Our nanoantenna consists of a narrow gold-coated carbon wire wound up in a screw-like shape forming a tiny helix (Fig. 1a). The gold-coated wire sustains a cutoff-free traveling surface plasmon, known as the TM0 mode32 (Fig. 1b). This mode, when propagated along a straight wire, features a radial polarization and thus an axially symmetrical field distribution, as shown in the inset of Fig. 1b. It is locally excited with the dipolar mode of a rectangular aperture nanoantenna that perforates a 100-nm-thick gold layer right at the helix's pedestal. An incident wave on the back of the aperture is transmitted as a subdiffraction guided surface plasmon, which is nonradiatively converted into the wire mode of the helix. The contact between the aperture and the helix's pedestal ensures efficient near-field coupling between the two plasmonic structures of high impedance. To identify the traveling-wave nature of the nanoantenna, we showed the intensity of the current along the metallic wire of a four-turn HTN (Fig. 1d). The thus-depicted mode closely resembles a traveling wave, as no clearly marked current nodes are evidenced. After strong attenuation along the first half-turn of the helix, the current remains almost constant over the rest of the structure, as is observed with the low-frequency traveling-wave helical antenna31. After half a turn, the nanoscale wire mode is nonresonantly converted into a helix-guided mode spreading over the overall structure cross section and propagating along the helix axis. This short transition length is indicative of a nanoscale plasmon coupling between the rectangle aperture nanoantenna and the helix. A far-field excitation of the helix from the aperture would require a longer distance for the helix mode to be installed, with important current inhomogeneities all along the helical wire (given the shifted position of the aperture with respect to the helix). The absence of well-defined nodes at the output end of the HTN denotes good impedance matching of the nanoantenna to vacuum (low reflection at the structure end).
In the course of propagation, the helix-guided mode acquires OAM oriented along the helix axis (0z). OAM is here transferred from the helix to the guided mode and is independent of the feed element, which enables ultracompact polarizers of subwavelength size. When circular polarization is generated by an HTN, this vortex mode (of charge 1 depending on the helix handedness) is released as freely propagating waves carrying SAM of 1 per photon (in ℏ units). The degree of circular polarization (DOCP) of the emitted waves refers to the distribution of photons prepared in the spin states +1 and -1. The DOCP is defined as $|I_{RCP} - I_{LCP}|/(I_{RCP} + I_{LCP})$, where IRCP and ILCP stand for the intensities of the right and left circularly polarized components of the nanoantenna radiation, respectively4. It corresponds to the normalized Stokes parameter S3/S0. An HTN designed to operate as a circular polarizer at λ = 1.5 μm has been predicted to emit light with polarization ellipticity and a DOCP peaking at 0.97 and 0.999, respectively (Fig. 1c).
We predicted from finite difference time domain (FDTD) simulations (Supplementary Section 1) that 61.2% of the light power coupled into the HTN is radiated in the far field (i.e., 38.8% of the incoupled power is absorbed by the nanoantenna due to ohmic losses). Remarkably, we found that only 14.7% of the incoupled power is dissipated by the plasmonic helix (i.e., approximately one-third of the total losses). This is in accordance with the slowly decaying current intensity of the helix's plasmon mode installed after the first turn (Fig. 1d). The guided mode of the helix is thus weakly dissipated.
Our fabrication of the corresponding structures started with the growth of carbon helices by focused-ion-beam-induced deposition (FIBID)33 on a 100-nm-thick gold film covering a glass substrate. Carbon was chosen for its excellent ability to be deposited by FIBID. The carbon helices were then coated with a thin layer of gold. The HTN was terminated by focused ion beam (FIB) milling of a rectangular aperture nanoantenna in contact with the helix pedestal and outside the winding area of the plasmonic wire (see Fig. S1 in the Supplementary Information). Figure 2a and the inset of Fig. 2b display scanning electron microscopy (SEM) images of a resulting structure. The HTNs were back-illuminated with polarized light from a tunable laser at telecommunication wavelengths, the nanoantenna output beams were measured and their polarization states were analysed (see "Methods"). The observed polarization properties (Fig. 2b, c) agree well with the theoretical model. As predicted numerically (by comparing Figs. 1c and 2b), a thinner gold coating may explain the noticeable redshift in the experimental spectra with respect to the theoretical expectations. The plasmon mode is then loaded by the high-refractive-index carbon skeleton of the helix.
