1. Introduction

Various types of metamaterial and frequency selective surfaces have been explored for use at infrared wavelengths, which have been engineered to give polarization sensitive responses, extraordinary optical transmission, directional emission, near perfect absorption, etc [1–9]. Another useful property to explore are higher order resonance modes, especially their angular dependence (azimuth and polar) where at certain angles a mode can become commonly referred to as “dark” or not able to be excited [10, 11]. This enables one way to manipulate the angular response of metamaterials by excitation of modes that are bright within a certain range of angles of incidence, but are dark at other angles of incidence. Generally, resonant metallic structures have potential applications involving sensing or other applications where strongly concentrated optical fields are desirable [12, 13]. Further, the prevalence of higher order modes at certain angles of incidence for these types of structures can provide for improved sensitivity for some applications because higher order modes can yield an electric field distribution having more nodes and, thus, provide a more uniform or less localized field across the structure. In particular, it has been suggested that metallic circular ring structures are promising for sensing applications because of their potential for providing more uniform field enhancement and greater tunability compared to other type structures like circular disk structures [13–15]. More specifically, gold circular rings and concentric ring/disk structures composed of silver have been suggested for this purpose as well as nonconcentric ring/disk structures composed of gold. Compared to a dimer antenna structure where the field enhancement is highly localized in the gap between the wires [16], the electric fields generated from these ring structures can be more evenly distributed across a surface, improving the efficiency for detecting target entities.

It has been shown that there can be a strong azimuthal angular dependence of fundamental and higher order resonances as well as hybridized modes for various structures. For instance, in one publication it was demonstrated for dimer antennas, composed of two metallic rods separated by a small gap, that by changing the azimuthal angle of illumination, hybridized, antisymmetric dark modes from the dimer could become excited [17]. Specifically, the authors rotated the sample with respect to the incident beam by 20°, which introduced a phase shift along the long axis of the antenna and, thus, broke the symmetry of the excitation. This allowed the antisymmetric mode from the dimer to become able to be excited or bright. However, when the sample was not rotated, then the antisymmetric dimer modes were dark and only the symmetric dimer modes were bright. Similar azimuthal angular dependence on the appearance of plasmonic modes has been observed for optical monopole antennas [18, 19]. In one publication near-field simulations and experimental data showed that odd order modes could be exited in gold monopole optical antennas with near-IR wavelength irradiation at 71° off-normal angle of incidence [18]. However, even order modes could not be excited under these conditions, except when the sample was rotated to a different azimuthal angle, which enabled for a phase delay to be experienced by the monopole antenna from the incident wave. In another publication similar results were observed in the far-field for gold nanorod antennas at optical wavelengths [19]. Generally, when the symmetry for the excitation is not broken, then odd order modes in monopole antennas are radiative due to having a net dipole moment while even order modes are dark due zero net dipole moment [20, 21].

In addition, several articles have showed that various other structures having different geometries displayed strong dependence of the even and odd order modes on the incident polar angle [10, 19, 22–25]. For instance, in one publication slot antennas of different lengths were fabricated in a thin gold film and measured in the near- and far-field [22]. Far-field IR microscope results performed between 18 and 40° off-normal angles of incidence showed the higher order resonances for several different length slots and the authors suggested that at normal incidence the even order resonances were dark modes, but no measured or simulated results were shown at this angle of incidence to support this claim. In these articles the geometry of the structure seems to dictate much of the angular response, in particular whether certain modes are able to be excited at different polar and azimuthal angles.

In previous work we investigated semi-infinite arrays composed of two different size aluminum square loops which were designed to have dipolar and quadrupolar resonances under s-polarized, 10.6 µm wavelength incident radiation at 60° off-normal angle of incidence [26]. These structures were measured at normal incidence in the far-field over the mid-infrared using FT-IR and with 10.6 µm wavelength illumination at 60° off-normal using scattering-type scanning near-field optical microscopy (s-SNOM). At 60° off-normal the s-SNOM measurement clearly showed that the quadrupolar mode could be excited and it was suggested that this mode would not be able to be excited near normal incidence. However, due to the overlap of the resonances from the BCB standoff layer and elements (along with the possibility that the antenna’s resonance enhances the organic layer’s vibrational modes), attempts to confirm this experimentally by FT-IR were not possible. To the best of our knowledge no other work exists exploring higher order resonances in square loop structures, especially considering the angular dependence.

