3D conductive coupling for efficient generation of prominent Fano resonances in metamaterials

We demonstrate a 3D conductive coupling mechanism for the efficient generation of prominent and robust Fano resonances in 3D metamaterials (MMs) formed by integrating vertical U-shape split-ring resonators (SRRs) or vertical rectangular plates along a planar metallic hole array with extraordinary optical transmission (EOT). In such a configuration, intensified vertical E-field is induced along the metallic holes and naturally excites the electric resonances of the vertical structures, which form non-radiative “dark” modes. These 3D conductive “dark” modes strongly interfere with the “bright” resonance mode of the EOT structure, generating significant Fano resonances with both prominent destructive and constructive interferences. The demonstrated 3D conductive coupling mechanism is highly universal in that both 3D MMs with vertical SRRs and vertical plates exhibit the same prominent Fano resonances despite their dramatic structural difference, which is conceptually different from conventional capacitive and inductive coupling mechanisms that degraded drastically upon small structural deviations.

ring-rod nanostructures 19 , and THz connected SRR structures 18 . The main reason is that the 2D connected elements were generally treated as single conductive structures and the resulted couplings were traditionally rationalized as the interference between the bright dipole modes and the dark high-order modes 19 .
Recently we observed significant Fano resonances from a "nanograter"-like 3D MM formed by integrating vertical U-shape SRRs along a planar metallic hole array and explained the observations phenomenologically and qualitatively by traditional plasmonic hybridizations 25 . In this work we demonstrate an even simpler 3D MMs with micro-plates to generate significant Fano resonance without the use of SRR-type building blocks. It is found that a 3D conductive coupling mechanism is the actual physical mechanism for the efficient generation of prominent Fano resonances in both 3D MMs. In this mechanism, when the metallic hole array with extraordinary optical transmission (EOT) is illuminated by normal incident light, the excited surface plasmon polaritons (SPPs) with electric-field (E-field) polarized perpendicular to the 2D array plane can efficiently activate vertical electric currents in the vertical nanostructures (vertical SRRs or vertical micro-plates), which naturally introduce "dark" modes. This 3D conductive "dark" mode strongly interferes with the "bright" dipole-like resonance mode of the EOT structure, which forms pronounced Fano resonances with both prominent destructive and constructive interferences. We show that once the conditions for this mechanism are satisfied, the prominent Fano resonances could be well preserved no matter the vertical structures are SRRs or micro-plates. Therefore, our 3D conductive coupling induced prominent Fano resonances are very robust and conceptually different from conventional capacitive and inductive coupling schemes that degrade drastically upon small structural deviations. Figure 1a illustrates the schematic of the 3D MMs in our studies, which are formed by vertical U-shape SRRs or vertical rectangular micro-plates standing along a planar metallic hole array. The U-shape SRRs have been the popular and widely accepted building blocks for various 2D and 3D MMs in which the electric resonances could be excited by E-field parallel to the two arms (E z ) and the magnetic resonances can be excited by E-field perpendicular to the two arms while parallel to the "U-plane" (E x ) 26 . It should be mentioned that in most cases, the SRR-based MMs employed isolated SRRs with planar 27 , vertical 28,29 or multi-layer arrangements 30 , which mainly relied on electric coupling, magnetic coupling or their combinations. In comparisons, the configurations like in Fig. 1a are not traditionally considered due to the lack of knowledge in conductive coupling, as well as the difficulties in fabrications of such 3D nanostructures. By using an in situ focused-ion-beam (FIB) irradiation-induced folding technique that we recently developed (see Methods) 25 , it is very sophisticated to realize such kinds of 3D MMs in free-standing Au films, as shown in Fig. 1b (a 3D MM with vertical SRRs) and Fig. 1c (a 3D MM with vertical plates), respectively. Surprisingly, the transmission spectra of both 3D MMs exhibit significant Fano-like resonances in both long wavelength and short wavelength regions (named as Fano resonance #1 and #2, respectively) as plotted in Fig. 1d, forming sharp contrast to the spectrum of the EOT structure without any vertical structures (grey line in Fig. 1d). This preservation of Fano resonances upon drastic structural changes is well verified by our numerical simulations in Fig. 1e, indicating that the central gap of the vertical SRRs does little effects to the generation of prominent Fano resonances. These findings are very important from two aspects. Firstly, compared to the 3D MMs with SRRs, the 3D MMs with micro-plates have obvious advantages on fabrication efficiency (33% reduction in fabrication time) due to their simpler geometry and mechanical stabilities due to the less overhanging structures. Secondly, these observations indicate an underlying physical mechanism responsible for the generation of prominent Fano resonances, which might be universal for the designs of other types of 3D MMs with versatile Fano resonances and thus deserves in-depth studies.