The radiation pattern of the HTN was measured by imaging individual nanoantennas with a 0.9 numerical aperture microscope objective (Fig. 2d). Despite their subwavelength sizes, an HTN produces a beam centered near polar angle θ = 0° (see inset of Fig. 2d) with a half-width at half-maximum of 26.9° in the (x0z)-plane and 23.7° in the (y0z)-plane. (x0z) and (y0z) are defined in the inset of Fig. 2d. These experimental results agree well with theoretical predictions (Fig. 2e). They confirm the axial mode operation of the HTN27, 31.
Figure 3 presents the spectrum of the far-field ellipticity factor (EF) of four helices showing an increasing number of turns. From one to four turns, the measured maximum EF varies from 0.64 to 0.96 while undergoing spectral redshift. The enhancement in the EF with the number of turns of the helix reveals the swirling plasmonic effect as the source of circular polarization. This result indicates the end-fired helix as the origin of the transmission process, which is confirmed experimentally in Supplementary Section 2.
We developed an HTN-based platform to convert linearly polarized incoming light into four closely packed circularly polarized beams: two right-handed and two left-handed circularly polarized beams (Fig. 4). To this end, we fabricated two couples of HTNs of opposite handedness, positioned at the corners of a 5-µm large fictive square, as shown in Fig. 4a. By using HTNs with various orientations of feed apertures, it is possible to tune the relative intensities of these beams by changing the polarization of the incident waves. With our HTNs of orthogonal apertures, we were able to excite all four helices (Fig. 4b; four output beams) or selectively address the right- or left-handed plasmonic structures (Fig. 4c, d, respectively; two output beams only) by rotating the input linear polarization. The polarization states of the HTN radiations were analysed by placing a rotating quarter-wave plate followed by a fixed linear polarizer in front of the camera (see Fig. S3). The resulting polarization diagram (Fig. 4e) shows that the beams produced by the right and left HTNs are right- and left-handed circularly polarized, respectively.
It is also possible to impart a different polarization state to each output beam in a controllable way simply by considering nanoantennas of various geometrical parameters (cf. Fig. S4). Moreover, as shown in Fig. 2b, the polarization state can be tuned by changing the wavelength of the incoming light. It is therefore possible to arrange at will a set of HTNs for locally converting an incoming light beam into an arbitrary distribution of directional beams of tunable polarizations and intensities, thereby obtaining unprecedented integrated devices for manipulating light polarization.
A more complex polarization response can be achieved with a spacing between the HTNs that is smaller than the wavelength, resulting in the near-field coupling of the light emission processes created by individual nanoantennas. We consider two couples of right and left HTNs with helices of opposite handedness that are spaced 560 nm apart and are made up of orthogonal apertures (Fig. 5a, d). This four-HTN structure is identical to that of Fig. 4 but with the nanoantennas packed in a volume smaller than a cubic wavelength. With this geometry, a single output beam is observed regardless of the incident polarization (inset of Fig. 5d). When the right or left HTNs are selectively excited (with two orthogonal incident linear polarizations), the output beam is no more right- or left-handed circularly polarized, as was observed in Fig. 4. By virtue of a plasmon coupling between helices of opposite handedness (Fig. S5), all four nanoantennas are excited and participate in the beam generation, regardless of the incoming polarization direction. As a result, two orthogonal linear polarizations of incident light are converted into right- and left-handed outcoming elliptical polarizations whose principal axes are parallel (Fig. 5b, e). Figure 5c, f compare the measured and calculated tilt angles 2ψ and ellipticity angles 2χ of the outcoming polarization (Poincare sphere approach) as a function of the direction angle ϕ of the incident linear polarization at two different wavelengths (1.61 μm and 1.47 μm), respectively. The measured curves in Fig. 5c, f reveal the theoretically anticipated tuning of the angular spacing Δϕ between the two right- and left-handed outcoming circular polarizations. Whereas Δϕ is fixed at 90° with conventional quarter-wave plates, it is here equal to 69° at λ = 1.61 μm and decreases to 52° at λ = 1.47 μm. This tunability in polarization manipulation is not standard at all. It provides a degree of freedom in polarization control that is unachievable when utilizing or artificially reproducing birefringent and dichroic materials. It arises from the possibility of generating circular polarizations from the combination of elliptically polarized waves of opposite handedness, parallel principal axes and tunable intensities (see Supplementary Section 3). By spectrally detuning the HTNs, the outcoming polarization ellipticities are modified, thereby resulting in a controlled and tunable angular spacing Δϕ. The above-described polarization properties appear to be robust to fabrication defects.