Here, we extend the above work by investigating arrays of different size square loops deposited on ZnS instead of BCB in order to explore the angular dependence of the higher order resonances and, especially, the conditions for which certain modes become bright or dark. ZnS has loss bands far removed from the 5 to 20 µm wavelength region of interest and, thus, avoids potential coupling or overlap between the resonances of the standoff layer and square loop elements that has been observed in our previous work [26]. Therefore, utilizing ZnS as the standoff layer we were able to investigate higher order resonances of square loops in the mid-infrared in near- and far-field without the added complication of other modes being excited in the standoff layer. Specifically, gold square loops having fundamental, second order, and third order modes at 10.6 µm wavelength were investigated, which we call the small, medium and large loops.

2. Materials and methods

2.1 Simulations and fabrication

The samples of interest consisted of three uniform arrays composed of different size square loops on ZnS and having an inter-element spacing of 5 µm, which were designed to have fundamental and higher order resonances under s-polarized (transverse electric), 10.6 µm wavelength illumination. For the purpose of optimizing near-field measurements in this work, the structures were designed to have peak fundamental and higher order resonances matching the illumination conditions of our s-SNOM, which is 10.6 µm wavelength illumination at 60° off-normal angle of incidence, with s-polarization. Briefly, electromagnetic simulations were performed using commercial finite element method software, Ansys HFSS. Variable angle spectroscopic ellipsometry was used to determine the wavelength dependent optical constants of all materials used in the simulations, which is important for increasing the confidence in simulations at infrared wavelengths where metals have a finite conductivity [27]. The simulated near- and far-field responses of infinitely repeating two dimensional arrays of the structures were performed using Floquet port analysis with periodic boundary conditions on opposite faces of the model. Far-field s-parameters were derived from the Floquet port analysis, which enabled the spectral absorptivity and relative phase change upon reflection to be determined. Also, values of the electric near-field were obtained from the same simulated results and were evaluated at 100 nm above the spacer layer. Parametric simulations were used to optimize the sizes of the loop structures to have fundamental and higher order resonances at 10.6 µm wavelength and 60° off-normal angle of incidence.

Based on parametric simulations, three different uniform arrays of square loops having a chromium ground plane and ZnS spacer layer were fabricated. The fabrication followed a similar procedure as was outlined in previous work [26, 28, 29]. First, a 150 nm layer of Cr was deposited by e-beam evaporation onto a clean silicon wafer to form the ground plane. Cr was employed as the ground plane because it was found previously that ZnS adheres relatively well to it [26]. Then, 0.32 µm of ZnS was thermally evaporated onto the ground plane where a baffled box was utilized to facilitate improved thickness uniformity and fewer defects for the deposited layer. E-beam lithography was used to define the areas to be patterned in a film of polymethyl methacrylate (PMMA) photo resist, which was followed by development of the resist. Metallization was done by e-beam evaporating 2.5 nm layer of titanium and 75 nm layer of gold. Lift-off was achieved by immersing the sample in n-methyl pyrrolidinone (NMP) for 24 hours, then rinsing with isopropyl alcohol (IPA) to yield the resulting loop structures. Figures 1(a)-1(c) shows scanning electron micrographs of the three uniform arrays of different size loop structures.

 

Fig. 1 SEM micrographs of the (a) small (b) medium and (c) large square loop structures on ZnS, each having a periodicity of 5 µm.

