further transmit along both sides forming the corner, and consequently no focused hotspot can be formed. Owning to the destructive interference between both the counter-propagating SPs from two sides forming the corner, there is no focused hotspot at both corner-1 and -2. Considering the cases shown in Figs. 3(b-2) to (b-4), it can be seen that there exist relatively strong converging hotspots on the lower surface of the silver film, and appear at corners-5 and -6, respectively, with a field enhancement factor of ∼11. This is due to the fact that it is the refractive lightwaves that drive the free-electron oscillations on the lower surface, breaking the symmetry of the destructive interference. Thus the tangential component ksp can be superimposed and then remarkably enhanced at concave corners. The above phenomenon causes an obvious enhancement of the surface wave amplitude and thus makes the net free-electron oscillate at the corner with a higher energy state. In addition, there is a greater net charge distribution density at the corner, which is responsible for the generation of converging hotspots.
Figure 3(c) shows four typical cross-sections Sup, Sblow, Sxoz, and Syoz of the DNRCA. The simulated electric field intensity of |Eup| and |Eblow| and |Exoz| and |Eyoz| at the peak wavelength in the above four cross-sections are shown in Figs. 3(d). As shown in Fig. 3(d-1), the electric fields distributed over the upper surface of the silver film present several converging hotspots at apexes-1 and -2 of the inner nano-rhombus-block. Similarly, the SPs wave vector ksp on the boundary of the nano-rhombus is also decomposed according to white arrows indicating the tangential components and pink arrows representing the vertical components. The vertical components will propagate to air and then be trapped in the nano-rhombus-annular cavity. And the tangential components will continuously propagate along the boundary. Since the ksp on the left and right sides are in the same phase, which transmit to the convex tips apex-1 and apex-2 are superimposed and then enhanced, resulting in relatively strong focused hotspots with a field enhancement factor of slightly less than 12. Combined with Figs. 3(d-2) to (d-4), it can be seen that on the lower surface of the silver film, as a metal-silicon interface, the much stronger converging hotspots with a field enhancement factor of ∼24 appear at apex-3 and -4. As shown, the magnitude of the ksp on the upper and lower surfaces is different, which depends on the materials for shaping the needed interface. Because the wave vector direction of the incident lightwaves is downward, the incident light energy tends to accumulate onto the lower surface, which will make the converging hotspot on the lower surface much stronger.
Considering the thickness of the silver film is only 125 nm, the SPs on the upper and lower surfaces will be closely coupled. An extraordinary transmission will occur and then correlate to a strong absorption peak, as shown in the absorption spectrum. So, the DNRCA exhibits the advantage that the convex tip of the inner nano-rhombus-block can effectively converge SPs into a hotspot, and the field enhancement factor also be greatly improved compared with the single nano-rhombus-aperture. It should be noted that the electric field is compressed into a smaller cavity, to highlight a light distribution limiting and then greatly enhance the capability for realizing a strong lightwave absorption of the optical array antenna.
4. Nano-focusing properties of DNRCAs with different size parameters
Four DNRCAs with different dimensional parameters are designed for comparing and analyzing their absorption spectrum and near-field nano-focusing properties. Both the structure schematic diagrams and surface morphology of the DNRCAs fabricated with different nano-structural parameters and the absorptivity curve simulated and measured, are shown in Fig. 4. Figure 4(a) are the schematic diagrams of the four DNRCAs, where the gray part is the silver film and the blue part the holes etched through downward, so as to expose the silicon substrate. The fabricated DNRCAs have the following specification: (structure-I) L1 = 800 nm, S1 = 400 nm, L2 = 300 nm, S2 = 150 nm, (structure-II) L1 = 800 nm, S1 = 400 nm, L2 = 500 nm, S2 = 250 nm, (structure-III) L1 = 600 nm, S1 = 300 nm, L2 = 300 nm, S2 = 150 nm, (structure-IV) L1 = 880 nm, S1 = 440 nm, L2 = 300 nm, S2 = 150 nm. The surface morphology of the obtained single nano-structure is characterized by a traditional scanning electron microscope (SEM), as shown in Fig. 4(b). The simulated absorption spectrums of the four nano-structures mentioned are shown in Fig. 4(c). The broadband light source is incident on the periodic structure at 45°, so the broadband fixed angle source technique (BFAST) is selected as the plane wave type. The PML boundary condition is selected at the z-axis, the simulation period is set as 1 µm, and the polarization angle φ 45°. Due to the wavelength of the spectrometer being limited to the wavelength of 0.4-1.8 µm, the simulation results in the same wavelength band are chosen to compare with the actual experimental results. The four curves colored orange, blue, yellow, and gray, represent the absorption curves of the structures-I, -II, -III, and -IV, respectively. The light absorptivity curves of the four nano-structures follow the same trend, and all of them exhibit obvious absorption peaks at the wavelength near ∼500 nm, ∼633 nm, and also ∼1300 nm, and troughs at the wavelength near ∼1000 nm and ∼1600 nm. And the strongest absorption peak is at 633 nm. In the whole band, the absorptivity is decreased according to a sequence of structures-III, -II, -I, and -IV.