Experimental observations.
Analysis and modellings. One may notice that except the emerging of both Fano resonances in similar wavelength regions with the same trend, some details of the measured and calculated results in Fig. 1d,e are not well matched. In comparison, the measured transmission spectrum of a 3D MM with SRRs in mid-infrared wavelength region, as plotted in Fig. 1f, is nearly perfectly matched with the calculation. This could be caused by the fact that in the realistic cases, the structures with tiny features normally suffer from relative larger fabrication imperfections than structures with larger sizes. Meanwhile, the material constants employed in modellings may deviate from realistic materials more seriously in high-frequency region than those in low-frequency region. Therefore, to effectively find out the underlying physical mechanism responsible for the Fano resonances, we move the studies to mid-infrared wavelength region, where experimental observations and numerical simulations are more consistent (Fig. 1f) and the principles can be generally applied.
On the other hand, since reported in 1998 by Ebbesen and co-workers 31 , the EOT in a metallic hole array has been well recognized as the result from two resonances, i.e. the surface plasmon resonances (SPRs) due to the periodicity and the localized plasmonic waveguide modes within the holes 32,33 . Importantly, the SPRs of the EOT structure could induce significantly enhanced E-field along the metallic holes in the z direction (E z ) when excited by y-polarized light, as plotted in Fig. 2a. Therefore, when a vertical SRR or vertical plate is placed within the intensified E z field (as the dashed outlines in Fig. 2a), the electric resonances of the vertical structure could be naturally and efficiently excited. The corresponding excitation efficiency will be the highest if the vertical structure is electrically connected to the edge of the metallic hole due to the fact that the intensified E z field is strongest at the air/metal interface. As a result, Fig. 2b-e plot two resonant electric current flows along the vertical SRRs and vertical plates of the 3D MMs, respectively. It can be seen that Mode #1 represents an in-phase conductive current flow while Mode #2 denotes an anti-phase current flow. Due to symmetry constraints, only currents that are parallel to the incident E-field can radiate into the far field 18 . Therefore, under y-polarized incident E-field, both modes (Modes #1 and #2) associated with vertical (z-direction) currents flows are non-radiative and naturally "dark" modes. These 3D conductive connection induced dark modes could strongly couple with the dipole-like SPR resonance of the EOT structure (the whole process is called as 3D conductive coupling), which finally results in prominent Fano-like resonances. As plotted in Fig. 2f, the sharp and asymmetric spectral profiles of the Fano resonance (red and black lines) in the 3D conductive MMs exhibit dramatic differences to that of the EOT structure (grey line). More importantly, it can be seen that the transmission spectra from the 3D MMs with vertical SRRs (red line) and vertical plates (black line) are almost the same, mainly caused by the fact that the 3D conductive coupling processes in both structures are mostly similar, as illustrated in Fig. 2b,e.
To further demonstrate the importance of the 3D conductive coupling mechanism, the vertical SRRs are intentionally lifted from the in-plane EOT structure in Fig. 2g, in the case of which capacitive coupling could be initiated when the gap distance (g) is larger than zero. It can be seen from Fig. 2f that when the gap distance is increased to 100 nm (corresponding to ~λ /45), i.e. when the condition changes from conductive coupling to capacitive coupling, the peak-to-dip depth of Fano resonance #1 degrades dramatically (blue curve). This observation clearly proves that the 3D conductive coupling mechanism plays a major role in the generation of prominent Fano resonance #1. It should be emphasized that the 3D conductive coupling induced Fano resonances only exist under y-polarized excitation. When excited by x-polarized incident light, as shown in Fig. 2h, the transmission of the 3D MMs with different gap distance shows little spectral shift. In this case, the spectra of the 3D MMs simply represent the linear spectral overlapping between the SRR and EOT structures, indicating there is almost no couplings between the SRR and EOT structures when g > 50 nm although the magnetic resonance of the SRR (plotted by the triangles in Fig. 2h) could be separately excited by x-polarized light. It should be mentioned that the tiny spectral dip at 4 μ m in the case of g = 0 results from the modified magnetic resonance of the SRR when it is connected to the EOT structure.