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2.2 Near-field measurements

The near-field signal polarized normal to the square loops was measured using a custom built s-SNOM setup, which has been described in previous works [26, 28–30]. The setup is shown in the schematic in Fig. 2, which utilizes a modified AFM (Innnova, Bruker) operating in tapping mode. The source is a CO₂ laser (L4S, Access Laser Company) operating at 10.6 µm, which provides a beam that is collimated and s-polarized with respect to the sample. A 50:50 beam splitter (BS) allows for comparable fractions of the incident to be reflected towards the sample and transmitted through into a reference path. The reflected beam is directed towards the sample at 60° off-normal relative to the surface plane (θ) using an off-axis parabolic (OAP) reflector, which focuses the beam to a roughly diffraction limited spot at the sample surface. A platinum coated AFM probe, operating in a frequency range of 240-280 kHz, is positioned within close proximity of the focused beam, which scatters the exited near-field into the far-field. The sample is raster scanned with the incident beam stationary, which allows for the region of interest to be imaged. The scattered far-field radiation is collected along the same beam path as the focused incident beam (reflection-mode backscattering configuration) [31]. The fraction of the beam that is transmitted through the BS is reflected off a moveable reference mirror (MRM). Here, the reference path contains a quarter-wave plate (QWP), which effectively rotates the polarization of the reference beam. The combined reference and scattered near-field radiation is directed from the BS through another polarizer which allows for p-polarized light to be transmitted, corresponding to signal sensitive to E_z. Then, this combined beam is focused onto a LN2 cooled mercury-cadmium-telluride (MCT) detector using another OAP where the following equation can be used to describe the various components that contribute to the detected far-field signal (S_d):

 

Fig. 2 Schematic of the s-SNOM apparatus which utilizes a modified AFM operating in tapping mode. An s-polarized beam having a wavelength of 10.6 µm from a CO₂ laser is reflected off a beam splitter (BS) towards an off-axis parabolic (OAP) reflector, which focuses the beam onto the sample at an angle of 60° off-normal (θ). The AFM tip, operating at a frequency of Ω and positioned within close proximity of the beam spot, scatters the near-field signal into the far-field. The scattered radiation is collected by the same OAP used for excitation and directed back towards the BS. Meanwhile, part of the incident beam is transmitted through the BS into a reference path. In this path a quarter wave plate (QWP) rotates the polarization and a moveable reference mirror (MRM) reflects the beam back to the BS. At the BS the reference beam is combined with the scattered radiation from the sample which is then focused to a MCT detector using another OAP. This configuration allows for determination of both amplitude and phase of the near-field polarized normal to the surface plane.

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2.3 Far-field measurements

Far-field characterization at predominantly normal incidence measurements were performed using an FT-IR with microscope attachment (Perkin Elmer). A circular aperture with a diameter of 100 µm was used to restrict the measurement to the center of the arrays. For far-field characterization at off-normal angles of incidence a hemispherical directional reflectometer (Surface Optics Corporation) was used. Here, a circular aperture with a diameter of 3.175 mm was used to restrict the interrogation area to the center of the arrays.

3. Results

3.1 Design simulations results

Three different size uniform arrays of gold square loop elements on ZnS were designed to exhibit dipolar (fundamental), quadrupolar (second order), and hexapolar (third order) modes at 10.6 µm and 60° angle of incidence. Parametric simulations of absorptance and reflected phase versus element size are often used to determine the resonant dimensions of elements designed to have various fundamental and higher order resonances at a particular wavelength and angle of illumination [30, 34–36]. Here, simulations using Floquet port analysis were performed where infinite arrays of square, Au loop elements having a range of different sizes and a periodicity of 5 µm were illuminated with s-polarized incident radiation having a wavelength of 10.6 µm and an angle of incidence of 60° off-normal. Fig. 3 shows the results from these simulations where absorptance (blue dashed line) and relative reflected phase (red solid line) are plotted as a function of edge length of the square loop. Here, due to the presence of an optically thick ground plane, absorptivity (A) was calculated from the resulting simulated reflectivity through: A(λ) = 1− R(λ). The graph shows absorptive fundamental, second order and third order resonances at three different edge length dimensions of 1.6, 2.8, and 4.4 µm, respectively. Based on these results, three different uniform arrays of square loops having edge lengths corresponding to these fundamental and higher order resonant modes were fabricated, which we refer to as the small, medium, and large loops.

 

Fig. 3 Graph showing simulated absorptance (blue dashed line) and reflected phase (red solid line) versus edge length for loops of 5 µm periodicity when the structures were illuminated with a 10.6 μm wavelength incident wave 60° off-normal to the surface plane.