Fig. 4. Simulated and measured absorption spectrums of the DNRCAs with four different size parameters. Structure-I, -II, -III, and -IV with different nano-structural size set of (structure-I) L1 = 800 nm, S1 = 400 nm, L2 = 300 nm, and S2 = 150 nm, (structure-II) L1 = 800 nm, S1 = 400 nm, L2 = 500 nm, S2 = 250 nm, (structure-III) L1 = 600 nm, S1 = 300 nm, L2 = 300 nm, S2 = 150 nm, and (structure-IV) L1 = 880 nm, S1 = 440 nm, L2 = 300 nm, S2 = 150 nm. (a) Structural schematics of the DNRCAs about structure-I, -II, -III, and -IV. (b) Surface morphology of the fabricated DNRCAs. (c) and (d) The simulated and measured absorption spectrums of the DNRCAs about structure-I, -II, -III, and -IV, as indicated by orange, blue, yellow, and gray curves, respectively.
The experimental environment is consistent with that of the simulations. The incident light with a polarization angle of 45° is incident at 45° over the sample. Figure 4(d) shows the experimental results. As demonstrated, the four curves indicated by orange, blue, yellow, and gray, represent the absorption characteristics of the structures-I, -II, -III, and -IV, respectively. Similar to the simulations, the four curves follow the same trend, such as with two large peaks ∼633 nm and ∼1300 nm and troughs ∼1000 nm and ∼1600 nm. And the absorptivity is decreased according to a sequence of the structures-III, -II, -I, and -IV. It is known that the absorption peaks indicate special near-field properties, usually SPs resonances. In other words, the structure-III with the highest absorptivity which is also with the smallest gap will produce the strongest resonance and the strongest near-field electric field intensity. Theoretically, the smaller the gap of the air nano-cavity is, the smaller the spatial extent of the light field is compressed, resulting in a large light energy density and strong nano-focusing performance.
The near-field properties at the strong absorption peak of 633 nm are experimentally tested to explore the nano-focusing performance of each nano-structure, and then the experiment results are shown in Fig. 5. The surface morphology of four kinds of nano-structure array is shown in Figs. 5(a-1) to (d-1), and the enlarged views of a single nano-structure are shown in Figs. 5(a-2) to (d-2). The near-field optical characteristics of the sample are measured using a scattering near-field optical microscope (NeaSNOM, Quantum Design, Ltd.). In experiments, a laser beam with a central wavelength of 633 nm is incident obliquely upon the patterned surface of the samples. Both the incidence angle θ and the polarization angle φ of the laser beams are 45°. An AFM probe with a curvature radius of ∼100 nm is performed to obtain the near-field lightwave vector distribution of the sample according to the initial incident direction and the polarization state of the laser beams. A non-contacting radar probe is further used to detect the electrical response signals of the near-field lightwaves over the measured facet of the measured sample. The scanned near-field lightwave intensity results from continuously accumulating lightwave energy signals measured during the measuring period.
Fig. 5. SEM micrographs and SNOM near-field measurements of the DNRCAs with different nano-structural parameters. Four nano-structures have the same arrangement period of 1 µm. A beam of 633 nm lightwave is incident at θ=φ=45° during experiments. (a-1) to (d-1) corresponds to the surface morphology of a 4×4 nano-structure array, and (a-2) to (d-2) to an enlarged nano-structure unit. The near-field lightwave intensity distribution scanned by SNOM including the planform shown in (a-3) to (d-3) and 3D views in (a-4) to (d-4), and the quantitative measurements about the electric field along specific trajectories marked by the arrows inserted on the right.
