3D coaxial out-of-plane metallic antennas for filtering and multi-spectral imaging in the infrared range

We fabricated and investigated a new configuration of 3D coaxial metallic antennas working in the infrared which combines the strong lateral light scattering of vertical plasmonic structures with the selective spectral transmission of 2D arrays of coaxial apertures. The coaxial structures are fabricated with a top-down method based on a template of hollow 3D antennas. Each antenna has a multilayer radial structure consisting of dielectric and metallic materials not achievable in a 2D configuration. A planar metallic layer is inserted normally to the antennas. The outer dielectric shell of the antenna defines a nanometric gap between the horizontal plane and the vertical walls. Thanks to this aperture, light can tunnel to the other side of the plane, and be transmitted to the far field in a set of resonances. These are investigated with finite-elements electromagnetic calculations and with Fourier-transform infrared spectroscopy measurements. The spectral position of the resonances can be tuned by changing the lattice period and/or the antenna length. Thanks to the strong scattering provided by the 3D geometry, the transmission peaks possess a high signal-to-noise ratio even when the illuminated area is less than 2 × 2 times the operation wavelength. This opens new possibilities for multispectral imaging in the IR with wavelength-scale spatial resolution.

Compared to the configuration adopted in the FTIR measurements, a plane wave is a good approximation of the incident focused beam at its focal plane. The presence of the focusing objective determines a spread in the angular distribution of the incident field. From FEM calculations (not shown), this spread induces a change in the absolute height of the peaks and in their width. While these effects might be significant for the transverse resonances at high energies, they do not substantially change the shape of the main longitudinal peaks. The full calculation of the scattered field taking into account the exact shape of the incident wave front would require a very large supercell, and this is out of our computational resources.
An exemplificative plot of the simulation mesh used in the antenna domains is reported in Fig. SI1. The top of the antenna (detail in the inset) is meshed with a triangular mesh. The maximum mesh size is tuned in order to allocate at least three mesh nodes within each layer. Along the vertical direction, the mesh is swept at constants steps equal to λ/10, where λ denotes the shortest wavelength in the simulation (typically λ=2 μm). The same method is used to mesh the planar domains (metallic mid-plane, TiO 2 and Si 3 N 4 membrane).
In this case, the triangular mesh is swept along the vertical direction with a distribution of five elements. The air and PMMA domains are meshed with a free tetrahedral mesh with TiO 2 Au Air Resist maximum cell size of λ/5 and λ/(5×n PMMA ), respectively (here n PMMA denotes the average real part of the refractive index of PMMA in the IR, which is approximately equal to 1.55).
With these settings, the unit cell of the array is meshed with a total of 20000 -80000 mesh elements, depending on the length of the antenna and on the lattice period. The calculation of each IR spectrum in the range 2-12 μm (wavelength step of 20-40 nm) takes between 2 and 10 hours on a modern workstation equipped with two Intel Xeon processors  Fig. SI2b). When a resonance is excited, a fraction of the incident power is always dissipated in the metallic walls of the antenna or in the mid-plane. PMMA presents a set of sharp vibrational bands all over the IR range, with a prominent absorption peak at λ=5.8 μm (red line of Fig. SI2b). This peak is responsible for the minimum in the transmission spectrum reported in Fig. SI2a and in Figs. 5a and 6a of the main text. TiO 2 has been chosen as the dielectric for the outer shell. This is a critical position. In fact, when the system is driven at resonance, strong field enhancements are present in the TiO2 shell, which is in direct contact with the metallic walls of the antenna. TiO 2 absorbs a substantial fraction of the incident power at wavelengths longer than 9 μm. Si 3 N 4 has similar absorption properties in the same spectral range. These two materials are responsible for the strong damping of the fundamental TM 0 resonance, which is barely visible in the transmission spectrum at λ=9.7 μm (Fig. SI2a).

SI#3: Angular dependence of the IR spectra
The angular dependence of the IR spectra for the array of coaxial antennas with P=3 μm, L=6 μm and D=550 nm is investigated by means of electromagnetic calculations for an angle of incidence in the range 0-60°. The results for TM and TE polarizations are illustrated in Fig. SI3a and SI3b, respectively. Due to the different orientations of the electric field (inset of Fig. 5 in the main text), the two polarizations can excite two distinct sets of transverse and longitudinal resonances.
At normal incidence (θ=0°), the IR spectra for TE and TM polarizations coincide (black curves in Figs. SI3a and SI3b). In this configuration, only the transverse resonances of the array can be excited. These produce small peaks in the transmission spectra (amplitude of just 7%), and they are thus not interesting for filtering applications.
At oblique incidence (θ>0°) the electric field for TM-polarized light has also a component parallel to the axis of the antenna. For this reason, both transverse and longitudinal resonances can be excited. Their angular dispersion is illustrated in Fig. SI3a.
The excitation efficiency of the TM0 mode around 9.7 μm (which is purely longitudinal) increases by increasing the incidence angle. However, due to the parasitic absorption, the maximum (theoretical) amplitude of this peak is just 16% at 60 degrees. In addition, the TM0 mode has a larger natural width compared to the longitudinal TM1 mode. These two facts make the TM0 mode less interesting for filtering applications. The excitation efficiency of the longitudinal TM1 mode around 5.3 μm is maximum between 30 and 45 degrees, with a theoretical transmission around 50%. For this reason, this is the most interesting resonance for filtering application. The longitudinal TM1 mode shows also a moderate redshift by increasing the angle of incidence (Fig. SI3a). The transverse TM1 peaks between 4 and 5 μm are excited by the in-plane component of the electric field (inset of Fig. 5 of the main text), and they produce shallow peaks in the transmission spectra.
TE-polarized light has the electric field polarized in the x-y plane of the array (inset of which are qualitatively analogous to the aforementioned transverse TM1 modes. Also in this case, the peaks in the transmission spectra (Fig. SI3b) are very small (less than 4% at θ>0°).