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3.2 Far-field results

Next, far-field measurements and simulations of absorptance as a function of polar incident angle and wavelength were performed for the small, medium and large loops. Figure 4 shows plots of experimental and simulated polar angle and spectral absorptivity for each uniform array of different size loop elements on ZnS. Measurements were made in the center of the array over a relatively large area, but away from the edges of the array to avoid effects of the array edge on the resonances, treated in previous work [29]. More specifically, Figs. 4(a) and 4(b) show plots of experimental and simulated spectral and polar angle absorptivity for the small loop, which was designed to have a fundamental mode at 10.6 µm wavelength irradiation and 60° off-normal angle of incidence. Similarly, Figs. 4(c) and 4(d) show experimental and simulated results for the medium loop, which was designed to have a second order mode at 10.6 µm wavelength irradiation and 60° off-normal angle of incidence. Lastly, Figs. 4(e) and 4(f) show experimental and simulated results for the large loop, which was designed to have a third order mode at 10.6 µm wavelength irradiation and 60° off-normal angle of incidence.

 

Fig. 4 Graphs of experimental absorptivity as a function of angle of incidence and wavelength for the (a) small, (c) medium, and (e) large square loop elements on ZnS. In addition, graphs of corresponding simulated spectral and polar angular absorptivity are shown for the (b) small, (d) medium, and (f) large square loops. Values for the z-axis, represented by the color bar, indicate absorptivity. The experimental results were obtained by FT-IR measurements under normal incidence and HDR under all other angle of incidence shown in the plot. The simulated results were obtained by calculating the reflection coefficient versus wavelength (µm) at all angles of incidence. Dashed lines indicate approximate locations of fundamental, second order, and third order modes for the small, medium and large loops, respectively. Dotted lines in (c) and (d) indicate the location of a fundamental resonance for the medium loop while the dash-dotted lines in (e) and (f) indicate the location of a second order resonance for the large loop.

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The simulated values for the absorptivity as a function of angle of incidence and wavelength qualitatively match the experimental results and show the same resonances. Small discrepancies between the simulated and experimental results can be attributed to differences in the geometry of the fabricated and simulated structure. More specifically, the fabricated loops structures include surface roughness and imperfections such as curvature around the edges of the structure, which are not included in the simulations. At wavelengths of roughly 4 um and less, the very high absorption can be attributed to thin-film interferences effects from the ZnS layer where this layer is acting as an AR coating. As expected, the resonant frequency for each mode is approximately linear with the resonance mode number (see Appendix).

In Fig. 4 several fundamental and other odd order modes are observed, which show an angular dependence with regards to their absorptivity. As was designed, there are fundamental and third order modes shown in Figs. 4(a) and 4(b) for the small loop and Figs. 4(e) and 4(f) for the large loop at ~10.6 µm wavelength illumination (indicated by the dashed lines). However, there are also other odd order modes that can be identified. For example, there is also a fundamental mode shown in Figs. 4(c) and 4(d) for the medium size loop at ~18.5 µm (indicated by the dotted line). Each of these fundamental modes for the small and medium loops indicated by the dashed lines in Figs. 4(a) and 4(b) and dotted lines in Figs. 4(c) and 4(d), respectively, shows a significant angular dependence with regards to the absorptivity, which becomes diminished at higher angles of incidence. Also, this is evident with the hexapolar mode for the large loops along the dashed line in Figs. 4(e) and 4(f) where at 60° off-normal angle of incidence the absorptivity becomes very small (point iii). This is consistent with previous work where the diminished absorptivity at higher angles of incidence was partly attributed to the appearance of the higher order modes and that the integral sum of all of the resonance peaks in the spectrum should remain constant at all angles of incidence [5, 24, 37, 38].