The near-field lightwave intensity distributions of the DNRCAs scanned via SNOM are shown in Figs. 5(a-3) to (d-3). As shown, the measured near-field lightwave intensity distributions can all be divided into bright nano-line-shaped and dark areas. The near-field lightwave signals are strongly localized in some linear regions of the DNRCAs. The white arrows in the figure point to the location of the “Hotspot” where the measurement signal are the strongest. For more visualization, the corresponding 3D views of the measured signals are also shown in Figs. 5(a-4) to (d-4). Several typical near-field lightwave intensity curves obtained by scanning a 300 nm length according to a measuring trajectory marked by a pair of arrows are inserted on the right. The size of the focused linear spot is quantified by the full width at half maximum (FWHM) of the scanning path curve.
As demonstrated, the near-field lightwaves of the structure-I are already converged into a bright linear spot at the edge of the outer nano-rhombus with a line width of ∼42 nm. In addition, a strongly focused spot is also formed on one corresponding side of the inner nano-rhombus-block with a near-field signal intensity up to ∼24 µV and a beam spot diameter of ∼21 nm. The measured near-field lightwave signal of the structure-II is relatively weak, and the strongest signal localized in the cavity between the inner nano-rhombus-block and the outer nano-rhombus already reaches ∼3.5 µV, and the diameter of the beam spot reaches ∼68 nm. To the structure-III, the measured near-field signal is also weak and has the strongest signal at the corner of the outer nano-rhombus reaching ∼4.6 µV, and the beam spot diameter reaching ∼24 nm. It is worth noting that the curvature radius of the AFM probe is ∼100 nm, and the size of the air gaps of structures-I, -II, -III, and -IV are 123 nm, 78 nm, 75 nm, and 130 nm, respectively. The reason for the relatively weak signal of the structure-II and -III is that their relatively large duty cycle and the very narrow air gap prevent the probe from effectively entering the cavity to accurately acquire the near-field signal located at the nano-rhombus sidewall. The situation of the structure-IV is similar to the structure-I, where the near-field lightwaves are also converged into a linear spot at the edge of the outer nano-rhombus with a linewidth of ∼40 nm. Moreover, a strong arc-shaped spot is formed near the apex of the inner nano-rhombus-block with a near-field signal up to ∼10.9 µV and a linewidth of ∼22 nm. Considering the excitation wavelength of 633 nm, the measured convergent light spot size has been reduced by an order of magnitude compared to the laser wavelength, so as to greatly exceed the light diffraction limit.
Compare measurement results with simulation results. As demonstrated, the simulated model is established based on actual measurements. The wavelength of incident light is 633 nm. Both the incidence angle θ and the polarization angle φ of the laser beams are 45°. Considering a structure of finite size 1 µm and utilizing common Bloch boundary conditions at both the x- and y-axes for oblique incidence, and PML boundary condition at the z-axis. A comparison between the simulations and the actual measurements of the structures-I, -II, -III, and -IV, is shown in Fig. 6. The simulated electric field vectors Eblow and Eup of the lower and upper surfaces of the functioned silver film are shown in Figs. 6(a) and (b). The red arrows in Figs. 6(a-1) and (b-1) indicate the projected component Exoy of the incident electric field in the x-y plane. It should be noted that since the surface electric field intensity is proportional to the surface net charge density, the electric field vector character also presents the distribution behaviors of the surface net charges stimulated. The positive electric field region labeled by red can be seen as a positive charge aggregation region, which is also marked with a plus sign. And the negative electric field region by blue corresponds to the negative charge aggregation region marked with a minus sign. The simulations indicate that the surface net charge distribution patterns are similar for all four structures mentioned. The net charge distribution on the lower surface of the functioned silver film presents a pair of dipoles formed on four sides of the air cavity along the inner and outer sidewalls marked by red-blue arrows, respectively. The electric field enhancement factors of Eblow of different DNRCA mentioned are similar with slightly different values of ±1.3, ±1.2, ±1.5, and ±1.3.
Fig. 6. Simulation and measurement results of the electric field vectors of four DNRCAs. The simulated electric field vector Eblow (a) and Eup (b) of the lower and upper surface of the silver film with the electric field intensity |E| curves scanned along the long axis of the rhombus inserted at the bottom. (c) The electric field vector Eexp by SNOM measurement.