For quantitative comparisons, in Fig. 3a we normalize the transmission spectra of the 3D MM to that of the EOT structure under y-polarized excitation when the coupling scheme varies gradually from 3D conductive coupling (g = 0 nm) towards capacitive coupling (g > 0 nm). One can clearly see that for g = 0 nm and near Fano resonance #1, significant constructive (enhanced by ~52% at the peak) and destructive (suppressed by ~92% at the dip) interference effects are observed in the case of y-polarized excitation. This is quite consistent with the classical understanding that Fano resonance describes both destructive and constructive interferences between a discrete state and a continuum state 2 . Meanwhile, it is found that for Fano resonance #1, both the resonance wavelength and the amplitude of constructive and destructive interferences are highly sensitive to the gap distance. Its peak-to-dip depth drops quickly by 75% when the 3D MM deviates slightly from conductive coupling (g = 0 nm) to capacitive coupling with a gap distance as small as λ /20 (g = 150 nm), as shown in Fig. 3b, further illustrating the critical role of the 3D conductive coupling. In comparison, both resonance wavelength and amplitude of Fano resonance #2 change more slowly with the gap distance. This is because for the anti-phase coupling case of Mode #2, the repelling currents in SRR and EOT structure are relatively independent even when the two structures are electrically conducted. Therefore, the 3D conductive coupling effect in Fano resonance #2 is much weaker than that in Fano resonance #1.
From above analysis, it is now clear that the prerequisites for 3D conductive coupling include two parts: the first part is a planar structure that couples efficiently with incident light and supports SPR-enhanced vertical E-field (E z ); the second part is a vertical structure that can sustain vertical electric resonances within the intensified E z field. As long as these two prerequisites are satisfied, prominent Fano resonances could be generated without the need of complicated formulas, models, or mechanisms 34 . Therefore, since the electric current flows are mostly along the outer edges of the SRRs under y-polarized excitation (Fig. 2b,c), simply replacing the SRR structure with a vertical rectangular plate of the same size does not change the two prerequisites for prominent Fano resonances (Fig. 2d). Consequently, the 3D MMs with vertical SRRs and vertical plates possess significant Fano resonances at nearly the same spectral positions, as shown in Fig. 1d-f, verifying the robust and universal generation of Fano resonances with the 3D conductive coupling mechanism. One may notice that the position and depth of the measured Fano resonance #1 in Fig. 1d are nearly unchanged while its width is broadened due to the less confinement of the electric charges, which induces extra non-radiative losses. Nevertheless, this preservation of Fano resonances when deviating dramatically from vertical SRRs to vertical plates clearly proves the robustness upon fabrications, which are highly desirable for large-scale or stream-lined fabrications. In other words, the introduction of Fano resonances in our 3D MMs is simply dependent on the effective conductive coupling length. Therefore, by engineering the 3D conductive coupling length through varying the size of the metallic holes, the width and height of the vertical structures, the Fano resonances in 3D MMs could be widely tuned from near-infrared to mid-infrared wavelength region, as illustrated in Fig. 1d,f, which are very preferable for applications in tunable MMs.

Polarization-independent features of Fano resonances.
Another important feature of the proposed 3D conductive coupling is that the induced Fano resonance #1 exhibits characteristics of localized resonance. As the simulation results shown in Fig. 4a, the position of Fano resonance is well preserved under normal incidence, irrespective of the polarization angles (except that both Fano resonances disappear under x-polarized excitation). The suppression factor at the Fano resonance (#1) dip versus the in-plane polarization angle exhibits a strong dipole-like pattern in the polar plot (as shown in Fig. 4b), indicating the strongly localized and anisotropic features of the Fano resonance. Interestingly, there is a crossing point near Fano resonance #1 where the transmission is fixed for all polarization angles (as indicated by the red arrow Fig. 4a), which is highly preferable for polarization-insensitive optical sensing. These features, including the crossing point, are well verified by our experimental results in Fig. 4c. Moreover, measurements under y-polarized excitation (Fig. 4d) also show that the position of Fano resonance #1 is almost independent on the illumination angle under y-polarized excitation, while Fano resonance #2 that is less affected by the 3D conductive coupling changes dramatically. This robustness of Fano resonance #1 (with wavelength variation of less than 2% for both simulations and measurements in Fig. 4a-d) results from the facts that except the excitation efficiency, the different illumination schemes in Fig. 4a-d do not change the basic conditions for the generation of Fano resonances, i.e. the E-field of the planar SPPs is intrinsically along the vertical direction and the SRRs are vertically connected with the planar structures. Therefore, it could be concluded that the 3D conductive coupling induced Fano resonance #1 is a type of localized resonance and thus its position is polarization-insensitive. These interesting polarization properties of the 3D conductive coupling induced Fano resonances may provide new prospects for the emerging areas of meta-surfaces 35,36 .