Also, Fig. 4 shows several even order resonances, especially 2nd order modes that appear to be dark at normal incidence, but can become excited at off-normal angles of incidence. For example, Figs. 4(a) and 4(b) shows that at 6 µm wavelength irradiation the second order mode for the small loop has very little absorptivity or is nearly dark at normal incidence and becomes more absorbing or bright at increasing angles of incidence, although it is slightly obscured by the thin-film interference effects of the ZnS standoff layer. However, in Figs. 4(c) and 4(d) the angular dependence of the second order mode at ~10.6 µm wavelength irradiation for the medium loop can be seen more clearly where at normal incidence there is only a small amount of absorptivity and at off-normal angles of incidence there is stronger absorptivity (indicated by the dashed line). In addition, a similar angular dependence is seen in Figs. 4(e) and 4(f) for the second order mode for the large loop at ~15.5 µm wavelength irradiation (indicated by the dash-dotted line).

3.3 Near-field results

Next, to verify the existence of the odd and even order modes at off-normal angles of incidence we performed near-field simulations and measurements at 60° off-normal angle of incidence and 10.6 µm wavelength illumination in the middle of the small, medium, and large square loop arrays. Figure 5 shows images of the experimental and simulated amplitude of the local electric field polarized normal to the surface plane for the small, medium, and large loops. The simulated amplitude images have been normalized to the experimental amplitude data for the small square loop structure to provide a better comparison to the experimental amplitude images. Note that each of the color bars corresponds to the amplitude of the near-field signal and has different ranges for each size loop. Corresponding near-field phase images are shown in Fig. 6.

 

Fig. 5 Measured (a, c, e) and simulated (b, d, f) amplitude near-field images for the small, medium, and large square loop array on ZnS with a periodicity of 5 µm when excited with a 10.6 µm wavelength radiation at 60° off-normal angle of incidence. In the measured amplitude images the values for the z-axis, represented by the color bar, are proportional to amplitude of E_z.

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Fig. 6 Measured (a, c, e) and simulated (b,d,f) near-field phase images for the small, medium and large square loop array on ZnS with a periodicity of 5 µm when excited with a 10.6 µm wavelength radiation at 60° off-normal angle of incidence.

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All of the amplitude images in Fig. 5 show a qualitative match between the simulations and experimental data. The experimental and simulated amplitude images in Figs. 5(a) and 5(b) show characteristic evidence of a strong dipolar (fundamental) resonance for the small loop. Further, the experimental and simulated phase images in Figs. 6(a) and 6(b) show a 180° phase shift across the elements, which is consistent with the presence of a dipolar mode. The experimental and simulated amplitude images in Figs. 5(c) and 5(d) show evidence of a quadrupolar mode for the medium loop, which is supported by the experimental and simulated phase images in Figs. 6(c) and 6(d). Interestingly, the magnitude of the experimental and simulated near-field response for the medium loop is comparable to the response for the small loop having a dipolar resonance. The experimental amplitude and phase images in Figs. 5(e) and 6(e) show evidence of a hexapolar mode for the large loop while the simulated amplitude and phase images in Figs. 5(f) and 6(f) show results consistent with the experimental results, although the experimental result is much weaker than with the other size loops. The weaker experimental near-field response of the large loop is actually predicted by simulations as well where the simulated signal is shown to be ~5 times weaker compared to the simulated results for the other size loops, although the experimental results shows that the signal is ~10 times weaker compared to the other size loops. The weaker near-field response of the large loop was also expected based on the graphs shown in Figs. 4(e) and 4(f).

To verify the absence of the second order mode at normal incidence for these square loops, especially the medium loops, we examined the expected near-field response at angles approaching normal incidence. Unfortunately, our near-field measurement setup limit measurements to only 60° off-normal angle of incidence, so we used simulations to predict the near-field response at other polar angles. The simulation shown in Fig. 7(a) shows the simulated near-field response for the medium loop when excited with 10.5 µm wavelength radiation at normal incidence, which shows a second order mode only at off-normal angles of incidence near this wavelength of excitation. Note that the second order resonance for the medium loop is slightly blue-shifted towards 10.5 µm when approaching normal incidence as shown in Figs. 4(c) and 4(d), so 10.5 µm wavelength radiation was used for these simulations. Here, the simulated near-field response from the medium loop is plotted across a 5x5 µm area as amplitude of the E_z field evaluated at 100 nm above the ZnS spacer layer. Similarly, these simulations were repeated with the small and large loops, which is shown in Figs. 9(a) and 9(b) (see Appendix). Also, simulations were performed where the amplitude of the E_z field was determined at the resonant wavelength for the second order mode for the medium loop, but at various angles of incidence. Here, these simulations were done at 0 to 80° angles of incidence. Specifically, the resulting amplitude of the E_z field was calculated by integrating this quantity over the whole unit cell. Figure 7(b) shows the results of these simulations where the integrated amplitude of the E_z field from the second order mode is plotted versus angle of incidence.