While on the upper surface of the functioned silver film, both the positive and negative net charge distribution is exactly opposite to that on the lower surface, due to already generating a dipole charge oscillation between the upper and lower surfaces excited by the incident electric field component in the z-axis. According to the colorbar, the electric field enhancement factor of Eup is much larger than that of Eblow, which are ±13, ±15, ±18, and ±11. This is due to the fact that the incident lightwaves with a central wavelength of 633 nm already excite the transmitted SPPs on the upper surface. Several obvious stripes can be seen on the lower right of the Eup distribution, which is also caused by the transmitted SPPs. According to the simulated Eup profile, the local electric field is the strongest at the left and right apex of the inner nano-rhombus-block. The corresponding electric field intensity |E| scanned along the long axis of the nano-rhombus is also displayed at the bottom of Fig. 6(b). The FWHM of the shaped peaks can be roughly used to represent the diameter of the converging spot, which are ∼16 nm and ∼15 nm and ∼15 nm and ∼16 nm corresponding to the structures-I, -II, -III, and -IV, respectively. The minimum size of ∼15 nm of the converging spot is slightly small than the measurement value of ∼21 nm. It is worth noting that the larger the duty cycle, i.e., the smaller the air gap, the stronger the dipole coupling between the inner and outer sidewalls of the nano-rhombus-annular cavity. This can be reflected in Fig. 6(b-3), where the four pairs of dipoles are circled in red dashed circles. The largest field enhancement factor of ±18 is obtained on the upper surface of the structure-III, which means that the nano-structure can be used to achieve the largest near-field convergence. Theoretically, a smaller size of near-field converging spot can also be achieved, thus continuously maximizing the breakthrough of the common light diffraction limit.
The SNOM measurements can be quantified in terms of AFM topography of the nano-tips, as well as the magnitude and phase of the near-field lightwaves. Their transient magnitude and the phase contain the needed information from the first-order to the fourth-order transformation of measurement data. Specifically, the amplitude s4 and phase φ4 of the near-field lightwaves can be extracted. Generally, the measured near-field signals express a direct response of the surface electric field excited, which can be described by a fluctuation formula of [21]
where T represents the time period of the near-field lightwaves. So, the near-field lightwave vector Eexp over the nano-structures, which also presents the distribution behavior of surface net charges stimulated, can be obtained, as shown in Fig. 6(c). It is shown that the charge distribution pattern measured generally agrees with the simulation prediction over the upper surface. The near-field signals of structures-I and -IV are stronger than structures-II and -III, which are (±20 µV, ±10 µV) and (±3 µV, ±4 µV). The reason for the relatively weak signal of the structures-II and -III is that their relatively large duty cycle and the narrow air gap prevent the probe from effectively entering the cavity to accurately acquire the near-field signal located at the cavity sidewall. In addition, there is a slight drift in the near-field optical micrographs due to a slight tilting of the sample during performing SNOM measurement, resulting in a slight difference between the measurements and the simulations. On the other hand, the presence of the oxide layer on the surface of the silver film also contributes to the deviations from the theoretical prediction in the SNOM experiment. Subsequent efforts will be devoted to improving the stability of the material to reduce the deviation of the actual measurement from the theoretical prediction, and thus ensure that the fabricated nano-structures present an excellent nano-focusing efficiency. The specific approach is to design bimetallic layer structures [22] based on surface plasmon resonance composed of Ag combined with stable metals such as Au, or the ridged metal heterostructures [23].5. Conclusion
In summary, a kind of optical metasurface composed of an arrayed nano-rhombus-shaped resonant cavity can be used to achieve a lightwave absorption modulation in a relatively broad wavelength range only by adjusting the thickness of the functioned silver film when excited by incident lightwaves polarized along the short axis of the nano-rhombus. And then a narrower band absorption is achieved by configuring the same thickness parameter when incident lightwaves are polarized along its long axis. Compared with a single nano-rhombus-aperture, the DNRCA can present a higher absorption peak and stronger near-field light convergence. The developed metasurfaces with the capability of performing a relatively strong incident lightwave collection and near-field light converging efficiency, and present an ideal nano-focusing performance with a minimum light-spot size of ∼21 nm, which is one order of magnitude smaller than the incident wavelength of 633 nm, thus greatly break the light diffraction limit.
Funding
National Natural Science Foundation of China (61176052).
Acknowledgment
The authors would like to thank Yan Zhu from Huazhong University of Science and Technology for the experimental support of FIB, Xiaolei Wen from the University of Science and Technology of China for the experimental support of SNOM, and Weihang Zhou from Wuhan National High Magnetic Field Center and School of Physics for the experimental support of the dispersive spectrometer.
Disclosures
The authors declare that there are no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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