Discussions and Conclusions
In summary, we have demonstrated a 3D conductive coupling mechanism for the efficient generation of robust and prominent Fano resonances in a new type of 3D MMs. Based on the 3D conductive coupling mechanism, only two simple prerequisites are required for the generation of Fano resonances, i.e. a planar structure providing intensified vertical E-field on the surface (like EOT structure) and a vertical structure sustaining electric resonances (like vertical SRRs or vertical plates). In such a configuration, electric "dark" modes could be naturally induced and strongly interfere with the "bright" dipole-like resonance mode of the EOT structure. As a result, we have observed pronounced Fano resonances with both prominent destructive and constructive interferences in both simulations and experiments. Moreover, we have shown that the 3D conductive coupling mechanism is highly universal in that both 3D MMs with vertical SRRs and vertical plates exhibited the same prominent Fano resonances although their structural geometries were largely different. Last but not least, the 3D conductive coupling induced Fano resonance exhibits characteristics of localized resonance, of which the  Fig. 2 except the gap distance g. Fano resonance #1 is mainly resulted from the 3D conductive coupling, which will be more discussed in following studies.
wavelength position is immune against certain changes in illumination polarizations. Therefore, our 3D conductive coupling mechanism is simple, universal, robust, and conceptually different from conventional capacitive and inductive coupling mechanisms that degraded drastically upon small structural deviations. This work could provide a new methodology for the efficient generation of Fano resonances with simple geometries, fast fabrications, stable mechanical strength, etc., holding potential applications in enhanced extraordinary optical transmission, color displays, optical sensing, etc., as well as opening up new prospects for the emerging areas of metasurfaces 35,36 .

Methods
Sample fabrications. The 3D MMs were fabricated with a focused-ion-beam (FIB) irradiation-induced folding technique on self-supporting Au films 25 . Specifically, Si substrates were cleaned and spin-coated with a 1.2 μ m layer of S1813 photoresist, then baked at 115 °C for 2 min and deposited an 80-nm-thick Au film using magnetron sputtering. To get suspended Au film, the sample was immersed in acetone for 24 h to fully dissolve the resist and a 100 μ m × 100 μ m Cu grid was dipped into the solution to pick the film up, which was then dried by N 2 in ultra-clean room to get a flat and self-supporting Au film. Pre-designed patterns were automatically cut by FIB system (FEI helios 600i). Subsequently, the FIB spot was continuously scanned along the bottom edge of the patterned structures, which folded the structures naturally by the ion-implantation induced stress. Through properly controlling the ion dose, a maximum folding angle of 90° could be realized. The acceleration voltage of Ga + was 30 kV. An ion-beam current of 40 pA was used for the structure processing.
Optical characterizations. Transmission spectra were collected by using a × 15, 0.4 numerical aperture reflective objective lens on an optical microscope (Hyperion 2000) and coupled to a Fourier-transform infrared spectrometer (Vertex 80, Bruker) through a 40 μ m × 40 μ m spatial aperture. A homemade aperture was inserted  Fig. 1f. The variations of dip wavelength of Fano resonance #1 in (a-d) are less than 2%, while the resonance strengths are changed due to the different excitation efficiency of SPPs under varied illumination schemes.
after the reflective objective to confine the illumination cone with a conical angle of ~5°, and the samples were tilted correspondingly to obtain normal incidence during measurement. The transmission spectra were calibrated using air (holes of the grid) as a reference.
Numerical simulations. The transmission spectra and E-field distributions of the structures were simulated by using the finite-difference time-domain (FDTD) method. The E-field monitors were placed 5 nm above the metal surface. The current distributions were calculated by the commercial software package CST Microwave Studio based on the finite integration method. We used realistic parameters describing gold's lossy properties, with an electric conductivity of 4.561 × 10 7 Sm −1 .The surface current distributions were obtained using an H-field/surface current monitor.