 

Fig. 7 (a) Simulated near-field amplitude image for the medium size loop on ZnS with a periodicity of 5 µm when excited with a 10.5 µm wavelength radiation at normal incidence. In the simulated amplitude image the values for the z-axis are |E_z|, which are represented by the color bar and have been normalized to the experimental amplitude data for the small square loop structure. This was done with all the simulated near-field data to provide for a better comparison with the experimental amplitude data. In the simulated amplitude image the values for the z-axis, represented by the color bar, shows amplitude of E_z (b) Graph showing simulated results of integrated |E_z| at the peak wavelength (λp) versus angle of incidence for the medium loop. The |E_z| was integrated across the whole unit cell 0.1 µm above the surface.

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Figure 7(a) shows a very weak near-field response for the medium size loop at normal incidence and 10.5 µm wavelength illumination, consistent with the results observed in Figs. 4(c) and 4(d). Interestingly, the weak field pattern is a characteristic of an asymmetric dipolar mode, similar to what was observed in previous work with circular ring structures [24]. Figure 7(b) shows that the integrated near-field amplitude becomes diminished to near zero approaching normal incidence, which is also consistent with the results in Figs. 4(c) and 4(d). However, the response shown in Fig. 7(b) does not clearly identify the type of resonance that is present, but based on Fig. 7(a) the only resonance present at normal incidence is the asymmetric dipolar mode while, at off-normal incidence, the near-field response becomes dominated by the quadrupolar mode. In contrast, the small and large loops, which have fundamental and third order modes at 10.6 µm wavelength and 60° angle of incidence, still show very clear fundamental and hexapolar modes at normal incidence (see Appendix).

4. Discussion

The observation that the second order mode (quadrupolar) is not observable at normal incidence, but is observable at off-normal incidence along with the odd order modes is consistent with some previous work, but contrary to others. As mentioned above, the geometry of the structure seems to be an important factor for determining what modes are present at different incident azimuthal and polar angles. In some of these articles the structures are quite different from our square loop structure, which can explain why the angular response is different. Still, in some work the structures are similar and should be expected to yield a similar angular response such as in one article where circular nanorings were investigated [10, 24]. Here, it was shown that at normal incidence a dipolar mode was excited in the circular nanorings with resonances in the near-IR to visible wavelengths, but at increasing angles of incidence higher order modes appeared and became more prominent. Specifically, they found that at increasing angles of incidence the dipolar mode became weaker as the higher order even and odd modes became more pronounced. However, inconsistent with the results in our work, it was claimed that all even and odd order modes were not able to be excited at normal incidence, except the 1st order symmetric and antisymmetric dipolar modes. In another article where a similar structure is investigated, results consistent with what we have observed is shown. Here, gold nanodisks were measured at near-IR to visible wavelengths in the far-field using a UV-Vis-NIR spectrophotometer [23]. These experimental results showed that at normal incidence the nanodisks displayed a dipolar resonance and the absence of a quadrupolar mode, but upon illumination at off-normal angles of incidence, the quadrupolar mode was observable. However, as with many related articles, a more comprehensive angular dependence was not shown and no other higher order modes beyond the quadrupolar mode were studied.

For square loop geometry structures, there is very little work investigating the higher order resonances and the angle of incidence dependence of these modes for these structures [39]. For example, our previous work discussed above was primarily done with square loops deposited on BCB, which has material absorption bands located near the higher order resonances for the structures studied, so there were no simulated or experimental results that gave significant insight into these modes and their angular dependence [26]. However, the results here clearly show a strong angular dependence of all the modes observed, especially the second order modes that are dark at normal incidence and become bright at off-normal angles. Here, at normal incidence the second order modes for the square loops have a charge distribution that yields a zero dipole moment and is dark. However, the structure has a sufficiently large enough dimensions along the surface to enable a phase delay to occur when excited at off-normal angles of incidence, allowing for the 2nd order to become bright, which is consistent with what has been claimed in other reports for similar circular ring and cross structures [25,40]. This is in contrast to the monopole and dimer antenna structures which do not allow for a phase delay to be experienced at off-normal angles of incidence when the incident beam is directed perpendicular to the long axis of the antenna so even order modes cannot be excited under these same conditions.

5. Conclusion

We investigated fundamental and higher order resonances in different size square loops on ZnS over a ground plane, especially the angle of incidence dependence of the far-field absorptivity. For instance, the medium size loop, which showed a second order resonance at 10.6 µm wavelength illumination and 60° off-normal, was dark at normal incidence and became bright at off-normal incidence. We expect that a similar angular response should be exhibited for all even order modes. Unexpectedly we found that the near-field signal was comparable in magnitude between the fundamental mode of the small square loop and the second order of the medium square loop at 10.6 µm wavelength illumination and 60° off-normal. Also, simulations showed that the small and large loop have similar magnitudes for their near-field signal at the same wavelength of excitation, but at normal incidence. The literature suggests that the angular dependence of higher order modes in a resonant metallic elements is strongly dependent on the geometry of the structure [10, 18, 19, 22–24]. For our particular square loop structure, the appearance of the second order mode (quadrupolar) at off-normal polar angles of incidence is a consequence of the phase delay of the incident beam across these structures whereas at normal incidence the whole structures is subjected to the same phase of the incident beam and there is no retardation effect.

These results are potentially useful for applications involving sensing where the second order mode of the medium loop can provide for a more uniform electric field under 60° off-normal angle of incidence and 10.6 µm illumination without sacrificing field strength [12]. Likewise, the large loop can provide similar field strength as the small loop structure at normal incidence and 10.6 µm illumination, but even more uniform electric field.

6 Appendix

6.1 Further analysis of far-field results

Here, we provide further analysis of the relationship of resonance mode number with resonant frequency in Fig. 4. Specifically, we looked at this relationship for the medium size loop in Fig. 4(d). Figure 8 shows a plot of the resonance frequency versus resonance mode number for the medium size loop, which, as expected, shows is an approximate linear relationship. The slight deviation from linearity is attributed to the finite conductivity at these wavelengths of the gold composing the elements and the presence of the substrate [22, 41, 42].

 

Fig. 8 Graph of resonance frequency versus resonance mode number derived for the medium size loop derived from the simulated data plotted in Fig. 4(d). Here, the angle of incidence is 60° off normal. The red line is present to act as a guide to the eye and illustrate the roughly linear relationship.

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6.2 Additional near-field simulations

In addition to the simulation in Fig. 7(a), we performed simulations to investigate the near-field response of the small and large loop at normal incidence and a wavelength of 10.5 µm, the expected fundamental and hexapolar resonant wavelength for each loop at this angle of incidence. As with the medium loop, the E_z field was evaluated at 100 nm above the ZnS spacer layer in the simulations and plotted across a 5x5 µm area as amplitude of the E_z field. As shown in Fig. 9(a) and 9(b), the small and large loop both still exhibit a fundamental and third order modes at 10.5 µm wavelength and normal incidence, similar to what was observed with the near-field measurements and simulations in Fig. 5 which were at 60° off-normal. As with the small and medium loops at 60° off-normal, the small and large loop show similar magnitudes for the near-field amplitude signal under normal incidence where the large loop only has ~4x less signal compared to the small loop.

 

Fig. 9 Simulated near-field amplitude images for the (a) small and (b) large size loops on ZnS with a periodicity of 5 µm when excited with a 10.5 µm wavelength radiation at normal incidence. In the simulated amplitude images the values for the z-axis are |E_z|, which are represented by the color bars and have been normalized to the experimental amplitude data for the small square loop structure. This was done with all the simulated near-field data to provide for a better comparison with the experimental amplitude data.

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Funding

National Science Foundation (NSF) (1204993, 1068050).

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